Solutions Manual for Financial Markets and Institutions 8th Edition by Anthony Saunders,Cornett & Er

SOLUTION MANUAL

SOLUTION MANUAL

PART 1: INTRODUCTION AND OVERVIEW OF FINANCIAL MARKETS Chapter 1 Introduction Chapter 2 Determinants of Interest Rates Chapter 3 Interest Rates and Security Valuation Chapter 4 The Federal Reserve System, Monetary Policy, and Interest Rates

PART 2: SECURITIES MARKETS Chapter 5 Money Markets Chapter 6 Bond Markets Chapter 7 Mortgage Markets Chapter 8 Stock Markets Chapter 9 Foreign Exchange Markets Chapter 10 Derivative Securities Markets

PART 3: COMMERCIAL BANKS Chapter 11 Commercial Banks Chapter 12 Commercial Banks’ Financial Statements and Analysis Chapter 13 Regulation of Commercial Banks

PART 4: OTHER FINANCIAL INSTITUTIONS Chapter 14 Other Lending Institutions Chapter 15 Insurance Companies Chapter 16 Securities Firms and Investment Banks Chapter 17 Investment Companies Chapter 18 Pension Funds Chapter 19 Fintech Companies

PART 5: RISK MANAGEMENT IN FINANCIAL INSTITUTIONS Chapter 20 Types of Risks Incurred by Financial Institutions Chapter 21 Managing Credit Risk on the Balance Sheet Chapter 22 Managing Liquidity Risk on the Balance Sheet Chapter 23 Managing Interest Rate Risk and Insolvency Risk on the Balance Sheet Chapter 24 Managing Risk off the Balance Sheet with Derivative Securities Chapter 25 Managing Risk off the Balance Sheet with Loan Sales and Securitization

Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Answers to Chapter 1 Questions: 1.

a. primary b. primary c. secondary d. secondary e. secondary

2.

a. money market b. money market c. capital market d. capital market e. capital market f. money market g. money market h. money market i. capital market j. money market

3. The capital markets are more likely to be characterized by actual physical locations such as the New York Stock Exchange. Money market transactions are more likely to occur via telephone, wire transfers, and computer trading.

4. According to Figure 1-4, federal funds and repurchase agreements, followed by Treasury bills, negotiable CDs, and commercial paper, had the largest amounts outstanding in 2019.

5. The major instruments traded in capital markets are corporate stocks, mortgages, corporate bonds, Treasury notes and bonds, state and local government bonds, U.S. government owned and sponsored agencies, and bank and consumer loans.

6. According to Figure 1-4, corporate stocks represent the largest capital market instrument in 2019, followed by mortgages, Treasury securities, and corporate bonds.

7. The bank would be most concerned about a depreciation of the yen against the dollar.

8. Financial institutions consist of: Commercial banks - depository institutions whose major assets are loans and major liabilities are deposits.

Commercial banks’ loans are broader in range, including consumer, commercial, and real estate loans, than other depository institutions. Commercial banks’ liabilities include more nondeposit sources of funds, such as subordinate notes and debentures, than other depository institutions.

Thrifts - depository institutions in the form of savings and loans, savings banks, and credit unions. Thrifts generally perform services similar to commercial banks, but they tend to concentrate their loans in one segment, such as real estate loans or consumer loans.

Insurance companies - financial institutions that protect individuals and corporations (policyholders) from adverse events. Life insurance companies provide protection in the event of untimely death, illness, and retirement. Property casualty insurance protects against personal injury and liability due to accidents, theft, fire, etc.

Securities firms and investment banks - financial institutions that underwrite securities and engage in related activities such as securities brokerage, securities trading, and making a market in which securities can trade.

Finance companies - financial intermediaries that make loans to both individual and businesses. Unlike depository institutions, finance companies do not accept deposits but instead rely on short- and long-term debt for funding.

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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Mutual funds and hedge funds - financial institutions that pool financial resources of individuals and companies and invest those resources in diversified portfolios of asset.

Pension funds - financial institutions that offer savings plans through which fund participants accumulated savings during their working years before withdrawing them during their retirement years. Funds originally invested in and accumulated in pension funds are exempt from current taxation.

9. If there were no FIs then the users of funds, such as corporations in the economy, would have to approach the savers of funds, such as households, directly in order to fund their investment projects and fill their borrowing needs.

This would be extremely costly because of the up-front information costs faced by potential lenders. These include costs associated with identifying potential borrowers, pooling small savings into loans of sufficient size to finance corporate activities, and assessing risk and investment opportunities. Moreover, lenders would have to monitor the activities of borrowers over each loan's life span, which is compounded by the free rider problem. The net result is an imperfect allocation of resources in an economy.

10. There are at least three reasons for this. First, once they have lent money in exchange for financial claims, suppliers of funds need to monitor or check the use of their funds. They must be sure that the user of funds neither absconds with nor wastes the funds on projects that have low or negative returns. Such monitoring actions are often extremely costly for any given fund supplier because they require considerable time, expense, and effort to collect this information relative to the size of the average fund supplier’s investment.

Second, the relatively long-term nature of some financial claims (e.g., mortgages, corporate stock, and bonds) creates a second disincentive for suppliers of funds to hold the direct financial claims issued by users of funds.

Specifically, given the choice between holding cash and long-term securities, fund suppliers may well choose to hold cash for liquidity reasons, especially if they plan to use savings to finance consumption expenditures in the near future and financial markets are not very deep in terms of active buyers and sellers.

Third, even though real-world financial markets provide some liquidity services, by allowing fund suppliers to trade financial securities among themselves, fund suppliers face a price risk upon the sale of securities. That is, the price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE) may well differ from the price they initially paid for the security either because investors change their valuation of the security between the time it was bought and when it was sold and/or because dealers, acting as intermediaries between buyers and sellers, charge transaction costs for completing a trade.

11. A suppler of funds who directly invests in a fund user’s financial claims faces a high cost of monitoring the fund user’s actions in a timely and complete fashion after purchasing securities. One solution to this problem is for a large number of small investors to place their funds with a single FI serving as a broker between the two parties. The FI groups the fund suppliers’ funds together and invests them in the direct or primary financial claims issued by fund users. This aggregation of funds resolves a number of problems. First, the “large” FI now has a much greater incentive to hire employees with superior skills and training in monitoring. This expertise can be used to collect information and monitor the ultimate fund user’s actions because the FI has far more at stake than any small individual fund supplier. Second, the monitoring function performed by the FI alleviates the “free-rider” problem that exists when small fund suppliers leave it to each other to collect information and monitor a fund user. In an economic sense, fund suppliers have appointed the financial institution as a delegated monitor to act on their behalf.

For example, full-service securities firms such as Morgan Stanley carry out investment research on new issues and make investment recommendations for their retail clients (or investors), while commercial banks collect deposits from fund suppliers and lend these funds to ultimate users such as corporations.

12. In addition to information costs, FIs help small savers alleviate liquidity and price risk. Often claims issued by financial institutions have liquidity attributes that are superior to those of primary securities. For example, banks and thrift institutions (e.g., savings associations) issue transaction account deposit contracts with a fixed principal value and often a guaranteed interest rate that can be withdrawn immediately, on demand, by investors. Money market mutual funds issue shares to household savers that allow them to enjoy almost fixed principal (depositlike) contracts while earning higher interest rates than on bank deposits, and that can be withdrawn immediately. Even life insurance companies allow policyholders to borrow against their policies held with the company at very short notice.

Notice that in reducing the liquidity risk of investing funds for fund suppliers, the FI transfers this risk to its own © 2022

2

Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e balance sheet. That is, FIs such as depository institutions offer highly liquid, low price-risk securities to fund suppliers on the liability side of their balance sheets, while investing in relatively less liquid and higher price-risk securities—such as the debt and equity—issued by fund users on the asset side.

13. As long as the returns on different investments are not perfectly positively correlated, by spreading their investments across a number of assets, FIs can diversify away significant amounts of their portfolio risk. Thus, FIs can exploit the law of large numbers in making their investment decisions, whereas due to their smaller wealth size, individual fund suppliers are constrained to holding relatively undiversified portfolios. As a result, diversification allows an FI to predict more accurately its expected return and risk on its investment portfolio so that it can credibly fulfill its promises to the suppliers of funds to provide highly liquid claims with little price risk. As long as an FI is sufficiently large, to gain from diversification and monitoring on the asset side of its balance sheet, its financial claims (it issues as liabilities) are likely to be viewed as liquid and attractive to small savers, especially when compared to direct investments in the capital market. A mutual fund invested in a diverse group of stocks and fixed income securities will best provide diversification for an investor.

14. If net borrowers and net lenders have different optimal time horizons, FIs can service both sectors by mismatching their asset and liability maturities. That is, by maturity mismatching, FIs can produce long-term contracts such as long-term, fixed-rate mortgage loans to households, while still raising funds with short-term liability contracts such as deposits. In addition, although such mismatches can subject an FI to interest rate, a large FI is better able than a small investor to manage this risk through its superior access to markets and instruments for hedging the risks of such loans.

15. Because they are sold in very large denominations, many assets are either out of reach of individual savers or would result in savers holding highly undiversified asset portfolios. For example, the minimum size of a negotiable CD is $100,000; commercial paper (short-term corporate debt) is often sold in minimum packages of $250,000 or more. Individual savers may be unable to purchase such instruments directly. However, by buying shares in a mutual fund with other small investors, household savers overcome the constraints to buying assets imposed by large minimum denomination sizes. Such indirect access to these markets may allow small savers to generate higher returns on their portfolios as well.

16. Other services provided by FIs that benefit the overall economy include: Money Supply Transmission - Depository institutions are the conduit through which monetary policy actions impact the rest of the financial system and the economy in general.

Credit Allocation - FIs are often viewed as the major, and sometimes only, source of financing for a particular sector of the economy, such as farming and residential real estate.

Intergenerational Wealth Transfers - FIs, especially life insurance companies and pension funds, provide savers the ability to transfer wealth from one generation to the next.

Payment Services - The efficiency with which depository institutions provide payment services directly benefits the economy.

17. As financial institutions perform the various services described above, they face many types of risk.

Specifically, all FIs hold some assets that are potentially subject to default or credit risk (such as loans, stocks, and bonds). As FIs expand their services to non-U.S. customers or even domestic customers with business outside the United States, they are exposed to both foreign exchange risk and country or sovereign risk as well. Further, FIs tend to mismatch the maturities of their balance sheet assets and liabilities to a greater or lesser extent and are thus exposed to interest rate risk. If FIs actively trade these assets and liabilities rather than hold them for longer-term investments, they are further exposed to market risk or asset price risk. Increasingly, FIs hold contingent assets and liabilities off the balance sheet, which presents an additional risk called off-balance-sheet risk. Moreover, all FIs are exposed to some degree of liability withdrawal or liquidity risk, depending on the type of claims they have sold to liability holders. All FIs are exposed to technology risk and operational risk because the production of financial services requires the use of real resources and back-office support systems (labor and technology combined to

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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e provide services). Finally, the risk that an FI may not have enough capital reserves to offset a sudden loss incurred as a result of one or more of the risks it faces creates insolvency risk for the FI. 18. FIs provide various services to sectors of the economy. Failure to provide these services, or a breakdown in their efficient provision, can be costly to both the ultimate suppliers (households) and users (firms) of funds as well as the overall economy. For example, bank failures may destroy household savings and at the same time restrict a firm’s access to credit. Insurance company failures may leave households totally exposed in old age to catastrophic illnesses and sudden drops in income on retirement. In addition, individual FI failures may create doubts in savers’ minds regarding the stability and solvency of FIs in general and cause panics and even runs on sound institutions.

FIs are regulated in an attempt to prevent these types of market failures.

19. A major event that changed and reshaped the financial services industry was the financial crisis of the late 2000s. As FIs adjusted to regulatory changes brought about by the likes of the FSM Act, one result was a dramatic increase in systemic risk of the financial system, caused in large part by a shift in the banking model from that of “originate and hold” to “originate to distribute.” In the traditional model, banks take short term deposits and other sources of funds and use them to fund longer term loans to businesses and consumers. Banks typically hold these loans to maturity, and thus have an incentive to screen and monitor borrower activities even after a loan is made.

However, the traditional banking model exposes the institution to potential liquidity, interest rate, and credit risk. In attempts to avoid these risk exposures and generate improved return-risk tradeoffs, banks have shifted to an underwriting model in which they originated or warehouse loans, and then quickly sell them. When loans trade, the secondary market produces information that can substitute for the information and monitoring of banks. Further, banks may have lower incentives to collect information and monitor borrowers if they sell loans rather than keep them as part of the bank’s portfolio of assets. Indeed, most large banks are organized as financial service holding companies to facilitate these new activities.

More recently activities of shadow banks, non-bank financial service firms that perform banking services, have facilitated the change from the originate and hold model of commercial banking to the originate and distribute banking model. In the shadow banking system savers place their funds with money market mutual7 and similar funds, which invest these funds in the liabilities of shadow banks. Borrowers get loans and leases from shadow banks rather than from banks. Like the traditional banking system, the shadow banking system intermediates the flow of funds between net savers and net borrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, or shadow bank, that intermediates. Further, unlike the traditional banking system, where the complete credit intermediation is performed by a single bank, in the shadow banking system it is performed through a series of steps involving many nonbank financial service firms.

These innovations remove risk from the balance sheet of financial institutions and shift risk off the balance sheet and to other parts of the financial system. Since the FIs, acting as underwriters, are not exposed to the credit, liquidity, and interest rate risks of traditional banking, they have little incentive to screen and monitor activities of borrowers to whom they originate loans. Thus, FIs role as specialists in risk measurement and management has been reduced.

20. The boom (“bubble”) in the housing markets began building in 2001, particularly after the terrorist attacks of 9/11. The immediate response by regulators to the terrorist attacks was to create stability in the financial markets by providing liquidity to FIs. For example, the Federal Reserve lowered the short-term interest rate that banks and other financial institutions pay in the Federal funds market and even made lender of last resort funds available to non-bank FIs such as investment banks. Perhaps not surprisingly, low interest rates and the increased liquidity provided by Central banks resulted in a rapid expansion in consumer, mortgage, and corporate debt financing. Demand for residential mortgages and credit card debt rose dramatically. As the demand for mortgage debt grew, especially among those who had previously been excluded from participating in the market because of their poor credit ratings, FIs began lowering their credit quality cut-off points. Moreover, to boost their earnings, in the market now popularly known as the “subprime market,” banks and other mortgage-supplying institutions often offered relatively low “teaser” rates on adjustable rate mortgages (ARMs) at exceptionally low initial interest rates, but with substantial step-up in rates after the initial rate period expired two or three year later and if market rates rose in the future.

Under the traditional banking structure, banks might have been reluctant to so aggressively pursue low credit quality borrowers for fear that the loans would default. However, under the originate-to-distribute model of banking, asset securitization and loan syndication allowed banks to retain little or no part of the loans, and hence the default risk on loans that they originated. Thus, as long as the borrower did not default within the first months after a loan’s © 2022

4

Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e issuance and the loans were sold or securitized without recourse back to the bank, the issuing bank could ignore longer term credit risk concerns. The result was deterioration in credit quality, at the same time as there was a dramatic increase in consumer and corporate leverage.

21. Measured as more than $1 trillion in international debt outstanding as of 2019 the biggest issuers are France, Germany, the Netherlands, the United Kingdom, and the United States.

22. China, France, Japan, the United Kingdom, and the United States have the biggest banks (in terms of total assets held in 2019).

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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Answers to Chapter 1 Questions: 1.

a. primary b. primary c. secondary d. secondary e. secondary

2.

a. money market b. money market c. capital market d. capital market e. capital market f. money market g. money market h. money market i. capital market j. money market

3. The capital markets are more likely to be characterized by actual physical locations such as the New York Stock Exchange. Money market transactions are more likely to occur via telephone, wire transfers, and computer trading.

4. According to Figure 1-4, federal funds and repurchase agreements, followed by Treasury bills, negotiable CDs, and commercial paper, had the largest amounts outstanding in 2019.

5. The major instruments traded in capital markets are corporate stocks, mortgages, corporate bonds, Treasury notes and bonds, state and local government bonds, U.S. government owned and sponsored agencies, and bank and consumer loans.

6. According to Figure 1-4, corporate stocks represent the largest capital market instrument in 2019, followed by mortgages, Treasury securities, and corporate bonds.

7. The bank would be most concerned about a depreciation of the yen against the dollar.

8. Financial institutions consist of: Commercial banks - depository institutions whose major assets are loans and major liabilities are deposits.

Commercial banks’ loans are broader in range, including consumer, commercial, and real estate loans, than other depository institutions. Commercial banks’ liabilities include more nondeposit sources of funds, such as subordinate notes and debentures, than other depository institutions.

Thrifts - depository institutions in the form of savings and loans, savings banks, and credit unions. Thrifts generally perform services similar to commercial banks, but they tend to concentrate their loans in one segment, such as real estate loans or consumer loans.

Insurance companies - financial institutions that protect individuals and corporations (policyholders) from adverse events. Life insurance companies provide protection in the event of untimely death, illness, and retirement. Property casualty insurance protects against personal injury and liability due to accidents, theft, fire, etc.

Securities firms and investment banks - financial institutions that underwrite securities and engage in related activities such as securities brokerage, securities trading, and making a market in which securities can trade.

Finance companies - financial intermediaries that make loans to both individual and businesses. Unlike depository institutions, finance companies do not accept deposits but instead rely on short- and long-term debt for funding.

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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Mutual funds and hedge funds - financial institutions that pool financial resources of individuals and companies and invest those resources in diversified portfolios of asset.

Pension funds - financial institutions that offer savings plans through which fund participants accumulated savings during their working years before withdrawing them during their retirement years. Funds originally invested in and accumulated in pension funds are exempt from current taxation.

9. If there were no FIs then the users of funds, such as corporations in the economy, would have to approach the savers of funds, such as households, directly in order to fund their investment projects and fill their borrowing needs.

This would be extremely costly because of the up-front information costs faced by potential lenders. These include costs associated with identifying potential borrowers, pooling small savings into loans of sufficient size to finance corporate activities, and assessing risk and investment opportunities. Moreover, lenders would have to monitor the activities of borrowers over each loan's life span, which is compounded by the free rider problem. The net result is an imperfect allocation of resources in an economy.

10. There are at least three reasons for this. First, once they have lent money in exchange for financial claims, suppliers of funds need to monitor or check the use of their funds. They must be sure that the user of funds neither absconds with nor wastes the funds on projects that have low or negative returns. Such monitoring actions are often extremely costly for any given fund supplier because they require considerable time, expense, and effort to collect this information relative to the size of the average fund supplier’s investment.

Second, the relatively long-term nature of some financial claims (e.g., mortgages, corporate stock, and bonds) creates a second disincentive for suppliers of funds to hold the direct financial claims issued by users of funds.

Specifically, given the choice between holding cash and long-term securities, fund suppliers may well choose to hold cash for liquidity reasons, especially if they plan to use savings to finance consumption expenditures in the near future and financial markets are not very deep in terms of active buyers and sellers.

Third, even though real-world financial markets provide some liquidity services, by allowing fund suppliers to trade financial securities among themselves, fund suppliers face a price risk upon the sale of securities. That is, the price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE) may well differ from the price they initially paid for the security either because investors change their valuation of the security between the time it was bought and when it was sold and/or because dealers, acting as intermediaries between buyers and sellers, charge transaction costs for completing a trade.

11. A suppler of funds who directly invests in a fund user’s financial claims faces a high cost of monitoring the fund user’s actions in a timely and complete fashion after purchasing securities. One solution to this problem is for a large number of small investors to place their funds with a single FI serving as a broker between the two parties. The FI groups the fund suppliers’ funds together and invests them in the direct or primary financial claims issued by fund users. This aggregation of funds resolves a number of problems. First, the “large” FI now has a much greater incentive to hire employees with superior skills and training in monitoring. This expertise can be used to collect information and monitor the ultimate fund user’s actions because the FI has far more at stake than any small individual fund supplier. Second, the monitoring function performed by the FI alleviates the “free-rider” problem that exists when small fund suppliers leave it to each other to collect information and monitor a fund user. In an economic sense, fund suppliers have appointed the financial institution as a delegated monitor to act on their behalf.

For example, full-service securities firms such as Morgan Stanley carry out investment research on new issues and make investment recommendations for their retail clients (or investors), while commercial banks collect deposits from fund suppliers and lend these funds to ultimate users such as corporations.

12. In addition to information costs, FIs help small savers alleviate liquidity and price risk. Often claims issued by financial institutions have liquidity attributes that are superior to those of primary securities. For example, banks and thrift institutions (e.g., savings associations) issue transaction account deposit contracts with a fixed principal value and often a guaranteed interest rate that can be withdrawn immediately, on demand, by investors. Money market mutual funds issue shares to household savers that allow them to enjoy almost fixed principal (depositlike) contracts while earning higher interest rates than on bank deposits, and that can be withdrawn immediately. Even life insurance companies allow policyholders to borrow against their policies held with the company at very short notice.

Notice that in reducing the liquidity risk of investing funds for fund suppliers, the FI transfers this risk to its own © 2022

2

Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e balance sheet. That is, FIs such as depository institutions offer highly liquid, low price-risk securities to fund suppliers on the liability side of their balance sheets, while investing in relatively less liquid and higher price-risk securities—such as the debt and equity—issued by fund users on the asset side.

13. As long as the returns on different investments are not perfectly positively correlated, by spreading their investments across a number of assets, FIs can diversify away significant amounts of their portfolio risk. Thus, FIs can exploit the law of large numbers in making their investment decisions, whereas due to their smaller wealth size, individual fund suppliers are constrained to holding relatively undiversified portfolios. As a result, diversification allows an FI to predict more accurately its expected return and risk on its investment portfolio so that it can credibly fulfill its promises to the suppliers of funds to provide highly liquid claims with little price risk. As long as an FI is sufficiently large, to gain from diversification and monitoring on the asset side of its balance sheet, its financial claims (it issues as liabilities) are likely to be viewed as liquid and attractive to small savers, especially when compared to direct investments in the capital market. A mutual fund invested in a diverse group of stocks and fixed income securities will best provide diversification for an investor.

14. If net borrowers and net lenders have different optimal time horizons, FIs can service both sectors by mismatching their asset and liability maturities. That is, by maturity mismatching, FIs can produce long-term contracts such as long-term, fixed-rate mortgage loans to households, while still raising funds with short-term liability contracts such as deposits. In addition, although such mismatches can subject an FI to interest rate, a large FI is better able than a small investor to manage this risk through its superior access to markets and instruments for hedging the risks of such loans.

15. Because they are sold in very large denominations, many assets are either out of reach of individual savers or would result in savers holding highly undiversified asset portfolios. For example, the minimum size of a negotiable CD is $100,000; commercial paper (short-term corporate debt) is often sold in minimum packages of $250,000 or more. Individual savers may be unable to purchase such instruments directly. However, by buying shares in a mutual fund with other small investors, household savers overcome the constraints to buying assets imposed by large minimum denomination sizes. Such indirect access to these markets may allow small savers to generate higher returns on their portfolios as well.

16. Other services provided by FIs that benefit the overall economy include: Money Supply Transmission - Depository institutions are the conduit through which monetary policy actions impact the rest of the financial system and the economy in general.

Credit Allocation - FIs are often viewed as the major, and sometimes only, source of financing for a particular sector of the economy, such as farming and residential real estate.

Intergenerational Wealth Transfers - FIs, especially life insurance companies and pension funds, provide savers the ability to transfer wealth from one generation to the next.

Payment Services - The efficiency with which depository institutions provide payment services directly benefits the economy.

17. As financial institutions perform the various services described above, they face many types of risk.

Specifically, all FIs hold some assets that are potentially subject to default or credit risk (such as loans, stocks, and bonds). As FIs expand their services to non-U.S. customers or even domestic customers with business outside the United States, they are exposed to both foreign exchange risk and country or sovereign risk as well. Further, FIs tend to mismatch the maturities of their balance sheet assets and liabilities to a greater or lesser extent and are thus exposed to interest rate risk. If FIs actively trade these assets and liabilities rather than hold them for longer-term investments, they are further exposed to market risk or asset price risk. Increasingly, FIs hold contingent assets and liabilities off the balance sheet, which presents an additional risk called off-balance-sheet risk. Moreover, all FIs are exposed to some degree of liability withdrawal or liquidity risk, depending on the type of claims they have sold to liability holders. All FIs are exposed to technology risk and operational risk because the production of financial services requires the use of real resources and back-office support systems (labor and technology combined to

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3

Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e provide services). Finally, the risk that an FI may not have enough capital reserves to offset a sudden loss incurred as a result of one or more of the risks it faces creates insolvency risk for the FI. 18. FIs provide various services to sectors of the economy. Failure to provide these services, or a breakdown in their efficient provision, can be costly to both the ultimate suppliers (households) and users (firms) of funds as well as the overall economy. For example, bank failures may destroy household savings and at the same time restrict a firm’s access to credit. Insurance company failures may leave households totally exposed in old age to catastrophic illnesses and sudden drops in income on retirement. In addition, individual FI failures may create doubts in savers’ minds regarding the stability and solvency of FIs in general and cause panics and even runs on sound institutions.

FIs are regulated in an attempt to prevent these types of market failures.

19. A major event that changed and reshaped the financial services industry was the financial crisis of the late 2000s. As FIs adjusted to regulatory changes brought about by the likes of the FSM Act, one result was a dramatic increase in systemic risk of the financial system, caused in large part by a shift in the banking model from that of “originate and hold” to “originate to distribute.” In the traditional model, banks take short term deposits and other sources of funds and use them to fund longer term loans to businesses and consumers. Banks typically hold these loans to maturity, and thus have an incentive to screen and monitor borrower activities even after a loan is made.

However, the traditional banking model exposes the institution to potential liquidity, interest rate, and credit risk. In attempts to avoid these risk exposures and generate improved return-risk tradeoffs, banks have shifted to an underwriting model in which they originated or warehouse loans, and then quickly sell them. When loans trade, the secondary market produces information that can substitute for the information and monitoring of banks. Further, banks may have lower incentives to collect information and monitor borrowers if they sell loans rather than keep them as part of the bank’s portfolio of assets. Indeed, most large banks are organized as financial service holding companies to facilitate these new activities.

More recently activities of shadow banks, non-bank financial service firms that perform banking services, have facilitated the change from the originate and hold model of commercial banking to the originate and distribute banking model. In the shadow banking system savers place their funds with money market mutual7 and similar funds, which invest these funds in the liabilities of shadow banks. Borrowers get loans and leases from shadow banks rather than from banks. Like the traditional banking system, the shadow banking system intermediates the flow of funds between net savers and net borrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, or shadow bank, that intermediates. Further, unlike the traditional banking system, where the complete credit intermediation is performed by a single bank, in the shadow banking system it is performed through a series of steps involving many nonbank financial service firms.

These innovations remove risk from the balance sheet of financial institutions and shift risk off the balance sheet and to other parts of the financial system. Since the FIs, acting as underwriters, are not exposed to the credit, liquidity, and interest rate risks of traditional banking, they have little incentive to screen and monitor activities of borrowers to whom they originate loans. Thus, FIs role as specialists in risk measurement and management has been reduced.

20. The boom (“bubble”) in the housing markets began building in 2001, particularly after the terrorist attacks of 9/11. The immediate response by regulators to the terrorist attacks was to create stability in the financial markets by providing liquidity to FIs. For example, the Federal Reserve lowered the short-term interest rate that banks and other financial institutions pay in the Federal funds market and even made lender of last resort funds available to non-bank FIs such as investment banks. Perhaps not surprisingly, low interest rates and the increased liquidity provided by Central banks resulted in a rapid expansion in consumer, mortgage, and corporate debt financing. Demand for residential mortgages and credit card debt rose dramatically. As the demand for mortgage debt grew, especially among those who had previously been excluded from participating in the market because of their poor credit ratings, FIs began lowering their credit quality cut-off points. Moreover, to boost their earnings, in the market now popularly known as the “subprime market,” banks and other mortgage-supplying institutions often offered relatively low “teaser” rates on adjustable rate mortgages (ARMs) at exceptionally low initial interest rates, but with substantial step-up in rates after the initial rate period expired two or three year later and if market rates rose in the future.

Under the traditional banking structure, banks might have been reluctant to so aggressively pursue low credit quality borrowers for fear that the loans would default. However, under the originate-to-distribute model of banking, asset securitization and loan syndication allowed banks to retain little or no part of the loans, and hence the default risk on loans that they originated. Thus, as long as the borrower did not default within the first months after a loan’s © 2022

4

Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e issuance and the loans were sold or securitized without recourse back to the bank, the issuing bank could ignore longer term credit risk concerns. The result was deterioration in credit quality, at the same time as there was a dramatic increase in consumer and corporate leverage.

21. Measured as more than $1 trillion in international debt outstanding as of 2019 the biggest issuers are France, Germany, the Netherlands, the United Kingdom, and the United States.

22. China, France, Japan, the United Kingdom, and the United States have the biggest banks (in terms of total assets held in 2019).

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Solutions for End-of-Chapter Questions and Problems: Chapter Three 1.

What is the primary function of finance companies? How do finance companies differ from depository institutions?

The primary function of finance companies is to make loans to individuals and corporations.

Finance companies differ from depository institutions in that they do not accept deposits, but borrow short- and long-term debt, such as commercial paper and bonds, to finance the loans. The heavy reliance on borrowed money has caused finance companies to generally hold more equity than depository institutions for the purpose of signaling solvency to potential creditors. Finally, finance companies are less regulated than depository institutions, in part because they do not rely on deposits as a source of funds.

2.

What are the three major types of finance companies? To which market segments do each of these types of companies provide service?

The three types of finance companies are (1) sales finance institutions, (2) personal credit institutions, and (3) business credit institutions. Sales finance companies specialize in making loans to customers of a particular retailer or manufacturer. An example is Ford Motor Credit.

Personal credit institutions specialize in making installment loans to consumers. An example is HSBC Finance. Business credit institutions provide specialty financing, such as equipment leasing and factoring, to corporations. Factoring involves the purchasing of accounts receivable at a discount from corporate customers and assuming the responsibility of collection. An example is U.S. Bancorp Equipment Finance.

3.

What have been the major changes in the accounts receivable balances of finance companies over the 38-year period from 1977 to 2015?

The biggest change in the accounts receivable balances of finance companies over the last 38 years is that the amount of consumer and business loans has decreased from 95.1 percent of assets to 71.2 percent of assets. Real estate loans have replaced some of the consumer and business loans and are now 7.3 percent of assets.

4.

What are the major types of consumer loans? Why are the rates charged by consumer finance companies typically higher than those charged by commercial banks?

Consumer loans include motor vehicle loans and leases, other consumer loans, and securitized loans, with motor vehicles loans and leases taking the largest share. Other consumer loans include loans for mobile homes, appliances, furniture, etc. The rates charged by finance companies typically are higher than the rates charged by banks because the customers are considered to be riskier. Customers who seek individual (or business) loans from finance companies are often those judged too risky to obtain loans from commercial banks.

5.

Why have home equity loans become popular? What are securitized mortgage assets?

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Since the enactment of the Tax Reform Act of 1986 only loans secured by an individual’s home offer tax-deductible interest for the borrower. Thus, these loans are more popular than loans without a tax deduction, and finance companies as well as banks, credit unions, and savings institutions have been attracted to this loan market.

Securitization of mortgages involves the pooling of a group of mortgages with similar characteristics, the removal of these mortgages from the balance sheet, and the subsequent sale of interests in the pool to secondary market investors. Securitization of mortgages results in the creation of mortgage-backed securities (e.g., government agency securities, collateralized mortgage obligations), which can be traded in secondary mortgage markets. While removed from its balance sheet, the finance company that originates the mortgage may still service the mortgage portfolio for a fee.

6.

What advantages do finance companies have over commercial banks in offering services to small business customers? What are the major subcategories of business loans? Which category is largest?

Finance companies have advantages in the following ways: (1) finance companies are not subject to regulations that restrict the types of products and services they can offer; (2) because they do not accept deposits, they do not have the extensive regulatory monitoring; (3) they are likely to have more product expertise because they generally are subsidiaries of industrial companies; (4) finance companies are more willing to take on riskier customers; and (5) finance companies typically have lower overhead than commercial banks.

The four categories of business loans are (1) retail and wholesale motor vehicle loans and leases, (2) equipment loans, (3) other business assets, and (4) securitized business assets. Equipment loans constitute over 40 percent of the business loans.

7.

What have been the primary sources of financing for finance companies?

Finance companies have relied primarily on short-term commercial paper and long-term notes and bonds. Over 60 percent of finance company funding comes from debt due to parents and debt not elsewhere classified.

Unlike banks and thrifts, finance companies cannot issue deposits. Rather, to finance assets, finance companies rely heavily on short-term commercial paper, with many having direct sale programs in which commercial paper is sold directly to mutual funds and other institutional investors on a continuous day-by-day basis. Indeed, finance companies are now the largest issuers in the short-term commercial paper market. Most commercial paper issues have maturities of 30 days or less, although they can be issued with maturities of up to 270 days.

8.

How do finance companies make money? What risks does this process entail? How do these risks differ for a finance company versus a commercial bank?

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Finance companies make a profit by borrowing money at a rate lower than the rate at which they lend. This is similar to a commercial bank, with the primary difference being the source of funds, principally deposits for a bank and money and capital market borrowing for a finance company.

The principal risk in relying heavily on public debt as a source of financing involves the continued depth of the commercial paper and other debt markets. As experienced during the financial crisis of 2008-2009, economic recessions can affect these markets more severely than the effect on deposit drains in the commercial banking sector. In addition, the riskier asset customers may have a greater impact on the finance companies.

9.

Compare Tables 3-1 and 2-5. Which firms have higher ratios of capital to total assets: finance companies or commercial banks? What does this comparison indicate about the relative strengths of these two types of firms?

Table 3-1 indicates that finance companies had a ratio of capital to total assets of 12.8 percent in 2015. Commercial banks (Table 2-5) have 11.3 percent of total capital to total assets. The difference may be partially due to the fact that the commercial banks have FDIC insured deposits. This insurance makes the debt safer from the depositors’ and stockholders’ perspective.

As a result, commercial banks can take on more debt than the uninsured finance companies.

The higher amount of capital for finance companies serves as a cushion for their own solvency and as a possible signal to the market place regarding their ability to borrow funds.

10.

Why do finance companies face less regulation than do commercial banks? How does this advantage translate into performance advantages? What is the major performance disadvantage?

By not accepting deposits, the need is eliminated for regulators to evaluate the potentially adverse safety and soundness effects of a finance company failure on the economy. The performance advantage involves the avoidance of dealing with the heavy regulatory burden, but the disadvantage is the loss of the use of a relatively cheaper source of deposit funds. However, because of the impact that non-bank FIs, including finance companies, had on the U.S. economy during the financial crisis and as a result of the need for the Federal Reserve to rescue several non-bank FIs, regulators proposed that non-bank FIs receive more oversight.

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Solutions for End-of-Chapter Questions and Problems: Chapter Four 1.

Explain how securities firms differ from investment banks. In what ways are they financial intermediaries?

Securities firms specialize primarily in the purchase, sale, and brokerage of securities, while investment banks primarily engage in originating, underwriting, and distributing issues of securities. In recent years, investment banks have undertaken increased corporate finance activities such as advising on mergers, acquisitions, and corporate restructuring. In both cases, these firms act as financial intermediaries in that they bring together economic units who need money with those units who wish to invest money.

Both segments have undergone substantial structural changes in recent years. Some of the most recent consolidations include the acquisition of Bears Stearns by J.P. Morgan Chase, the bankruptcy of Lehman Brothers and the acquisition of Merrill Lynch by Bank of America.

Indeed, as discussed later in the chapter, the investment banking industry has seen the failure or acquisition of all but two of its major firms (Goldman Sachs and Morgan Stanley) and these two firms converted to commercial bank holding companies in 2008.

2.

In what ways have changes in the investment banking industry mirrored changes in the commercial banking industry?

First, both industries have seen a concentration of business among the larger firms. This concentration has occurred primarily through the merger and acquisition activities of several of the largest firms. Second, firms in both industries tend to be divided along product line services provided to customers. Some national full-line firms provide service to both retail customers, in the form of brokerage services, and corporate customers, in the form of new issue underwriting.

Other national full-line firms specialize in corporate finance and security trading activities.

Third, the remaining firms specialize in more limited activities such as discount brokerage, regional full service retail activities, etc. This business line division is not dissimilar to that of the banking industry with money center banks, regional banks, and community banks. Clearly product line overlap occurs between the different firm divisions in each industry.

3.

What are the different types of firms in the securities industry and how does each type differ from the others?

Firms in the industry can be divided along a number of dimensions. The largest firms, the socalled national full-line firms, service both retail customers (especially in acting as broker– dealers, thus assisting in the trading of existing securities) and corporate customers (such as underwriting, thus assisting in the issue of new securities). With the changes in the past few years, national full-line firms now fall into three subgroups. First are the commercial bank holding companies that are the largest of the full service investment banks. They have extensive domestic and international operations and offer advice, underwriting, brokerage, trading, and asset management services. The largest of these firms include Bank of America (through their acquisition of Merrill Lynch), Morgan Stanley, and J.P. Morgan Chase (through its many 1 © 2022

acquisitions, including that of Bear Stearns, for $240 million in 2008). Second are the national full-line firms that specialize more in corporate business with customers and are highly active in trading securities. Examples are Goldman Sachs and Salomon Brothers/Smith Barney, the investment banking arm of Citigroup (created from the merger of Travelers and Citicorp in 1998). Third are the large investment banks. These firms maintain more limited branch networks concentrated in major cities operating with predominantly institutional client bases. These firms include Lazard Ltd. and Greenhill & Co. The rest of the industry is comprised of firms that perform a mix of primary and secondary market services for a particular segment of the financial markets: 1. Regional securities firms that are often subdivided into large, medium, and small categories and concentrate on servicing customers in a particular region, e.g., New York or California (such as Raymond James Financial).

2. Specialized discount brokers that effect trades for customers on- or offline without offering investment advice or tips (such as Charles Schwab).

3. Specialized electronic trading securities firms (such as E*trade) that provide a platform for customers to trade without the use of a broker. Rather, trades are enacted on a computer via the Internet.

4. Venture capital firms that pool money from individual investors and other FIs (e.g., hedge funds, pension funds, and insurance companies) to fund relatively small and new businesses (e.g., in biotechnology).

5. Other firms in this industry include research boutiques, floor specialists, companies with large clearing operations, and other firms that do not fit into one of the preceding categories. This would include firms such as Knight Capital Group (a leading firm in off-exchange trading of U.S. equities) and floor specialist LaBranche & Co. 4.

What are the key activity areas for investment banks and securities firms? How does each activity area assist in the generation of profits and what are the major risks for each area?

The seven major activity areas of security firms are: a) Investment Banking: Investment banks specialize in underwriting and distributing both debt and equity issues in the corporate market. New issues can be placed either privately or publicly and can represent either a first issued (IPO) or a secondary issue.

Secondary issues of seasoned firms typically will generate lower fees than an IPO. Securities underwritings can be undertaken through either public offerings or private offerings. In a private offering the investment bank receives a fee for acting as the agent in the transaction. In best-efforts public offerings, the firm acts as the agent and receives a fee based on the success of the offering. The firm serves as a principal by actually takes ownership of the securities in a firm commitment underwriting. Thus, the risk of loss is higher. Finally, the firm may perform similar functions in the government markets and the asset-backed derivative markets. In all cases, the investment bank receives fees related to the difficulty and risk in placing the issue.

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b) Venture Capital: A difficulty for new and small firms in obtaining debt financing from commercial banks is that CBs are generally not willing or able to make loans to new companies with no assets and business history. In this case, new and small firms often turn to investment banks (and other firms) that make venture capital investments to get capital financing as well as advice. Venture capital is a professionally managed pool of money used to finance new and often high-risk firms. Venture capital is generally provided to back an untried company and its managers in return for an equity investment in the firm. Venture capital firms do not make outright loans. Rather, they purchase an equity interest in the firm that gives them the same rights and privileges associated with an equity investment made by the firm’s other owners. c) Market Making: Security firms assist in the market-making function by acting as brokers to assist customers in the purchase or sale of an asset. Market making can involve either agency or principal transactions. Agency transactions are two-way transactions on behalf of customers, for example, acting as a stockbroker or dealer for a fee or commission. In principal transactions, the market maker seeks to profit on the price movements of securities and takes either long or short inventory positions for its own account. (Or an inventory position may be taken to stabilize the market in the securities.) These principal positions can be profitable if prices increase, but they can also create downside risk in volatile markets. d) Trading: Trading activities can be conducted on behalf of a customer or the firm. The activities usually involve position trading, pure arbitrage, risk arbitrage, program trading, stock brokerage, and electronic brokerage. Position trading involves the purchase of large blocks of stock to facilitate the smooth functioning of the market.

Pure arbitrage involves the purchase and simultaneous sale of an asset in different markets because of different prices in the two markets. Risk arbitrage involves establishing positions prior to some anticipated information release or event. Program trading involves positioning with the aid of computers and futures contracts to benefit from small market movements. In each case, the potential risk involves the movements of the asset prices, and the benefits are aided by the lack of most transaction costs and the immediate information that is available to investment banks. Stock brokerage involves the trading of securities on behalf of individuals who want to transact in the money or capital markets. Electronic brokerage, offered by major brokers, involves direct access, via the Internet, to the trading floor, therefore bypassing traditional brokers. e) Investing: Securities firms act as agents for individuals with funds to invest by establishing and managing mutual funds and by managing pension funds. The securities firms generate fees that affect directly the revenue stream of the companies. f) Cash Management: Cash management accounts are checking accounts that earn interest and may be covered by FDIC insurance. The accounts have been beneficial in providing full-service financial products to customers, especially at the retail level.

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g) Mergers and Acquisitions: Most investment banks provide advice to corporate clients who are involved in mergers and acquisitions. This activity has been extremely beneficial from a fee standpoint during the 1990s and 2000s. h) Back-Office and Other Service Functions: Security firms offer clearing and settlement services, research and information services, and other brokerage services on a fee basis.

5.

What is the difference between an IPO and a secondary issue?

An IPO is the first time issue of a company’s securities, whereas a secondary offering is a new issue of a security that is already offered.

6.

What is the difference between a private placement and a public offering?

A public offering represents the sale of a security to the public at large. A private placement involves the sale of securities to one or several large investors such as an insurance company or a pension fund.

7.

What are the risk implications to an investment bank from underwriting on a best-efforts basis versus a firm commitment basis? If you operated a company issuing stock for the first time, which type of underwriting would you prefer? Why? What factors may cause you to choose the alternative?

In a best efforts underwriting, the investment bank acts as an agent of the company issuing the security and receives a fee based on the number of securities sold. With a firm commitment underwriting, the investment bank purchases the securities from the company at a negotiated price and sells them to the investing public at what it hopes will be a higher price. Thus, the investment bank has greater risk with the firm commitment underwriting, since the investment bank will absorb any adverse price movements in the security before the entire issue is sold.

Factors causing preference to the issuing firm include general volatility in the market, stability and maturity of the financial health of the issuing firm, and the perceived appetite for new issues in the market place. The investment bank will also consider these factors when negotiating the fees and/or pricing spread in making its decision regarding the offering process.

8.

An investment bank agrees to underwrite an issue of 15 million shares of stock for Looney Landscaping Corp. a. If the investment bank underwrites the stock on a firm commitment basis, it agrees to pay $12.50 per share to Looney Landscaping Corp. for the 15 million shares of stock. It can then sell those shares to the public for $13.25 per share. How much money does Looney Landscaping Corp. receive? What is the profit to the investment bank? If the investment bank can sell the shares for only $11.95, how much money does Looney Landscaping Corp. receive? What is the profit to the investment bank?

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If the investment bank sells the stock for $13.25 per share, Looney Landscaping Corp. receives $12.50 x 15,000,000 shares = $187,500,000. The profit to the investment bank is ($13.25 $12.50) x 15,000,000 shares = $11,250,000. The stock price of Looney Landscaping Corp. is $13.25 since that is what the public agrees to pay. From the perspective of Looney Landscaping Corp., the $11.25 million represents the commission that it must pay to issue the stock.

If the investment bank sells the stock for $11.95 per share, Looney Landscaping Corp. still receives $12.50 x 15,000,000 shares = $187,500,000. The profit to the investment bank is ($11.95 - $12.50) x 15,000,000 shares = -$8,250,000. The stock price of Looney Landscaping Corp. is $11.95 since that is what the public agrees to pay. From the perspective of the investment bank, the -$8.25 million represents a loss for the firm commitment it made to Looney Landscaping Corp. to issue the stock. b. Suppose, instead, that the investment bank agrees to underwrite the 15 million shares on a best-efforts basis. The investment bank is able to sell 13.6 million shares for $12.50 per share, and it charges Looney Landscaping Corp. $0.275 per share sold. How much money does Looney Landscaping Corp. receive? What is the profit to the investment bank? If the investment bank can sell the shares for only $11.95, how much money does Looney Landscaping Corp. receive? What is the profit to the investment bank?

If the investment bank sells the stock for $12.50 per share, Looney Landscaping Corp. receives ($12.50 - $0.275) x 13,600,000 shares = $166,260,000, the investment bank’s profit is $0.275 x 13,600,000 shares = $3,740,000, and the stock price is $12.50 per share since that is what the public pays.

If the investment bank sells the stock for $11.95 per share, Looney Landscaping Corp. receives ($11.95 - $0.275) x 13,600,000 shares = $158,780,000, the investment bank’s profit is still $0.275 - 13,600,000 shares = $3,740,000, and the stock price is $11.95 per share since that is what the public pays.

9.

An investment bank agrees to underwrite a $500 million, 10-year, 8 percent semiannual bond issue for KDO Corporation on a firm commitment basis. The investment bank pays KDO on Thursday and plans to begin a public sale on Friday. What type of interest rate movement does the investment bank fear while holding these securities? If interest rates rise 0.05 percent, or five basis points, overnight, what will be the impact on the profits of the investment bank? What if the market interest rate falls five basis points?

An increase in interest rates will cause the value of the bonds to fall. If rates increase 5 basis points over night, the bonds will lose $1,695,036.32 in value. The investment bank will absorb the decrease in market value, since the issuing firm has already received its payment for the bonds. If market rates decrease by 5 basis points, the investment bank will benefit by the $1,702,557.67 increase in market value of the bonds. These two changes in price can be found with the following two equations respectively: 5 © 2022

− $1,695,036.32 = $20,000,000PVAi=4.025%,n=20 + $500,000,000PVi=4.025%,n=20 − $500,000,000 $1,702,557.67 = $20,000,000PVAi=3.975%,n=20 + $500,000,000PVi=3.975%,n=20 − $500,000,000 10.

An investment bank pays $23.50 per share for 4 million shares of JCN Company. It then sells those shares to the public for $25 per share. How much money does JCN receive?

What is the profit to the investment bank? What is the stock price of JCN?

JCN receives $23.50 x 4,000,000 shares = $94,000,000. The profit to the investment bank is ($25.00 - $23.50) x 4,000,000 shares = $6,000,000. The stock price of JCN is $25.00 since that is what the public must pay. From the perspective of JCN, the $6,000,000 represents the commission that it must pay to issue the stock.

11.

XYZ, Inc., has issued 10 million new shares of stock. An investment bank agrees to underwrite these shares on a best-efforts basis. The investment bank is able to sell 8.4 million shares for $27 per share, and it charges XYZ $0.675 per share sold. How much money does XYZ receive? What is the profit to the investment bank? What is the stock price of XYZ?

XYZ receives ($27.00 - $0.675) x 8,400,000 shares = $221,130,000, the investment bank’s profit is $0.675 x 8,400,000 shares = $5,670,000, and the stock price is $27 per share since that is what the public pays.

12. What is venture capital?

Venture capital is a professionally managed pool of money used to finance new and often highrisk firms. Venture capital is generally provided by investment institutions or private individuals willing to back an untried company and its managers in return for an equity investment in the firm. Venture capital firms do not make outright loans. Rather, they purchase an equity interest in the firm that gives them the same rights and privileges associated with an equity investment made by the firm’s other owners. As equity holders, venture capital firms are not generally passive investors. Rather, they provide valuable expertise to the firm’s managers and sometimes even help in recruiting senior managers for the firm. They also generally expect to be fully informed about the firm’s operations, any problems, and whether the joint goals of all of the firm’s owners are being met.

13. What are the different types of venture capital firms? How do institutional venture capital firms differ from angel venture capital firms?

Institutional venture capital firms are business entities whose sole purpose is to find and fund the most promising new firms. Private-sector institutional venture capital firms include venture capital limited partnerships (that are established by professional venture capital firms, acting as general partners in the firm: organizing and managing the firm and eventually liquidating their 6 © 2022

equity investment), financial venture capital firms (subsidiaries of investment or commercial banks), and corporate venture capital firms (subsidiaries of nonfinancial corporations which generally specialize in making start-up investments in high-tech firms). Limited partner venture capital firms dominate the industry. In addition to these private sector institutional venture capital firms, the federal government, through the SBA, operates Small Business Investment Companies (SBICs). SBICs are privately organized venture capital firms licensed by the SBA that make equity investments (as well as loans) to entrepreneurs for start-up activities and expansions. As federally sponsored entities, SBICs have relied on their unique opportunity to obtain investment funds from the U.S. Treasury at very low rates relative to private-sector institutional venture capital firms. In contrast to institutional venture capital firms angel venture capitalists (or angels) are wealthy individuals who make equity investments. Angel venture capitalists have invested much more in new and small firms than institutional venture capital firms.

14. What are the advantages and disadvantages to a new or small firm of getting capital funding from a venture capital firm?

A difficulty for new and small firms in obtaining debt financing from banks is that banks are generally not willing or able to make loans to new companies with no assets and business history. In this case, new and small firms often turn to venture capital firms to get capital financing as well as advice. As equity holders, venture capital firms are not generally passive investors. Rather, they provide valuable expertise to the firm’s managers and sometimes even help in recruiting senior managers for the firm. They also generally expect to be fully informed about the firm’s operations, any problems, and whether the joint goals of all of the firm’s owners are being met. Venture capital firms look for two things in making their decisions to invest in a firm. The first is a high return. Venture capital firms are willing to invest in high-risk new and small firms. However, they require high levels of returns (sometimes as high as 700 percent within five to seven years) to take on these risks. The second is an easy exit. Venture capital firms realize a profit on their investments by eventually selling their interests in the firm. They want a quick and easy exit opportunity when it comes time to sell. Basically, venture capital firms provide equity funds to new, unproven, and young firms. This separates venture capital firms from commercial banks and investment firms, which prefer to invest in existing, financially secure businesses.

15.

How do agency transactions differ from principal transactions for market makers?

Agency transactions are done on behalf of a customer. Thus, the investment bank is acting as a stockbroker, and the company earns a fee or commission. In a principal transaction, the investment bank is trading on its own account. In this case, the profit is made from the difference in the price that the company pays for the security and the price at which it is sold. In the first case the company bears no risk, but in the second case the company is risking its own capital.

16.

One of the major activity areas of securities firms is trading.

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a. What is the difference between pure arbitrage and risk arbitrage?

Pure arbitrage involves the buying and selling of similar assets trading at different prices. Pure arbitrage has a lock or assurance of the profits that are available in the market. This profit position usually occurs with no equity investment, the use of only very short-term borrowed funds, and reduced transaction costs for securities firms.

Risk arbitrage also is based on the principle of buying low and selling high a similar asset (or an asset with the same payoff). The difference between risk arbitrage and pure arbitrage is that the prices are not locked in, leaving open a certain speculative component that could result in real economic losses. b. What is the difference between position trading and program trading?

Position trading involves the purchase of large blocks of stock for the purpose of providing consistency and continuity to the secondary markets. In most cases, these trades are held in inventory for a period of time, either after or prior to the trade. Program trading involves the ability to buy or sell entire portfolios of stocks quickly and often times simultaneously in an effort to capture differences between the actual futures price of a stock index and the theoretically correct price. The program trading process is useful when conducting index arbitrage. If the futures price is too high, an arbitrager would short futures contract and buy the stocks in the underlying index. The program trading process in effect is a coordinated trading program that allows for this arbitrage process to be accomplished.

17.

If an investor observes that the price of a stock trading in one exchange is different from the price in another exchange, what form of arbitrage is applicable, and how can the investor participate in that arbitrage?

The investor should short sell the more expensive asset and use the proceeds to purchase the cheaper stock to lock in a given spread. This transaction would be an example of a pure arbitrage rather than risk arbitrage. The actual spread realized would be affected by the amount of transaction costs involved in executing the transactions.

18.

An investor notices that an ounce of gold is priced at $1,018 in London and $1,025 in New York. a. What action could the investor take to try to profit from the price discrepancy?

An investor would try to buy gold in London at $1,018 and sell it in New York for $1,025 yielding a riskless profit of $7 per ounce. b. Under which of the four trading activities would this action be classified?

This transaction is an example of pure arbitrage.

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c. If the investor is correct in identifying the discrepancy, what pattern should the two prices take in the short-term?

The prices of gold in the two separate markets should converge or move toward each other. In all likelihood, the prices will not become exactly the same. It does not matter which price moves most, since the investor should unwind both positions when the prices are nearly equal. d. What may be some impediments to the success of the transaction?

The success or profitability of this arbitrage opportunity will depend on transaction costs and the speed at which the investor can execute the transactions. If the price disparity is sufficiently large, other investors will seize the opportunity to attempt to achieve the same arbitrage results, thus causing the prices to converge quickly.

19.

What three factors are given credit for the steady decline in brokerage commissions as a percent of total revenues over the period beginning in 1977 and ending in 1991?

The reasons often offered for the decline in brokerage commissions over this period are the abolition of fixed commissions by the SEC in 1975, the resulting competition among firms, and the stock market crash of 1987. The stock market crash caused a decline in the amount of equity and debt underwriting which subsequently had a negative effect on income. Although the equity markets rebounded during the 1990s, the continued growth of discount brokerage firms by depository institutions and the advances of electronic trade continued to affect commissions.

20.

What factors are given credit for the resurgence of profitability in the securities industry beginning in 1991? Are firms that trade in fixed-income securities more or less likely to have volatile profits? Why?

Profits for securities firms increased beginning in 1991 because of (a) the resurgence of stock markets and trading volume, (b) increased growth in the underwriting of new issues, especially corporate debt issues, and (c) growth in the asset-backed securities market as a result of increased securitization of mortgages. However, rising oil prices and the subprime mortgage market collapse and the eventual full market crash in 2008 through 2009 pushed stock market values down. As a result, commission income in the securities industry declined as well. As the economy and the stock market recovered in the early 2010s, commission income again rose to almost 20 percent of total revenues.

The continued slowdown of the U.S. economy in 2001 and the terrorist attacks on the World Trade Center (which housed offices of many securities firms and investment banks) in September 2001, however, brought an end to these record profits. Also impacting profit, the securities industry was rocked by several allegations of securities law violations as well as a loss of investor confidence in Wall Street and corporate America as a result of a number of corporate governance failures and accounting scandals involving Enron, Merck, WorldCom, and other major U.S. corporations.

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21.

Using Table 4-6, which type of security accounts for most underwriting in the United States? Which is likely to be more costly to underwrite: corporate debt or equity? Why?

According to Table 4-6, debt issues were greater than equity issues by a ratio of roughly four to one in the middle 1980s and late 2000s, and a ratio of thirteen to one in the mid-2000s. Debt is less risky than equity, so there is less risk of an adverse price movement with debt compared to equity. Further, debt is more likely to be bought in larger blocks by fewer investors, a transaction characteristic that makes the selling process less costly.

22. How did the financial crisis affect the performance of securities firms and investment banks?

Signs of the impending financial crisis arose in 2007. The industry began 2007 on a strong note, but hit by the subprime mortgage market meltdown that began in the summer of 2007, ended the year with pretax profits of just $0.78 billion. Many revenue lines showed solid growth in 2007 and total revenues reached a record high of $474.2 billion in 2007. However, trading and investment account loses were large; totaling a loss of $6 billion in 2007 compared to a gain of $43 billion in 2006. Further, expenses grew faster than revenues, to a record $473.4 billion in 2007. The worst of the financial crisis hit in 2008 as the industry reported a record loss for the year of $34.1 billion. Revenues were $290.5 billion, down 38.7 percent from 2007. Nearly all revenue lines decreased from 2007 levels, with trading and investment account losses being the largest (-$65.0 billion in 2008).

As quickly as industry profits plunged during the financial crisis, they recovered in 2009. Pretax profits were a record $61.4 billion. Revenues totaled $288.1 billion for the year. Commission and fee income was $49.0 billion of the total, reflecting improved trading volume. Trading revenues, which had been negative for six consecutive quarters, grew to $45.3 billion. Industry expenses for 2009 were $212.4 billion, 33.7 percent below 2008 levels. Of this, interest expenses fell to just $21.9 billion, 82.2 percent below 2008 levels. While still in a fragile state, the industry seemed to be recovering along with the economy.

The U.S. and world economies grew very slowly after the financial crisis. While interest rates remained at historic lows, concerns about the health of Eurozone economies and the U.S. fiscal cliff kept economic growth at a standstill. Memories of the financial crisis were still fresh in the minds of investors. Events such as the May 2010 “flash crash,” the October 2011 collapse of MF Global Holdings, and the August 2012 trading glitch at Knight Capital, caused individual and institutional investors to limit capital market activity. Industry pretax profits fell to $34.8 billion, $16.8 billion, and $34.6 billion in 2010, 2011, and 2012, respectively.

By the mid-2010s, while the industry had put most problems from the financial crisis behind it, the industry was affected by post-crisis consequences, with increased regulation on risk taking and capital requirements. Since 2013, many companies undertook strategic initiatives to respond to new regulations and to de-risk their firms. This has led to balance sheet reductions as well as to downsizing or disposition of select businesses, trading products, and investments. In addition, corporate strategies increasingly focus on client services and away from making large bets through principal investments like hedge funds or risky trading activity for using the firm’s 10 © 2022

capital. As regulation became stricter following the 2008 crisis, many large banks across the globe have sold assets or are selling, and/or discontinuing, lines of operations, and are focusing more on their core competencies. A result of the new regulations is that profitability is down: pre-tax profits in 2013 and 2014 fell to $28.6 billion and $27.6 billion, respectively.

23.

How do the operating activities, and thus the balance sheet structures, of securities firms differ from the operating activities of depository institutions? How are the balance sheet structures of securities firms similar to depository institutions?

Securities firms and investment banks primarily help net suppliers of funds (e.g., households) transfer funds to net users of funds (e.g., businesses) at a low cost and with a maximum degree of efficiency. Unlike other types of FIs, securities firms and investment banks do not transform the securities issued by the net users of funds into claims that may be “more” attractive to the net suppliers of funds (e.g., banks and their creation of bank deposits and loans). Rather, they serve as brokers intermediating between fund suppliers and users.

The short-term nature of many of the assets in the portfolios of securities firms demonstrates that an important activity is trading/brokerage. As a broker, the securities firm receives a commission for handling the trade but does not take either an asset or liability position. Thus, many of the assets appearing on the balance sheets of securities firms are cash-like money market instruments, not capital market positions. In the case of depository institutions, assets tend to be medium-term from the lending position of the depository institutions.

A major similarity between securities firms and all other types of FIs is a high degree of financial leverage. That is, all of these firms use high levels of debt that is used to finance an asset portfolio consisting primarily of financial securities. A difference in the funding is that securities firms tend to use liabilities that are extremely short term (see the balance sheet in Table 4-7).

Nearly 35 percent of the total liability financing is payables incurred in the transaction process.

In contrast, depository institutions have fixed-term time and savings deposit liabilities.

24.

Based on the data in Table 4-7, what were the largest assets and liabilities of securities firms in 2015? Are these asset and liability categories related? Exactly how does a repurchase agreement work?

The largest asset categories are reverse repurchase agreements (securities purchased under agreements to resell (i.e., the broker gives a short-term loan to the repurchase agreement seller)) and receivables from other broker–dealers, and the largest liabilities are repurchase agreements.

When a financial institution needs to borrow funds, one source is to sell an asset. In the case of financial assets, the institution often finds it more beneficial to sell the asset under an agreement to repurchase the asset at a later time. In his case, the current money market rate of interest is built into the agreed upon repurchase price, and the asset literally does not leave the balance sheet of the borrowing institution. The borrowing institution receives cash and a liability representing the agreement to repurchase. The lending institution, which has excess funds, replaces cash as an asset with the reverse repurchase agreement.

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25.

How did the National Securities Markets Improvement Act of 1996 (NSMIA) change the regulatory structure of the securities industry?

The NSMIA removed most of the regulatory burden that had been imposed by individual states, effectively giving the SEC exclusive regulatory jurisdiction over securities firms.

26.

Identify the major regulatory organizations that are involved in the daily operations of the investment securities industry, and explain their role in providing smoothly operating markets.

The primary regulator of the securities industry is the Securities and Exchange Commission (SEC), established in 1934 largely in response to abuses by securities firms that many at the time felt were partly responsible for the economic problems in the United States. The primary role of the SEC includes administration of securities laws, review and evaluation of registrations of new securities offerings (ensuring that all relevant information is revealed to potential investors), review and evaluation of annual and semiannual reports summarizing the financial status of all publicly held corporations, and the prohibition of any form of security market manipulation. The National Securities Markets Improvement Act (NSMIA) of 1996 reaffirmed the significance of the SEC as the primary regulator of securities firms. According to the NSMIA, states are no longer allowed to require federally registered securities firms to be registered in a state as well.

States are also now prohibited from requiring registration of securities firms’ transactions and from imposing substantive requirements on private placements. Prior to the NSMIA, most securities firms were subject to regulation from the SEC and from each state in which they operated. While the NSMIA provides that states may still require securities firms to pay fees and file documents to be submitted to the SEC, most of the regulatory burden imposed by states has been removed. Thus, the NSMIA effectively gives the SEC the exclusive regulatory jurisdiction over securities firms.

The early 2000s saw a reversal of this trend toward the dominance of the SEC, with states— especially their attorneys general—increasingly intervening through securities-related investigations. Several highly publicized securities violations resulted in criminal cases brought against securities law violators by mainly state and some federal prosecutors. In the spring of 2003 the issue culminated in an agreement between regulators and 10 of the nation’s largest securities firms to pay a record $1.4 billion in penalties to settle charges involving investor abuse. The long-awaited settlement centered on civil charges that securities firms routinely issued overly optimistic stock research to investors in order to gain favor with corporate clients and win their investment banking business.

Subsequent to these investigations, the SEC instituted rules requiring Wall Street analysts to vouch that their stock picks are not influenced by investment banking colleagues and that analysts disclose details of their compensation that would flag investors to any possible conflicts.

If evidence surfaces that analysts have falsely attested to the independence of their work, it could be used to bring enforcement actions. Violators could face a wide array of sanctions, including fines and other penalties, such as a suspension or a bar from the securities industry. In addition, 12 © 2022

the SEC now requires that top officials from all public companies sign off on financial statements.

While the SEC sets the overall regulatory standards for the industry, the Financial Industry Regulatory Authority (FINRA) is involved in the day-to-day regulation of trading practices. In contrast to the SEC which is a government run regulator, FINRA is an independent, not-forprofit organization authorized by Congress to protect America’s investors by making sure the securities industry operates fairly and honestly. Specifically, FINRA writes and enforces rules governing the activities of securities firms, examines firms for compliance with those rules, works to foster market transparency, and supports investor education. FINRA monitors trading abuses (such as insider trading) trading rule violations, and securities firms’ capital (solvency) positions. FINRA’s expanded oversight is intended to monitor and determine whether orders placed in dark pools are indeed attempts at moving stock prices. FINRA also announced that it is increasing its surveillance of high speed trading and rapid-fire trading across exchanges.

Also overseeing this industry at the federal level is the U.S. Congress. For example, the U.S. Senate Permanent Subcommittee on Investigations was created with the broad mandate to determine whether any changes are required in U.S. law to better protect the public from actions of investment banks and securities firms. In the spring of 2010, a subcommittee hearing focused on the role of investment banks in contributing to the financial crisis. The 2010 Wall Street Reform and Consumer Protection Act, passed in response to the financial crisis, set forth many changes in the way securities firms and investment banks are regulated. The bill’s Financial Services Oversight Council of financial regulators was given oversight of the industry in its charge to identify emerging systemic risks. Also under the act, effective July 21, 2011, the dollar threshold for determining whether an investment advisor must register under federal or state law increased. Specifically, all advisors with assets under management of under $100 million must register with state regulators and those with over $100 million under management must register with the SEC. Prior to that date, only advisors with assets under management of under $25 million registered with a state regulator. The bill also gave new authority for the Federal Reserve to supervise all firms that could pose a threat to financial stability and called for stronger capital and other prudential standards for all financial firms, and even higher standards for large, interconnected firms. Investment banks also saw stricter oversight as the bill called for the regulation of securitization markets, stronger regulation of credit rating agencies, a requirement that issuers and originators retain a financial interest in securitized loans, comprehensive regulation of all over-the-counter derivatives, and new authority for the Federal Reserve to oversee payment, clearing, and settlement systems. Finally, the bill gave authority to the government to resolve nonbank financial institutions whose failure could have serious systemic effects and revised the Federal Reserve’s emergency lending authority to improve accountability.

Finally, the Securities Investor Protection Corporation (SIPC) protects investors against losses of up to $500,000 caused by securities firm failures. SIPC is not an agency or establishment of the U.S. government and it has no authority to investigate or regulate its member broker-dealers.

Rather, the SIPC was created under the Securities Investor Protection Act of 1970 as a non-profit membership corporation. SIPC oversees the liquidation of member broker-dealers that close when the broker-dealer is bankrupt or in financial trouble and customer assets are missing. While 13 © 2022

agencies such as the SEC and FINRA deal with cases of investment fund fraud, the SIPC's focus is both different and narrow: restoring customer cash and securities left in the hands of bankrupt or otherwise financially troubled brokerage firms. The fund does not protect against losses on a customer’s account due to poor investment choices that reduce the value of a portfolio. The SIPC is funded with premium contributions from member firms.

27.

What are the three requirements of the U.S.A. Patriot Act that financial service firms must implement after October 1, 2003?

FIs must (1) verify the identity of people opening new accounts; (2) maintain records of the information used to verify the identity; and (3) determine whether the person opening an account is on a suspected terrorist list.

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Solutions for End-of-Chapter Questions and Problems: Chapter Five 1.

What is a mutual fund? In what sense is it a financial institution?

A mutual fund represents a pool of financial resources obtained from individuals and companies, which is invested in the money and capital markets. This process represents another method for economic savers to channel funds to companies and government units that need extra funds.

2.

What are money market mutual funds? In what assets do these funds typically invest? What factors have caused the strong growth in this type of fund since the late 1970s?

Money market mutual funds (MMMFs) invest in various mixtures of money market securities.

These securities primarily are Treasury bills, negotiable certificates of deposit, repurchase agreements, and commercial paper. The growth in MMMFs since the late 1970s initially occurred because of rising interest rates in the money markets, while Regulation Q restricted interest rates on accounts in depository institutions. Many investors moved their short-term savings from the depository institutions to the MMMFs as the spread in the earnings rate reached double digits. A result of this activity was to introduce many investors to the capital markets for the first time.

At the end of 2008, the share of long-term funds plunged to 59.1 percent of all funds, while money market funds increased to 40.9 percent. Part of the move to money market funds was the fact that during the worst of the financial crisis, the U.S. Treasury extended government insurance to all money market mutual fund accounts on a temporary basis. As financial markets tumbled in 2008, money market mutual funds moved investments out of corporate and foreign bonds (12.4 percent of the total in 2007 and 6.1 percent in 2008) into safer securities such as U.S. government securities (13.6 percent of the total investments in 2007 and 35.5 percent in 2008).

3.

What are long-term mutual funds? In what assets do these funds usually invest? What factors caused the strong growth in this type of fund from 1992 through 2007, the slowdown in growth in 2007-2008, and the return to growth after 2008?

Long-term funds include equity funds (comprised of common and preferred stock securities), bond funds (comprised of fixed-income securities with a maturity of longer than one year), and hybrid funds (comprised of both bond and stock securities). Some money market assets are included for liquidity purposes. The growth in these funds in the 1990s and 2000s reflected the dramatic increase in equity returns, the reduction in transaction costs, and the recognition of diversification benefits achievable through mutual funds.

The financial crisis and the collapse in stock and other security prices produced a sharp drop in mutual fund activity. At the end of 2008, total assets fell to $9,603.6 billion and the number of accounts to 264.6 million (of this, $5,771.3 billion and 226.5 million accounts were long-term funds). Investor demand for certain types of mutual funds plummeted, driven in large part by deteriorating financial market conditions. Stock market funds suffered substantial outflows, while inflow to U.S. government money market funds reached record highs. As the economy 1 © 2022

recovered in 2009-2012, so did assets invested in mutual funds, growing to $15.94 trillion by the end of 2015 (of this, $13.22 trillion were invested in long-term funds).

4.

Using the data in Table 5-2, discuss the growth and ownership holdings over the last 35 years of long-term funds versus short-term funds.

The dollar investment in the money market mutual funds (MMMF) exceeded the investment in the long-term funds in 1980. However, by 2007, long-term funds had more than a two to one advantage on the MMMFs, $7,829 billion to $3,033 billion. Long-term funds grew at an annualized rate of 19.6 percent, and the MMMF grew at an annualized rate of 14.6 percent. In each type of fund, the largest investment source was the household sector, owning 61.7 percent of all long-term funds and 44.4 percent of MMMFs in 2007. Household sector growth from 1980 through 2008 was 18.3 percent annual rate for long-term funds and 11.9 percent for the MMMF. The financial crisis and the collapse in stock and other security prices produced a sharp drop in long-term mutual fund activity. In 2008, investments in long-term funds fell to $5,435.3 billion, while MMMFs grew to $3,757.3 billion. However, as the economy recovered, long-term funds grew back to $12,574.6 billion by 2015, while MMMF fell to $2,627.1 billion. In each type of fund, the household sector remained the largest investment source, owning 63.0 percent of all long-term funds and 37.7 percent of MMMFs in 2015.

5.

Why did the proportion of equities in long-term funds increase from 38.3 percent in 1990 to more than 70 percent by 2000 and then decrease to 56.4 percent in 2015? How might an investor’s preference for a mutual funds objectives change over time?

The primary reason for the increased proportion of funds in equities during the 1990s was the strength of the equity market that was driven by the underlying strength of the economy during this period. Contrarily, the economy experienced its worst recession since the Great Depression in the late 2000s, causing investors to retreat from equities as preferred investments.

As might be expected, the proportion of equities in long-term funds reflects the popularity of different types of bond or equity funds at any point in time. For example, underscoring the attractiveness of equity funds in 2007 was the fact that stocks comprised over 70.0 percent of total long-term mutual fund asset portfolios. Credit market instruments were the next most popular assets (28.1 percent of the asset portfolio). In contrast, look at the distribution of assets in 2008, when the equity markets were plummeting. Equities made up only 55.5 percent of the long-term mutual fund portfolios and credit market instruments were 41.9 percent of total assets.

Note too that total financial assets fell from $7,829.0 billion in 2007 (before the start of the financial crisis) to just $5,435.3 billion in 2008 (at the height of the crisis), a drop of 30.6 percent. As the economy and financial markets recovered (in 2010), financial assets held by long-term mutual funds increased to $7,934.5 billion, of which only 60.0 percent were corporate equities. In 2015, long-term funds held financial assets totaling $12,574.6 billion, of which 56.4 percent were corporate equities. Thus, even seven years after the start of the financial crisis, long-term funds had not switched their holdings of corporate equities back to pre-crisis levels.

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6.

How does the risk of short-term funds differ from the risk of long-term funds?

The principal type of risk for short-term funds is interest rate risk, because of the predominance of fixed-income securities. Because of the shortness of maturity of the assets, which often is less than 60 days, this risk is mitigated to a large extent. Short-term funds generally have virtually no liquidity or default risk because of the types of assets held. An exception occurred during the financial crisis of 2008-2009. In September 2008, Primary Reserve Fund, a large and reputedly conservative money market fund had holdings of $785 million in commercial paper issued by Lehman. As a result of Lehman’s failure, shares in Primary Reserve Fund ‘broke the buck’ (i.e., fell below $1), meaning that its investors lost principal. This was the first incidence of a share price dip below a dollar for any money market mutual fund open to the general public. This fund had built a reputation for safe investment. Hence its exposure to Lehman scared investors, leading to a broad run on money market mutual funds. Within a few days more than $200 billion had flowed out of these funds. The U.S. Treasury stopped the run by extending government insurance to all money market mutual fund accounts held in participating money market funds as of the close of business on September 19, 2008. The insurance coverage lasted for one year (through September 18, 2009).

Long-term equity funds typically are well diversified, and the risk is more systematic or market based. Bond funds have extensive interest rate risk because of their long-term, fixed-rate nature.

Sector, or industry-specific, funds have systematic (market) and unsystematic risk, regardless of whether they are equity or bond funds.

7.

What are the economic reasons for the existence of mutual funds; that is, what benefits do mutual funds provide for investors? Why do individuals rather than corporations hold most mutual funds?

One major economic reason for the existence of mutual funds is the ability to achieve diversification through risk pooling for small investors. By pooling investments from a large number of small investors, fund managers are able to hold well-diversified portfolios of assets. In addition, managers can obtain lower transaction costs because of the volume of transactions, both in dollars and numbers, and they benefit from research, information, and monitoring activities at reduced costs.

Many small investors are able to gain benefits of the money and capital markets by using mutual funds. Once an account is opened in a fund, a small amount of money can be invested on a periodic basis. In many cases, the amount of the investment would be insufficient for direct access to the money and capital markets. On the other hand, corporations are more likely to be able to diversify by holding a large bundle of individual securities and assets, and money and capital markets are easily accessible by direct investment. Further, an argument can be made that the goal of corporations should be to maximize shareholder wealth, not to be diversified.

8.

What are the principal demographics of household owners who own mutual funds? What are the primary reasons why household owners invest in mutual funds?

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As of 2015, 53.6 million (43.0 percent of) U.S. households owned mutual funds. This was down from 56.3 million (52 percent) in 2001. Most are long-term owners, with 29 percent making their first purchases before 1990. While mutual fund investors come from all age groups, ownership is concentrated among individuals in their prime saving and investing years. Two-thirds of households owning mutual funds in 2015 were headed by individuals between the ages of 35 and 64. Interestingly, the number of families headed by a person with less than a college degree investing in mutual funds is 49 percent. The bull markets of the 1990s, the low transaction costs of purchasing mutual funds shares, as well as the diversification benefits achievable through mutual fund investments are again the likely reasons for these trends. The typical fund-owning household had $103,000 invested in a median number of four mutual funds. Compared to 1995, 2015 has seen an increase in the median age of mutual fund holders (from 44 to 51 years) and a large increase in median household financial assets owned (from $50,000 to $200,000) and median mutual fund assets owned (from $18,000 to $103,000). Further, holdings of equity funds have increased from 73 to 88 percent of all households.

9.

What change in regulatory guidelines occurred in 2009 that had the primary purpose of giving investors a better understanding of the risks and objectives of a fund?

In March 2009, the SEC adopted amendments to the form used by mutual funds to register under the Investment Company Act of 1940 and to offer their securities under the Securities Act of 1933 in order to enhance the disclosures that are provided to mutual fund investors. The amendments (first proposed in November 2007) required key information to appear in plain English in a standardized order at the front of the mutual fund statutory prospectus. The new amendment also included a new option for satisfying prospectus delivery obligations with respect to mutual fund securities under the Securities Act. Under the option, key information is sent or given to investors in the form of a summary prospectus and the statutory prospectus is provided on an Internet Web site. The improved disclosure framework was intended to provide investors with information that is easier to use and more readily accessible, while retaining the comprehensive quality of the information that was previously available.

10.

What are the three possible components reflected in the return an investor receives from a mutual fund?

The investor receives the income and dividends paid by the companies, the capital gains from the sale of securities by the mutual fund, and the capital appreciation of the underlying assets.

11.

How is the net asset value (NAV) of a mutual fund determined? What is meant by the term marked-to-market daily?

Net Asset Value (NAV) is the market value of each ownership share of the mutual fund. The total market value of the fund is determined by summing the total value of each asset in the fund.

The value of each asset can be found by multiplying the number of shares of the asset by the corresponding price of the asset. Dividing this total fund value by the number of shares in the mutual fund will give the NAV for the fund.

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The NAV is calculated at the end of each daily trading session, and thus reflects any adjustments in value caused by (a) changes in value of the underlying assets, (b) dividend distributions of the companies held, or (c) changes in ownership of the fund. This process of daily recalculation of the NAV is called marking-to-market.

12.

Suppose today a mutual fund contains 2,000 shares of J.P. Morgan Chase, currently trading at $64.75, 1,000 shares of Wal-mart, currently trading at $63.10, and 2,500 shares of Pfizer, currently trading at $31.50. The mutual fund has no liabilities and 10,000 shares outstanding held by investors. a. What is the NAV of the fund?

NAV = (2,000 x $64.75 + 1,000 x $63.10 + 2,500 x $31.50)/10,000 = $271,350/10,000 = $27.135 b. Calculate the change in the NAV of the fund if tomorrow J.P. Morgan’s shares increase to $66, Wal-mart’s shares increase to $68, and Pfizer’s shares increase to $30.

NAV = (2,000 x $66 + 1,000 x $68 + 2,500 x $34)/10,000 = $285,000/10,000 = $28.500, or an increase of $1.365. c. Suppose that today 1,000 additional investors buy one share each of the mutual fund at the NAV of $27.135. This means that the fund manager has $27,135 additional funds to invest. The fund manager decides to use these additional funds to buy additional shares in Wal-mart. Calculate tomorrow’s NAV given the same rise in share values as assumed in part b.

At today’s market price, the manager could buy 430 additional shares ($27,135/$63.10) of Walmart. Thus, its new portfolio of shares has 2,000 in J.P. Morgan Chase, 1,430 in Wal-mart, and 2,500 in Pfizer.

NAV = (2,000 x $66 + 1,430 x $68 + 2,500 x $34)/11,000 = $314,240/11,000 = $28.567, or an increase of $1.432. Note that the fund’s value changed over the month due to both capital appreciation and investment size. A comparison of the NAV in part b. with the one in this part indicates that the additional shares and the profitable investments made with the new funds from these shares resulted in a slightly higher NAV than had the number of shares remained static ($28.500 versus $28.567).

13.

A mutual fund owns 300 shares of General Electric, currently trading at $30, and 400 shares of Microsoft, Inc., currently trading at $54. The fund has 1,000 shares outstanding. a. What is the net asset value (NAV) of the fund?

NAV = (300 x $30 + 400 x $54)/1,000 = $30,600/1,000 = $30.60.

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b. If investors expect the price of General Electric shares to increase to $34 and the price of Microsoft shares to decrease to $48 by the end of the year, what is the expected NAV at the end of the year?

Expected NAV = (300 x $34 + 400 x $48)/1,000 = $29,400/1,000 = $29.4, or a decline of 3.92% c. Assume that the expected price of the General Electric shares is realized at $34. What is the maximum price decrease that can occur to the Microsoft shares to realize an end-ofyear NAV equal to the NAV estimated in part (a)? [(300 x $34) + (400 x PM)]/1,000 = $30.60, implies that PM = $51.00, a decrease of $3.00.

14.

What is the difference between open-end and closed-end mutual funds? Which type of fund tends to be more specialized in asset selection? How does a closed-end fund provide another source of return from which an investor may either gain or lose?

Open-end funds allow shares to be purchased and redeemed according to investor demand. The NAV of open-ended funds is determined only by changes in the value of the assets owned. In closed-end funds, the number of shares of the fund is fixed. If investors need to redeem their shares, they sell them to another investor. Thus, the demand for the fund shares can provide another source of return for the investors as the market price of the fund may exceed the NAV of the fund. Closed-end funds, such as real estate investment trusts, tend to be more specialized.

15.

Open-end fund A owns 165 shares of AT&T valued at $35 each and 30 shares of Toro valued at $75 each. Closed-end fund B owns 75 shares of AT&T and 72 shares of Toro.

Each fund has 1,000 shares of stock outstanding. a. What are the NAVs of both funds using these prices?

NAVopen-end = (165 x $35 + 30 x $75)/1,000 = $8.025.

NAVclosed-end = (75 x $35 + 72 x $75)/1,000 = $8.025. b. Assume that in one month the price of AT&T stock has increased to $36.25 and the price of Toro stock has decreased to $72.292. How do these changes impact the NAV of both funds? If the funds were purchased at the NAV prices in part (a) and sold at month end, what would be the realized returns on the investments?

NAVopen-end = (165 x $36.25 + 30 x $72.292)/1,000 = $8.15.

Percentage change in NAV = ($8.15 - $8.025)/$8.025 = 1.56%.

NAVclosed-end = (75 x $36.25 + 72 x $72.292)/1,000 = $7.92377.

Percentage change in NAV = ($7.92377 - $8.025)/$8.025 = -1.26%.

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c. Assume that another 155 shares of AT&T are added to fund A. The funds needed to buy the new shares are obtained by selling 676 more shares in fund A. What is the effect on fund A’s NAV if the stock prices remain unchanged from the original prices?

NAVopen-end = ((165 + 155) x $35 + 30 x $75)/(1,000 + 676) = $8.025.

Percentage change in NAV = ($8.025 - $8.025)/$8.025 = 0.00%.

16.

What is the difference between a load fund and a no-load fund? Is the argument that load funds are more closely managed and therefore have higher returns supported by the evidence presented in Table 5-6?

A load fund charges an up-front fee that often is called a sales charge and is used as a commission payment for sales representatives. These fees can be as high as 5.75 percent. A noload fund does not charge a sales fee, although a small annual fee can be charged to cover certain administrative expenses. This small fee, which is called a 12b-1 fee, usually ranges between 0.25 and 1.00 percent of assets. According to the data in Table 5-6, the load funds have adjusted returns that are decreased after the fee is removed. In each case the relative performance ranking of the fund decreases after the load is subtracted.

17.

What is a 12b-1 fee? Suppose you have a choice between a load fund with no annual 12b-1 fee and a no-load fund with an annual 12b-1 fee of 25 basis points. How would the length of your expected investment horizon, or holding period, influence your choice between these two funds?

The 12b-1 fee is allowed by the SEC to provide assistance in covering administrative expenses for no-load funds. Thus, in terms of fees and without consideration of time value issues, a 4.00 percent load would be equivalent to the 12b-1 fee for 16 years. This comparison would have to be adjusted for change in the value of the fund’s assets over time, since the 12b-1 fee is administered on an annual basis against the fund value at that time.

18.

Suppose an individual invests $10,000 in a load mutual fund for two years. The load fee entails an up-front commission charge of 4 percent of the amount invested and is deducted from the original funds invested. In addition, annual fund operating expenses (or 12b-1 fees) are 0.85 percent. The annual fees are charged on the average net asset value invested in the fund and are recorded at the end of each year. Investments in the fund return 5 percent each year paid on the last day of the year. If the investor reinvests the annual returns paid on the investment, calculate the annual return on the mutual fund over the twoyear investment period.

Annual Return Calculation Based on Text Example 5-4: Annualized load fee = 4%  2 years = 2.00% Annual fund operating expense = 0.85% Total annual cost = 2.85%  Annual return = 5.00% - 2.85% = 2.15%

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Annual Return Calculation Based on Present Value of Investment: Initial investment in the fund = $10,000 Front-end load of 4.00% = $400 Total investable funds = $9,600 Investment value at end of year one = $9,600 x 1.05 = $10,080.00 Operating expenses based on average NAV = $9,840 x 0.0085 = $83.64 Net investable funds for year two = $9,996.36 Investment value at end of year two = $9,996.36 x 1.05 = $10,496.18 Operating expenses based on average NAV = $10,246.27 x 0.0085 = $87.09 Net investment at end of year two = $10,409.09 Average annual compound return: $10,409.09 = $10,000(1 + g)2 => g = 2.025% 19.

Who are the primary regulators of the mutual fund industry? How do their regulatory goals differ from those of other types of financial institutions?

The Securities and Exchange Commission (SEC) is the primary regulator of the mutual fund industry. The SEC is not concerned with the administration of sound economic monetary policy, which is part of the goal of the Federal Reserve System, but rather is primarily concerned with the protection of investors from possible abuses by managers of mutual funds.

Several pieces of legislation have been enacted to clarify and assist this regulatory process.

Under the Securities Act of 1933, mutual funds must file a registration statement with the SEC and abide by the rules established under the act for the distribution of prospectuses to investors.

The Securities Exchange Act of 1934 establishes antifraud provisions aimed at the accurate transmission of information to prospective investors. The 1934 act also appointed the National Association of Securities Dealers to supervise the distribution of mutual fund shares. The Investment Advisors Act of 1940 regulates the activities of mutual fund advisors, and the Investment Company Act establishes rules involving fees and charges. The Insider Trading and Securities Fraud Enforcement Act of 1988 addresses issues of insider trading, and the Market Reform Act of 1990 provides for the establishment of circuit breakers to halt trading in case of severe market downturns. The National Securities Markets Improvement Act of 1996 exempts mutual funds from the regulatory burden of state securities regulators. Finally, in March 2009, the SEC adopted amendments to the form used by mutual funds to register under the Investment Company Act of 1940 and to offer their securities under the Securities Act of 1933 in order to enhance the disclosures that are provided to mutual fund investors. The amendments (first proposed in November 2007) required key information to appear in plain English in a standardized order at the front of the mutual fund statutory prospectus. The new amendment also included a new option for satisfying prospectus delivery obligations with respect to mutual fund securities under the Securities Act. Under the option, key information is sent or given to investors in the form of a summary prospectus and the statutory prospectus is provided on an 8 © 2022

Internet Web site. The improved disclosure framework was intended to provide investors with information that is easier to use and more readily accessible, while retaining the comprehensive quality of the information that was previously available.

After the financial crisis, in a February 2013 letter sent to the Financial Stability Oversight Council (FSOC) (set up as a result of the Wall Street Reform and Consumer Protection Act to oversee the financial system), the leaders of all 12 regional Federal Reserve banks called for a significant overhaul of the money market industry. The letter stated that even four years after the financial crisis, without reform money, market mutual fund activities could spread the risk of significant credit problems from the funds to banks to the broader financial system. New York Fed president William Dudley stated that the risk of a run on money market funds was potentially higher in 2013 than before the crisis because banks increasingly used these funds as a source of financing and because Congress blocked the Fed and Treasury from using certain emergency tools that could stabilize the funds during a market panic. As a result of the calls for reform, in 2014, the SEC adopted amendments to the rules that govern money market mutual funds. The amendments make structural and operational reforms to address risks of investor runs in money market funds, while preserving the benefits of the funds. The new rules require a floating net asset value (NAV) for institutional prime money market funds. Floating NAV allows the daily share prices of these funds to fluctuate along with changes in the market value of fund assets. Further, liquidity fees and redemption gates were instituted, giving money market fund boards the ability to impose fees and gates during periods of stress. The final rules also include enhanced diversification, disclosure and stress testing requirements, as well as updated reporting by money market funds and private funds that operate like money market funds.

Also, in 2015 the SEC proposed rules and amendments to modernize and enhance the reporting and disclosure of information by investment companies and investment advisers. The new rules would enhance the quality of information available to investors and would allow the Commission to more effectively collect and use data provided by investment companies and investment advisers. The SEC also proposed a comprehensive package of rule reforms designed to enhance effective liquidity risk management by open-end funds, including mutual funds and exchange-traded funds (ETFs). Under the proposed reforms, mutual funds and ETFs would be required to implement liquidity risk management programs and enhance disclosure regarding fund liquidity and redemption practices. The proposal is designed to better ensure investors can redeem their shares and receive their assets in a timely manner. A fund’s liquidity risk management program would be required to contain multiple elements, including: classification of the liquidity of fund portfolio assets based on the amount of time an asset would be able to be converted to cash without a market impact; assessment, periodic review and management of a fund’s liquidity risk; establishment of a fund’s three-day liquid asset minimum; and board approval and review.

20.

What is a hedge fund and how is it different from a mutual fund?

Hedge funds are a type of investment pool that solicits funds from (wealthy) individuals and other investors (e.g., commercial banks) and invests these funds on their behalf. Hedge funds are similar to mutual funds in that they are pooled investment vehicles that accept investors’ money 9 © 2022

and generally invest it on a collective basis. Hedge funds are, however, not subject to the numerous regulations that apply to mutual funds for the protection of individuals, such as regulations requiring a certain degree of liquidity, regulations requiring that mutual fund shares be redeemable at any time, regulations protecting against conflicts of interest, regulations to ensure fairness in the pricing of funds shares, disclosure regulations, and regulations limiting the use of leverage. Further, hedge funds do not have to disclose their full activities to third parties.

Thus, they offer a high degree of privacy for their investors. Until 2010, hedge funds were not required to register with the SEC. Thus, they were subject to virtually no regulatory oversight (e.g., by the SEC under the Securities Act and Investment Advisors Act) and generally took significant risk. Even after 2010, hedge funds offered in the United States avoid regulations by limiting the asset size of the fund.

Historically, hedge funds avoided regulations by limiting the number of investors to less than 100 individuals (below that required for SEC registration), who must be deemed “accredited investors.” To be accredited, an investor must have a net worth of over $1 million or have an annual income of at least $200,000 ($300,000 if married). These stiff financial requirements allowed hedge funds to avoid regulation under the theory that individuals with such wealth should be able to evaluate the risk and return on their investments. According to the SEC, these types of investors should be expected to make more informed decisions and take on higher levels of risk. However, as a result of some heavily publicized hedge fund failures and near failures (the result of fraud by fund managers, e.g., Bernard L. Madoff Investment Securities, and the financial crisis, e.g., Bear Stearns High Grade Structured Credit Strategies Fund), in 2010 federal regulators increased the oversight of hedge funds.

Because hedge funds have been exempt from many of the rules and regulations governing mutual funds, they can use aggressive strategies that are unavailable to mutual funds, including short selling, leveraging, program trading, arbitrage, and derivatives trading. Further, since hedge funds that do not exceed $100 million in assets under management do not register with the SEC, their actual data cannot be independently tracked. Therefore, much hedge fund data are selfreported. It is estimated that in 2015 there were over 8,000 hedge funds in the world, with managed assets estimated at $3.17 trillion.

21.

What are the different categories of hedge funds?

Most hedge funds are highly specialized, relying on the specific expertise of the fund manager(s) to produce a profit. Hedge fund managers follow a variety of investment strategies, some of which use leverage and derivatives, others use more conservative strategies and involve little or no leverage. Generally, hedge funds are set up with specific parameters so investors can forecast a risk-return profile.

“More risk” funds are the most aggressive and may produce profits in many types of market environments. Funds in this group are classified by objectives such as: aggressive growth, emerging markets, macro, market timing, and short selling. Aggressive growth funds invest in equities expected to experience acceleration in growth of earnings per share. Generally, high price-to-earnings ratios, low or no dividend companies are included. These funds hedge by 10 © 2022

shorting equities where earnings disappointment is expected or by shorting stock indexes.

Emerging market funds invest in equity or debt securities of emerging markets which tend to have higher inflation and volatile growth. Macro funds aim to profit form changes in global economies, typically brought about by shifts in government policy which impact interest rates.

These funds include investments in equities, bonds, currencies and commodities. They use leverage and derivatives to accentuate the impact of market moves. Market timing funds allocate asset among different asset classes depending on the manager’s view of the economic or market outlook. Thus, portfolio emphasis may swing widely between assets classes. Unpredictability of market movements and the difficulty of timing entry and exit from markets adds significant risk to this strategy. Short selling funds sell securities in anticipation of being able to buy them back in the future at a lower price based on the manager’s assessment of the overvaluation of the securities or in anticipation of earnings disappointments.

“Moderate risk” funds are more traditional funds, similar to mutual funds, with only a portion of the portfolio being hedged. Funds in this group are classified by objectives such as: distressed securities, fund of funds, opportunistic, multi strategy, and special situations. Distressed securities funds buy equity, debt or trade claims at deep discounts of companies in or facing bankruptcy or reorganization. Profits opportunities come from the market’s lack of understanding of the true value of these deep discount securities and from the fact that the majority of institutional investor cannot own below investment grade securities. Fund of funds mix hedge funds and other pooled investment vehicles. This blending of different strategies and asset classes aims to provide a more stable long term investment return than any of the individual funds. Returns and risk can be controlled by the mix of underlying strategies and funds. Capital preservation is generally an important consideration for these funds. Opportunistic funds change their investment strategy as opportunities arise to profit from events such as IPOs, sudden price changes resulting from a disappointing earnings announcement, and hostile takeover bids. These funds may utilize several investing styles at any point in time. and are not restricted to any particular investment approach or asset class. Multi strategy funds take a diversified investment approach by implementing various strategies simultaneously to realize short and long term gains.

This style of investment allows the manager to overweight or underweight different strategies to best capitalize on current investment opportunities. Special situation funds invest in event driven situations such as mergers, hostile takeovers, reoganizations, or leveraged buyouts. These funds may undertake simultaneous purchases of stock in companies being acquired, and the sale of stock in its bidder, hoping to profit from the spread between the current market price an the final purchase price of the company.

“Risk avoidance” funds are also more traditional funds, emphasizing consistent but moderate returns while avoiding risk. Funds in this group are classified by objectives such as: income, market neutral-arbitrage, market neutral-securities hedging, and value. Income funds invest with the primary focus on yield or current income rather than solely on capital gains. These funds use leverage to buy bonds and some fixed income derivatives, profiting from principal appreciation and interest income. Market neutral-arbitrage funds attempt to hedge market risk by taking offsetting positions, often in different securities of the same issuer, e.g., long convertible bonds and short the firm’s equity. Their focus is on obtaining returns with low or no correlation to both the equity and bond markets. Market neutral-securities hedging funds invest equally in long and short equity portfolios in particular market sectors. Market risk is reduced but effective stock 11 © 2022

analysis is critical to obtaining a profit. These funds use leverage to magnify their returns. They also sometimes use market index futures to hedge systematic risk. Value funds invest in securities perceived to be selling at deep discounts relative to their intrinsic values. Securities include those that may be out of favor or underfollowed by analysts.

22.

What types of fees do hedge funds charge?

Hedge fund managers generally charge two types of fees: management fees and performance fees. As with mutual funds, the management fee is computed as a percentage of the total assets under management and typically run between 1.5 to 2.0 percent. Performance fees are unique to hedge funds. Performance fees give the fund manager a share of any positive returns on a hedge fund. The average performance fee on hedge funds is approximately 20 percent but varies widely. For example, Steven Cohen’s SAC Capital Partners charges a performance fee of 50 percent. Performance fees are paid to the hedge fund manager before returns are paid to the funds investors. Hedge funds often specify a “hurdle” rate, which is a minimum annualized performance benchmark that must be realized before a performance fee can be assessed. Further, a “high water mark” is usually used for hedge funds in which the manager does not receive a performance fee unless the value of the fund exceeds the highest net asset value it has previously achieved. High water marks are used to link the fund manager’s incentives more closely to those of the fund investors and to reduce the manager’s incentive to increase the risk of trades.

23.

What is the difference between domestic hedge funds and offshore hedge funds?

Describe the advantages of offshore hedge funds over domestic hedge funds.

Hedge funds that are organized in the U.S. are designated as domestic hedge funds. These funds require investors to pay income taxes on all earnings from the hedge fund. Funds located outside of the U.S. and structured under foreign laws are designated as offshore hedge funds. Many offshore financial centers encourage hedge funds to locate in their countries. The major centers include the Cayman Islands, Bermuda, Dublin, and Luxembourg. /the Cayman Islands is estimated to be the location of approximately 75 percent of all hedge funds. Offshore hedge funds are regulated in that they must obey the rules of the host country. However, the rules in most of these countries are not generally burdensome and provide anonymity to fund investors.

Further, offshore hedge funds are not subject to U.S. income taxes on distributions of profit or to U.S. estate taxes on funds shares.

When compared to domestic hedge funds, offshore hedge funds have been found to trade more intensely than domestic funds, due to the zero or lower capital gains tax for offshore funds.

Further, offshore hedge funds tend to engage less often in positive feedback trading (rushing to buy when the market is booming and rushing to sell when the market is declining) than domestic hedge funds. Finally, offshore hedge funds have been found to herd (mimic each other’s behavior when trading while ignoring information about the fundamentals of valuation) less than domestic hedge funds. Many hedge fund managers maintain both domestic and offshore hedge funds. Given the needs of their client investors, hedge fund managers want to have both types of funds so as to attract all types of investors.

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Solutions for End-of-Chapter Questions and Problems: Chapter Six 1.

What is the primary function of an insurance company? How does this function compare with the primary function of a depository institution?

The primary function of an insurance company is to provide protection from adverse events.

Insurance companies accept premium payments in exchange for compensation in the event that certain specified events occur.

The primary function of depository institutions is to provide financial intermediation for individual and corporate savers. By accepting deposits and making loans, depository institutions allow savers with predominantly small, short-term financial assets to benefit from investments in larger, longer-term assets. These long-term assets typically yield a higher rate of return than short-term assets.

2.

What is the adverse selection problem? How does adverse selection affect the profitable management of an insurance company?

The adverse selection problem occurs because customers who are most in need of insurance are most likely to acquire insurance. However, the premium structure for various types of insurance typically is based on an average population proportionately representing all categories of risk.

Thus, the existence of a proportionately larger share of high-risk customers may cause the premium revenue received by the insurance provider to underestimate the revenue needed to cover the insured liabilities and to provide a reasonable profit for the insurance company.

Insurance companies deal with the adverse selection problem by establishing different pools of the population based on health and related characteristics (such as income). By altering the pool used to determine the probability of losses to a particular customer’s health characteristics, the insurance company can more accurately determine the probability of having to pay out on a policy and can adjust the insurance premium accordingly.

3.

What are the similarities and differences among the four basic lines of life insurance products?

The four basic lines of life insurance products are (1) ordinary life, (2) group life, (3) industrial life, and (4) credit life. Ordinary life is sold on an individual basis and represents the largest segment (79%) of the life insurance market. The insurance policy can be structured as pure life insurance (term life) or may contain a savings component (whole life or universal life). Group policies (20%) are similar to ordinary life insurance policies except that they are centrally administered, providing cost economies in evaluating, screening, selling, and servicing the policies. Industrial life (<1%) has largely been replaced by group life since cost economies have made group life more affordable. Industrial life was historically marketed to individuals who would make small, very frequent payments and would require personal collection services.

Credit life (<1%) typically is term life sold in conjunction with some debt contract 1 © 2022

4.

Explain how annuity activities represent the reverse of life insurance activities.

Whereas life insurance involves different contractual methods of building up a fund, annuities involve different methods of liquidating a fund, such as paying out a fund’s proceeds. A typical life insurance contract requires a periodic payment by one party for a promised payment of either a lump sum or an annuity if a particular event occurs, such as death or an accident. An annuity represents a reverse contract where the party purchases the right to receive periodic payments depending on the market conditions. The contract may be initiated by investing a lump sum or by making periodic payments before the annuity payments begin.

5.

Explain how life insurance and annuity products can be used to create a steady stream of cash disbursements and payments to avoid paying or receiving a single-lump sum cash amount.

A life insurance policy (whole life or universal life) requires regular premium payments that entitle the beneficiary to the receipt of a single lump sum payment. Upon receipt of such a lump sum, a single annuity could be obtained which would generate regular cash payments until the value of the insurance policy is depleted.

6.

a. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $200,000 for 20 years? Assume that the annuity will earn 10 percent per year.

The required payment is the present value of $200,000 per year for 20 years at 10 percent. $1,702,712.74 = $200,000 (PVAi =10%, n = 20) b. Calculate the annual cash flows from a $1 million, 20-year fixed-payment annuity earning a guaranteed 10 percent per year if payments are to begin at the end of the current year.

The annual cash flows are given by X: $1,000,000= X ( PVAi=10%,n= 20 ) where PVA is obtained from a financial calculator with i = 10 percent and n = 20 years. The value for X is $117,459.62. c. Calculate the annual cash flows from a $1 million, 20-year fixed-payment annuity earning a guaranteed 10 percent per year if payments are to begin at the end of year 5.

In this case, the first annuity is to be received five years from today. The initial sum today will have to be compounded by four periods to estimate the annuities: X = $189,169.90 2 © 2022

$1,000,000 (1 + 0.10 )5 = X (PVAi = 10%, n = 20)

7.

You deposit $10,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 8 percent, what will be the amount of retirement funds at the end of year 10? $156,454.8 7 = $10,000FVA Beg i=8%, n=10

b. Instead of a lump sum, you wish to receive annuities for the next 20 years (years 11 through 30). What is the constant annual payment you expect to receive at the beginning of each year if you assume an interest rate of 8 percent during the distribution period?

In this case, the first annuity is to be received ten years from today. The amount of retirement funds at the end of year ten (the answer to part (a) of $156,454.87) will be paid out over twenty years with the first payment to be received immediately. $156,454.87 = X (PVA Beg i=8%,n=20 )

X = $14,754,88 c. Repeat parts (a) and (b) above assuming earning rates of 7 percent and 9 percent during the deposit period and earning rates of 7 percent and 9 percent during the distribution period. During which period does the change in the earning rate have the greatest impact?

Deposit Period 7 percent

Value at 10 Years $147,835.99

Distribution Period 7 percent 9 percent

Annual Payment $13,041.75 $14,857.72

9 percent

$165,602.93

7 percent 9 percent

$14,609.11 $16,643.32

If you earn only 7 percent during the deposit period, earning 9 percent during the distribution period will barely allow you to better the distribution of the 8 percent/8 percent pattern in parts (a) and (b). But if you earn 9 percent during the deposit period, the distribution amount at 7 percent will almost match the 8 percent/8 percent pattern.

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8.

You deposit $12,000 annually into a life insurance fund for the next 10 years, at which time you plan to retire. Instead of a lump sum, you wish to receive annuities for the next 20 years. What is the annual payment you expect to receive beginning in year 11 if you assume an interest rate of 6 percent for the whole time period?

The value of $12,000 deposited annually in a fund will amount to the following in ten years: $158,169.5 4 = $12,000FVA i=6%, n=10 $158,169.54 = X (PVAi=6%,n=20 )

The annuities per year over the next twenty years at 6% can be found by solving for X, annual cash flows, X = $13,789.94 9.

a. Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $20,000 per year until the end of that person’s life. The insurance company expects this person to live for 15 more years and would be willing to pay 6 percent on the annuity. How much should the insurance company ask this person to pay for the annuity?

Lumpsum = $20,000 x PVAi=6%,n=15 = $194,244.98 b. A second 65-year-old person wants the same $20,000 annuity, but this person is much healthier and is expected to live for 20 years. If the same 6 percent interest rate applies, how much should this healthier person be charged for the annuity?

Lumpsum = $20,000 x PVAi=6%,n=20 = $229,398.42 c. In each case, what is the difference in the purchase price of the annuity if the distribution payments are made at the beginning of the year?

For 15 years, the lump sum value is $205,899.68. So, the difference in the purchase price is $11,654.70. For 20 years, the lump sum value is $243,162.33. So, the difference in the purchase price is $13,763.91.

10.

Contrast the balance sheet of a life insurance company (Table 6-3) with the balance sheet of a commercial bank (Table 2-5) and that of a savings institution (Table 2-9). Explain the balance sheet differences in terms of the differences in the primary functions of the three organizations.

Life insurance companies have long-term liabilities because of the life insurance products that they sell. As a result, the asset side of the balance sheet predominantly includes long-term 4 © 2022

government and corporate bonds, corporate equities, and a declining amount of mortgage products. The asset side of a commercial bank’s balance sheet is comprised primarily of shortand medium-term loans to corporations and individuals and some liquid investment securities (e.g., Treasury securities). The principal asset category for a savings institution is long-term mortgages.

In effect, all three companies use large degrees of financial leverage to fund assets that primarily consist of debt securities. While the face value of deposits is fixed for banks and savings institutions, the composition of liabilities for insurance companies is stochastic. The primary liability category for a life insurance company is policy reserves that reflect the expected payment commitments on existing policy contracts. Insurance companies also sell short- and medium-term debt instruments called GICs that are used to fund their pension plan business. The liabilities of savings institutions are primarily short-term deposit accounts, while banks utilize short-term deposits and short-term borrowed funds, depending on the size of the bank.

11.

Using the data in Table 6-2, how has the composition of assets of U.S. life insurance companies changed over time?

Table 6-2 indicates that life insurance companies have increased their holdings of bonds and stocks and decreased their holdings of mortgages and policy loans over the period. Government securities comprise the second largest component, although the proportion has been decreasing in recent years as the yields have decreased. The major trends have been a long-term increase in the proportion of bonds and equities and a decline in the proportion of mortgages in the balance sheet.

12.

How do life insurance companies earn a profit?

Insurance companies earn profits by taking in more premium income than they pay out in policy payments. Firms can increase their spread between premium income and policy payouts in two ways. The first way is to decrease future required payouts for any given level of premium payments. This can be accomplished by reducing the risk of the insured pool (provided the policyholders do not demand premium rebates that fully reflect lower expected future payouts).

The second way is to increase the profitability of interest income on net policy reserves. Since insurance liabilities typically are long term, the insurance company has long periods of time to invest premium payments in interest earning asset portfolios. The higher is the yield on the insurance company's investments, the greater is the difference between the premium income stream and the policy payouts (except in the case of variable life insurance) and the greater is the insurance company's profitability.

13.

How would the balance sheet of a life insurance company change if it offered to run a private pension fund for another company?

The primary change in the balance sheet of a life insurance company would be an increase in the liability accounts that reflect these pension plans. Guaranteed investment contracts (GICs) and separate account categories likely would increase, depending on the type of pension plans 5 © 2022

provided to the customers. The premiums and contributions would be invested in the normal asset categories of the insurance company, except in cases where the pension fund requires aggressive investment strategies. In this case, the funds may be invested in specific equity mutual funds.

14.

How does the regulation of insurance companies differ from the regulation of depository institutions? What are the major pieces of life insurance regulatory legislation?

Insurance companies are more exclusively subject to state regulations compared to banks and savings institutions. Although there are national insurance organizations such as the National Association of Insurance Commissioners, the companies are chartered and regulated at the state level. Banks and thrifts are typically subject to both national and state oversight. While both banks and insurance companies receive regulatory scrutiny as to the quality of their assets and liabilities, bank regulations also dictate minimum reserve and capital requirements. Both insurance companies and banks are limited in the products that they can offer. The primary legislation is the McCarran-Ferguson Act of 1945. This legislation provides that federal regulation is subordinate to state regulation.

In 2009, the U.S. Congress considered establishing an optional federal insurance charter. The move behind such a charter picked up steam following the failure of the existing state by state regulatory system to act in preventing the problems at insurance giant AIG from becoming a systemic risk to the national economy. Those in favor of an optional federal insurance charter noted that under the current state by state system, insurers face obstacles such as inconsistent regulations, barriers to innovation, conflicting agent licensing, and education requirements. While the House version of the 2010 Financial Services Regulatory Overhaul Bill (approved in December 2009) contained no provision for federal regulation of insurance companies, Financial Services Chairman Barney Frank stated that this would still be a possibility as the bill moved through the regulatory process towards final passage.

The final version of the overhaul bill, the Wall Street Reform and Consumer Protection Act of 2010 established the Federal Insurance Office (FIO) that reports to Congress and the President on matters pertaining to the insurance industry. While the industry’s main regulator continues to be the states in which firms operate, the FIO has the authority to monitor the insurance industry, identify regulatory gaps or systemic risk, deal with international insurance matters and monitor the extent to which underserved communities have access to affordable insurance products. The Wall Street Reform and Consumer Protection Act also called for the establishment of the Financial Stability Oversight Council (FSOC), which is charged with designating any financial institution (including insurance companies) that presents a systemic risk to the economy and subjecting them to greater regulation.

Also the result of the Wall Street Reform and Consumer Protection Act, the Federal Reserve has become a major supervisor of insurance firms. The Fed extended much of its authority over the insurance industry through the designation of three of the largest insurers (American International Group, Prudential Financial, and MetLife) as “systemically important financial institutions.” However, with the closure of the Office of Thrift Supervision in 2011, the Fed also 6 © 2022

supervises 14 insurance companies that own savings institutions. In total, the Fed supervises about one-third of U.S. insurance industry assets. This increased oversight by the Fed has incited concern among insurance companies and state regulators that the Fed will enact onerous capital rules and supervise insurance firms like banks. Promoting the concerns are cases like that of MetLife that failed the Fed’s “stress tests” in 2012 despite the firm’s protests the Fed misunderstood its business model. In 2015, MetLife sued the U.S. to overturn its designation as a non-bank systemically important financial institution. The insurer argued that its failure would not pose a risk to the financial system. MetLife further argued that, because it is harder for a customer to pull money from an insurance contract than it is for a depositor to withdraw money from a bank deposit account during a crisis, the insurance industry is safer than banking.

15.

How do state guarantee funds for life insurance companies compare with deposit insurance for depository institutions?

State guarantee funds are different from deposit insurance in several ways. First, the insurance guarantee funds are administered by the life insurance companies as opposed to a separate company like the FDIC for deposit institutions. Second, insurance companies do not generally pay premiums into the guarantee fund until after the failure of an insurance company. The FDIC requires annual premium payments from all depository institutions. Third, while the FDIC requires premium payments to be based on the amount of deposits and the risk of the assets of the depository institutions, the contributions by insurance companies typically are based on the relative amount of premium income received by the surviving insurance companies. Finally, because contributions to the insurance guarantee funds are requested only after the failure of a company, the transmission of the benefits to the policyholders occurs only after a reasonable delay. In contrast, the FDIC normally pays depositors within a few days after the failure of a depository institution.

16.

What are the two major activity lines of property-casualty insurance firms?

The two major lines of property-casualty insurance are: a) Property insurance: Property insurance involves insurance coverages related to the loss of real and personal property. Insurance compensating the insured, fully or partially, for personal or commercial property damage as a result of accidents and other events; and b) Liability insurance: Liability insurance concerns protection against legal liability exposures. Insurance compensating a third party, fully or partially, because its personal or commercial property was damaged as a result of the accidental actions of the insured.

In many cases, property and liability insurance is sold together, such as personal or commercial multiple peril and auto insurance. Fire insurance is usually are sold as property insurance only.

Liability insurance is sold separately for coverage such as malpractice or product liability hazards. In addition, reinsurance provides a means for primary insurers to pool their risk by transferring some of the risk and premium to a reinsurer.

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17.

How have the product lines of property-casualty insurance companies changed over time?

Product lines based on net premiums typically are included in the property-casualty insurance arena. Large decreases have occurred in the fire and allied categories, while the multiple peril (or umbrella) and liability policies have shown the large increases. The changes are related in that much of the decreased coverage has been subsumed into the multiple peril policies.

18.

Contrast the balance sheet of a property-casualty insurance company (Table 6-5) with the balance sheet of a commercial bank (Table 2-5). Explain the balance sheet differences in terms of the differences in the primary functions of the two organizations.

The balance sheet of a PC company is similar to that of a life insurance company. Long-term financial assets such as bonds, common equities, and preferred stock comprise the majority of the assets, while loss reserves, loss adjustment expenses, and unearned premiums dominate the liabilities. In contrast, short- and medium-term financial assets dominate the asset side of the balance sheets of most banks and borrowed funds in the form of deposits are the primary liability for commercial banks. Whereas banks provide time and size intermediation for depositors, PC insurance companies use premium payments to provide assurance against certain types of risk for customers. For a bank the deposits represent borrowed funds, while the premiums to an insurance company represent the actual price for the risk coverage.

19.

What are the three sources of underwriting risk in the property-casualty insurance industry?

The three sources of underwriting risk in the PC industry are (a) unexpected increases in loss rates, (b) unexpected increases in expenses, and (c) unexpected decreases in investment yields.

Loss rates are influenced by whether the product lines are property or liability (with the latter being less predictable), whether they are low-severity high-frequency lines or high-severity lowfrequency lines (with the latter being more difficult to estimate), and whether they are long-tail or short-tail lines (with the former being more difficult to estimate). Loss rates also are affected by product and social inflation. Unexpected increases in expenses are a result of increases in commission costs to brokers, general expenses, taxes, and other expenses related to acquisitions.

Finally, investment yields depend on the stock and bond markets as well as on the asset allocations of the portfolios.

20.

How do unexpected increases in inflation affect property-casualty insurers?

Inflation generally has an adverse effect on the cost of providing benefits that have been purchased by the insured, particularly if the policy is written in terms of the replacement cost of the asset and the premiums are not adjusted for inflation. In addition, the investment value of bonds and other fixed-rate assets of insurers from which claims proceeds are derived may decrease in value from unexpected inflation.

21.

Identify the four characteristics or features of the perils insured against by propertycasualty insurance. Rank the features in terms of actuarial predictability and total loss potential.

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• • • •

22.

Property versus liability: Maximum levels of losses are more predictable for property lines than for liability lines.

Severity versus frequency: Loss rates are more predictable on low-severity, high-frequency lines than they are on high-severity, low-frequency lines.

Time of exposure (long-tail versus short tail): The extent of expected losses is more difficult for long-tail risk exposure phenomenon than for short-tail exposures.

Inflation: The inflation risk of property lines is likely to reflect the underlying inflation of the economy, while the inflation risk of liability lines may be subject to the changing values or social risk of the society.

Insurance companies will charge a higher premium for which of the insurance lines listed below? Why? a. Low-severity, high-frequency lines versus high-severity, low-frequency lines.

Insurance companies have a more difficult time predicting the severity of losses for highseverity, low-frequency lines of business, such as earthquakes and hurricanes. In addition, these catastrophic events cause severe damage, meaning the individual risks in the insured pool are not independent. As a result, premiums for high-severity, low-frequency lines will be higher than premiums for low-severity, high-frequency lines. b. Long-tail versus short-tail lines.

Losses in long-tail lines of business are harder to predict than in short-tail lines, because claims can be made years after the premiums have been made. Thus, premiums in this category of business will be higher. Modern day examples of such lines include coverage for product liabilities, such as exposure to asbestos.

23.

What does the loss ratio measure? What has been the long-term trend of the loss ratio?

Why?

The loss ratio measures the actual losses incurred on a line of insurance relative to the premiums earned on the line. A ratio greater than 100 implies that the premiums earned did not cover the losses on the product line. The loss ratio has increased from the 60 percent range in the early 1950s to the 70 and 80 percent range in the 1990s into the 2010s. Increases in social inflation and the long-tail risk exposure phenomenon have caused some insurance companies to invest in shorter-term assets that have lower yields and thus generate lower premium earnings. In addition, increased coverage in areas with higher uncertainty of losses has occurred within the industry.

24.

What does the expense ratio measure? Identify and explain the two major sources of expense risk to a property-casualty insurer. Why has the long-term trend in this ratio been decreasing?

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The expense ratio measures the expenses incurred relative to premiums written. Expense risk is comprised primarily of loss adjustment expenses, which relate to the cost surrounding the loss settlement process, and commission costs paid to insurance brokers and sales agents in an effort to attract business. Large insurance companies have found expense efficiencies in using their own brokers rather than using independent brokers to sell insurance.

25.

How is the combined ratio defined? What does it measure?

The combined ratio is equal to the loss ratio plus the expense ratio. The ratio may be stated before or after dividends paid to policyholders. The ratio basically measures the underwriting profitability of an insurance line. If the combined ratio is less than 100, the premiums on the insurance have been sufficient to cover both losses and expenses on line.

26.

What is the investment yield on premiums earned? Why has this ratio become so important to property-casualty insurers?

The investment yield on premiums earned is the return earned on the firm’s investment of premiums relative to premiums earned on a line of insurance. In cases where the combined ratio is greater than 100, the insurer must rely on investment income from premiums to achieve profitability. Since the 1980s, the combined ratio most often has been greater than 100. That is, the loss ratio and the expense ratio have exceeded the amount of premiums received on the insurance lines. Thus, the yield on invested premiums has become critical to the overall profitability of the property-casualty insurance industry.

27.

Consider the data in Table 6-6. Since 1980, what has been the necessary investment yield for the industry to enable the operating ratio to be less than 100 in each year? How is this requirement related to the interest rate risk and credit risk faced by a property-casualty insurer?

The minimum investment yield required to achieve an operating ratio of 100 or less ranged from a low of -7.6 percent in 2006 to a high of 16.2 percent in 1985. The average yield over this period (for the years reported) was 3.30 percent. In effect, PC insurers required an average annual yield of 3.30 percent on invested premiums during a time when interest rates were seldom this high and operating losses were significant. Year-by-year values are given below based on data given in Table 6-6.

Year 1980 1985 1990 1995 1997 2000

Combined Ratio after Dividends 103.1% 116.2% 109.6% 106.4% 101.6% 110.5%

Required Combined Ratio 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

Minimum Investment Yield 3.1% 16.2% 9.6% 6.4% 1.6% 10.5% 10

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2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

116.0% 107.2% 100.1% 98.7% 100.9% 92.4% 95.6% 105.1% 101.0% 102.4% 108.2% 103.2% 96.3% 97.0% 97.6%

100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

16.0% 7.2% 0.1% -1.3% 0.9% -7.6% -4.4% 5.1% 1.1% 2.4% 8.2% 3.2% -3.7% -3.0% -2.4%

Arithmetic Average = Minimum = Maximum = 28.

3.30% -7.6% 16.2%

a. What is the combined ratio for a property insurer that has a loss ratio of 73 percent, a loss adjustment expense of 12.5 percent, and a ratio of commissions and other acquisition expenses of 18 percent?

The combined ratio is 73% + 12.5% + 18% = 103.5%. b. What is the combined ratio adjusted for investment yield if the company earns an investment yield of 8 percent?

The combined ratio adjusted for investment yield is 103.5% - 8% = 95.5%.

29.

An insurance company’s projected loss ratio is 77.5 percent and its expense ratio is 23.9 percent. The company estimates that dividends to policyholders will be 5 percent. What must be the minimum yield on investments to achieve a positive operating ratio?

The combined ratio = 77.5% + 23.9% + 5.0% = 106.4%. In order to be profitable, the yield on investments has to be greater than 6.4%.

30.

An insurance company collected $3.6 million in premiums and disbursed $1.96 million in losses. Expenses amounted to 6.6 percent and dividends paid to policyholders totaled 1.2 percent. The total income generated from the company’s investments was $170,000 after all expenses were paid. What is the net profitability in dollars?

Pure loss = $3.6 million - $1.96 million = $1,640,000 Expenses = 0.066 x $3,600,000 = $237,600 11 © 2022

Dividends = 0.012 x $3,600,000 = $43,200 Investment returns = $170,000 Net profits = $1,640,000 - $237,600 - $43,200 + $170,000 = $1,529,200 31.

A property–casualty insurer brings in $6.25 million in premiums on its homeowners multiple line of insurance. The line’s losses amount to $4,343,750, expenses are $1,593,750, and dividends are $156,250. The insurer earns $218,750 in the investment of its premiums. Calculate the line’s loss ratio, expense ratio, dividend ratio, combined ratio, investment ratio, operating ratio, and overall profitability.

Loss ratio = $4,343,750/$6,250,000 = 69.5% Expense ratio = $1,593,750/$6,250,000 = 25.5% Dividend ratio = $156,250/$6,250,000 = 2.5% Combined ratio = 69.5% + 25.5% + 2.5% = 97.5% Investment ratio = $218,750/$6,250,000 = 3.5% Operating ratio = 97.5% - 3.5% = 94.0% Overall profitability = 100.0% - 94.0% = 6.0%

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Solutions for End-of-Chapter Questions and Problems: Chapter Seven 1.

What is the process of asset transformation performed by a financial institution? Why does this process often lead to the creation of interest rate risk? What is interest rate risk?

Asset transformation by an FI involves purchasing primary assets and issuing secondary assets as a source of funds. The primary securities purchased by the FI often have maturity and liquidity characteristics that are different from the secondary securities issued by the FI. For example, a bank buys medium- to long-term bonds and makes medium-term loans with funds raised by issuing short-term deposits.

Interest rate risk occurs because the prices and reinvestment income characteristics of long-term assets react differently to changes in market interest rates than the prices and interest expense characteristics of short-term deposits. Interest rate risk is the risk incurred by an FI when the maturities of its assets and liabilities are mismatched.

2.

What is refinancing risk? How is refinancing risk part of interest rate risk? If an FI funds long-term assets with short-term liabilities, what will be the impact on earnings of an increase in the rate of interest? A decrease in the rate of interest?

Refinancing risk is the risk that the cost of rolling over or reborrowing funds will rise above the returns being earned on asset investments. This risk occurs when an FI is holding assets with maturities greater than the maturities of its liabilities. For example, if a bank has a ten-year fixedrate loan funded by a 2-year time deposit, the bank faces a risk in that new deposits may only be obtained, and the loans refinanced, at a higher rate in two years. These interest rate increases would reduce net interest income. The bank would benefit if interest rates decrease as the cost of renewing the deposits would decrease, while the interest rate earned on the loan would not change. In this case, net interest income would increase.

3.

What is reinvestment risk? How is reinvestment risk part of interest rate risk? If an FI funds short-term assets with long-term liabilities, what will be the impact on earnings of a decrease in the rate of interest? An increase in the rate of interest?

Reinvestment risk is the risk that the return on funds to be reinvested will fall below the cost of funds. This risk occurs when an FI holds assets with maturities that are shorter than the maturities of its liabilities. For example, if a bank has a two-year loan funded by a ten-year fixedrate time deposit, the bank faces the risk that interest rates might decrease. In this case, it might be forced to lend or reinvest the money at lower rates after two years, perhaps even below the deposit rates. Also, if the bank receives periodic cash flows, such as coupon payments from a bond or monthly payments on a loan, these periodic cash flows will also be reinvested at the new lower interest rates. In this case, net interest income would decrease. If interest rates increase, the bank would be able to lend or reinvest the money at higher rates after two years. In this case, net interest income would increase. Besides the effect on the income statement, reinvestment risk may cause realized yields on assets to differ from the a priori expected yields.

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4.

The sales literature of a mutual fund claims that the fund has no risk exposure since it invests exclusively in federal government securities which are free of default risk. Is this claim true? Explain why or why not.

Although the fund's asset portfolio is comprised of securities with no default risk, the securities are exposed to interest rate risk. For example, if interest rates increase, the market value of the fund's Treasury security portfolio will decrease. Further, if interest rates decrease, the realized yield on these securities will be less than the expected rate of return because of reinvestment risk.

In either case, investors who liquidate their positions in the fund may sell at a Net Asset Value (NAV) that is lower than the purchase price.

5.

How can interest rate risk adversely affect the economic or market value of an FI?

When interest rates increase (or decrease), the values of fixed-rate assets decrease (or increase) because of the discounted present value of the cash flows. To the extent that the change in market value of the assets differs from the change in market value of the liabilities, the difference is realized in the economic or market value of the equity of the FI. For example, for most depository institutions, an increase in interest rates will cause asset values to decrease more than liability values. The difference will cause the market value, or share price, of equity to decrease.

6.

Consider an FI that issues $100 million of liabilities with one year to maturity to finance the purchase of $100 million of assets with a two year maturity. Suppose that the cost of funds (liabilities) for the FI is 5 percent per year and the return on the assets is 8 percent per year. a.

Calculate the FI’s profit spread and dollar value of profit in year 1.

Over the first year, the FI can lock in a profit spread of 3 percent (8 percent - 5 percent) by borrowing short term (for one year) and lending long term (for two years). Thus, its profit is $3 million (0.03 x $100m). Its profit for the second year, however, is uncertain. The risk always exists that interest rates will change between years 1 and 2. b. Calculate the profit spread and dollar value of profit in year 2, if the FI can refinance its liabilities at 5 percent.

If the level of interest rates does not change, the FI will receive a profit spread of 3 percent or $3 million profit for the second year as well. c.

If interest rates rise and the FI can borrow new one-year liabilities at 9 percent in the second year, calculate the FI’s profit spread and dollar value of profit in year 2.

In this case the FI’s profit spread in the second year is negative: 8 percent -9 percent = -1 percent, or the FI loses $1 million (-0.01 x 100m). The positive spread earned in the first year by the FI from holding assets with a longer maturity than its liabilities is offset by a negative spread in the second year. As a result, when an FI holds longer-term assets relative to liabilities, it 2 © 2022

potentially exposes itself to the interest rate risk that the cost of refinancing can be more than the return earned on asset investments. d.

If interest rates fall and the FI can borrow new one-year liabilities at 3 percent in the second year, calculate the FI’s profit spread and dollar value of profit in year 2.

If interest rates rise and the FI can borrow new one-year liabilities at 3 percent in the second year, its profit spread in the second year is positive: 8 percent - 3 percent = 5 percent, or the FI gains $5 million (0.05 x 100m). The positive spread earned in the first year by the FI from holding assets with a longer maturity than its liabilities is even greater in the second year.

7.

Consider an FI that issues $200 million of liabilities with two years to maturity to finance the purchase of $200 million of assets with a one year maturity. Suppose that the cost of funds (liabilities) for the FI is 5 percent per year and the return on the assets is 9 percent per year. a.

Calculate the FI’s profit spread and dollar value of profit in year 1.

Over the first year, the FI can lock in a profit spread of 4 percent (9 percent - 5 percent) by borrowing long term (for two years) and lending short term (for one year). Thus, its profit is $8 million (0.04 x $200m). In this case, the FI is exposed to an interest rate risk; by holding shorter term assets relative to liabilities, it faces uncertainty about the interest rate at which it can reinvest funds in the second period. b.

Calculate the profit spread and dollar value of profit in year 2, if the FI can reinvest its assets at 9 percent.

If the level of interest rates does not change, the FI will receive a profit spread of 4 percent or $8 million profit for the second year as well. c.

If interest rates fall and the FI can invest in one-year assets at 6 percent in the second year, calculate the FI’s profit spread and dollar value of profit in year 2.

If in the second year interest rates on $200 million invested in new one-year assets decreases to 6 percent, the FI’s profit spread falls to 1 percent (6 percent - 5 percent), or the FI profit falls to $2 million (0.01 x $200m). As a result, when an FI holds longer term liabilities relative to assets, it potentially exposes itself to the interest rate risk that borrowed funds can only be reinvested at a rate lower than their cost. d.

If interest rates rise and the FI can invest in one-year assets at 11 percent in the second year, calculate the FI’s profit spread and dollar value of profit in year 2.

If in the second year interest rates on $200 million invested in new one-year assets increases to 11 percent, the FI’s profit spread rises to 6 percent (11 percent - 5 percent), or the FI profit increases to $12 million (0.06 x $200m).

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8.

A financial institution has the following market value balance sheet structure: Assets Cash Bond Total assets

Liabilities and Equity Certificate of deposit Equity Total liabilities and equity

$1,000 $10,000 $11,000

$10,000 $1,000 $11,000

a. The bond has a 10-year maturity, a fixed-rate coupon of 10 percent paid at the end of each year, and a par value of $10,000. The certificate of deposit has a 1-year maturity and a 6 percent rate of interest. The FI expects no additional asset growth. What will be the net interest income at the end of the first year? Note: Net interest income equals interest income minus interest expense.

Interest income Interest expense Net interest income (NII)

$1,000 600 $400

$10,000 x 0.10 $10,000 x 0.06

b. If at the end of year 1 market interest rates have increased 100 basis points (1 percent), what will be the net interest income for the second year? Is this result caused by reinvestment risk or refinancing risk?

Interest income Interest expense Net interest income (NII)

$1,000 700 $300

$10,000 x 0.10 $10,000 x 0.07

The decrease in net interest income is caused by the increase in financing cost without a corresponding increase in the earnings rate. Thus, the change in NII is caused by refinancing risk. The increase in market interest rates does not affect the interest income because the bond has a fixed-rate coupon for ten years. Note: this answer makes no assumption about reinvesting the first year’s interest income at the new higher rate. c. Assuming that market interest rates increase 1 percent, the bond will have a value of $9,446 at the end of year 1. What will be the market value of the equity for the FI? Assume that all of the NII in part (a) is used to cover operating expenses or dividends.

Cash Bond Total assets

$1,000 $9,446 $10,446

Certificate of deposit $10,000 Equity $ 446 Total liabilities and equity $10,446

d. If market interest rates had decreased 100 basis points by the end of year 1, would the market value of equity be higher or lower than $1,000? Why? The market value of the equity would be higher ($1,600) because the value of the bond would be higher ($10,600) and the value of the CD would remain unchanged.

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e. What factors have caused the changes in operating performance and market value for this FI? The operating performance has been affected by changes in market interest rates that have caused corresponding changes in interest income, interest expense, and net interest income.

These specific changes have occurred because of the unique maturities of the fixed-rate assets and variable-rate liabilities. Similarly, the economic or market value of the FI has changed because of the effect of the changing rates on the market value of the bond.

9.

How does a policy of matching the maturities of assets and liabilities work (a) to minimize interest rate risk and (b) against the asset-transformation function of FIs?

A policy of maturity matching will allow changes in market interest rates to have approximately the same effect on both interest income and interest expense. An increase in rates will tend to increase both income and expense, and a decrease in rates will tend to decrease both income and expense. The changes in income and expense may not be equal because of different cash flow characteristics of the assets and liabilities. The asset-transformation function of an FI involves investing short-term liabilities in long-term assets. Maturity matching clearly works against successful implementation of this process.

10.

Corporate bonds usually pay interest semiannually. If an FI decided to change from semiannual to annual interest payments, how would this affect the bond’s interest rate risk?

The interest rate risk would increase as the bonds are being paid back more slowly and therefore the cash flows would be exposed to interest rate changes for a longer period of time. Thus, any change in interest rates would cause a larger inverse change in the value of the bonds.

11.

Two 10-year bonds are being considered for an investment that may have to be liquidated before the maturity of the bonds. The first bond is a 10-year premium bond with a coupon rate higher than its required rate of return, and the second bond is a zero-coupon bond that pays only a lump-sum payment after 10 years with no interest over its life. Which bond would have more interest rate risk? That is, which bond’s price would change by a larger amount for a given change in interest rates? Explain your answer.

The zero-coupon bond would have more interest rate risk. Because the entire cash flow is not received until the bond matures, the entire cash flow is exposed to interest rate changes over the entire life of the bond. The cash flows of the coupon-paying bond are returned with periodic regularity, thus allowing less exposure to interest rate changes. In effect, some of the cash flows may be received before interest rates change.

12.

Consider again the two bonds in problem 11. If the investment goal is to leave the assets untouched until maturity, such as for a child’s education or for one’s retirement, which of the two bonds has more interest rate risk? What is the source of this risk?

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In this case the coupon-paying bond has more interest rate risk. The zero-coupon bond will generate exactly the expected return at the time of purchase because no interim cash flows will be realized. Thus, the zero-coupon bond has no reinvestment risk. The coupon-paying bond faces reinvestment risk each time a coupon payment is received. The results of reinvestment will be beneficial if interest rates rise, but decreases in interest rates will cause the realized return to be less than the expected return.

13.

A money market mutual fund bought $1 million of two-year Treasury notes six months ago. During this time, the value of the securities has increased, but for tax reasons the mutual fund wants to postpone any sale for two more months. What type of risk does the mutual fund face for the next two months?

The mutual fund faces the risk of interest rates rising and the value of the securities falling.

14.

A bank invested $50 million in a two-year asset paying 10 percent interest per year and simultaneously issued a $50 million, one-year liability paying 8 percent interest per year.

The liability will be rolled over after one year at the current market rate. What will be the impact on the bank’s net interest income if at the end of the first year all interest rates have increased by 1 percent (100 basis points)?

Net interest income is not affected in the first year, but NII will decrease in the second year.

Interest income Interest expense Net interest income

Year 1 $5,000,000 $4,000,000 $1,000,000

Year 2 $5,000,000 $4,500,000 $500,000

The bank’s net interest income decreases in year 2 by $500,000 as the result of refinancing risk.

15.

What is credit risk? Which types of FIs are more susceptible to this type of risk? Why?

Credit risk is the risk that promised cash flows from loans and securities held by FIs may not be paid in full. FIs that lend money for long periods of time, whether as loans or by buying bonds, are more susceptible to this risk than those FIs that have short investment horizons. For example, life insurance companies and depository institutions generally must wait a longer time for returns to be realized than money market mutual funds and property-casualty insurance companies.

16.

What is the difference between firm-specific credit risk and systematic credit risk? How can an FI alleviate firm-specific credit risk?

Firm-specific credit risk refers to the likelihood that a single asset may deteriorate in quality, while systematic credit risk involves macroeconomic factors that may increase the default risk of all firms in the economy. Thus, if S&P lowers its rating on IBM stock and if an investor is holding only this particular stock, he may face significant losses as a result of this downgrading.

However, portfolio theory in finance has shown that firm-specific credit risk can be diversified 6 © 2022

away if a portfolio of well-diversified stocks is held. Similarly, if an FI holds a well-diversified portfolio of assets, the FI will face only systematic credit risk that will be affected by the general condition of the economy. The risks specific to any one customer will not be a significant portion of the FIs overall credit risk.

17.

Many banks and savings institutions that failed in the 1980s had made loans to oil companies in Louisiana, Texas, and Oklahoma. When oil prices fell, these companies, the regional economy, and the banks and savings institutions all experienced financial problems. What types of risk were inherent in the loans that were made by these banks and savings institutions?

The loans in question involved credit risk. Although the geographic area covered a large region of the United States, the risk more closely characterized firm-specific risk than systematic risk.

More extensive diversification by the FIs to other types of industries would have decreased the amount of financial hardship these institutions had to endure.

18.

What is liquidity risk? What routine operating factors allow FIs to deal with this risk in times of normal economic activity? What market reality can create severe financial difficulty for an FI in times of extreme liquidity crises?

Liquidity risk is the risk that a sudden surge in liability withdrawals may require an FI to liquidate assets in a very short period of time and at less than fair market prices. In times of normal economic activity, depository institutions meet cash withdrawals by accepting new deposits and borrowing funds in the short-term money markets. However, in times of harsh liquidity crises, the FI may need to sell assets at significant losses in order to generate cash quickly.

19.

Consider the simple FI balance sheet below (in millions of dollars).

Before the Withdrawal Assets Liabilities/Equity Cash assets $ 20 Deposit $150 Nonliquid assets 155 Equity 25 $175 $175

Suppose that depositors unexpectedly withdraw $50 million in deposits and the FI receives no new deposits to replace them. Assume that the FI cannot borrow any more funds in the short-term money markets, and because it cannot wait to get better prices for its assets in the future (as it needs the cash now to meet immediate depositor withdrawals), the FI has to sell any nonliquid assets at 75 cents on the dollar. Show the FI’s balance sheet after adjustments are made for the $50 million of deposit withdrawals. .

Before the Withdrawal

After the Withdrawal 7 © 2022

Assets Cash assets $ 20 Nonliquid assets 155 $175

Liabilities/Equity Deposit $150 Equity

Assets Liabilities/Equity Cash assets $ 0 Deposits $100 Nonliquid assets 115 Equity 15 $115 $115

25 $175

.

To meet these deposit withdrawals, the FI first uses the $20 million it has in cash assets and then seeks to sell some of its nonliquid assets to raise an additional $30 million in cash. To cover the remaining $30 million in deposit withdrawals, the FI must sell $40 million in nonliquid assets, incurring a loss of $10 million from the face value of those assets. The FI must then write off any such losses against its capital or equity funds. Since its capital was only $25 million before the deposit withdrawal, the loss on the fire-sale of assets of $10 million leaves the FI with $15 million.

20.

What two factors provide potential benefits to FIs that expand their asset holdings and liability funding sources beyond their domestic borders?

FIs can realize operational and financial benefits from direct foreign investment and foreign portfolio investments in two ways. First, the technologies and firms across various economies differ from each other in terms of growth rates, extent of development, etc. Second, exchange rate changes may not be perfectly correlated across various economies.

21.

What is foreign exchange risk? What does it mean for an FI to be net long in foreign assets? What does it mean for an FI to be net short in foreign assets? In each case, what must happen to the foreign exchange rate to cause the FI to suffer losses?

Foreign exchange risk is the risk that exchange rate changes can affect the value of an FI’s assets and liabilities denominated in foreign currencies. An FI is net long in foreign assets when the foreign currency-denominated assets exceed the foreign currency-denominated liabilities. In this case, an FI will suffer potential losses if the domestic currency strengthens relative to the foreign currency when repayment of the assets will occur in the foreign currency. An FI is net short in foreign assets when the foreign currency-denominated liabilities exceed the foreign currencydenominated assets. In this case, an FI will suffer potential losses if the domestic currency weakens relative to the foreign currency when repayment of the liabilities will occur in the domestic currency.

22.

If the Swiss franc is expected to depreciate in the near future, would a U.S.-based FI in Bern City prefer to be net long or net short in its asset positions? Discuss.

The U.S. FI would prefer to be net short (liabilities greater than assets) in its asset position. The depreciation of the Swiss franc relative to the dollar means that the U.S. FI would pay back the net liability position with fewer dollars. In other words, the decrease in the foreign assets in dollar value after conversion will be less than the decrease in the value of the foreign liabilities in dollar value after conversion.

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23.

If the British pound is expected to appreciate in the near future, would a U.S.-based FI in London prefer to be net long or net short in its asset positions? Discuss.

The U.S. FI would prefer to be net long (assets greater than liabilities) in its asset position. The appreciation of the British pound relative to the dollar means that the U.S. FI would pay back the net liability position with fewer dollars. In other words, the decrease in the foreign assets in dollar value after conversion will be less than the decrease in the value of the foreign liabilities in dollar value after conversion.

24.

If an FI has the same amount of foreign assets and foreign liabilities in the same currency, has that FI necessarily reduced the risk involved in these international transactions to zero?

Explain.

Matching the size of the foreign currency book will not eliminate the risk of the international transactions if the maturities of the assets and liabilities are mismatched. To the extent that the assets and liabilities are mismatched in terms of maturities, or more importantly durations, the FI will be exposed to foreign interest rate risk.

25.

A U.S. insurance company invests $1,000,000 in a private placement of British bonds.

Each bond pays £300 in interest per year for 20 years. If the current exchange rate is £1.564/$, what is the nature of the insurance company’s exchange rate risk? Specifically, what type of exchange rate movement concerns this insurance company?

In this case, the insurance company is worried about the value of the £ falling. If this happens, the insurance company would be able to buy fewer dollars with the £s received. This would happen if the exchange rate rose to say £1.68/$ since now it would take more £s to buy one dollar, but the bond contract is paying a fixed amount of interest and principal.

26.

Assume that a bank has assets located in London that are worth £150 million on which it earns an average of 8 percent per year. The bank has £100 million in liabilities on which it pays an average of 6 percent per year. The current spot exchange rate is £1.50/$. a. If the exchange rate at the end of the year is £2.00/$, will the dollar have appreciated or depreciated against the pound?

The dollar will have appreciated, or conversely, the £ will have depreciated. b. Given the change in the exchange rate, what is the effect in dollars on the net interest income from the foreign assets and liabilities? Note: The net interest income is interest income minus interest expense.

Measurement in £ Interest received Interest paid Net interest income

= = =

£12 million £6 million £6 million 9 © 2022

Measurement in $ before £ devaluation Interest received in dollars = Interest paid in dollars = Net interest income =

$8 million $4 million $4 million

Measurement in $ after £ devaluation Interest received in dollars = Interest paid in dollars = Net interest income =

$6 million $3 million $3 million

Thus, net interest income decreases by $1 million as a result of foreign exchange risk. c. What is the effect of the exchange rate change on the value of assets and liabilities in dollars?

The assets were worth $100 million (£150m/1.50) before depreciation, but after depreciation they are worth only $75 million. The liabilities were worth $66.67 million before depreciation, but they are worth only $50 million after devaluation. Since assets decline by $25 million and liabilities by $16.67 million, net worth decreases by $8.33 million using spot rates at the end of the year.

27.

Six months ago, Qualitybank issued a $100 million, one-year maturity CD denominated in euros. On the same date, $60 million was invested in a €-denominated loan and $40 million was invested in a U.S. Treasury bill. The exchange rate on this date was €1.5675/$.

Assume no repayment of principal and an exchange rate today of €1.2540/$. a. What is the current value of the CD principal (in euros and dollars)?

The current principal value on the CD is €156.75m and $125m (€156.75m/1.2540). b. What is the current value of the euro-denominated loan principal (in euros and dollars)?

The current principal value on the loan is €94.050m and $75m (€94.050m/1.2540). c. What is the current value of the U.S. Treasury bill (in euros and dollars)?

The current principal value on the U.S. Treasury bill is $40m and €50.16m ($40m x 1.2540). For a U.S. bank this does not change in value. d. What is Qualitybank’s profit/loss from this transaction (in euros and dollars)?

Qualitybank's loss is €12.540m (($40m x 1.5675) - €50.16m) or $10m (($125m - $100m) – ($75m - $60m)).

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Solution matrix for problem 27: At Issue Date: Dollar Transaction Values (in millions) Euro loan $60 Euro CD $100 U.S T-bill $40 $100 $100 Today: Dollar Transaction Values (in millions) Euro loan $75 Euro CD $125 U.S. T-bill $40 $115 $125 Loss -$ 10 28.

Euro Transaction Values (in millions) Euro loan €94.050 Euro CD €156.75 U.S. T-bill €62.700 €156.750 €156.75 Euro Transaction Values (in millions) Euro loan €94.050 Euro CD €156.75 U.S. T-bill €50.160 €144.210 €156.75 Loss -€12.540

Suppose you purchase a 10-year, AAA-rated Swiss bond for par that is paying an annual coupon of 6 percent. The bond has a face value of 1,000 Swiss francs (SF). The spot rate at the time of purchase is SF1.15/$. At the end of the year, the bond is downgraded to AA and the yield increases to 8 percent. In addition, the SF appreciates to SF1.05/$. a. What is the loss or gain to a Swiss investor who holds this bond for a year? What portion of this loss or gain is due to foreign exchange risk? What portion is due to interest rate risk?

Beginning of the Year Price of Bond = SF 60 * PVAi =6,n =10 + SF1,000 * PVi=6,n=10 = SF1,000 End of the Year Price of Bond = SF 60 * PVAi =8,n=9 + SF1,000 * PVi=8,n =9 = SF 875.06 The loss to the Swiss investor (SF875.06 + SF60 - SF1,000)/SF1,000 = -6.49 percent. The entire amount of the loss is due to interest rate risk. b. What is the loss or gain to a U.S. investor who holds this bond for a year? What portion of this loss or gain is due to foreign exchange risk? What portion is due to interest rate risk?

Price at beginning of year = SF1,000/SF1.15 = $869.565 Price at end of year = SF875.06/SF1.05 = $833.393 Interest received at end of year = SF60/SF1.05 = $57.143 Gain to U.S. investor = ($833.393 + $57.143 - $869.565)/$869.565 = +2.41%.

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The U.S. investor had an equivalent loss of 6.49 percent ([((SF875.06 + SF60)/SF1.15) $869.565]/$869.565) from interest rate risk, but had a gain of 8.90 percent (2.41% - (-6.49%)) from foreign exchange risk.

29.

What is country or sovereign risk? What remedy does an FI realistically have in the event of a collapsing country or currency?

Country or sovereign risk is the risk that repayments to foreign lenders or investors may be interrupted because of restrictions, intervention, or interference from foreign governments. A lender FI has very little recourse in this situation unless the FI is able to restructure the debt or demonstrate influence over the future supply of funds to the country in question. This influence likely would involve significant working relationships with the IMF and the World Bank.

30.

What is market risk? How does this risk affect the operating performance of financial institutions? What actions can be taken by an FI’s management to minimize the effects of this risk?

Market risk is the risk incurred from assets and liabilities in an FI’s trading book due to changes in interest rates, exchange rates, and other asset prices. Market risk affects any firm that trades assets and liabilities. The risk can surface because of changes in interest rates, exchange rates, or any other prices of financial assets that are traded rather than held on the balance sheet. Market risk can be minimized by using appropriate hedging techniques such as futures, options, and swaps, and by implementing controls that limit the amount of exposure taken by market makers.

31.

What is the nature of an off-balance-sheet activity? How does an FI benefit from such activities? Identify the various risks that these activities generate for an FI, and explain how these risks can create varying degrees of financial stress for the FI at a later time.

Off-balance-sheet activities are contingent commitments to undertake future on-balance-sheet investments. The usual benefit of committing to a future activity is the generation of immediate fee income without the normal recognition of the activity on the balance sheet. As such, these contingent investments may expose the FI to credit risk (if there is some default risk probability), interest rate risk (if there is some price and/or interest rate sensitivity), and foreign exchange rate risk (if there is a cross currency commitment).

32.

What is technology risk? What is the difference between economies of scale and economies of scope? How can these economies create benefits for an FI? How can these economies prove harmful to an FI?

Technology risk occurs when investment in new technologies does not generate the cost savings expected in the production and expansion of financial services. Economies of scale occur when the average cost of production decreases with the production of or an expansion in the amount of financial services provided. Economies of scope occur when an FI is able to lower overall costs by producing new products with inputs similar to those used for other products. In financial service industries, the use of data from existing customer databases to assist in providing new 12 © 2022

service products is an example of economies of scope. Failure to produce the perceived synergies or costs savings can result in major losses in competitive efficiency of an FI and, ultimately, in an FI’s long-term failure.

33.

What is the difference between technology risk and operational risk? How does internationalizing the payments system among banks increase operational risk?

Technology risk is the risk incurred by an FI when its technological investments do not produce anticipated cost savings. For example, if an FI spends millions on upgrading its computer systems, but is not able to recapture its costs because its productivity has not increased commensurately or because the technology has already become obsolete, it has invested in a negative NPV investment in technology.

Operational risk refers to the risk that existing technology, auditing, monitoring, and other support systems may malfunction or break down. This includes the failure of the back-room support operations necessary to maintain the smooth functioning of the operation of FIs, including settlement, clearing, and other transaction-related activities. For example, computerized payment systems such as CHIPS allow modern financial intermediaries to transfer funds, securities, and messages across the world in seconds of real time. This creates the opportunity to engage in global financial transactions over a short time in an extremely costefficient manner. However, the interdependence of such transactions also creates settlement risk.

Typically, any given transaction leads to other transactions as funds and securities trade across the globe. If there is either a transmittal failure or high-tech fraud affecting any one of the intermediate transactions, this could cause an unraveling of all subsequent transactions.

34.

Why can insolvency risk be classified as a consequence or outcome of any or all of the other types of risks?

Insolvency risk is the risk that an FI may not have enough capital to offset a sudden decline in the value of its assets relative to its liabilities. This risk involves the shortfall of capital in times when the operating performance of the institution generates accounting losses. These losses may be the result of one or more of interest rate, credit, liquidity, sovereign, foreign exchange, market, off-balance-sheet, and technological risks.

35.

Discuss the interrelationships among the different sources of FI risk exposure. Why would the construction of an FI risk management model to measure and manage only one type of risk be incomplete?

Measuring each source of FI risk exposure individually creates the false impression that they are independent of each other. For example, the interest rate risk exposure of an FI could be reduced by requiring customers to take on more interest rate risk exposure through the use of floating-rate products. However, this reduction in FI risk may be obtained only at the possible expense of increased credit risk. That is, customers experiencing losses resulting from unanticipated interest rate changes may be forced into insolvency, thereby increasing the FI’s default risk. Similarly, off-balance-sheet risk encompasses several risks since off-balance-sheet contingent contracts 13 © 2022

typically have credit risk and interest rate risk as well as currency risk. Moreover, the failure of collection and payment systems may lead corporate customers into bankruptcy. Thus, technology risk may influence the credit risk of FIs. As a result of these interdependencies, FIs must focus on developing sophisticated models that attempt to measure all of the risks faced by the FI at any point in time.

36.

Characterize the risk exposure(s) of the following FI transactions by choosing one or more of the risk types listed below: a. Interest rate risk b. Credit risk c. Off-balance-sheet risk (1) (2) (3) (4) (5) (6) (7)

37.

d. Technology risk e. Foreign exchange rate risk f. Country or sovereign risk

A bank finances a $10 million, six-year fixed-rate commercial loan by selling oneyear certificates of deposit. a, b An insurance company invests its policy premiums in a long-term municipal bond portfolio. a, b A French bank sells two-year fixed-rate notes to finance a two-year fixed-rate loan to a British entrepreneur. b, e, f A Japanese bank acquires an Austrian bank to facilitate clearing operations. a, b, c, d, e, f A mutual fund completely hedges its interest rate risk exposure by using forward contingent contracts. b, c A bond dealer uses his own equity to buy Mexican debt on the less developed country (LDC) bond market. a, b, e, f A securities firm sells a package of mortgage loans as mortgage-backed securities. a, b, c

Consider these four types of risks: credit, foreign exchange, market, and sovereign. These risks can be separated into two pairs of risk types in which each pair consists of two related risk types, with one being a subset of the other. How would you pair off the risk types, and which risk type could be considered a subset of the other type in the pair?

Credit risk and sovereign risk comprise one pair, while FX and market risk make up the other.

Sovereign risk is a type of credit risk in that one reason why a loan may default is because of political upheaval in the country in which the borrower resides. FX risk is a type of market risk in that one reason why the market value of an outstanding loan or security may change is due to a change in exchange rates.

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Solutions for End-of-Chapter Questions and Problems: Chapter Eight 1.

How do monetary policy actions made by the Federal Reserve impact interest rates?

Through its daily open market operations, such as buying and selling Treasury bonds and Treasury bills, the Fed seeks to influence the money supply, inflation, and the level of interest rates. When the Fed finds it necessary to slow down the economy, it tightens monetary policy by raising interest rates. The normal result is a decrease in business and household spending (especially that financed by credit or borrowing). Conversely, if business and household spending decline to the extent that the Fed finds it necessary to stimulate the economy it allows interest rates to fall (an expansionary monetary policy). The drop in rates promotes borrowing and spending.

2.

How has the increased level of financial market integration affected interest rates?

Increased financial market integration, or globalization, increases the speed with which interest rate changes and volatility are transmitted among countries. The result of this quickening of global economic adjustment is to increase the difficulty and uncertainty faced by the Federal Reserve as it attempts to manage economic activity within the U.S. Further, because FIs have become increasingly more global in their activities, any change in interest rate levels or volatility caused by Federal Reserve actions more quickly creates additional interest rate risk issues for these companies.

3.

What is the repricing gap? In using this model to evaluate interest rate risk, what is meant by rate sensitivity? On what financial performance variable does the repricing model focus? Explain.

The repricing gap is a measure of the difference between the dollar value of assets that will reprice and the dollar value of liabilities that will reprice within a specific time period, where repricing can be the result of a roll over of an asset or liability (e.g., a loan is paid off at or prior to maturity and the funds are used to issue a new loan at current market rates) or because the asset or liability is a variable rate instrument (e.g., a variable rate mortgage whose interest rate is reset every quarter based on movements in a prime rate). Rate sensitivity represents the time interval where repricing can occur. The model focuses on the potential changes in the net interest income variable. In effect, if interest rates change, interest income and interest expense will change as the various assets and liabilities are repriced, that is, receive new interest rates.

4.

What is a maturity bucket in the repricing model? Why is the length of time selected for repricing assets and liabilities important when using the repricing model?

The maturity bucket is the time window over which the dollar amounts of assets and liabilities are measured. The length of the repricing period determines which of the securities in a portfolio are rate-sensitive. The longer the repricing period, the more securities either mature or will be repriced, and, therefore, the more the interest rate risk exposure. An excessively short repricing period omits consideration of the interest rate risk exposure of assets and liabilities are that repriced in the period immediately following the end of the repricing period. That is, it 1 © 2022

understates the rate sensitivity of the balance sheet. An excessively long repricing period includes many securities that are repriced at different times within the repricing period, thereby overstating the rate sensitivity of the balance sheet.

5.

What is the CGAP effect? According to the CGAP effect, what is the relation between changes in interest rates and changes in net interest income when CGAP is positive? When CGAP is negative?

The CGAP effect describes the relation between changes in interest rates and changes in net interest income. According to the CGAP effect, when CGAP is positive the change in NII is positively related to the change in interest rates. Thus, an FI would want its CGAP to be positive when interest rates are expected to rise. According to the CGAP effect, when CGAP is negative the change in NII is negatively related to the change in interest rates. Thus, an FI would want its CGAP to be negative when interest rates are expected to fall.

6.

Which of the following is an appropriate change to make on a bank’s balance sheet when GAP is negative, spread is expected to remain unchanged, and interest rates are expected to rise?

According to the CGAP effect, when GAP, or CGAP, is positive the change in NII is positively related to the change in interest rates. Thus, an FI would want its GAP to be positive when interest rates are expected to rise. a. Replace fixed-rate loans with rate-sensitive loans.

Yes. This change will increase RSAs, which will increase GAP. b. Replace marketable securities with fixed-rate loans.

No. This change will decrease RSAs, which will decrease GAP. c. Replace fixed-rate CDs with rate-sensitive CDs. No. This change will increase RSLs, which will decrease GAP. d. Replace equity with demand deposits.

No. This change will have no impact on either RSAs or RSLs. So, will have no impact on GAP. e. Replace vault cash with marketable securities.

Yes. This change will increase RSAs, which will increase GAP. 7.

If a bank manager was quite certain that interest rates were going to rise within the next six months, how should the bank manager adjust the bank’s six-month repricing gap to take 2 © 2022

advantage of this anticipated rise? What if the manger believed rates would fall in the next six months.

When interest rates are expected to rise, a bank should set its repricing gap to a positive position.

In this case, as rates rise, interest income will rise by more than interest expense. The result is an increase in net interest income. When interest rates are expected to fall, a bank should set its repricing gap to a negative position. In this case, as rates fall, interest income will fall by less than interest expense. The result is an increase in net interest income.

8.

Consider the following balance sheet positions for a financial institution: •

Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million

•

Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million

•

Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million

a. Calculate the repricing gap and the impact on net interest income of a 1 percent increase in interest rates for each position.

•

Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.

Repricing gap = RSA - RSL = $200 - $100 million = +$100 million. NII = ($100 million)(0.01) = +$1.0 million, or $1,000,000.

•

Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.

Repricing gap = RSA - RSL = $100 - $150 million = -$50 million. NII = (-$50 million)(0.01) = -$0.5 million, or -$500,000.

•

Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.

Repricing gap = RSA - RSL = $150 - $140 million = +$10 million. NII = ($10 million)(0.01) = +$0.1 million, or $100,000. b. Calculate the impact on net interest income on each of the above situations assuming a 1 percent decrease in interest rates.

•

NII = ($100 million)(-0.01) = -$1.0 million, or -$1,000,000.

•

NII = (-$50 million)(-0.01) = +$0.5 million, or $500,000.

•

NII = ($10 million)(-0.01) = -$0.1 million, or -$100,000. c. What conclusion can you draw about the repricing model from these results?

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The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap), while the FI in part (2) is exposed to interest rate increases. The FI in part (3) has the lowest interest rate risk exposure since the absolute value of the repricing gap is the lowest, while the opposite is true for the FI in part (1).

9.

Consider the following balance sheet for MMC Bancorp (in millions of dollars):

Assets 1. Cash and due from 2. Short-term consumer loans (one-year maturity) 3. Long-term consumer loans (two-year maturity) 4. Three-month T-bills 5. Six-month T-notes

$ 6.25 62.50

Liabilities/Equity 1. Equity capital (fixed)

$25.00

2. Demand deposits

50.00

3. One-month CDs 4. Three-month CDs 5. Three-month bankers’ acceptances 6. Six-month commercial paper 7. One-year time deposits

37.50 50.00 25.00 75.00 25.00

8. Two-year time deposits

50.00

31.25 37.50 43.75

6. Three-year T-bonds 75.00 7. 10-year, fixed-rate mortgages 25.00 8. 30-year, floating-rate mortgages 50.00 9. Premises 6.25 $337.50

$337.50

a. Calculate the value of MMC’s rate-sensitive assets, rate sensitive liabilities, and repricing gap over the next year.

Looking down the asset side of the balance sheet, we see the following one-year rate-sensitive assets (RSA): 1. Short-term consumer loans: $62.50 million, which are repriced at the end of the year and just make the one-year cutoff.

2. Three-month T-bills: $37.50 million, which are repriced on maturity (rollover) every three months.

3. Six-month T-notes: $43.75 million, which are repriced on maturity (rollover) every six months.

4. 30-year floating-rate mortgages: $50.00 million, which are repriced (i.e., the mortgage rate is reset) every nine months. Thus, these long-term assets are RSA in the context of the repricing model with a one-year repricing horizon.

Summing these four items produces one-year RSA of $193.75 million. The remaining $143.75 million is not rate sensitive over the one-year repricing horizon. A change in the level of interest rates will not affect the interest revenue generated by these assets over the next year. The $6.25 million in the cash and due from category and the $6.25 million in premises are nonearning assets. Although the $131.25 million in long-term consumer loans, three-year Treasury bonds, and 10-year, fixed-rate mortgages generate interest revenue, the level of revenue generated will 4 © 2022

not change over the next year since the interest rates on these assets are not expected to change (i.e., they are fixed over the next year).

Looking down the liability side of the balance sheet, we see that the following liability items clearly fit the one-year rate or repricing sensitivity test: 1. One-month CDs: $37.50 million, which mature in one months and are repriced on rollover.

2. Three-month CDs: $50 million, which mature in three months and are repriced on rollover.

3. Three-month bankers’ acceptances: $25 million, which mature in three months and are repriced on rollover.

4. Six-month commercial paper: $75 million, which mature and are repriced every six months.

5. One-year time deposits: $25 million, which are repriced at the end of the one-year gap horizon.

Summing these five items produces one-year rate-sensitive liabilities (RSL) of $212.5 million.

The remaining $125 million is not rate sensitive over the one-year period. The $25 million in equity capital and $50 million in demand deposits do not pay interest and are therefore classified as nonpaying. The $50 million in two-year time deposits generate interest expense over the next year, but the level of the interest generated will not change if the general level of interest rates change. Thus, we classify these items as fixed-rate liabilities.

The five repriced liabilities ($37.50 + $50 + $25 + $75 + $25) sum to $212.5 million, and the four repriced assets of $62.50 + $37.50 + $43.75 + $50 sum to $193.75 million. Given this, the cumulative one-year repricing gap (CGAP) for the bank is: CGAP = (One-year RSA) - (One-year RSL) = RSA - RSL = $193.75 million - $212.5 million = -$18.80 million b. Calculate the expected change in the net interest income for the bank if interest rates rise by 1 percent on both RSAs and RSLs. If interest rates fall by 1 percent on both RSAs and RSLs. The CGAP would project the expected annual change in net interest income ()NII) of the bank is: )NII = CGAP x )R = (-$18.80 million) x 0.01 = -$188,000 Similarly, if interest rates fall equally for RSAs and RSLs, NII will fall by: = (-$18.80 million) x (-0.01) = $188,000 c. Calculate the expected change in the net interest income for the bank if interest rates rise by 1.2 percent on RSAs and by 1 percent on RSLs. If interest rates fall by 1.2 percent on RSAs and by 1 percent on RSLs. The resulting change in NII is calculated as: 5 © 2022

)NII = [RSA x )RRSA] - [RSL x )RRSL] = [$193.75 million x 1.2%] - [$212.5 million x 1.0%] = $2.325 million - $2.125 million = $200,000 10.

What are the reasons for not including demand deposits as rate-sensitive liabilities in the repricing analysis for a commercial bank? What is the subtle but potentially strong reason for including demand deposits in the total of rate sensitive liabilities? Can the same argument be made for passbook savings accounts?

The regulatory rate available on demand deposit accounts is zero. Although many banks are able to offer NOW accounts on which interest can be paid, this interest rate seldom is changed and thus the accounts are not really interest rate sensitive. However, demand deposit accounts do pay implicit interest in the form of not charging fully for checking and other services. Further, when market interest rates rise, customers draw down their demand deposit accounts, which may cause the bank to use higher cost sources of funds. The same or similar arguments can be made for passbook savings accounts.

11.

What is the gap to total assets ratio? What is the value of this ratio to interest rate risk managers and regulators?

The gap to total assets ratio is the ratio of the cumulative gap position to the total assets of the FI. The cumulative gap position is the sum of the individual gaps over several time buckets. The value of this ratio is that it tells the direction of the interest rate exposure and the scale of that exposure relative to the size of the FI. 12.

Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test?

3-month U.S. Treasury bills Yes 1-year U.S. Treasury notes Yes 20-year U.S. Treasury bonds No 20-year floating-rate corporate bonds with annual repricing Yes 30-year floating-rate mortgages with repricing every two years No 30-year floating-rate mortgages with repricing every six months Yes Overnight fed funds Yes 9-month fixed-rate CDs Yes 1-year fixed-rate CDs Yes 5-year floating-rate CDs with annual repricing Yes Common stock No

13.

What is the spread effect?

The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has on net interest income as interest rates change. The spread effect is such that, regardless of the direction of the change in interest rates, a positive relation exists between changes in the spread and changes in NII. Whenever the spread increases (decreases), NII increases (decreases).

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14.

A bank manager is quite certain that interest rates are going to fall within the next six months. How should the bank manager adjust the bank’s six-month repricing gap and spread to take advantage of this anticipated rise? What if the manger believes rates will rise in the next six months.

When interest rates are expected to fall, a bank should set its repricing gap to a negative position.

Further, the manager would want to increase the spread between the return on RSAs and RSLs. In this case, as rates fall, interest income will fall by less than interest expense. The result is an increase in net interest income. When interest rates are expected to rise, a bank should set its repricing gap to a positive position. Again, the manager would want to increase the spread between the return on RSAs and RSLs. In this case, as rates rise, interest income will rise by more than interest expense. The result is an increase in net interest income.

15.

Consider the following balance sheet for WatchoverU Savings, Inc. (in millions): Assets Floating-rate mortgages (currently 10% annually) 30-year fixed-rate loans (currently 7% annually) Total assets

Liabilities and Equity 1-year time deposits (currently 6% annually) 3-year time deposits (currently 7% annually) Equity Total liabilities & equity

$50 $50 $100

$70 $20 $10 $100

a. What is WatchoverU’s expected net interest income (for year 2) at year-end?

Current expected interest income: $50m(0.10) + $50m(0.07) = $8.5m.

Expected interest expense: $70m(0.06) + $20m(0.07) = $5.6m.

Expected net interest income : $8.5m - $5.6m = $2.9m. b. What will expected net interest income (for year 2) be at year-end if interest rates rise by 2 percent?

After the 2 percent interest rate increase, net interest income is: 50(0.12) + 50(0.07) - 70(0.08) - 20(.07) = $9.5m - $7.0m = $2.5m, a decline of $0.4m. c. Using the cumulative repricing gap model, what is the expected net interest income (for year 2) for a 2 percent increase in interest rates?

WatchoverU’s repricing or funding gap is $50m - $70m = -$20m. The change in net interest income using the funding gap model is (-$20m)(0.02) = -$0.4m. d. What will expected net interest income (for year 2) be at year-end if interest rates on RSAs increase by 2 percent but interest rates on RSLs increase by 1 percent? Is it reasonable for changes in interest rates on RSAs and RSLs to differ? Why? 7 © 2022

After the unequal rate increases, net interest income will be 50(0.12) + 50(0.07) – 70(0.07) – 20(0.07) = $9.5m - $6.3m = $3.2m, an increase of $0.3m. It is not uncommon for interest rates to adjust in an unequal manner on RSAs versus RSLs. Interest rates often do not adjust solely because of market pressures. In many cases, the changes are affected by decisions of management. Thus, you can see the difference between this answer and the answer for part a.

16.

Use the following information about a hypothetical government security dealer named M. P. Jorgan. Market yields are in parenthesis, and amounts are in millions.

Assets Cash 1-month T-bills (7.05%) 3-month T-bills (7.25%) 2-year business loans (7.50%) 8-year mortgage loans (8.96%) 5-year munis (floating rate) (8.20% reset every 6 months) Total assets

Liabilities and Equity Overnight repos Subordinated debt 7-year fixed rate (8.55%)

$10 75 75 50 100 25 $335

Equity Total liabilities & equity

$170 150

15 $335

a. What is the repricing gap if the planning period is 30 days? 3 months? 2 years? Recall that cash is a non-interest-earning asset.

Repricing gap using a 30-day planning period = $75m - $170m = -$95 million.

Repricing gap using a 3-month planning period = ($75m + $75m) - $170m = -$20 million.

Reprising gap using a 2-year planning period = ($75m + $75m + $50m + $25m) - $170m = +$55 million. b. What is the impact over the next 30 days on net interest income if interest rates increase 50 basis points? Decrease 75 basis points?

If interest rates increase 50 basis points, net interest income will decrease by $475,000. NII = CGAP(R) = -$95m(0.005) = -$0.475m.

If interest rates decrease by 75 basis points, net interest income will increase by $712,500. NII = CGAP(R) = -$95m(-0.0075) = $0.7125m. c. The following one-year runoffs are expected: $10 million for two-year business loans and $20 million for eight-year mortgage loans. What is the one-year repricing gap?

The repricing gap over the 1-year planning period = ($75m. + $75m. + $10m. + $20m. + $25m.) - $170m. = +$35 million. d. If runoffs are considered, what is the effect on net interest income at year-end if interest rates increase 50 basis points? Decrease 75 basis points?

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If interest rates increase 50 basis points, net interest income will increase by $175,000. NII = CGAP(R) = $35m(0.005) = $0.175m.

If interest rates decrease 75 basis points, net interest income will decrease by $262,500. NII = CGAP(R) = $35m(-0.0075) = -$0.2625m.

17.

A bank has the following balance sheet: Assets Rate sensitive Fixed rate Nonearning Total

$550,000 755,000 265,000 $1,570,000

Avg. Rate 7.75% 8.75

Liabilities/Equity Rate sensitive $375,000 Fixed rate 805,000 Nonpaying 390,000 Total $1,570,000

Avg. Rate 6.25% 7.50

Suppose interest rates rise such that the average yield on rate-sensitive assets increases by 45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis points. a.

Calculate the bank’s CGAP and gap ratio.

Repricing GAP = $550,000 - $375,000 = $175,000 Gap ratio = $175,000/$1,570,000 = 11.15% b.

Assuming the bank does not change the composition of its balance sheet, calculate the resulting change in the bank’s interest income, interest expense, and net interest income.

II = $550,000(0.0045) = $2,475 IE = $375,000(0.0035) = $1,312.50 NII = $2,475 - $1,312.50 = $1,162.50 c.

Explain how the CGAP and spread effects influenced the change in net interest income.

The CGAP affect worked to increase net interest income. That is, the CGAP was positive while interest rates increased. Thus, interest income increased by more than interest expense. The result is an increase in NII. The spread effect also worked to increase net interest income. The spread increased by 10 basis points. According to the spread affect, as spread increases, so does net interest income.

18.

A bank has the following balance sheet: Assets Rate sensitive Fixed rate Nonearning Total

$550,000 755,000 265,000 $1,570,000

Avg. Rate 7.75% 8.75

Liabilities/Equity Rate sensitive $575,000 Fixed rate 605,000 Nonpaying 390,000 Total $1,570,000 9

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Avg. Rate 6.25% 7.50

Suppose interest rates fall such that the average yield on rate-sensitive assets decreases by 15 basis points and the average yield on rate-sensitive liabilities decreases by 5 basis points. a.

Calculate the bank’s CGAP and gap ratio.

CGAP = $550,000 - $575,000 = -$25,000 Gap ratio = -$25,000/$1,570,000 = -1.59% b.

Assuming the bank does not change the composition of its balance sheet, calculate the resulting change in the bank’s interest income, interest expense, and net interest income.

II = $550,000(-0.0015) = -$825 IE = $575,000(-0.0005) = -$287.50 NII = -$825 – (-$287.50) = -$537.50 c.

The bank’s CGAP is negative and interest rates decreased, yet net interest income decreased. Explain how the CGAP and spread effects influenced this decrease in net interest income.

The CGAP affect worked to increase net interest income. That is, the CGAP was negative while interest rates decreased. Thus, interest income decreased by less than interest expense. The result is an increase in NII. The spread effect, on the other hand, worked to decrease net interest income. The spread decreased by 10 basis points. According to the spread affect, as spread decreases, so does net interest income. In this case, the increase in NII due to the CGAP effect was dominated by the decrease in NII due to the spread effect.

19.

The balance sheet of A. G. Fredwards, a government security dealer, is listed below.

Market yields are in parentheses, and amounts are in millions.

Assets Cash 1-month T-bills (7.05%) 3-month T-bills (7.25%) 2-year T-notes (7.50%) 8-year T-notes (8.96%) 5-year munis (floating rate) (8.20% reset every 6 months) Total assets

Liabilities and Equity Overnight repos Subordinated debt 7-year fixed rate (8.55%)

$20 150 150 100 200 50 $670

Equity Total liabilities and equity

$340 300

30 $670

a. What is the repricing gap if the planning period is 30 days? 3 months? 2 years?

Repricing gap using a 30-day planning period = $150m - $340m = -$190 million.

Repricing gap using a 3-month planning period = ($150m + $150m) - $340m = -$40 million.

Repricing gap using a 2-year planning period = ($150m + $150m + $100m + $50m) - $340m = $110 million.

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b. What is the impact over the next three months on net interest income if interest rates on RSAs increase 50 basis points and on RSLs increase 60 basis points? II = ($150m. + $150m.)(0.005) = $1.5m. IE = $340m.(0.006) = $2.04m. NII = $1.5m. – ($2.04m.) = -$0.54m. c. What is the impact over the next two years on net interest income if interest rates on RSAs increase 50 basis points and on RSLs increase 75 basis points? II = ($150m. + $150m. + $100m. + $50m.)(0.005) = $2.25m. IE = $340m.(0.0075) = $2.04m. NII = $2.25m. – ($2.04m.) = $0.21m. d. Explain the difference in your answers to parts (b) and (c). Why is one answer a negative change in NII, while the other is positive?

For the 3-month analysis, the CGAP affect worked to decrease net interest income. That is, the CGAP was negative while interest rates increased. Thus, interest income increased by less than interest expense. The result is a decrease in NII. For the 3-year analysis, the CGAP affect worked to increase net interest income. That is, the CGAP was positive while interest rates increased.

Thus, interest income increased by more than interest expense. The result is an increase in NII. 20.

A bank has the following balance sheet: Assets Rate sensitive Fixed rate Nonearning Total

$225,000 550,000 120,000 $895,000

Avg. Rate 6.35% 7.55

Liabilities/Equity Rate sensitive $300,000 Fixed rate 505,000 Nonpaying 90,000 Total $895,000

Avg. Rate 4.25% 6.15

Suppose interest rates rise such that the average yield on rate-sensitive assets increases by 45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis points. a. Calculate the bank’s repricing GAP. Repricing GAP = $225,000 - $300,000 = -$75,000 b.

Assuming the bank does not change the composition of its balance sheet, calculate the net interest income for the bank before and after the interest rate changes. What is the resulting change in net interest income?

NIIb = ($225,000(0.0635) +$550,000(0.0755)) – ($300,000(0.0425) + $505,000(0.0615)) = $55,812.50 - $43,807.50 = $12,005 11 © 2022

NIIa = ($225,000(0.0635 + 0.0045) +$550,000(0.0755)) – ($300,000(0.0425 + 0.0035) + $505,000(0.0615)) = $56,825 - $44,857.50 = $11,967.50 NII = $11,967.50 - $12,005 = -$37.50 c.

Explain how the CGAP and spread effects influenced this increase in net interest income.

The CGAP affect worked to decrease net interest income. That is, the CGAP was negative while interest rates increased. Thus, interest income increased by less than interest expense. The result is a decrease in NII. In contrast, the spread effect worked to increase net interest income. The spread increased by 10 basis points. According to the spread affect, as spread increases, so does net interest income. However, in this case, the increase in NII due to the spread effect was dominated by the decrease in NII due to the CGAP effect.

21.

What are some of the weakness of the repricing model? How have large banks solved the problem of choosing the optimal time period for repricing? What is runoff cash flow, and how does this amount affect the repricing model’s analysis?

The repricing model has four general weaknesses: (1)

It ignores market value effects.

(2)

It does not take into account the fact that the dollar value of rate-sensitive assets and liabilities within a bucket are not similar. Thus, if assets, on average, are repriced earlier in the bucket than liabilities, and if interest rates fall, FIs are subject to reinvestment risks.

(3)

It ignores the problem of runoffs. That is, that some assets are prepaid and some liabilities are withdrawn before the maturity date.

(4)

It ignores income generated from off-balance-sheet activities.

Large banks are able to reprice securities every day using their own internal models so reinvestment and repricing risks can be estimated for each day of the year.

Runoff cash flow reflects the assets that are repaid before maturity and the liabilities that are withdrawn unexpectedly. To the extent that either of these amounts is significantly greater than expected, the estimated interest rate sensitivity of the FI will be in error.

The following questions and problems are based on material in Appendix 8A, located on the website (www.mhhe.com/saunders9e).

22.

What is a maturity gap? How can the maturity model be used to immunize an FI’s portfolio? What is the critical requirement that allows maturity matching to have some success in immunizing the balance sheet of an FI? 12 © 2022

Maturity gap is the difference between the average maturity of an FI’s assets and liabilities. If the maturity gap is zero, it is possible to immunize the portfolio so that changes in interest rates will result in equal but offsetting changes in the value of assets and liabilities. Thus, if interest rates increase (decrease), the fall (rise) in the value of the assets will be offset by an identical fall (rise) in the value of the liabilities. The critical assumption is that the timing of the cash flows on the assets and liabilities must be the same.

23.

Nearby Bank has the following balance sheet (in millions): Assets Cash 5-year Treasury notes 30-year mortgages Total assets

$60 60 200 $320

Liabilities and Equity Demand deposits 1-year certificates of deposit Equity Total liabilities and equity

$140 160 20 $320

What is the maturity gap for Nearby Bank? Is Nearby Bank more exposed to an increase or decrease in interest rates? Explain why?

MA = [0x$60m + 5x$60m + 30x$200m]/$320m = 19.6875 years, and ML = [0x$140m + 1x$160m]/$300m = 0.5333 years. Therefore, the maturity gap = MGAP = 19.6875 – 0.5333 = 19.1542 years. Nearby Bank is exposed to an increase in interest rates. If rates rise, the value of assets will decrease by more than the value of liabilities.

24.

County Bank has the following market value balance sheet (in millions, all interest at annual rates). All securities are selling at par equal to book value.

Assets Cash $20 15-year commercial loan at 10% interest, balloon payment 160 30-year mortgages at 8% interest, balloon payment 300 Total assets

$480

Liabilities and Equity Demand deposits 5-year CDs at 6% interest, balloon payment 20-year debentures at 7% interest, balloon payment Equity Total liabilities and equity

$100 210 120 50 $480

a. What is the maturity gap for County Bank?

MA = [0x$20m + 15x$160m + 30x$300m]/$480m = 23.75 years.

ML = [0x$100m + 5x$210m + 20x$120m]/$430m = 8.02 years.

MGAP = 23.75 – 8.02 = 15.73 years. b. What will be the maturity gap if the interest rates on all assets and liabilities increase by 1 percent?

If interest rates increase one percent, the value and average maturity of the assets will be: 13 © 2022

Cash = $20m Commercial loans = $16mxPVAn=15, i=11% + $160mxPVn=15,i=11% = $148.49m Mortgages = $24mxPVAn=30,i=9% + $300mxPVn=30,i=9% = $269.18m MA = [0x$20m + 15x$148.49m + 30x$269.18m]/($20m + $148.49m + $269.18m) = 23.54 years The value and average maturity of the liabilities will be: Demand deposits = $100m CDs = $12.60mxPVAn=5,i=7% + $210mxPVn=5,i=7% = $201.39m Debentures = $8.4mxPVAn=20,i=8% + $120mxPVn=20,i=8% = $108.22m ML = [0x$100m + 5x$201.39m + 20x$108.22m]/($100m + $201.39m + $108.22m) = 7.74 years The maturity gap = MGAP = 23.54 – 7.74 = 15.80 years. The maturity gap increased because the average maturity of the liabilities decreased more than the average maturity of the assets. This result occurred primarily because of the differences in the cash flow streams for the mortgages and the debentures. c. What will happen to the market value of the equity?

The market value of the assets has decreased from $480m to $437.67m, or $42.33m. The market value of the liabilities has decreased from $430m to $409.61m, or $20.39m. Therefore, the market value of the equity will decrease by $42.33m - $20.39m = $21.94m, or 43.88 percent.

25.

If a bank manager is certain that interest rates were going to increase within the next six months, how should the bank manager adjust the bank’s maturity gap to take advantage of this anticipated increase? What if the manager believes rates will fall? Would your suggested adjustments be difficult or easy to achieve?

When rates rise, the value of the longer-lived assets will fall by more the shorter-lived liabilities.

If the maturity gap is positive, the bank manager will want to shorten the maturity gap or make it negative. If the maturity gap is negative, the manager might do nothing. If rates are expected to decrease, the manager should reverse these strategies. Changing the maturity on the balance sheet often involves changing the mix of assets and liabilities. Attempts to make these changes may involve changes in financial strategy for the bank which may not be easy to accomplish.

Later in the text, methods of achieving the same results using derivatives will be explored.

26.

An insurance company has invested in the following fixed-income securities: (a) $10,000,000 of five-year Treasury notes paying 5 percent interest and selling at par value, (b) $5,800,000 of 10-year bonds paying 7 percent interest with a par value of $6,000,000, and (c) $6,200,000 of 20-year subordinated debentures paying 9 percent interest with a par value of $6,000,000. a. What is the weighted-average maturity of this portfolio of assets?

MA = [5x$10m + 10x$5.8m + 20x$6.2m]/$22m = 232/22 = 10.55 years 14 © 2022

b. If interest rates change so that the yields on all of the securities decrease 1 percent, how does the weighted-average maturity of the portfolio change?

To determine the weighted-average maturity of the portfolio for a rate decrease of 1 percent, the new value of each security must be determined. This calculation will require knowing the yield to maturity of each security before the rate change.

T-notes are selling at par, so the yield to maturity = 5 percent. Therefore, the new value will be PV = $500,000xPVAn=5,i=4% + $10,000,000xPVn=5,i=4% = $10,445,182.

10-year bonds: Par = $6,000,000, PV = $5,800,000, Cpn = 7 percent  YTM = 7.485%. The new PV = $420,000xPVAn=10,i=6.485% + $6,000,000xPVn=10,i=6.485% = $6,222,161.

Debentures: Par = $6,000,000, PV = $6,200,000, Cpn = 9 percent  8.644 percent. The new PV = $540,000xPVAn=20,i=7.644% + $6,000,000xPVn=20,i=7.644 = $6,820,378.

The total value of the assets after the change in rates will be $23,487,721, and the weightedaverage maturity will be [5x$10,445,182 + 10x$6,222,030 + 20x$6,820,378]/$23,487,721 = 250,855,080/23,487,721 = 10.68 years. c. Explain the changes in the weighted-average maturity of the portfolio if the yields increase by 1 percent.

When interest rates increase 1 percent, the value of the T-note is $9,578,764, the value of the 10year bond is $5,414,885, and the value of the debenture is $5,662,851, and the new value of the assets is $20,656,500. The weighted-average maturity is 10.42 years. d. Assume that the insurance company has no other assets. What will be the effect on the market value of the company’s equity if the interest rate changes in (b) and (c) occur?

Assuming that the company is financed entirely with equity, the market value will increase $1,487,721 when interest rates decrease 1 percent, and the market value will decrease $1,343,500 when rates increase 1 percent. Notice that for the same absolute rate change, the increase in value is greater than the decrease in value.

27.

The following is a simplified FI balance sheet: Assets Loans

$1,000

Total assets

$1,000

Liabilities and Equity Deposits Equity Total liabilities & equity

$850 $150 $1,000

The average maturity of loans is four years and the average maturity of deposits is two years. Assume loan and deposit balances are reported as book value, zero-coupon items.

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a. Assume that interest rate on both loans and deposits is 9 percent. What is the market value of equity?

The market value of loans = $1,000/(1.09)4 = $708.4252, and the market value of deposits = $850/(1.09)2 = $715.4280. The net worth = $708.4252 - $715.4280 = -$7.0028. (That is, net worth is negative.) b. What must be the interest rate on deposits to force the market value of equity to be zero? What economic market conditions must exist to make this situation possible?

In this case the deposit value should equal the loan value. Thus, $850/(1 + x)2 = $708.4252.

Solving for x, we get 9.5374%. That is, deposit rates will have to increase more because they have a shorter maturity. Further, this result suggests that deposit rates would have to be higher than loan rates. c. Assume that interest rate on both loans and deposits is 9 percent. What must be the average maturity of deposits for the market value of equity to be zero?

In this case, we need to solve the equation in part (b) for N, i.e., $850/(1 + 0.09)N = $708.4252.

The result is N = 2.1141 years. If interest rates remain at 9 percent, then the average maturity of deposits has to be higher in order to match the value of a 4-year loan.

28.

Gunnison Insurance has reported the following balance sheet (in thousands): Assets 2-year Treasury note 15-year munis

$175 165

Total assets

$340

Liabilities and Equity 1-year commercial paper 5-year note Equity Total liabilities and equity

$135 160 45 $340

All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year munis are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8 percent. All instruments pay interest annually. a. What is the weighted-average maturity of the assets for Gunnison?

MA = [2x$175 + 15x$165]/$340 = 8.31 years b. What is the weighted-average maturity of the liabilities for Gunnison?

ML = [1x$135 + 5x$160]/$295 = 3.17 years c. What is the maturity gap for Gunnison?

MGAP = 8.31- 3.17 = 5.14 years 16 © 2022

d. What does your answer to part (c) imply about the interest rate exposure of Gunnison Insurance?

Gunnison Insurance is exposed to interest rate risk. If interest rates rise, net worth will decrease because the average maturity of the assets is higher than the average maturity of the liabilities.

The opposite holds true if interest rates fall. That is, net worth will increase. e. Calculate the values of all four securities on Gunnison Insurance’s balance sheet assuming that all interest rates increase 2 percent. What is the dollar change in the total asset and total liability values? What is the percentage change in these values?

T-notes: PV = 8.75xPVAi=7%,n=2 + 175xPVi=7%,n=2 = $168.67 Munis: PV = 14.85xPVAi=11%,n=15 + 165xPVi=11%,n=15 = $141.27 Commercial Paper: PV = 6.075xPVAi=6.5%,n=1 + 135xPVi=6.5%,n=1 = $132.46 Note: PV = 12.80xPVAi=10%,n=5 + 160xPVi=10%,n=5 = $147.87 Total assets = $168.67 + $141.27 = $309.94  A = -$30.06 or -8.84 percent change Total liabilities = $132.46 + $147.87 = $280.33  L = -$14.67 or -4.97 percent change f. What is the dollar impact on the market value of equity for Gunnison? What is the percentage change in the value of the equity? E = A - L = -$30.06 – (-$14.67) = -$15.39  -34.2 percent g. What would be the impact on Gunnison’s market value of equity if the liabilities paid interest semiannually instead of annually?

The value of liabilities will be lower with semi-annual compounding, increasing the value of net worth. The one-year CP will decline in value to $132.43. The five-year note will decline in value to $147.64. The value of equity will decrease to $29.87 = ($168.67 + $141.27) - ($132.43 + $147.64).

29.

Scandia Bank has issued a one-year, $1million CD paying 5.75 percent to fund a one-year loan paying an interest rate of 6 percent. The principal of the loan will be paid in two installments: $500,000 in six months and the balance at the end of the year. a. What is the maturity gap of Scandia Bank? According to the maturity model, what does this maturity gap imply about the interest rate risk exposure faced by Scandia Bank?

The maturity gap is 1 year – 1 year = 0. The maturity gap model would state that the bank is immunized against changes in interest rates because assets and liabilities are of equal maturity. b. Assuming no change in interest rates over the year, what is the expected net interest income at the end of the year?

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Principal received in six months Interest received in six months (0.03 x $1,000,000) Total

$500,000 30,000 $530,000

Principal received at the end of the year Interest received at the end of the year (0.03 x $500,000) Future value of interest received in six months ($530,000 x 1.03) Total principal and interest received

$500,000 15,000 545,900 $1,060,900

Principal and interest paid on deposits ($1,000,000 x 0.0575) Net interest income received

$1,057,500 $3,400

c. What would be the effect on annual net interest income of a 2 percent interest rate increase that occurred immediately after the loan was made? What would be the effect of a 2 percent decrease in rates?

If interest rates increase 2 percent, then the reinvestment benefits of cash flows in six months will be higher: Principal received in six months Interest received in six months (0.03 x $1,000,000) Total

$500,000 30,000 $530,000

Principal received at the end of the year Interest received at the end of the year (0.03 x $500,000) Future value of interest received in six months ($530,000 x 1.04) Total principal and interest received

$500,000 15,000 551,200 $1,066,200

Principal and interest paid on deposits ($1,000,000 x 0.0575) Net interest income received

$1,057,500 $8,700

If interest rates decrease by 2 percent, then reinvestment income is reduced.

Principal received in six months Interest received in six months (0.03 x $1,000,000) Total

$500,000 30,000 $530,000

Principal received at the end of the year Interest received at the end of the year (0.03 x $500,000) Future value of interest received in six months ($530,000 x 1.02) Total principal and interest received

$500,000 15,000 540,600 $1,055,600

Principal and interest paid on deposits ($1,000,000 x 0.0575) Net income received

$1,057,500 -$1,900

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d. What do these results indicate about the ability of the maturity model to immunize portfolios against interest rate exposure?

The results indicate that just matching assets and liabilities by maturity is not sufficient to immunize a portfolio against interest rate risk. If the timing of the cash flows within a period is different for assets and liabilities, the effects of interest rate changes are different. For a truly effective immunization strategy, one also needs to account for the timing of cash flows.

30.

EDF Bank has a very simple balance sheet. Assets consist of a two-year, $1 million loan that pays an interest rate of LIBOR plus 4 percent annually. The loan is funded with a twoyear deposit on which the bank pays LIBOR plus 3.5 percent interest annually. LIBOR currently is 4 percent, and both the loan and the deposit principal will be paid at maturity. a. What is the maturity gap of this balance sheet?

Maturity gap = 2 - 2 = 0 years b. What is the expected net interest income in year 1 and year 2?

Interest received in year 1 Interest paid in year 1 Net interest income in year 1

$80,000 75,000 $5,000

Interest received in year 2 Interest paid in year 2 Net interest income in year 2

$80,000 75,000 $5,000

c. Immediately prior to the beginning of year 2, LIBOR rates increased to 6 percent. What is the expected net interest income in year 2? What would be the effect on net interest income of a 2 percent decrease in LIBOR? Year 2: If interest rates increase 2 percent Interest received in year 2 $100,000 Interest paid in year 2 95,000 Net interest income in year 2 $5,000

Year 2: If interest rates decrease 2 percent Interest received in year 2 $60,000 Interest paid in year 2 55,000 Net interest income in year 2 $5,000

d. What do the answers to parts (b) and (c) of this question suggest about the use of maturity gap to immunize an FI against interest rate risk?

The solutions above suggest that, as long as the FI’s assets are financed entirely with liabilities and the timing of the cash flows on the assets and liabilities of the FI are perfectly matched, setting the maturity gap equal to zero immunizes the FI against interest rate risk.

31.

What are the weaknesses of the maturity gap model?

First, the maturity gap model does not consider the degree of leverage on the balance sheet. For example, if assets are not financed entirely with deposits, a change in interest rates may cause the assets to change in value by a different amount than the liabilities. Second, the maturity model does not take into account the timing of the cash flows of either the assets or the liabilities, and 19 © 2022

thus reinvestment and/or refinancing risk may become important factors in profitability and valuation as interest rates change.

The following questions and problems are based on material in Appendix 8B to the chapter.

32.

Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 6%

E(2r1) = 7%

E(3r1) = 7.5%

E(4r1) = 7.85%

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve.

1R1 = 6.00% 1R2 = [(1 + 0.06)(1 + 0.07)]

½

- 1= 6.50%

1R3 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)]

1/3

- 1 = 6.83%

1R4 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)(1 + 0.0785)]

1/4

- 1 = 7.09%

and the current yield to maturity curve will be upward sloping as shown: Yield to Maturity 7.09% 6.83%

6.50%

6.00% 0 33.

1

2

3

4

Term to Maturity (in years)

The current one-year Treasury bill rate is 5.2 percent, and the expected one-year rate 12 months from now is 5.8 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security?

(1.052)(1.058) = (1 + 1R2)2 = 1.113016; (1 + 1R2) = 1.054996  1R2 = 0.0550 or 5.50 percent 34. The Wall Street Journal reported interest rates of 6 percent, 6.35 percent, 6.65 percent, and 6.75 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively.

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According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6?

[1 + E(ir1)] = (1 + 1Ri)i  (1 + 1Ri-1)i-1 [1 + E(4r1)] = (1.0635)4  (1.06)3 = 1.0741  E(4r1) = 7.41 percent for period 4 [1 + E(5r1)] = (1.0665)5  (1.0635)4 = 1.0786  E(5r1) = 7.86 percent for period 5 [1 + E(6r1)] = (1.0675)6  (1.0665)5 = 1.0725  E(6r1) = 7.25 percent for period 6 35.

The Wall Street Journal reports that the rate on three-year Treasury securities is 5.60 percent and the rate on four-year Treasury securities is 5.65 percent. According to the unbiased expectations hypothesis, what does the market expect the one-year Treasury rate to be in year 4, E(4r1)?

1R4 = [(1+1R1)(1+E(2r1))(1+E(3r1)) (1+E(4r1))]

Thus,

0.0565 = [(1+0.056)3(1+ E(4r1))]1/4- 1

and

E(4r1) = [(1+0.0565)4/(1+0.056)3] – 1 = 5.80%

36.

1/4 -1

How does the liquidity premium theory of the term structure of interest rates differ from the unbiased expectations theory? In a normal economic environment, that is, an upwardsloping yield curve, what is the relationship of liquidity premiums for successive years into the future? Why?

The unbiased expectations theory asserts that long-term rates are a geometric average of current and expected short-term rates. The liquidity premium theory asserts that long-term rates are a geometric average of current and expected short-term rates plus a liquidity risk premium. The premium is assumed to increase with the maturity of the security because the uncertainty of future returns grows as maturity increases.

37.

Based on economists= forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: 1R1 = 5.65%

E(2r1) = 6.75%

L2 = 0.05%

E(3r1) = 6.85%

L3 = 0.10%

E(4r1) = 7.15%

L4 = 0.12%

Using the liquidity premium hypothesis, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself.

1R1 = 5.65%

21 © 2022

½ 1R2 = [(1 + 0.0565)(1 + 0.0675 + 0.0005)] -

1= 6.22%

+ 0.0675 + 0.0005)(1 + 0.0685 + 0.001)]1/3- 1 = 6.47%

1R3 = [(1 + 0.0565)(1

1R4 = [(1 + 0.0565)(1 + 0.0675 + 0.0005)(1 + 0.0685 + 0.001)(1 + 0.0715 + 0.0012)]

1/4

-1

= 6.67% and the current yield curve will be upward sloping as shown:

Yield to Maturity

∙

6.67% ∙

6.47% ∙

6.22% ∙

5.65% 0 38.

1

2

3

4

Term to Maturity (in years)

The Wall Street Journal reports that the rate on three-year Treasury securities is 5.25 percent and the rate on four-year Treasury securities is 5.50 percent. The one-year interest rate expected in year four, E(4r1), is 6.10 percent. According to the liquidity premium hypothesis, what is the liquidity premium on the four-year Treasury security, L4?

1R4 = [(1+1R1)(1+E(2r1)+L2)(1+E(3r1)+L3)(1+E(4r1)+L4)]

1/4 -1

Thus,

0.055 = [(1 + 0.0525)3(1 + E(4r1) + L4)]1/4- 1

and

0.061 + L4 = [(1 + 0.055)4/(1 + 0.0525)3] – 1 => L4 = 0.00154 = 0.154%

39.

You note the following yield curve in The Wall Street Journal. According to the unbiased expectations hypothesis, what is the one-year forward rate for the period beginning two years from today, 2f1?

Maturity One day One year Two years Three years

Yield 2.00% 5.50 6.50 9.00 22 © 2022

2 2f1 = [(1 + 1R2) /(1 + 1R1)] – 1 2 2f1 = [(1.065) /(1.055)] - 1 = 7.51%

Integrated Mini Case: Calculating and Using the Repricing GAP State Bank’s balance sheet is listed below. Market yields are in parenthesis, and amounts are in millions.

Assets Cash $20 Fed funds (1.05%) 150 3-month T-bills (5.25%) 150 2-year T-notes (6.50%) 100 8-year T-bonds (7.50%) 200 5-year munis (floating rate) (8.20%, repriced @ 6 months) 50 6-month consumer loans (6%) 250 1-year consumer loans (5.8%) 300 5-year car loans (7%) 350 7-month C&I loans (5.8%) 200 2-year C&I loans (floating rate) (5.15%, repriced @ 6-months) 275 15-year variable rate mortgages (5.8%, repriced @ 6-months) 200 15-year variable rate mortgages (6.1%, repriced @ year) 400 15-year fixed-rate mortgages (7.85%) 300 30-year variable rate mortgages (6.3%, repriced @ quarter) 225 30-year variable rate mortgages (6.4%, repriced @ month) 355 30-year fixed-rate mortgages (8.2%) 400 Premises and equipment 20 Total assets $3,945

Liabilities and Equity Demand deposits $250 Savings accounts (1.5%) 20 MMDAs (2.5%) (no minimum balance requirement) 340 3-month CDs (4.2%) 120 6-month CDs (4.3%) 220 1-year CDs (4.5%) 375 2-year CDs (5%) 425 4-year CDs (5.5%) 330 5-year CDs (6%) 350 Fed funds (1%) 225 Overnight repos (1.25%) 290 6-month commercial paper (3%) 300 Subordinate notes: 3-year fixed rate (6.55%) 200 Subordinated debt: 7-year fixed rate (7.25%) 100 Total liabilities $3,545

Equity Total liabilities and equity

400 $3,945

a. What is the repricing gap if the planning period is 30 days? 6 months? 1 year? 2 years? 5 years?

Assets Repricing period Cash $20 Not rate sensitive Fed funds (1.05%) 150 30-days 3-month T-bills (5.25%) 150 6-months 2-year T-notes (6.50%) 100 2-years 8-year T-bonds (7.50%) 200 Not rate sensitive 5-year munis (floating rate) 23 © 2022

(8.20%, repriced @ 6 months) 50 6-month consumer loans (6%) 250 1- year consumer loans (5.8%) 300 5-year car loans (7%) 350 7-month C&I loans (5.8%) 200 2-year C&I loans (floating rate) (5.15%, repriced @ 6-months) 275 15-year variable rate mortgages (5.8%, repriced @ 6-months) 200 15-year variable rate mortgages (6.1%, repriced @ year) 400 15-year fixed-rate mortgages (7.85%) 300 30-year variable rate mortgages (6.3%, repriced @ quarter) 225 30-year variable rate mortgages (6.4%, repriced @ month) 355 30-year fixed-rate mortgages (8.2%) 400 Premises and equipment 20

6-months 6-months 1-year 5-years 1-year

Liabilities and Equity Demand deposits $250 Savings accounts (1.5%) 20 MMDAs (4.5%) (no minimum balance requirement) 340 3-month CDs (4.2%) 120 6-month CDs (4.3%) 220 1- year CDs (4.5%) 375 2- year CDs (5%) 425 4- year CDs (5.5%) 330 5- year CDs (6%) 350 Fed funds (1%) 225 Overnight repos (1.25%) 290 6- month commercial paper (3%) 300 Subordinate notes 3- year fixed rate (6.55%) 200 Subordinated debt 7- year fixed rate (7.25%) 100 Equity 400

Repricing Period Not rate sensitive 30-days

6-months 6-months 1-year Not rate sensitive 6-months 30-days Not rate sensitive Not rate sensitive

30-days 6-months 6-months 1-year 2-years 5-years 5-years 30-days 30-days 6-months 5-years Not rate sensitive Not rate sensitive

30-day repricing gap: RSAs = $150m. + $355m. = $505m.

RSLs = $20m. + $340m. + $225m. + $290m. = $875m.

CGAP = $505m. - $875m. = -$370m.

6-month repricing gap: RSAs = $505m. + $150m. + $50m. + $250m. + $275m. + $200m. + $225m. = $1655m.

RSLs = $875m. + $120m. + $220m. + $300m. = $1515m.

CGAP = $1655m. - $1515m. = $140m.

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1-year repricing gap:

2- year repricing gap:

5-year repricing gap:

RSAs = $1655m. + $300m. + $200m. + $400m. = $2555m.

RSLs = $1515m. + $375m. = $1890m.

CGAP = $2555m. - $1890m. = $665m.

RSAs = $2555m. + $100m. = $2655m.

RSLs = $1890m. + $425m. = $2315m.

CGAP = $2655m. - $2315m. = $340m.

RSAs = $2655m. + $350m. = $3005m.

RSLs = $2315m. + $330m. + $350m. + $200m. = $3195m.

CGAP = $3005m. - $3195m. = -$190m.

b. What is the impact over the next six months on net interest income if interest rates on RSAs increase 60 basis points and on RSLs increase 40 basis points? ΔNII (6-months) = ΔII (6-months) – ΔIE (6-months) = $1655m.(0.0060) - $1515m.(0.0040) = $3.87m. c. What is the impact over the next year on net interest income if interest rates on RSAs increase 60 basis points and on RSLs increase 40 basis points? ΔNII (1-year) = ΔII (1-year) – ΔIE (1-year) = $2555m.(0.0060) - $1890m.(0.0040) = $7.77m.

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Solutions for End-of-Chapter Questions and Problems: Chapter Nine 1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the two methods?

What is marking to market?

Book value accounting reports assets and liabilities at the original issue values. Market value accounting reports assets and liabilities at their current market values. Current market values may be different from book values because they reflect current market conditions, such as current interest rates. FIs generally report their balance sheets using book value accounting methods.

This is a problem if an asset or liability has to be liquidated immediately. If the asset or liability is held until maturity, then the reporting of book values does not pose a problem.

For an FI, a major factor affecting asset and liability values is interest rate changes. If interest rates increase, the value of both loans (assets) and deposits and other debt (liabilities) fall. If assets and liabilities are held until maturity, interest rate changes do not affect the valuation of the FI. However, if deposits or loans have to be refinanced, then market value accounting presents a better picture of the condition of the FI. The process by which changes in the economic value of assets and liabilities are accounted is called marking to market. The changes can be beneficial as well as detrimental to the total economic value of the FI. 2.

What are the two different general interpretations of the concept of duration, and what is the technical definition of this term? How does duration differ from maturity?

Duration measures the weighted-average life of an asset or liability in economic terms. As such, duration has economic meaning as the interest rate sensitivity (or interest elasticity) of an asset’s value to changes in the interest rate. Duration differs from maturity as a measure of interest rate sensitivity because duration takes into account the time of arrival and the rate of reinvestment of all cash flows during the assets life. Technically, duration is the weighted-average time to maturity using the relative present values of the cash flows as the weights.

3.

A one-year, $100,000 loan carries a coupon rate and a market interest rate of 12 percent.

The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year. a. What will be the cash flows at the end of six months and at the end of the year?

CF1/2 = ($100,000 x 0.12 x ½) + $50,000 = $56,000 interest and principal.

CF1 = ($50,000 x 0.12 x ½) + $50,000 = $53,000 interest and principal. b. What is the present value of each cash flow discounted at the market rate? What is the total present value?

PV of CF1/2 = $56,000/1.06 = $52,830.19 PV of CF1 = $53,000/(1.06)2 = 47,169.81 1 © 2022

PV Total CF = $100,000.00 c. What proportion of the total present value of cash flows occurs at the end of six months? What proportion occurs at the end of the year?

X1/2 = $52,830.19  $100,000 = 0.5283 = 52.83% X1 = $47,169.81  $100,000 = 0.4717 = 47.17% d. What is the duration of this loan?

Duration = 0.5283(1/2) + 0.4717(1) = 0.7358 OR t ½ 1

CF $56,000 53,000

PVof CF $52,830.19 47,169.81 $100,000.00

PV of CF x t $26,415.09 47,169.81 $73,584.91

Duration = $73,584.91/$100,000.00 = 0.7358 years 4.

Two bonds are available for purchase in the financial markets. The first bond is a two-year, $1,000 bond that pays an annual coupon of 10 percent. The second bond is a two-year, $1,000, zero-coupon bond. a. What is the duration of the coupon bond if the current yield to maturity (R) is 8 percent? 10 percent? 12 percent? (Hint: You may wish to create a spreadsheet program to assist in the calculations.)

Coupon Bond: Par value = $1,000 R = 8% t 1 2

CFt $100 1,100

Coupon rate = 10% Maturity = 2 years

DFt 0.9259 0.8573

CFt x DFt $92.59 943.07 $1,035.67 Duration = $1,978.74/$1,035.67 = 1.9106

Maturity = 2 years CF x DF CFt x DFt x t t t t 1 $90.91 $90.91 2 909.09 1,818.18 $1,000.00 $1,909.09 Duration = $1,909.09/$1,000.00 = 1.9091 CFt $100 1,100

R = 10% DFt 0.9091 0.8264

CFt x DFt x t $92.59 1,886.15 $1,978.74

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Annual payments

Maturity = 2 years CFt x DFt CFt x DFt x t $89.29 $89.23 876.91 1,753.83 $966.20 $1,843.11 Duration = $1,843.11/$966.20 = 1.9076 t 1 2

CFt $100 1,100

R = 12% DFt 0.8929 0.7972

b. How does the change in the yield to maturity affect the duration of this coupon bond?

Increasing the yield to maturity decreases the duration of the bond. c. Calculate the duration of the zero-coupon bond with a yield to maturity of 8 percent, 10 percent, and 12 percent.

Zero Coupon Bond:

Par value = $1,000 R = 8% t CFt DFt CFt x DFt 2 $1,000 0.8573 $857.34 $857.34 Duration = $1,714.68/$857.34 = 2.0000

Coupon rate = 0% Maturity = 2 years CFt x DFt x t $1,714.68 $1,714.68

R = 10% DFt CFt x DFt 0.8264 $826.45 $826.45 Duration = $1,652.89/$826.45 = 2.0000

Maturity = 2 years CFt x DFt x t $1,652.89 $1,652.89

R = 12% DFt CFt x DFt 0.7972 $797.19 $797.19 Duration = $1,594.39/$797.19 = 2.0000

Maturity = 2 years CFt x DFt x t $1,594.39 $1,594.39

t 2

t 2

CFt $1,000

CFt $1,000

d. How does the change in the yield to maturity affect the duration of the zero-coupon bond?

Changing the yield to maturity does not affect the duration of the zero coupon bond. e. Why does the change in the yield to maturity affect the coupon bond differently than it affects the zero-coupon bond?

Increasing the yield to maturity on the coupon bond allows for higher reinvestment income that more quickly recovers the initial investment. The zero-coupon bond, on the other hand, has no cash flow (and therefore no reinvestment of income) until maturity.

3 © 2022

5.

What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this relationship exist?

Five-year Treasury Bond: Par value = $1,000

Coupon rate = 10%

R = 10% CFt t 0.5 50 1.0 50 1.5 50 2.0 50 2.5 50 3.0 50 3.5 50 4.0 50 4.5 50 5.0 1,050

Maturity = 5 years DFt CFt x DFt CFt x DFt x t 0.9524 47.620 23.810 0.9070 45.350 45.350 0.8638 43.190 64.785 0.8227 41.135 82.270 0.7835 39.175 97.937 0.7462 37.310 111.930 0.7107 35.535 124.373 0.6768 33.842 135.368 0.6446 32.230 145.035 0.6139 644.595 3,222.975 1,000.00 4,053.833 Duration = $4,053.91/$1,000.00 = 4.0539 R = 12% CFt t 0.5 50 1.0 50 1.5 50 2.0 50 2.5 50 3.0 50 3.5 50 4.0 50 4.5 50 5.0 1,050

Maturity = 5 years CFt x DFt CFt x DFt x t 47.17 23.58 44.50 44.50 41.98 62.97 39.60 79.21 37.36 93.41 35.25 105.74 33.25 116.38 31.37 125.48 29.59 133.18 586.31 2,931.57 926.40 3,716.03 Duration = $3,716.03/$926.40 = 4.0113 R = 14% CFt t 0.5 50 1.0 50 1.5 50 2.0 50 2.5 50 3.0 50

Maturity = 5 years CFt x DFt CFt x DFt x t 46.73 23.36 43.67 43.67 40.81 61.22 38.14 76.29 35.65 89.12 33.32 99.95 4 © 2022

Semiannual payments

3.5 4.0 4.5 5.0

50 50 50 1,050

31.14 29.10 27.20 533.77 859.53

108.98 116.40 122.39 2,668.83 3,410.22

Duration = $3, 410.22/$859.53 = 3.9676 Duration and YTM

4.08

4.0539

Years

4.04

4.0113

4.00

3.9676

3.96 3.92 0.10

0.12

0.14

Yield to Maturity

As the yield to maturity increases, the higher yields discount later cash flows more heavily and the relative importance, or weights, of those later cash flows decline when compared with earlier cash flows on the bond.

6.

Consider three Treasury bonds each of which has a 10 percent semiannual coupon and trades at par. a. Calculate the duration for a bond that has a maturity of four years, three years, and two years.

Four-year Treasury Bond: Par value = $1,000 Coupon rate = 10% Semiannual payments R = 10% t CFt 0.5 50 1.0 50 1.5 50 2.0 50 2.5 50 3.0 50 3.5 50 4.0 1,050

Maturity = 4 years DFt CFt x DFt 0.9524 47.62 0.9070 45.35 0.8638 43.19 0.8227 41.14 0.7835 39.18 0.7462 37.31 0.7107 35.53 0.6768 710.68 1,000.00

Duration = $3,393.19/$1,000.00 = 3.3932 R = 10%

Maturity = 3 years 5 © 2022

CFt x DFt x t 23.81 45.35 64.79 82.27 97.94 111.93 124.37 2,842.72 3,393.19

t 0.5 1.0 1.5 2.0 2.5 3.0

CFt 50 50 50 50 50 1,050

DFt 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462

CFt x DFt 47.62 45.35 43.19 41.14 39.18 783.53 1,000.00

CFt x DFt x t 23.81 45.35 64.79 82.27 97.94 2,350.58 2,664.74

Maturity = 2 years DFt CFt x DFt 0.9524 47.62 0.9070 45.35 0.8638 43.19 0.8227 863.84 1,000.00

CFt x DFt x t 23.81 45.35 64.79 1,727.68 1,861.62

Duration = $2,664.74/$1,000.00 = 2.6647 R = 10% CFt t 0.5 50 1.0 50 1.5 50 2.0 1,050

Duration = $1,861.62/$1,000.00 = 1.8616 b. What conclusions can you reach about the relationship between duration and the time to maturity? Plot the relationship.

As maturity decreases, duration decreases at a decreasing rate. Although the graph below does not illustrate with great precision, the change in duration is less than the change in time to maturity.

4.00

3.3932

3.00

Years

Duration 1.8616 2.6647 3.3932

Duration and Maturity

Change in Maturity Duration 2 3 0.8031 4 0.7285

2.6647 2.00 1.8616 1.00

0.00 2

3

4

Time to Maturity

7.

A six-year, $10,000 CD pays 6 percent interest annually and has a 6 percent yield to maturity. What is the duration of the CD? What would be the duration if interest were paid semiannually? What is the relationship of duration to the relative frequency of interest payments?

6 © 2022

Six-year CD: Par value = $10,000

Coupon rate = 6%

R = 6% CFt t 1 600 2 600 3 600 4 600 5 600 6 10,600

Maturity = 6 years DFt CFt x DFt 0.9434 566.04 0.8900 534.00 0.8396 503.77 0.7921 475.26 0.7423 448.35 0.7050 7.472.58 10,000.00 Duration = $52,123.64/$1,000.00 = 5.2124

Annual payments CFt x DFt x t 566.04 1,068.00 1,511.31 1,901.02 2,241.77 44,835.49 52,123.64

R = 6% CFt t 0.5 300 1 300 1.5 300 2 300 2.5 300 3 300 3.5 300 4 300 4.5 300 5 300 5.5 300 6 10,300

Semiannual payments CFt x DFt x t 145.63 282.78 411.81 533.09 646.96 753.74 853.75 947.29 1,034.66 1,116.14 1,192.00 43,345.28 51,263.12

Maturity = 6 years DFt CFt x DFt 0.9709 291.26 0.9425 282.78 0.9151 274.54 0.8885 266.55 0.8626 258.78 0.8375 251.25 0.8131 243.93 0.7894 236.82 0.7664 229.93 0.7441 223.23 0.7224 216.73 0.7014 7,224.21 10,000.00 Duration = $51,263.12/$10,000.00 = 5.1263

Duration decreases as the frequency of payments increases. This relationship occurs because (a) cash is being received more quickly and (b) reinvestment income will occur more quickly from the earlier cash flows.

8.

What is a consol bond? What is the duration of a consol bond that sells at a yield to maturity of 8 percent? 10 percent? 12 percent? Would a consol bond trading at a yield to maturity of 10 percent have a greater duration than a 20-year zero-coupon bond trading at the same yield to maturity? Why?

A consol bond is a bond that pays a fixed coupon each year forever.

A consol bond trading at a yield to maturity of 10 percent has a duration of 11 years, while a 20-year zero-coupon bond trading at a ytm of 10 percent, or any other ytm, has a duration of 20 years because no cash flows occur before the twentieth year.

7 © 2022

R 0.08 0.10 0.12

Consol Bond D = 1 + 1/R 13.50 years 11.00 years 9.33 years

9.

Maximum Pension Fund is attempting to manage one of the bond portfolios under its management. The fund has identified three bonds that have five year maturities and trade at a yield to maturity of 9 percent. The bonds differ only in that the coupons are 7 percent, 9 percent, and 11 percent. a. What is the duration for each bond?

Five-year Bond: Par value = $1,000 Maturity = 5 years Annual payments R = 9% Coupon rate = 7% CFt DFt CFt x DFt CFt x DFt x t t 1 70 0.9174 64.22 64.22 2 70 0.8417 58.92 117.84 3 70 0.7722 54.05 162.16 4 70 0.7084 49.59 198.36 5 1,070 0.6499 695.43 3,477.13 922.21 4,019.71 Duration = $4,019.71/$922.21 = 4.3588 R = 9% CFt t 1 $90 2 $90 3 $90 4 $90 5 $1,090

Coupon rate = 9% DFt CFt x DFt 0.9174 82.57 0.8417 75.75 0.7722 69.50 0.7084 63.76 0.6499 708.43 1,000.00 Duration = $4,239.72/$1,000.00 = 4.2397 R = 9% CFt t 1 $110 2 $110 3 $110 4 $110 5 $1,110

Coupon rate = 11% DFt CFt x DFt 0.9174 100.92 0.8417 92.58 0.7722 84.94 0.7084 77.93 0.6499 721.42 1,077.79 Duration = $4,459.73/$1,077.79 = 4.1378

CFt x DFt x t 82.57 151.50 208.49 255.03 3,542.13 4,239.72

CFt x DFt x t 100.92 185.17 254.82 311.71 3,607.12 4,459.73

b. What is the relationship between duration and the amount of coupon interest that is paid? Plot the relationship.

8 © 2022

Duration and Coupon Rates

Duration decreases as the amount of coupon interest increases.

Change in Duration Coupon Duration 4.3588 7% 4.2397 9% -0.1191 4.1378 11% -0.1019

Years

4.3588 4.2397 4.1378 4.00 7%

9%

11%

Coupon Rates

10.

An insurance company is analyzing three bonds and is using duration as the measure of interest rate risk. All three bonds trade at a yield to maturity of 10 percent, have $10,000 par values, and have five years to maturity. The bonds differ only in the amount of annual coupon interest that they pay: 8, 10, and 12 percent. a. What is the duration for each five-year bond?

Five-year Bond: Par value = $10,000 Coupon rate = 8% CFt t 1 800 2 800 3 800 4 800 5 10,800

DFt 0.9091 0.8264 0.7513 0.6830 0.6209

R = 10%

Maturity = 5 years

CFt x DFt 727.27 661.16 601.06 546.41 6,705.95 9,241.84

CFt x DFt x t 727.27 1,322.31 1,803.16 2,185.64 33,529.75 39,568.14

Duration = $39,568.14/9,241.84 = 4.2814 Coupon rate = 10% CFt DFt t 1 $1,000 0.9091 2 $1,000 0.8264 3 $1,000 0.7513 4 $1,000 0.6830 5 $11,000 0.6209

CFt x DFt 909.09 826.45 751.31 683.01 6,830.13 10,000.00

CFt x DFt x t 909.09 1,652.89 2,253.94 2,732.05 34,150.67 41,698.65

Duration = $41.698.65/10,000.00 = 4.1699 Coupon rate = 12% CFt DFt t 1 $1,200 0.9091

CFt x DFt 1,090.91 9 © 2022

CFt x DFt x t 1,090.91

Annual payments

2 3 4 5

$1,200 $1,200 $1,200 $11,200

0.8264 0.7513 0.6830 0.6209

991.74 901.58 819.62 6,954.32 10,758.16

1,983.47 2,704.73 3,278.46 34,771.59 43,829.17

Duration = $43,829.17/10,758.16 = 4.0740 b.

What is the relationship between duration and the amount of coupon interest that is paid?

Duration and Coupon Rates

4.50

Years

4.2814 4.1699 4.0740 4.00 8%

10%

12%

Duration decreases as the amount of coupon interest increases.

Change in Duration Coupon Duration 4.2814 8% 4.1699 10% -0.1115 4.0740 12% -0.0959

Coupon Rates

11.

You can obtain a loan of $100,000 at a rate of 10 percent for two years. You have a choice of (i) paying the interest (10 percent) each year and the total principal at the end of the second year or (ii) amortizing the loan, that is, paying interest (10 percent) and principal in equal payments each year. The loan is priced at par. a. What is the duration of the loan under both methods of payment?

Two-year loan: Interest at end of year one; Principal and interest at end of year two Par value = $100,000 Coupon rate = 10% Annual payments R = 10% Maturity = 2 years CFt DFt CFt x DFt CFt x DFt x t t 1 $10,000 0.9091 9,090.91 9,090.91 2 $110,000 0.8264 90,909.09 181,818.18 100,000.00 190,909.09 Duration = $190,909.09/$100,000 = 1.9091 Two-year loan: Amortized over two years Par value = $100,000 Coupon rate = 10% Annual amortized payments R = 10% Maturity = 2 years = $57,619.05 CFt DFt CFt x DFt CFt x DFt x t t 1 $57,619.05 0.9091 52,380.95 52,380.95 2 $57,619.05 0.8264 47,619.05 95,238.10 100,000.00 147,619.05 Duration = $147,619.05/$100,000 = 1.4762 10 © 2022

b. Explain the difference in the two results Duration decreases dramatically when a portion of the principal is repaid at the end of year one.

Duration is the weighted-average maturity of an asset. If more weight is given to early payments, the effective maturity of the asset is reduced.

12.

How is duration related to the interest elasticity of a fixed-income security? What is the relationship between duration and the price of the fixed-income security?

Taking the first derivative of a bond’s (or any fixed-income security) price (P) with respect to the yield to maturity (R) provides the following: dP P =−D dR (1 + R) The economic interpretation is that D is a measure of the percentage change in the price of a bond for a given percentage change in yield to maturity (interest elasticity). This equation can be rewritten to provide a practical application:  dR  dP = − D P 1+ R In other words, if duration is known, then the change in the price of a bond due to small changes in interest rates, R, can be estimated using the above formula.

13.

You have discovered that the price of a bond rose from $975 to $995 when the yield to maturity fell from 9.75 percent to 9.25 percent. What is the duration of the bond?

We know − D=

14.

PP R

20

=− 4.5 years D= 4.5 years 975 − 0.005 (1+ R) 1.0975 =

A 10-year, 10 percent annual coupon, $1,000 bond trades at a yield to maturity of 8 percent. The bond has a duration of 6.994 years. What is the modified duration of this bond? What is the practical value of calculating modified duration? Does modified duration change the result of using the duration relationship to estimate price sensitivity?

Modified duration = Duration/(1+ R) = 6.994/1.08 = 6.4759. Some practitioners find this value easier to use because the percentage change in value can be estimated simply by multiplying the existing value times the basis point change in interest rates rather than by the relative change in interest rates. Using modified duration will not change the estimated price sensitivity of the asset.

15.

What is dollar duration? How is dollar duration different from duration?

11 © 2022

Dollar duration is the dollar value change in the price of a security to a one percent change in the return on the security. Duration is a measure of the percentage change in the price of a security for a one percent change in the return on the security. The dollar duration is intuitively appealing in that we multiply the dollar duration by the change in the interest rate to get the actual dollar change in the value of a security to a change in interest rates.

16.

Calculate the duration of a two-year, $1,000 bond that pays an annual coupon of 10 percent and trades at a yield of 14 percent. What is the expected change in the price of the bond if interest rates fall by 0.50 percent (50 basis points)?

Two-year Bond: Par value = $1,000 Coupon rate = 10% Annual payments R = 14% Maturity = 2 years CFt DFt CFt x DFt CFt x DFt x t t 1 100 0.8772 87.72 87.72 2 1,100 0.7695 846.41 1,692.83 934.13 1,780.55 Duration = $1,780.55/$934.13 = 1.9061 The expected change in price = - dollar duration x ∆R = − D

R 1+ R

P = - MD x ∆R =

- (1.9061/1.14) x (-0.0050) x $934.13 = $7.81. This implies a new price of $941.94 ($934.13 + $7.81). The actual price using conventional bond price discounting would be $941.99. The difference of $0.05 is due to convexity, which is not considered in the duration elasticity measure.

17.

The duration of an 11-year, $1,000 Treasury bond paying a 10 percent semiannual coupon and selling at par has been estimated at 6.763 years. a. What is the modified duration of the bond? What is the dollar duration of the bond?

Modified duration = D/(1 + R/2) = 6.763/(1 + 0.10/2) = 6.441 years Dollar duration = MD x P = 6.441 x $1,000 = 6441 b. What will be the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points)? If rates decrease 0.20 percent (20 basis points)?

For an interest rate increase of 0.10 percent: Estimated change in price = - dollar duration x R = -6441 x 0.001 = -$6.441 => new price = $1,000 - $6.441 = $993.559 For an interest rate decrease of 0.20 percent: Estimated change in price = -6441 x -0.002 = $12.882 => new price = $1,000 + $12.882 = $1,012.882 12 © 2022

c. What would the actual price of the bond be under each rate change situation in part (b) using the traditional present value bond pricing techniques? What is the amount of error in each case?

Rate Change + 0.001 - 0.002

Price Estimated $993.559 $1,012.882

Actual Price $993.535 $1,013.111

Error $0.024 -$0.229

18. Suppose you purchase a six-year, 8 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000. a. Show that the duration of this bond is equal to five years.

Coupon rate = 8% Annual payments Maturity = 6 years CFt x DFt CFt x DFt x t 73.39 73.39 67.33 134.67 61.77 185.32 56.67 226.70 51.99 259.97 643.97 3,863.81 955.14 4,743.87 Duration = $4,743.87/955.14 = 4.97  5 years Six-year Bond: Par value = $1,000 R = 9% CFt DFt t 1 80 0.9174 2 80 0.8417 3 80 0.7722 4 80 0.7084 5 80 0.6499 6 1,080 0.5963

b. Show that if interest rates rise to 10 percent within the next year and your investment horizon is five years from today, you will still earn a 9 percent yield on your investment.

Value of bond at end of year five: PV = ($80 + $1,000)/1.10 = $981.82 Future value of interest payments at end of year five: $80FVn=4, i=10% = $488.41 Future value of all cash flows at n = 5: Coupon interest payments over five years $400.00 Interest on interest at 10 percent 88.41 Value of bond at end of year five $981.82 Total future value of investment $1,470.23 Yield on purchase of asset at $955.14 = $1,470.23xPVn=5, i=?%  i = 9.00924% c. Show that a 9 percent yield also will be earned if interest rates fall next year to 8 percent.

Value of bond at end of year five: PV = ($80 + $1,000)/1.08 = $1,000 Future value of interest payments at end of year five: $80xFVn=5, i=8% = $469.33 13 © 2022

Future value of all cash flows at n = 5: Coupon interest payments over five years Interest on interest at 8 percent Value of bond at end of year five Total future value of investment

$400.00 69.33 $1,000.00 $1,469.33

Yield on purchase of asset at $955.14 = $1,469.33xPVn=5, i=?%  i = 8.99596 percent.

19.

Suppose you purchase a five-year, 15 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000. a. Show that the duration of this bond is equal to four years.

Five-year Bond: Par value = $1,000 Coupon rate = 15% Annual payments R = 9% Maturity = 5 years CFt DFt CFt x DFt CFt x DFt x t t 1 $150 0.9174 137.62 137.62 2 $150 0.8417 126.25 252.50 3 $150 0.7722 115.83 347.48 4 $150 0.7084 106.26 425.06 5 $1,150 0.6499 747.42 3,737.10 1,233.38 4,899.76 Duration = $4899.76/1,233.38 = 3.97  4 years b. Show that if interest rates rise to 10 percent within the next year and your investment horizon is four years from today, you will still earn a 9 percent yield on your investment.

Value of bond at end of year four: PV = ($150 + $1,000)/1.10 = $1,045.45 Future value of interest payments at end of year four: $150xFVn=4, i=10% = $696.15 Future value of all cash flows at n = 4: Coupon interest payments over four years $600.00 Interest on interest at 10 percent 96.15 Value of bond at end of year four $1,045.45 Total future value of investment $1,741.60 Yield on purchase of asset at $1,233.38 = $1,741.60xPVn=4, i=?%  i = 9.00% c. Show that a 9 percent yield also will be earned if interest rates fall next year to 8 percent.

Value of bond at end of year four: PV = ($150 + $1,000)/1.08 = $1,064.81 Future value of interest payments at end of year four: $150xFVn=4, i=8% = $675.92 Future value of all cash flows at n = 4: 14 © 2022

Coupon interest payments over four years Interest on interest at 8 percent Value of bond at end of year four Total future value of investment

$600.00 75.92 $1,064.81 $1,740.73

Yield on purchase of asset at $1,233.38 = $1,740.73xPVn=4, i=?%  i = 9.00 percent.

20.

Consider the case in which an investor holds a bond for a period of time longer than the duration of the bond, that is, longer than the original investment horizon. a. If interest rates rise, will the return that is earned exceed or fall short of the original required rate of return? Explain.

In this case, the actual return earned would exceed the yield expected at the time of purchase.

The benefits from a higher reinvestment rate would exceed the price reduction effect if the investor holds the bond for a sufficient length of time. b. What will happen to the realized return if interest rates decrease? Explain.

If interest rates decrease, the realized yield on the bond will be less than the expected yield because the decrease in reinvestment earnings will be greater than the gain in bond value. c. Recalculate parts (b) and (c) of problem 18 above, assuming that the bond is held for all five years, to verify your answers to parts (a) and (b) of this problem.

The case where interest rates rise to 10 percent, n = five years: Future value of interest payments at end of year five: $150xFVn=5, i=10% = $915.76 Future value of all cash flows at n = 5: Coupon interest payments over five years $750.00 Interest on interest at 10 percent 165.76 Value of bond at end of year five $1,000.00 Total future value of investment $1,915.76 Yield on purchase of asset at $1,233.38 = $1,915.76xPVn=5, i=?%  i = 9.2066% The case where interest rates fall to 8 percent, n = five years: Future value of interest payments at end of year five: $150xFVn=5, i=8% = $879.99 Future value of all cash flows at n = 5: Coupon interest payments over five years $750.00 Interest on interest at 8 percent 129.99 Value of bond at end of year five $1,000.00 Total future value of investment $1,879.99 Yield on purchase of asset at $1,233.38 = $1,879.99xPVn=5, i=?%  i = 8.7957% 15 © 2022

d. If either calculation in part (c) is greater than the original required rate of return, why would an investor ever try to match the duration of an asset with his or her investment horizon?

The answer has to do with the ability to forecast interest rates. Forecasting interest rates is a very difficult task, one that most financial institution money managers are unwilling to do. For most managers, betting that rates would rise to 10 percent to provide a realized yield of 9.20 percent over five years is not a sufficient return to offset the possibility that rates could fall to 8 percent and thus give a yield of only 8.8 percent over five years.

21.

Two banks are being examined by regulators to determine the interest rate sensitivity of their balance sheets. Bank A has assets composed solely of a 10-year $1 million loan with a coupon rate and yield of 12 percent. The loan is financed with a 10-year $1 million CD with a coupon rate and yield of 10 percent. Bank B has assets composed solely of a 7-year, 12 percent zero-coupon bond with a current (market) value of $894,006.20 and a maturity (principal) value of $1,976,362.88. The bond is financed with a 10-year, 8.275 percent coupon $1,000,000 face value CD with a yield to maturity of 10 percent. The loan and the CDs pay interest annually, with principal due at maturity. a. If market interest rates increase 1 percent (100 basis points), how do the market values of the assets and liabilities of each bank change? That is, what will be the net effect on the market value of the equity for each bank?

For Bank A, an increase of 100 basis points in interest rate will cause the market values of assets and liabilities to decrease as follows: Loan: $120,000xPVAn=10,i=13% + $1,000,000xPVn=10,i=13% = $945,737.57 CD: $100,000xPVAn=10,i=11% + $1,000,000xPVn=10,i=11% = $941,107.68 The loan value decreases $54,262.43 and the CD value falls $58,892.32. Therefore, the decrease in value of the asset is $4,629.89 less than the liability, which is, in turn, the increase in the market value of equity for Bank A. For Bank B: Bond: $1,976,362.88xPVn=7,i=13% = $840,074.08 CD: $82,750xPVAn=10,i=11% + $1,000,000xPVn=10,i=11% = $839,518.43 The bond value decreases $53,932.12 and the CD value falls $54,487.79. Therefore, the decrease in value of the asset is $555.67 less than the liability, which is, in turn, the increase in the market value of equity for Bank B. b. What accounts for the differences in the changes in the market value of equity between the two banks?

The assets and liabilities of Bank A change in value by different amounts because the durations of the assets and liabilities are not the same, even though the face values and maturities are the same. For Bank B, the maturities of the assets and liabilities are different, but the current market 16 © 2022

values and durations are the same. Thus, the change in interest rates causes a smaller change in value for both liabilities and assets. c. Verify your results above by calculating the duration for the assets and liabilities of each bank, and estimate the changes in value for the expected change in interest rates.

Summarize your results.

Ten-year CD Bank B (values in thousands of $s) Par value = $1,000 Coupon rate = 8.275% Annual payments R = 10% Maturity = 10 years CFt DFt CFt x DFt CFt x DFt x t t 1 82.75 0.9091 75.23 75.23 2 82.75 0.8264 68.39 136.78 3 82.75 0.7513 62.17 186.51 4 82.75 0.6830 56.52 226.08 5 82.75 0.6209 51.38 256.91 6 82.75 0.5645 46.71 280.26 7 82.75 0.5132 42.46 297.25 8 82.75 0.4665 38.60 308.83 9 82.75 0.4241 35.09 315.85 10 1,082.75 0.3855 417.45 4,174.47 894.01 6,258.15 Duration = $6,258.15/894.01 = 7.00 The duration on the CD of Bank B is calculated above to be 7.00 years. Since the bond is a zerocoupon, the duration is equal to the maturity of 7 years.

Using the duration formula to estimate the change in value: R P = − 7.00 0.01 $894,006.20 =− $55,875.39 Bond: Value = − D 1+ R 1.12 CD:

Value = − D

R 1+ R

P = − 7.00

0.01

$894,006.20 = − $56,891.30

1.10

The difference in the change in value of the assets and liabilities for Bank B is $1,015.91 using the duration estimation model. The difference in this estimate and the estimate found in part (a) above is due to the convexity of the two financial assets.

The duration estimates for the loan and CD for Bank A are presented below: Ten-year Loan Bank A Par value = $1,000 R = 12%

(values in thousands of $s) Coupon rate = 12% Maturity = 10 years 17 © 2022

Annual payments

t

CFt

DFt

CFt x DFt

18 © 2022

CFt x DFt x t

1 2 3 4 5 6 7 8 9 10

120 120 120 120 120 120 120 120 120 1,120

0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220

107.14 95.66 85.41 76.26 68.09 60.80 54.28 48.47 43.27 360.61 1,000.00

107.14 191.33 256.24 305.05 340.46 364.77 379.97 387.73 389.46 3,606.10 6,328.25

Duration = $6,328.25/$1,000 = 6.3282 Ten-year CD Bank A (values in thousands of $s) Par value = $1,000 Coupon rate = 10% Annual payments R = 10% Maturity = 10 years CFt DFt CFt x DFt CFt x DFt x t t 1 100 0.9091 90.91 90.91 2 100 0.8264 82.64 165.29 3 100 0.7513 75.13 225.39 4 100 0.6830 68.30 273.21 5 100 0.6209 62.09 310.46 6 100 0.5645 56.45 338.68 7 100 0.5132 51.32 359.21 8 100 0.4665 46.65 373.21 9 100 0.4241 42.41 381.69 10 1,100 03855 424.10 4,240.98 1,000.00 6,759.02 Duration = $6,759.02/$1,000 = 6.7590 Using the duration formula to estimate the change in value: R P = − 6.3282 0.01 $1,000,000 =− $56,501.79 Loan: Value = − D 1+ R 1.12 CD:

Value = − D

R P =− 6.7590 0.01 $1,000,000 =− $61,445.45 1+ R

1.10

The difference in the change in value of the assets and liabilities for Bank A is $4,943.66 using the duration estimation model. The difference in this estimate and the estimate found in part (a) above is due to the convexity of the two financial assets. The reason the change in asset values for Bank A is considerably larger than for Bank B is because of the difference in the durations of the loan and CD for Bank A. 19 © 2022

22.

If an FI uses only duration to immunize its portfolio, what three factors affect changes in the net worth of the FI when interest rates change?

The change in net worth for a given change in interest rates is given by the following equation: L R where k = E = − DA − DL k * A * A 1+ R

Thus, three factors are important in determining E. 1) [DA - D L k] or the leveraged adjusted duration gap. The larger this gap, the more exposed is the FI to changes in interest rates.

2) A, or the size of the FI. The larger is A, the larger is the exposure to interest rate changes.

3) ΔR/(1 + R), or the interest rate shock. The larger is the shock, the larger is the interest rate risk exposure.

23.

Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9.94 years. The assets are financed with equity and a $900,000, two-year, 7.25 percent semiannual coupon capital note selling at par. a. What is the leverage adjusted duration gap of Financial Institution XY?

The duration of the capital note is 1.8975 years.

Two-year Capital Note (values in thousands of $s) Par value = $900 Coupon rate = 7.25% Semiannual payments R = 7.25% Maturity = 2 years CFt DFt CFt x DFt CFt x DFt x t t 0.5 32.625 0.9650 31.48 15.74 1 32.625 0.9313 30.38 30.38 1.5 32.625 0.8987 29.32 43.98 2 932.625 0.8672 808.81 1,617.63 900.00 1,707.73 Duration = $1,707.73/$900.00 = 1.8975 The leverage-adjusted duration gap can be found as follows: Leverage− adjusteddurationgap=DA

− DL k=9.94−1.8975

$900,000 $1,000,000

=8.23225years

b. What is the impact on equity value if the relative change in all market interest rates is a 20 © 2022

decrease of 20 basis points? Note: The relative change in interest rates is R/(1+R/2) = -0.0020.

21 © 2022

The change in net worth using leverage adjusted duration gap is given by: E = − DA − DL k* A *

R 1+



= − 9.94 − (1.8975) R

(1,000,000)(−0.0020) = $16,464

2 c. Using the information calculated in parts (a) and (b), what can be said about the desired duration gap for the financial institution if interest rates are expected to increase or decrease.

If the FI wishes to be immune from the effects of interest rate risk (either positive or negative changes in interest rates), a desirable leverage-adjusted duration gap (DGAP) is zero. If the FI is confident that interest rates will fall, a positive DGAP will provide the greatest benefit. If the FI is confident that rates will increase, then negative DGAP would be beneficial. d. Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points. R E =− DA − DL k* A * R = −8.23225(1,000,000)(0.003) = − $24,697 1+ 2 e. What would the duration of the assets need to be to immunize the equity from changes in market interest rates?

Immunizing the equity from changes in interest rates requires that the DGAP be 0. Thus, (DADLk) = 0  DA = DLk, or DA = 1.8975x0.9 = 1.70775 years.

24.

The balance sheet for Gotbucks Bank, Inc. (GBI), is presented below ($ millions): Assets Cash Federal funds Loans (floating) Loans (fixed) Total assets

Liabilities and Equity Core deposits Federal funds Euro CDs Equity Total liabilities and equity

$30 20 105 65 $220

$20 50 130 20 $220

Notes to the balance sheet: The fed funds rate is 8.5 percent, the floating loan rate is LIBOR + 4 percent, and currently LIBOR is 11 percent. Fixed rate loans have five-year maturities, are priced at par, and pay 12 percent annual interest. The principal is repaid at maturity. Core deposits are fixed rate for two years at 8 percent paid annually. The principal is repaid at maturity. Euro CDs currently yield 9 percent. a. What is the duration of the fixed-rate loan portfolio of Gotbucks Bank?

22 © 2022

Five-year Loan (values in millions of $s)

23 © 2022

Par value = $65 R = 12% CFt t 1 7.8 2 7.8 3 7.8 4 7.8 5 72.8

Coupon rate = 12% Annual payments Maturity = 5 years DFt CFt x DFt CFt x DFt x t 0.8929 6.964 6.964 0.7972 6.218 12.436 0.7118 5.552 16.656 0.6355 4.957 19.828 05674 41.309 206.543 65.000 262.427 Duration = $262.427/$65.000 = 4.0373 b. If the duration of the floating-rate loans and fed funds is 0.36 year, what is the duration of GBI’s assets?

DA = [$30(0) + $20(0.36) + $105(0.36) + $65(4.0373)]/$220 = 1.3974 years c. What is the duration of the core deposits if they are priced at par?

Two-year Core Deposits (values in millions of $s) Par value = $20 Coupon rate = 8% Annual payments R = 8% Maturity = 2 years CFt DFt CFt x DFt CFt x DFt x t t 1 1.6 0.9259 1.481 1.481 2 21.6 0.8573 18.519 37.037 20.000 38.519 Duration = $38.519/$20.000 = 1.9259 d. If the duration of the Euro CDs and fed funds liabilities is 0.401 year, what is the duration of GBI’s liabilities?

DL = [$20(1.9259) + $50(0.401) + $130(0.401)]/$200 = 0.5535 years e. What is GBI’s duration gap? What is its interest rate risk exposure?

GBI’s leveraged adjusted duration gap is: 1.3974 - 200/220 x (0.5535) = 0.8942 years Since GBI’s duration gap is positive, an increase in interest rates will lead to a decrease in the market value of equity. f. What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 percent (100 basis points)? Note that the relative change in interest rates is R/(1+R) = 0.01.

For a 1 percent increase, the change in equity value is: 24 © 2022

ΔE = -0.8942 x $220,000,000 x (0.01) = -$1,967,280 (new net worth will be $18,032,720). g. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of 0.5 percent (-50 basis points)?

For a 0.5 percent decrease, the change in equity value is: ΔE = -0.8942 x $220,000,000 x (-0.005) = $983,647 (new net worth will be $20,983,647). h. What variables are available to GBI to immunize the bank? How much would each variable need to change to get DGAP equal to zero?

Immunization requires the bank to have a leverage adjusted duration gap of 0. Therefore, GBI could reduce the duration of its assets to 0.5032 (0.5535 x 200/220) years by using more fed funds and floating rate loans. Or GBI could use a combination of reducing asset duration and increasing liability duration in such a manner that DGAP is 0.

25.

Hands Insurance Company issued a $90 million, one-year note at 8 percent add-on annual interest (paying one coupon at the end of the year) or with an 8 percent yield. The proceeds, plus $10 million in equity, were used to fund a $100 million, two-year commercial loan with a 10 percent coupon rate and a 10 percent yield. Immediately after these transactions were simultaneously closed, all market interest rates increased 1.5 percent (150 basis points). a. What is the true market value of the loan investment and the liability after the change in interest rates?

The market value of the loan decreases by $2,551,831 to $97,448,169.

MVA = $10,000,000 x PVAn=2, i=11.5% + $100,000,000 x PVn=2, i=11.5% = $97,448,169 The market value of the note decrease $1,232,877 to $88,767,123 MVL = $97,200,000 x PVn=1, i=9.5% = $88,767,123 b. What impact did these changes in market value have on the market value of the FI’s equity? E = A - L = -$2,551,831 – (-$1,232,877) = -$1,318,954 The increase in interest rates caused the asset to decrease in value more than the liability which caused the market value of equity to decrease by $1,318,954. c. What was the duration of the loan investment and the liability at the time of issuance?

Two-year Loan (values in millions of $s) 25 © 2022

Par value = $100 R = 10% CFt t 1 $10 2 $110

Coupon rate = 10% Annual payments Maturity = 2 years DFt CFt x DFt CFt x DFt x t 0.9091 9.091 9.091 0.8264 90.909 181.818 100.000 190.909 Duration = $190.909/$100.00 = 1.9091 The duration of the loan investment is 1.9091 years. The duration of the liability is one year since it is a one year note that pays interest and principal at the end of the year. d. Use these duration values to calculate the expected change in the value of the loan and the liability for the predicted increase of 1.5 percent in interest rates.

The approximate change in the market value of the loan for a 1.5 percent change is: .015 A= − 1.9091 * * $100,000,000 = − $2,603,300. The expected market value of the loan using 1.10 the above formula is $97,396,700.

The approximate change in the market value of the note for a 1.5 percent change is: 0.015 L = − 1.0 x x $90,000,000 = − $1,250,000. The expected market value of the note 1.08 using the above formula is $88,750,000. e. What is the duration gap of Hands Insurance Company after the issuance of the asset and note?

The leverage adjusted duration gap is [1.9091 – (0.9)1.0] = 1.0091 years. f. What is the change in equity value forecasted by this duration gap for the predicted increase in interest rates of 1.5 percent? E = -1.0091 x $100,000,000 x [0.015/(1.10)] = -$1,376,045. Note that this calculation assumes that the change in interest rates is relative to the rate on the loan. Further, this estimated change in equity value compares with the estimates above in part (d) as follows: E = A - L = -$2,603,300 - (-$1,250,000) = -$1,353,300. g. If the interest rate prediction had been available during the time period in which the loan and the liability were being negotiated, what suggestions would you have offered to reduce the possible effect on the equity of the company? What are the difficulties in implementing your ideas?

Obviously, the duration of the loan could be shortened relative to the liability, or the liability duration could be lengthened relative to the loan, or some combination of both. Shortening the 26 © 2022

loan duration would mean the possible use of variable rates, or some earlier payment of principal. The duration of the liability cannot be lengthened without extending the maturity life of the note. In either case, the loan officer may have been up against market or competitive constraints in that the borrower or investor may have had other options. Other methods to reduce the interest rate risk under conditions of this nature include using derivatives such as options, futures, and swaps.

26.

The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution: Amount Duration T-bills $90 0.50 T-notes 55 0.90 T-bonds 176 x Loans 2,724 7.00 Deposits 2,092 1.00 Federal funds 238 0.01 Equity 715 Treasury bonds are five-year maturities paying 6 percent semiannually and selling at par. a. What is the duration of the T-bond portfolio?

Five-year Treasury Bond Coupon rate = 6% Par value = $176 R = 6% Maturity = 5 years CFt DFt CFt x DFt t 0.5 5.28 0.9709 5.13 1 5.28 0.9426 4.98 1.5 5.28 0.9151 4.83 2 5.28 0.8885 4.69 2.5 5.28 0.8626 4.55 3 5.28 0.8375 4.42 3.5 5.28 0.8131 4.29 4 5.28 0.7894 4.17 4.5 5.28 0.7664 4.05 5 181.28 0.7441 134.89 176.00 Duration = $773.18/$176.00 = 4.3931

Semiannual payments CFt x DFt x t 2.56 4.98 7.25 9.38 11.39 13.27 15.03 16.67 18.21 674.45 773.18

b. What is the average duration of all the assets? [(0.5)($90) + (0.9)($55) + (4.3931)($176) + (7)($2,724)]/$3,045 = 6.5470 years c. What is the average duration of all the liabilities?

27 © 2022

[(1)($2,092) + (0.01)($238)]/$2,330 = 0.8989 years d. What is the leverage adjusted duration gap? What is the interest rate risk exposure?

DGAP = DA - kDL = 6.5470 - ($2,330/$3,045)(0.8989) = 5.8592 years The duration gap is positive, indicating that an increase in interest rates will lead to a decrease in the market value of equity. e. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 0.5 percent [i.e., R/(1+R) = 0.0050]?

The market value of the equity will change by: ΔMVE = -DGAP x A x ΔR/(1 + R) = -5.8592($3,045)(0.0050) = -$89.207. The loss in equity of $89,207 will reduce the market value of equity to $625,793. f. If the yield curve shifts downward by 0.25 percent [i.e., R/(1+R) = -0.0025], what is the forecasted impact on the market value of equity?

The change in the value of equity is ΔMVE = -5.8592($3,045)(-0.0025) = $44,603. Thus, the market value of equity will increase by $44,603, to $759,603. g. What variables are available to the financial institution to immunize the balance sheet?

How much would each variable need to change to get DGAP equal to 0?

Immunization requires the bank to have a leverage adjusted duration gap of 0. Therefore, the FI could reduce the duration of its assets to 0.6878 years by using more T-bills and floating rate loans. Or, the FI could try to increase the duration of its deposits possibly by using fixed-rate CDs with a maturity of 3 or 4 years. Finally, the FI could use a combination of reducing asset duration and increasing liability duration in such a manner that DGAP is 0. This duration gap of 5.8592 years is quite large and it is not likely that the FI will be able to reduce it to zero by using only balance sheet adjustments. For example, even if the FI moved all of its loans into T-bills, the duration of the assets still would exceed the duration of the liabilities after adjusting for leverage. This adjustment in asset mix would imply foregoing a large yield advantage from the loan portfolio relative to the T-bill yields in most economic environments.

27.

Refer again to the financial institution in problem 26. a. What is the change in the value of the firm’s assets for relative upward shift in the entire yield curve of 0.5 percent?

A= − 6.5470 *0.005*$3,045 =− $99.678428 . The expected change in the market value of the assets using the above formula is $99,678,428.

28 © 2022

b. What is the change in the value of the firm’s liabilities for relative upward shift in the entire yield curve of 0.4 percent? L=− 0.8989 x 0.004 x $2,330 =− $8.37752. The expected change in the market value of the liabilities using the above formula is $8,377,520.

c. What is the resulting change in the value of equity for the firm? ΔMVE = ΔMVA – ΔMVL = $99,678,428– ($8,377,520) = $91,300,908 28.

Assume that a goal of the regulatory agencies of financial institutions is to immunize the ratio of equity to total assets, that is, (E/A) = 0. Explain how this goal changes the desired duration gap for the institution. Why does this differ from the duration gap necessary to immunize the total equity? How would your answers to part (h) in problem 24 and part (g) in problem 26 change if immunizing equity to total assets was the goal?

In this case, the duration of the assets and liabilities should be equal. Thus, if E = A, then by definition the leveraged adjusted duration gap is positive, since E would exceed kA by the amount of (1 – k) and the FI would face the risk of increases in interest rates. In reference to problems 24 and 26, the adjustments on the asset side of the balance sheet would not need to be as strong, although the difference likely would not be large if the FI in question is a depository institution such as a bank or savings institution.

29.

Identify and discuss three criticisms of using the duration gap model to immunize the portfolio of a financial institution.

The three criticisms are: a Immunization is a dynamic problem because duration changes over time. Thus, it is necessary to rebalance the portfolio as the duration of the assets and liabilities change over time. b Duration matching can be costly because it is not easy to restructure the balance sheet periodically, especially for large FIs. c Duration is not an appropriate tool for immunizing portfolios when the expected interest rate changes are large because of the existence of convexity. Convexity exists because the relationship between security price changes and interest rate changes is not linear, which is assumed in the estimation of duration. Using convexity to immunize a portfolio will reduce the problem.

30.

In general, what changes have occurred in the financial markets that would allow financial institutions to restructure their balance sheets more rapidly and efficiently to meet desired goals? Why is it critical for an FI manager who has a portfolio immunized to match a desired investment horizon to rebalance the portfolio periodically? What is convexity?

Why is convexity a desirable feature to capture in a portfolio of assets?

29 © 2022

The growth of purchased funds markets, asset securitization, and loan sales markets have considerably increased the speed of major balance sheet restructurings. Further, as these markets have developed, the cost of the necessary transactions has also decreased. Finally, the growth and development of the derivative securities markets provides significant alternatives to managing the risk of interest rate movements only with on-balance-sheet adjustments.

Assets approach maturity at different rates of speed than the duration of the same assets approaches zero. Thus, after a period of time, a portfolio of assets that was immunized against interest rate risk will no longer be immunized. In fact, portfolio duration will exceed the remaining time in the investment or target horizon, and changes in interest rates could prove costly to the institution.

Convexity is a property of fixed-rate assets that reflects nonlinearity in the reflection of priceyield relationships. This characteristic is similar to buying insurance to cover part of the interest rate risk faced by the FI. The more convexity in the price-yield relationship for a given asset, the more insurance against interest rate changes is purchased.

31.

A financial institution has an investment horizon of two years 9.33 months (or 2.777 years).

The institution has converted all assets into a portfolio of 8 percent, $1,000, three-year bonds that are trading at a yield to maturity of 10 percent. The bonds pay interest annually.

The portfolio manager believes that the assets are immunized against interest rate changes. a. Is the portfolio immunized at the time of bond purchase? What is the duration of the bonds?

Three-year Bonds Par value = $1,000 R = 10% CFt DFt t 1 80 0.9091 2 80 0.8264 3 1,080 0.7513

Coupon rate = 8% Annual payments Maturity = 3 years CFt x DFt CFt x DFt x t 72.73 72.73 66.12 132.23 811.42 2,434.26 950.26 2,639.22 Duration = $2,639.22/$950.26 = 2.777 The bonds have a duration of 2.777 years, which is 33.33 months. For practical purposes, the bond investment horizon is immunized at the time of purchase. b. Will the portfolio be immunized one year later?

After one year, the investment horizon will be 1 year, 9.33 months (or 1.777 years). At this time, the bonds will have a duration of 1.9247 years, or 1 year, 11+ months. Thus, the bonds will no longer be immunized.

Two-year Bonds 30 © 2022

Par value = $1,000 R = 10% CFt DFt t 1 $80 0.9091 2 $1,080 0.8264

Coupon rate = 8% Annual payments Maturity = 2 years CFt x DFt CFt x DFt x t 72.73 72.73 892.56 1,785.12 965.29 1,857.85 Duration = $1,857.85/$965.29 = 1.9247 c. Assume that one-year, 8 percent zero-coupon bonds are available in one year. What proportion of the original portfolio should be placed in these bonds to rebalance the portfolio?

The investment horizon is 1 year, 9.33 months, or 21.33 months. Thus, the proportion of bonds that should be replaced with the zero-coupon bonds can be determined by the following analysis: 21.33 months = wzero x 12 months + (1 – wzero)x1.9247x12 months  wzero = 15.92 percent Thus, 15.92 percent of the bond portfolio should be replaced with the zero-coupon bonds after one year.

The following questions and problems are based on material in Appendix 9A, at the book’s website (www.mhhe.com/saunders9e).

32.

Consider a 12-year, 12 percent annual coupon bond with a required return of 10 percent.

The bond has a face value of $1,000. a.

What is the price of the bond?

PV = $120 x PVAi=10%,n=12 + $1,000 x PVi=10%,n=12 = $1,136.27 b. If interest rates rise to 11 percent, what is the price of the bond?

PV = $120 x PVAi=11%,n=12 + $1,000 x PVi=11%,n=12 = $1,064.92 c. What has been the percentage change in price? P = ($1,064.92 - $1,136.27)/$1,136.27 = -0.0628 or –6.28 percent. d. Repeat parts (a), (b), and (c) for a 16-year bond.

PV = $120 x PVAi=10%,n=16 + $1,000 x PVi=10%,n=16 = $1,156.47 PV = $120 x PVAi=11%,n=16 + $1,000 x PVi=11%,n=16 = $1,073.79 P = ($1,073.79 - $1,156.47)/$1,156.47 = -0.0715 or –7.15 percent.

31 © 2022

e. What do the respective changes in bond prices indicate?

For the same change in interest rates, longer-term fixed-rate assets experience a greater change in price.

33. Consider a five-year, 15 percent annual coupon bond with a face value of $1,000. The bond is trading at a yield to maturity of 12 percent. a.

What is the price of the bond?

PV = $150 x PVAi=12%,n=5 + $1,000 x PVi=12%,n=5 = $1,108.14 If the yield to maturity increases 1 percent, what will be the bond’s new price?

b.

PV = $150 x PVAi=13%,n=5 + $1,000 x PVi=13%,n=5 = $1,070.34 Using your answers to parts (a) and (b), what is the percentage change in the bond’s price as a result of the 1 percent increase in interest rates?

c.

P = ($1,070.34 - $1,108.14)/$1,108.14 = -0.0341 or –3.41 percent. d.

Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates.

PV = $150 x PVAi=11%,n=5 + $1,000 x PVi=11%,n=5 = $1,147.84 P = ($1,147.84 - $1,108.14)/$1,108.14 = 0.0358 or 3.58 percent e.

What do the differences in your answers indicate about the interest rate-price relationships of fixed-rate assets?

For a given percentage change in interest rates, the absolute value of the increase in price caused by a decrease in rates is greater than the absolute value of the decrease in price caused by an increase in rates.

34.

Consider a $1,000 bond with a fixed-rate 10 percent annual coupon rate and a maturity (N) of 10 years. The bond currently is trading at a yield to maturity (YTM) of 10 percent. a.

Complete the following table:

N 8 9

Change Coupon Rate 10% 10

YTM 9% 9

Price $1,055.35 1,059.95

$ Change in Price from Par $55.35 59.95

32 © 2022

% Change in Price from Par 5.535% 5.995

b.

10 10 10

10 10 10

9 10 11

1,064.18 1,000.00 941.11

64.18 0.00 -58.89

6.418 0.00 -5.889

11 12

10 10

11 11

937.93 935.07

-62.07 -64.93

-6.207 -6.493

Use this information to verify the principles of interest rate-price relationships for fixed-rate financial assets.

Rule 1. Interest rates and prices of fixed-rate financial assets move inversely.

See the change in price from $1,000 to $941.11 for the change in interest rates from 10 percent to 11 percent, or from $1,000 to $1,064.18 when rates change from 10 percent to 9 percent.

Rule 2. The longer is the maturity of a fixed-income financial asset, the greater is the change in price for a given change in interest rates.

A change in rates from 10 percent to 11 percent caused the 10-year bond to decrease in value $58.89, but the 11-year bond decreased in value $62.07, and the 12-year bond decreased $64.93.

Rule 3. The change in value of longer-term fixed-rate financial assets increases at a decreasing rate.

For the increase in rates from 10 percent to 11 percent, the difference in the change in price between the 10-year and 11-year assets is $3.18 ($62.07 - $58.89), while the difference in the change in price between the 11-year and 12-year assets is $2.86 ($64.93 - $62.07).

Rule 4. Although not mentioned in Appendix 9A, for a given percentage () change in interest rates, the increase in price for a decrease in rates is greater than the decrease in value for an increase in rates.

For rates decreasing from 10 percent to 9 percent, the 10-year bond increases $64.18. But for rates increasing from 10 percent to 11 percent, the 10-year bond decreases $58.89.

The following questions and problems are based on material in Appendix 9B to the chapter.

35.

MLK Bank has an asset portfolio that consists of $100 million of 30-year, 8 percent coupon, $1,000 bonds that sell at par. a. What will be the bonds’ new prices if market yields change immediately by  0.10 percent? What will be the new prices if market yields change immediately by  2.00 percent?

33 © 2022

At +0.10%: At –0.10%:

Price = $80 x PVAn=30, i=8.1% + $1,000 x PVn=30, i=8.1% = $988.85 Price = $80 x PVAn=30, i=7.9% + $1,000 x PVn=30, i=7.9% = $1,011.36

At +2.0%: At –2.0%:

Price = $80 x PVAn=30, i=10% + $1,000 x PVn=30, i=10% = $811.46 Price = $80 x PVAn=30, i=6.0% + $1,000 x PVn=30, i=6.0% = $1,275.30

b. The duration of these bonds is 12.1608 years. What are the predicted bond prices in each of the four cases using the duration rule? What is the amount of error between the duration prediction and the actual market values? P = -D x [R/(1+R)] x P At +0.10%: At -0.10%:

P = -12.1608 x 0.001/1.08 x $1,000 = -$11.26  P’ = $988.74 P = -12.1608 x (-0.001/1.08) x $1,000 = $11.26  P’ = $1,011.26

At +2.0%: At -2.0%:

P = -12.1608 x 0.02/1.08) x $1,000 = -$225.20  P’ = $774.80 P = -12.1608 x (-0.02/1.08) x $1,000 = $225.20  P’ = $1,225.20

Price - market determined At +0.10%: $988.85 At -0.10%: $1,011.36 At +2.0%: $811.46 At -2.0%: $1,275.30

Price - duration estimation $988.74 $1,011.26 $774.80 $1,225.20

Amount of error $0.11 $0.10 $36.66 $50.10

c. Given that convexity is 212.4, what are the bond price predictions in each of the four cases using the duration plus convexity relationship? What is the amount of error in these predictions? P = {-D x [R/(1+R)] + ½ x CX x (R)2} x P At +0.10%: At -0.10%: At +2.0%: At -2.0%:

At +0.10%: At -0.10%: At +2.0%: At -2.0%:

P = {-12.1608 x 0.001/1.08 + 0.5 x 212.4 x (0.001)2} x $1,000 = -$11.15 P = {-12.1608 x (-0.001/1.08) + 0.5 x 212.4 x (-0.001)2} x $1,000 = $11.366 P = {-12.1608 x 0.02/1.08 + 0.5 x 212.4 x (0.02)2} x $1,000 = -$182.72 P = {-12.1608 x (-0.02/1.08) + 0.5 x 212.4 x (-0.02)2} x $1,000 = $267.68

Price market determined $988.85 $1,011.36 $811.46 $1,275.30

Price duration & convexity estimation -$11.15 $11.37 -$182.72 $267.68 34 © 2022

Price duration & convexity estimation $988.85 $1,011.37 $817.28 $1,267.68

Amount of error $0.00 $0.01 $5.82 $7.62

d. Diagram and label clearly the results in parts (a), (b) and (c).

Rate-Price Relationships

$1,400 Actual Market Price

$1,275.30 $1,225.20 Duration Profile

$1,000

The duration and convexity profile is virtually on the actual market price profile, and thus is barely visible in the graph.

$811.46 $774.80

$600 4

6

8

10

12

Percent Yield-to-Maturity

The profiles for the estimates based on only  0.10 percent changes in rates are very close together and do not show clearly in a graph. However, the profile relationship would be similar to that shown above for the  2.0 percent changes in market rates.

36.

Estimate the convexity for each of the following three bonds, all of which trade at yield to maturity of 8 percent and have face values of $1,000.

A 7-year, zero-coupon bond.

A 7-year, 10 percent annual coupon bond.

A 10-year, 10 percent annual coupon bond that has a duration value of 6.994 years (i.e., approximately 7 years).

7-year zero

Market Value at 8.01 percent -0.37804819

Market Value at 7.99 percent 0.37832833 35 © 2022

Capital Loss + Capital Gain Divided by Original Price 0.00000048

7-year coupon 10-year coupon

-0.55606169 -0.73121585

0.55643682 0.73186329

0.00000034 0.00000057

Convexity = 108 x (Capital Loss + Capital Gain) ÷ Original Price at 8.00 percent 7-year zero 7-year coupon 10-year coupon

CX = 100,000,000 x 0.00000048 = 48 CX = 100,000,000 x 0.00000034 = 34 CX = 100,000,000 x 0.00000057 = 57

An alternative method of calculating convexity for these three bonds using the following equation is illustrated at the end of this problem. n  CFt  1 Convexity = x   t  (1+ t) P x (1+ R)2 t= 1 (1+ R) t   Rank the bonds in terms of convexity, and express the convexity relationship between zeros and coupon bonds in terms of maturity and duration equivalencies.

Ranking, from least to most convexity: 7-year coupon bond, 7-year zero, 10-year coupon Convexity relationships: Given the same yield-to-maturity, a zero-coupon bond with the same maturity as a coupon bond will have more convexity.

Given the same yield-to-maturity, a zero-coupon bond with the same duration as a coupon bond will have less convexity.

Zero-coupon Bond Par value = $1,000 R = 8% t .

CF PV of CF 1 0.00 0.00 2 0.00 0.00 3 0.00 0.00 4 0.00 0.00 5 0.00 0.00 6 0.00 0.00 7 1,000.00 583.49 583.49

7-year Coupon Bond Par value = $1,000

Coupon = 0% Maturity = 7 years PV of CF x t x(1+t) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4,084.43 32,675.46 4,084.43 32,675.46

Coupon = 10% 36 © 2022

x(1+R)2

680.58 Duration 7.0000 Convexity 48.011

t .

1 2 3 4 5 6 7

R = 8% CF 100.00 100.00 100.00 100.00 100.00 100.00 1,100.00

PVof CF 92.59 85.73 79.38 73.50 68.06 63.02 641.84 1,104.13

Maturity = 7 years PV of CF x t x(1+t) 92.59 185.19 171.47 514.40 238.15 952.60 294.01 1,470.06 340.29 2,041.75 378.10 2,646.71 4,492.88 35,943.01 6,007.49 43,753.72

x(1+R)2

1287.9 Duration = 5.4409 Convexity = 33.974

10-year Coupon Bond

t 1 2 3 4 5 6 7 8 9 10

Par value = $1,000 R = 8% .

CF PV of CF 100.00 92.59 100.00 85.73 100.00 79.38 100.00 73.50 100.00 68.06 100.00 63.02 100.00 58.35 100.00 54.03 100.00 50.02 1,100.0 509.51 1,134.20

Coupon = 10% Maturity = 10 years PV of CF x t x(1+t) 92.59 185.19 171.47 514.40 238.15 952.60 294.01 1,470.06 340.29 2,041.75 378.10 2,646.71 408.44 3,267.55 432.22 3,889.94 450.22 4,502.24 5,095.13 56,046.41 7,900.63 75,516.84

x(1+R)2

1322.9 Duration = 6.9658 Convexity = 57.083

Integrated Mini Case: Calculating and Using Duration GAP State Bank’s balance sheet is listed below. Market yields and durations (in years) are in parenthesis, and amounts are in millions.

Assets Cash Fed funds (1.05%, 0.02) T-bills (5.25%, 0.22) T-bonds (7.50%, 7.55) Consumer loans (6%, 2.50)

$20 150 300 200 900

Liabilities and Equity $250 Demand deposits MMDAs (2.5%, 0.50) (no minimum balance requirement) 360 CDs (4.3%, 0.48) 715 CDs (6%, 4.45) 1,105 37

© 2022

C&I loans (5.8%, 6.58)

475

Fed funds (1%, 0.02)

38 © 2022

515

Fixed-rate mortgages (7.85%, 19.50) 1,200 Variable-rate mortgages, repriced @ quarter (6.3%, 0.25) 580 Premises and equipment 120 Total assets

Commercial paper (3%, 0.45) Subordinated debt: Fixed-rate (7.25%, 6.65) Total liabilities Equity Total liabilities and equity

$3,945

400 200 $3,545 400 $3,945

a. What is State Bank’s duration gap?

DA = [20(0) + 150(0.02) + 300(0.22) + 200(7.55) + 900(2.50) + 475(6.85) + 1,200(19.50) + 580(0.25) + 120(0)]/3,945 = 7.76369 year DL = [250(0) + 360(0.50) + 715(0.48) + 1,105(4.45) + 515(0.02) + 400(0.45) + 200(6.65))]/3,545 = 1.96354 years DGAP = DA - kDL = 7.76369 - ($3,545/$3,945)(1.96354) = 5.99924 years b. Use these duration values to calculate the expected change in the value of the assets and liabilities of State Bank for a predicted increase of 1.5 percent in interest rates. ΔMVfedfunds = -0.02 x 0.015/1.0105 x 150m ΔMVT-bills = -0.22 x 0.015/1.0525 x 300m ΔMVT-bonds = -7.55 x 0.015/1.0750 x 200m ΔMVconsumerloans = -2.50 x 0.015/1.0600 x 900m ΔMVC&Iloans = -6.58 x 0.015/1.0580 x 475m ΔMVfixed-ratemortgages = -19.50 x 0.015/1.0785 x 1,200m ΔMVvariable-ratemortgages = -0.25 x 0.015/1.0630 x 580m =>ΔMVA ΔMVMMDAs = -0.50 x 0.015/1.025 x 360m ΔMVCDs = -0.48 x 0.015/1.0430 x 715m ΔMVCDs = -4.45 x 0.015/1.0600 x 1,105m ΔMVfedfunds = -0.02 x 0.015/1.0100 x 515m ΔMVcommericalpaper = -0.45 x 0.015/1.0300 x 400m ΔMVfixed-ratesubordinatedebt = -6.65 x 0.015/1.0725 x 200m =>ΔMVL

= -$44,532 = -$940,618 = -$21,069,767 = -$31,839,623 = -$44,312,382 = -$325,452,017 = -$2,046,096 = -$425,705,035 = = = = = =

-$2,634,146 -$4,935,762 -$69,583,726 -$152,970 -$2,621,359 -$18,601,399

= -$98,529,362

c. What is the change in equity value forecasted from the duration values for a predicted increase in interest rates of 1.5 percent? ΔMVE = ΔMVA – ΔMVL = -$425,705,035 – (-$98,529,362) = -$327,175,673 39 © 2022

Integrated Mini Case Chapters 8 and 9: Calculating and Using Repricing and Duration GAP State Bank’s balance sheet is listed below. Market yields and durations (in years) are in parenthesis, and amounts are in millions.

Assets Cash $31 Fed funds (2.05%, 0.02) 150 3-month T-bills (3.25%, 0.22) 200 8-year T-bonds (6.50%, 7.55) 250 5-year munis (7.20%, 4.25) 50 6-month consumer loans (5%, 0.42) 250 5-year car loans (6%, 3.78) 350 7-month C&I loans (4.8%, 0.55) 200 2-year C&I loans (4.15%, 1.65) 275 Fixed-rate mortgages (5.10%, 0.48) 450 (maturing in 5 months) Fixed-rate mortgages (6.85%, 0.85) (maturing in 1 year) 300 Fixed-rate mortgages (5.30%, 4.45) (maturing in 5 years) 275 Fixed-rate mortgages (5.40%, 18.25) (maturing in 20 years) 355 Premises and equipment 20 Total assets $3,156

Liabilities and Equity Demand deposits $253 Savings accounts (0.5%, 1.25) 50 MMDAs (3.5%, 0.50) (no minimum balance requirement) 460 3-month CDs (3.2%, 0.20) 175 1-year CDs (3.5%, 0.95) 375 5-year CDs (5%, 4.85) 350 Fed funds (2%, 0.02) 225 Repos (2%, 0.05) 290 6-month commercial paper (4.05%, 0.55) 300 Subordinate notes: 1-year fixed rate (5.55%, 0.92) 200 Subordinated debt: 7-year fixed rate (6.25%, 6.65) 100 Total liabilities $2,778 Equity Total liabilities and equity

a. What is the repricing gap if the planning period is six months? One year?

Assets Cash Fed funds (2.05%) 3-month T-bills (3.25%) 8-year T-bonds (6.50%) 5-year munis (7.20%) 6-month consumer loans (5%) 5-year car loans (6%) 7-month C&I loans (4.8%) 2-year C&I loans (4.15%) Fixed-rate mortgages (5.10%) (maturing in 5 months) Fixed-rate mortgages (6.85%) (maturing in 1 year) Fixed-rate mortgages (5.30%) (maturing in 5 years) Fixed-rate mortgages (5.40%)

$31 150 200 250 50 250 350 200 275

Repricing period Not rate sensitive 6-months 6-months Not rate sensitive Not rate sensitive 6-months Not rate sensitive 1-year Not rate sensitive

450

6-months

300

1-year

275

Not rate sensitive 40

© 2022

378 $3,156

(maturing in 20 years) Premises and equipment

355 20

Not rate sensitive Not rate sensitive

Liabilities and Equity Demand deposits $253 Savings accounts (0.5%) 50 MMDAs (3.5%) (no minimum balance requirement) 460 3-month CDs (3.2%) 175 1-year CDs (3.5%) 375 5- year CDs (5%) 350 Fed funds (2%) 225 Repos (2%) 290 6- month commercial paper (4.05%) 300 Subordinate notes 1-year fixed rate (5.55%) 200 Subordinated debt 7- year fixed rate (6.25%) 100 Equity 400

Repricing Period Not rate sensitive 6-months 6-months 6-months 1-year Not rate sensitive 6-months 6-months 6-months 1-year Not rate sensitive Not rate sensitive

6-month repricing gap: RSAs = $150m. + $200m. + $250m. + $450m. = $1050m.

RSLs = $50m. + $460m. + $175m. + $225m. + $290m. + $300m. = $1500m.

CGAP = $1050m. - $1500m. = -$450m.

1-year repricing gap: RSAs = $1050m. + $200m. + $300m. = $1550m.

RSLs = $1500m. + $375m. + $200m. = $2075m.

CGAP = $1550m. - $2075m. = -$525m. b. What is State Bank’s duration gap?

DA = [31(0) + 150(0.02) + 200(0.22) + 250(7.55) + 50(4.25) + 250(0.42) + 350(3.78) + 200(0.55) + 275(1.65) + 450(0.48) + 300(0.85) + 275(4.45) + 355(18.25) + 20(0)]/3,156 = 3.90122 years DL = [253(0) + 50(1.25) + 460(0.50) + 175(0.20) + 375(0.95) + 350(4.85) + 225(0.02) + 290(0.05) + 300(0.55) + 200(0.92) + 100(6.65))]/2,778 = 1.22903 years DGAP = DA - kDL = 3.90122 - ($2,778/$3,156)(1.22903) = 2.81939 years c. What is the impact over the next six months on net interest income if interest rates on RSAs increase 50 basis points and on RSLs increase 35 basis points? Explain the results. ΔNII (6-months) = ΔII (6-months) – ΔIE (6-months) = $1050m.(0.0050) - $1500m.(0.0035) = $0m.

41 © 2022

GAP is negative and interest rates are expected to go up. Therefore, the GAP effect pushes NII down. However, at the same time the spread increases. So, the spread affect pushes NII up. Thus, despite the fact that the GAP works against the bank, reducing its NII, the spread affect exactly offsets this, increasing NII by the same amount. The net effect is no change in NII. d. What is the impact over the next year on net interest income if interest rates on RSAs decrease (increase) 35 basis points and on RSLs decrease (increase) 50 basis points?

Explain the results. ΔNII (1-year) = ΔII (1-year) – ΔIE (1-year) = $1505m.(-0.0035) - $2075m.(-0.0050) = $4.95m.

GAP is negative and interest rates are expected to go down. Therefore, the GAP effect pushes NII up. At the same time the spread decreases. So, the spread affect pushes NII up. Thus, both the GAP effect and the spread affect work to increase NII. ΔNII (1-year) = ΔII (1-year) – ΔIE (1-year) = $1550m.(0.0035) - $2075m.(0.0050) = $4.95m.

GAP is negative and interest rates are expected to go up. Therefore, the GAP effect pushes NII down. At the same time the spread decreases. So, the spread affect pushes NII down. Thus, both the GAP effect and the spread affect work to decrease NII. e. Use these duration values to calculate the expected change in the value of the assets and liabilities of State Bank for a predicted decrease of 0.35 percent in interest rates on assets and 0.50 percent on liabilities. ΔMVfedfunds = -0.02 x -0.0035/1.0205 x 150m ΔMVT-bills = -0.22 x -0.0035/1.0325 x 200m ΔMVT-bonds = -7.55 x -0.0035/1.0650 x 250m ΔMVmunis = -4.55 x -0.0035/1.0720 x 50m ΔMVconsumerloans = -0.42 x -0.0035/1.0500 x 250m ΔMVcarloans = -3.78 x -0.0035/1.0600 x 350m ΔMVC&Iloans = -0.55 x -0.0035/1.0480 x 200m ΔMVC&Iloans = -1.65 x -0.0035/1.0415 x 275m ΔMVfixed-ratemortgages = -0.48 x -0.0035/1.0510 x 450m ΔMVfixed-ratemortgages = -0.85 x -0.0035/1.0685 x 300m ΔMVfixed-ratemortgages = -4.45 x -0.0035/1.0530 x 275m ΔMVfixed-ratemortgages = -18.25 x -0.0035/1.0540 x 355m =>ΔMVA ΔMVsavings = -1.25 x -0.005/1.0050 x 50m ΔMVMMDAs = -0.50 x -0.005/1.0350 x 460m

= = = = = = = = = = = =

= $40,851,889 = =

42 © 2022

$10,289 $149,153 $6,203,052 $742,771 $350,000 $4,368,396 $367,366 $1,524,844 $719,315 $835,283 $4,067,544 $2,046,096

$310,945 $1,111,111

ΔMVCDs = -0.20 x -0.005/1.0320 x 175m ΔMVCDs = -0.95 x -0.005/1.0350 x 375m ΔMVCDs = -4.85 x -0.005/1.0500 x 350m ΔMVfedfunds = -0.02 x -0.005/1.0200 x 225m ΔMVrepos = -0.05 x -0.005/1.0200 x 290m ΔMVcommericalpaper = -0.55 x -0.005/1.0405 x 300m ΔMVsubordinatedebt = -0.92 x -0.005/1.0555 x 200m ΔMVsubordinatedebt = -6.65 x -0.005/1.0625 x 100m =>ΔMVL

= = = = = = = =

$169,574 $1,721,015 $8,083,333 $22,059 $71,078 $792,888 $871,625 $3,129,412

=

$16,283,040

f. What is the change in equity value forecasted from the duration values for decrease of 0.35 percent in interest rates on assets and 0.50 percent on liabilities? ΔMVE = ΔMVA – ΔMVL = $40,851,889 – ($16,283,040) = $24,568,849 g. Use the duration gap model to calculate the change in equity value if the relative change in all market interest rates is a decrease of 50 basis points. ΔMVE = - DGAP x A x ΔR/(1 + R) = -2.81939 years x 3,156m x (-0.0050) = $44.49m

Additional Example for Chapter 9 This example is to estimate both the duration and convexity of a 6-year bond paying 5 percent coupon annually and the annual yield to maturity is 6 percent.

6-year Coupon Bond Par value = $1,000 R = 6% t .

CF PV of CF 1 $50.00 $47.17 2 $50.00 $44.50 3 $50.00 $41.98 4 $50.00 $39.60 5 $50.00 $37.36 6 $1,050.00 $740.21 $950.83

Coupon = 5% Maturity = 6 years PV of CF x t x(1+t) $47.17 $94.34 $89.00 $267.00 $125.94 $503.77 $158.42 $792.09 $186.81 1,120.89 $4,441.25 31,088.76 $5,048.60 33,866.85

x(1+R)2

1068.3

Duration = 5.3097 Convexity = 31.7 Using the textbook method: CX

= 108 [(950.3506-950.8268)/950.8268 + (951.3032-950.8268)/950.8268] 43 © 2022

= 108[-0.0005007559 + 0.0005501073] = 31.70

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What is the effect of a 2 percent increase in interest rates, from 6 percent to 8 percent?

Using Present Values, the percentage change is: = ($950.8268 - $861.3136)/ $950.8268 = -9.41% ΔMVA = -D x ΔR/(1 + R) + 0.5CX(R)2 = -5.3097 x [(0.02)/1.06] + 0.5(31.7)(0.02)2 = -0.1002 + .0063 = -9.38% Adding convexity adds more precision. Duration alone would have given the answer of -10.02%.

Using the duration formula:

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Solutions for End-of-Chapter Questions and Problems: Chapter Ten 1.

Why is credit risk analysis an important component of FI risk management? What recent activities by FIs have made the task of credit risk assessment more difficult for both FI managers and regulators?

Credit risk management is important for FI managers because it determines several features of a loan: interest rate, maturity, collateral and other covenants. Riskier projects require more analysis before loans are approved. If credit risk analysis is inadequate, default rates could be higher and push a bank into insolvency, especially if the markets are competitive and the margins are low.

Credit risk management has become more complicated over time because of the increase in offbalance-sheet activities that create implicit contracts and obligations between prospective lenders and buyers. Credit risks of some off-balance-sheet products, such as loan commitments, credit guarantees, and interest rate swaps, are difficult to assess because the contingent payoffs are not deterministic, making the pricing of these products complicated.

2.

Differentiate between a secured and an unsecured loan. Who bears most of the risk in a fixed-rate loan? Why would FI managers prefer to charge floating rates, especially for longer-maturity loans?

A secured loan is backed by some of the collateral that is pledged to the lender in the event of default. A lender has rights to the collateral, which can be liquidated to pay all or part of the loan.

With a fixed-rate loan, the lender bears the risk of interest rate changes. If interest rates rise, the opportunity cost of lending is higher, while if interest rates fall the lender benefits. Since it is harder to predict longer-term rates, FIs prefer to charge floating rates for longer-term loans and pass the interest rate risk on to the borrower.

3.

How does a spot loan differ from a loan commitment? What are the advantages and disadvantages of borrowing through a loan commitment?

A spot loan involves the immediate takedown of the loan amount by the borrower, while a loan commitment allows a borrower the option to take down the loan any time during a fixed period at a predetermined rate. This can be advantageous during periods of rising rates in that the borrower can borrow as needed at a predetermined rate. If rates decline, the borrower can borrow from other sources. The disadvantage is the cost: often an up-front fee is required in addition to a back-end fee for the unused portion of the commitment.

4.

Why is commercial lending declining in importance in the U.S.? What effect does this decline have on overall commercial lending activities?

Commercial bank lending has been declining in importance because of disintermediation, a process in which customers are able to access financial markets directly such as by issuing commercial paper. The total amount of commercial paper outstanding in the U.S. has grown dramatically over the last thirty years. Historically, only the most creditworthy borrowers had 1 © 2022

access the commercial paper market, but more middle-market firms and financial institutions now have access to this market. As a consequence of this growth, the pool of borrowers available to banks has become smaller and riskier. This makes the credit assessment and monitoring of loans more difficult, yet important.

5.

What are the primary characteristics of residential mortgage loans? Why does the ratio of adjustable-rate mortgages to fixed-rate mortgages in the economy vary over an interest rate cycle? When would the ratio be highest?

Residential mortgage contracts differ in size, the ratio of the loan amount to the value of the property, the maturity of the loan, the rate of interest of the loan, and whether the interest rate is fixed or adjustable. In addition, mortgage agreements differ in the amount of fees, commissions, discounts, and points that are paid by the borrower.

The ratio of adjustable-rate mortgages to fixed-rate mortgages is lowest when interest rates are low because borrowers prefer to lock in the low market rates for long periods of time. When rates are high, adjustable-rate mortgages allow borrowers the potential to realize relief from high interest rates in the future when rates decline.

6.

What are the two major classes of consumer loans at U.S. banks? How do revolving loans differ from nonrevolving loans?

Consumer loans can be classified as either nonrevolving or revolving loans. Automobile loans and fixed-term personal loans usually have a maturity date at which time the loan is expected to have a zero balance, and thus they are considered to be nonrevolving loans. Revolving loans usually involve credit card debt, or similar lines of credit, and as a result the balance will rise and fall as borrowers make payments and utilize the accounts. Many banks often recognize high rates of return on these loans, even though in recent years, banks have faced chargeoff rates in the range of four to eight percent.

7.

Why are rates on credit card loans generally higher than rates on car loans?

Car loans are backed by collateral (the car), while credit card loans are not. Thus, in the event of default on a car loan, the FI can take possession of the car to recoup at least some the lost interest and principal payments. In the event of a default on a credit card loan, the FI has no such collateral available with which to recover lost interest and principal payments. Accordingly, the FI charges a higher rate on the credit card loan.

8.

What are compensating balances? What is the relationship between the amount of compensating balance requirement and the return on the loan to the FI?

A compensating balance is the portion of a loan that a borrower must keep on deposit with the credit-granting FI. Thus, the funds are not available for use by the borrower. As the amount of compensating balance for a given loan size increases, the effective return on the loan increases for the lending institution.

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9.

Suppose that a bank does the following: a. Sets a loan rate on a prospective loan at 8 percent (where BR = 5% and ϕ = 3%). b. Charges a 1/10 percent (or 0.10 percent) loan origination fee to the borrower. c. Imposes a 5 percent compensating balance requirement to be held as noninterest-bearing demand deposits. d. Holds reserve requirements of 10 percent imposed by the Federal Reserve on the bank’s demand deposits.

Calculate the bank’s ROA on this loan.

1 + k = 1 + 0.0010 + (0.05 + 0.03) = 1 + 0.081 = 1.0848 or k = 8.48% 1 - [(0.05)(1 - 0.10)] 0.955 10.

County Bank offers one-year loans with a stated rate of 9 percent, but requires a compensating balance of 10 percent. What is the true cost of this loan to the borrower?

How does the cost change if the compensating balance is 15 percent? If the compensating balance is 20 percent? In each case, assume origination fees and the reserve requirement are zero.

The true cost is the loan rate ÷ (1 – compensating balance rate) = 9% ÷ (1.0 – 0.1) = 10 percent.

For compensating balance rates of 15 percent and 20 percent, the true cost of the loan would be 10.59 percent (= 9% ÷ (1.0 – 0.15)) and 11.25 percent (= 9% ÷ (1.0 – 0.2)), respectively. Note that as the compensating balance rate increases by a constant amount, the true cost of the loan increases at an increasing rate.

11.

Metrobank offers one-year loans with a 9 percent stated or base rate, charges a 0.25 percent loan origination fee, imposes a 10 percent compensating balance requirement, and must hold a 6 percent reserve requirement at the Federal Reserve. The loans typically are repaid at maturity. a. If the risk premium for a given customer is 2.5 percent, what is the simple promised interest return on the loan?

The simple promised interest return on the loan is BR + ϕ = 0.09 + 0.025 = 0.115 or 11.5%. b. What is the contractually promised gross return on the loan per dollar lent?

1+ k =1+

of + (BR + ) 1−[b(1− RR)]

=1+

0.0025 + (0.09 + 0.025) 1−[0.1(1− 0.06)]

=1+

0.1175

=1.1297 or k = 0.1297 = 12.97%

0.906

c. Which of the fee items has the greatest impact on the gross return?

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The compensating balance has the strongest effect on the gross return on the loan. Without the compensating balance, the gross return would equal 11.75 percent, a reduction of 1.22 percent.

Without the origination fee, the gross return would be 12.69 percent, a reduction of only 0.28 percent. Eliminating the reserve requirement would cause the gross return to increase to 13.06 percent, an increase of 0.09 percent.

12.

Why are most retail borrowers charged the same rate of interest, implying the same risk premium or class? What is credit rationing? How is it used to control credit risks with respect to retail and wholesale loans?

Most retail loans are small in size relative to the overall investment portfolio of an FI, and the cost of collecting information on household borrowers is high. As a result, most retail borrowers are charged the same rate of interest that implies the same level of risk.

Credit rationing involves restricting the amount of loans that are available to individual borrowers. On the retail side, the amount of loans provided to borrowers may be determined solely by the proportion of loans desired in this category rather than price or interest rate differences, thus the actual credit quality of the individual borrowers. On the wholesale side, the FI may use both credit quantity and interest rates to control credit risk. Typically, more risky borrowers are charged a higher risk premium to control credit risk. However, the expected returns from increasingly higher interest rates that reflect higher credit risk at some point will be offset by higher default rates. Thus, rationing credit through quantity limits will occur at some interest rate level even though positive loan demand exists at even higher risk premiums.

13.

Why could a lender’s expected return be lower when the risk premium is increased on a loan? In addition to the risk premium, how can a lender increase the expected return on a wholesale loan? A retail loan?

An increase in risk premiums indicates a riskier pool of clients who are more likely to default by taking on riskier projects. This reduces the repayment probability and lowers the expected return to the lender. The lender often is able to charge fees that increase the return on the loan.

However, the fees may become sufficiently high as to increase the risk of nonpayment or default on the loan.

14.

What are covenants in a loan agreement? What are the objectives of covenants? How can these covenants be negative? Positive?

Covenants are restrictions that are written into loan or bond contracts that affect the actions of the borrower. Negative covenants in effect restrict actions, that is, they are “thou shall not...” conditions. Common examples include the nonincrease of dividend payments without permission of the lender, or the maintenance of net working capital above some minimum level. Positive covenants encourage actions such as the submission of quarterly financial statements. In effect both types of covenants are designed and implemented to assist the lender in the monitoring and control of credit risk.

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15.

Identify and define the borrower-specific and market-specific factors that enter into the credit decision. What is the impact of each type of factor on the risk premium?

The borrower-specific factors are: Reputation: Based on the lending history of the borrower; better reputation implies a lower risk premium.

Leverage: A measure of the existing debt of the borrower; the larger the debt, the higher the risk premium.

Volatility of earnings: The more stable the earnings, the lower the risk premium.

Collateral: If collateral is offered, the risk premium is lower.

Market-specific factors include: Business cycle: Lenders are less likely to lend if a recession is forecasted.

Level of interest rates: A higher level of interest rates may lead to higher default rates, so lenders are more reluctant to lend under such conditions. a. Which of these factors is more likely to adversely affect small businesses rather than large businesses in the credit assessment process by lenders?

Because reputation involves a history of performance over an extended time period, small businesses that are fairly young in operating time may suffer. b. How does the existence of a high debt ratio typically affect the risk of the borrower?

Increasing amounts of debt increase the interest charges that must be paid by the borrower, and thus, decrease the amount of cash flows available to repay the debt principal. c. Why is the volatility of the earnings stream of a borrower important to a lender?

A highly volatile earnings stream increases the probability that the borrower cannot meet the fixed interest and principal payments for any given capital structure.

16.

Why is the degree of collateral as specified in the loan agreement of importance to a lender? If the book value of the collateral is greater than or equal to the amount of the loan, is the credit risk of a lender fully covered? Why, or why not?

Collateral provides the lender with some assets that can be used against the amount of the loan in the case of default. However, collateral has value only to the extent of its market value, and thus a loan fully collateralized at book value may not be fully collateralized at market value. Further, errors in the recording of collateralized positions may limit or severely reduce the protected positions of a lender.

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17.

Why are FIs consistently interested in the expected level of economic activity in the markets in which they operate? Why is monetary policy of the Federal Reserve System important to FIs?

During recessions firms in certain industries are much more likely to suffer financial distress because of the slowdown in economic activity. Specifically, the consumer durables industries are particularly hard hit because of cutbacks in spending by consumers. Further, Fed monetary policy actions that increase interest rates cause FIs to sustain a higher cost of funds and cause borrowers to increase the risk of investments. The higher cost of funds to the FI can be passed along to the borrower, but the increased risk in the investment portfolio necessary to generate returns to cover the higher funding cost to the borrower may lead to increased default risk realization. Thus, actions by the Fed often are signals of future economic activity.

18.

What are the purposes of credit scoring models? How do these models assist an FI manager to better administer credit?

Credit scoring models are used to calculate the probability of default or to sort borrowers into different default risk classes. The primary benefit of credit scoring models is to improve the accuracy of predicting borrower’s performance without using additional resources. This benefit results in fewer defaults and charge-offs to the FI. The models use data on observed economic and financial borrower characteristics to assist an FI manager in (a) identifying factors of importance in explaining default risk, (b) evaluating the relative degree of importance of these factors, (c) improving the pricing of default risk, (d) screening bad loan applicants, and (e) more efficiently calculating the necessary reserves to protect against future loan losses.

19.

Suppose there were two factors influencing the past default behavior of borrowers: the leverage or debt–assets ratio (D/A) and the profit margin ratio (PM). Based on past default (repayment) experience, the linear probability model is estimated as: PDi = 0.105(D/Ai ) - 0.35(PMi ) Prospective borrower A has a D/A = 0.65 and a PM = 5%, and prospective borrower B has a D/A = 0.45 and PM = 1%. Calculate the prospective borrowers’ expected probabilities of default (PDi). Which borrower is the better loan candidate? Explain your answer.

PDA = 0.105(0.65) - 0.35(0.05) = 0.05075 or 5.075% PDB = 0.105(0.45) - 0.35(0.01) = 0.04375 or 4.375%

Prospective borrower B is the better loan candidate. Even though B’s profit margin is lower than A’s, A’s higher debt-asset ratio increases the firm’s probability of default to be higher than firm B’s.

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20.

Suppose the estimated linear probability model used by an FI to predict business loan applicant default probabilities is PD = 0.03X1 + 0.02X2 - 0.05X3 + error, where X1 is the borrower's debt/equity ratio, X2 is the volatility of borrower earnings, and X3 is the borrower’s profit ratio. For a particular loan applicant, X1 = 0.75, X2 = 0.25, and X3 = 0.10. a. What is the projected probability of default for the borrower?

PD = 0.03(0.75) + 0.02(0.25) – 0.05(0.10) = 0.0225 b. What is the projected probability of repayment if the debt/equity ratio is 2.5?

PD = 0.03(2.5) + 0.02(0.25) - 0.05(0.10) = 0.075 The expected probability of repayment is 1 - 0.075 = 0.925. c. What is a major weakness of the linear probability model?

A major weakness of this model is that the estimated probabilities can be below 0 percent or above 100 percent, an occurrence that does not make economic or statistical sense.

21.

Describe how a linear discriminant analysis model works. Identify and discuss the criticisms which have been made regarding the use of this type of model to make credit risk evaluations.

Linear discriminant models divide borrowers into high or low default classes contingent on their observed characteristics. The overall measure of default risk classification (Z) depends on the values of various financial ratios and the weighted importance of these ratios based on the past or observed experience of borrowers. These weights are derived from a discriminant analysis model.

Several criticisms have been levied against these types of models. First, the models identify only two extreme categories of risk: default or no default. The real world considers several categories of default severity. Second, the relative weights of the variables may change over time. Further, the actual variables to be included in the model may change over time. Third, hard to define, but potentially important, qualitative variables are omitted from the analysis. Fourth, no centralized database on defaulted business loans for proprietary and other reasons exists. This constrains the ability of many FIs to use traditional credit scoring models (and quantitative models in general) for larger business loans.

22.

Suppose that the financial ratios of a potential borrowing firm take the following values: Working capital/total assets ratio (X1) = 0.75 Retained earnings/total assets ratio (X2) = 0.10 Earnings before interest and taxes/total assets ratio (X3) = 0.05 Market value of equity/book value of total liabilities ratio (X4) = 0.10 Sales/total assets ratio (X5) = 0.65 7 © 2022

Calculate the Altman’s Z score for the borrower in question. How is this number a sign of the borrower’s default risk?

Z = 1.2(0.75) + 1.4(0.10) + 3.3(0.05) + 0.6(0.10) + 1.0(0.65) = 0.90 + 0.14 + 0.165 + 0.06 + 0.65 = 1.915 With a Z score between 1.81 and 2.99, the firm is in the indeterminant default risk region. The ratios X2 and X3 are small, indicating that the firm has low earnings or even losses in recent periods. The ratio X5 indicates that the firm may be unable to produce sales efficiently. Also, X4 indicates that the borrower is highly leveraged. Finally, the working capital ratio (X1) is high, indicating that the firm is investing the large majority of its funding in zero or low earning assets.

The FI should not make a loan to this borrower until it improves its earnings.

23.

MNO Inc., a publicly traded manufacturing firm in the United States, has provided the following financial information in its application for a loan. All numbers are in thousands of dollars.

Assets Cash Accounts receivables Inventory

$ 20 90 90

Plant and equipment Total assets

500 $700

Liabilities and Equity Accounts payable Notes payable Accruals Long-term debt Equity (ret. earnings = $300) Total liabilities and equity

$ 30 40 30 150 450 $700

Also assume sales = $500,000; cost of goods sold = $360,000; and the market value of equity is equal to the book value. a. What is the Altman discriminant function value for MNO Inc.? Recall that: Net working capital = Current assets - Current liabilities.

Current assets = Cash + Accounts receivable + Inventories.

Current liabilities = Accounts payable + Accruals + Notes payable.

EBIT = Revenues - Cost of goods sold.

Altman’s discriminant function is given by: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5 All numbers are in $000s.

X1 = (20 + 90 + 90 – 30 – 40 – 30) / 700 = 0.1429 X2 = 300 / 700 = 0.4286

X1 = Working capital/total assets (TA) X2 = Retained earnings/TA

X3 = (500 – 360) / 700 = 0.20 X4 = 450 / (30+40+30+150) = 1.80

X3 = EBIT/TA X4 = Market value of equity/Book value of long-term debt 8 © 2022

X5 = 500 / 700 = 0.7143

X5 = Sales/TA

Z = 1.2(0.1429) + 1.4(0.4286) + 3.3(0.20) + 0.6(1.80) + 1.0(0.7143) = 3.2257 = 0.1714 + 0.6000 + 0.6600 + 1.0800 + 0.7143 = 3.2257 b. Based on the Altman’s Z score only, should you approve MNO Inc.'s application to your bank for a $500,000 capital expansion loan?

Since the Z score of 3.2257 is greater than 2.99, ABC Inc.’s application for a capital expansion loan should be approved. c. If sales for MNO were $250,000, the market value of equity was only half of book value, and all other values are unchanged, would your credit decision change?

ABC’s EBIT would be $300,000 - $360,000 = -$60,000.

X1 = (20 + 90 + 90 - 30 - 40 - 30) / 700 = 0.1429 X2 = 300 / 700 = 0.4286 X3 = -110 / 700 = -0.1571 X4 = 225 / (30+40+30+150) = 0.9000 X5 = 250 / 700 = 0.3571 Z = 1.2(0.1429) + 1.4(0.4286) + 3.3(-0.1571) + 0.6(0.9000) + 1.0(0.3571) = 1.1500 Since ABC's Z-score falls to 1.1500 < 1.81, credit should be denied. d. Would the discriminant function change for firms in different industries? Would the function be different for manufacturing firms in different geographic sections of the country? What are the implications for the use of these types of models by FIs? Discriminant function models are very sensitive to the weights for the different variables. Since different industries have different operating characteristics, a reasonable answer would be yes with the condition that there is no reason that the functions could not be similar for different industries. In the retail market, the demographics of the market play a big role in the value of the weights. For example, credit card companies often evaluate different models for different areas of the country. Because of the sensitivity of the models, extreme care should be taken in the process of selecting the correct sample to validate the model for use.

24.

Consider the coefficients of Altman’s Z score. Can you tell by the size of the coefficients which ratio appears most important in assessing the creditworthiness of a loan applicant?

Explain.

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Although X3, or EBIT/Total assets, has the highest coefficient (3.3), it is not necessarily the most important variable. Since the value of X3 is likely to be small, the product of 3.3 and X3 may be quite small. For some firms, particularly those in the retail business, the asset turnover ratio, X 5 may be quite large and the product of the X5 coefficient (1.0) and X5 may be substantially larger than the corresponding number for X3. Generally, the factor that adds most to the Z-score varies from firm to firm and industry to industry.

25.

If the rate on one-year Treasury strips currently is 6 percent, what is the repayment probability for each of the following two securities? Assume that if the loan is defaulted, no payments are expected. What is the market-determined risk premium for the corresponding probability of default for each security? a. One-year AA-rated zero coupon bond yielding 9.5 percent.

Probability of repayment = p = (1 + i)/(1 + k) For an AA-rated bond = (1 + 0.06)/ (1 + 0.095) = 0.9680, or 96.80 percent => probability of default = 1 – 0.9680 = 0.0320, or 3.20%

The market determined risk premium is 0.095 – 0.060 = 0.035 or 3.5 percent. This implies a probability of default of 3.2 percent on an AA-rated corporate bond requires an FI to set a risk premium of 3.5 percent. b. One-year BB-rated zero coupon bond yielding 13.5 percent.

Probability of repayment = p = (1 + i)/(1 + k) For BB-rated bond = (1 + 0.06)/(1 + 0.135) = 93.39 percent => probability of default = 1 – 0.9339 = 0.0661, or 6.61% The market determined risk premium is 0.135 – 0.060 = 0.075 or 7.50 percent. This implies a probability of default of 6.61 percent on a BB-rated corporate bond requires an FI to set a risk premium of 7.5 percent.

26.

A bank has made a loan charging a base lending rate of 10 percent. It expects a probability of default of 5 percent. If the loan is defaulted, the bank expects to recover 50 percent of its money through the sale of its collateral. What is the expected return on this loan?

E(r) = p(1 + k) + (1 - p)(1 + k)(γ) where γ is the percentage generated when the loan is defaulted.

E(r) = 0.95(1 + 0.10) + 0.05(1 + 0.10)(0.50) = 1.0450 + 0.0275 = 1.0725 - 1.0 = 7.25% 27.

Assume a one-year Treasury strip is currently yielding 5.5 percent and an AAA-rated discount bond with similar maturity is yielding 8.5 percent. a. If the expected recovery from collateral in the event of default is 50 percent of principal and interest, what is the probability of repayment of the AAA-rated bond? What is the probability of default?

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p(1 + k) +  (1 - p)(1 + k) = 1 + i. Solving for the probability of repayment (p): p=

1+ i 1.055 1+ k −  = 1.085 − 0.5 1− 

= 0.9447 or 94.47 percent

1− 0.5

Therefore the probability of default is 1.0 - 0.9447 = 0.0553 or 5.53 percent. b. What is the probability of repayment of the AAA-rated bond if the expected recovery from collateral in the case of default is 94.47 percent of principal and interest? What is the probability of default?

p=

1+ i − 1+ k 1− 

1.055

− 0.9447 = 1.085 = 0.5000 or 50.00 percent 1− 0.9447

Therefore the probability of default is 1.0 – 0.5000 = 0.5000 or 50.00 percent. c. What is the relationship between the probability of default and the proportion of principal and interest that may be recovered in case of default on the loan?

The proportion of the loan’s principal and interest that is collectible on default is a perfect substitute for the probability of repayment should such defaults occur.

28.

What is meant by the phrase marginal default probability? How does this term differ from cumulative default probability? How are the two terms related?

Marginal default probability is the probability of default in a given year, whereas cumulative default probability is the probability of default across several years. For example, the cumulative default probability across two years is given below, where (pt) is the probability of nondefault in a given year.

Cp = 1 – (p1) (p2) 29.

Suppose an FI manager wants to find the probability of default on a two-year loan. For the one-year loan, 1 - p1 = 0.03 is the marginal and total or cumulative probability (Cp) of default in year 1. For the second year, suppose that 1 - p2 = 0.05. Calculate the cumulative probability of default over the next two years.

1 - p1 = 0.03 = marginal probability of default in year 1 1 - p2 = 0.05 = marginal probability of default in year 2 The probability of the borrower surviving—not defaulting at any time between now (time 0) and 11 © 2022

the end of year 2—is: p1 × p2 = (0.97)(0.95) = 0.9215. Thus,

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Cp = 1- [(0.97)(0.95)] = 0.785, or 7.85% There is an 7.85 percent probability of default over this period.

30.

From the Treasury strip yield curve, the current required yields on one- and two-year Treasuries are i1 = 4.65 percent and i2 = 5.50 percent, respectively. Further, the current yield curve indicates that appropriate one-year discount bonds are yielding k1 = 8.5 percent, and two-year bonds are yielding k2 = 10.25 percent. a. Calculate the one-year forward rate on the Treasuries and the corporate bond.

The one-year forward rate, f1, on the Treasury is: f1 = (1.0550)2 / 1.0465 = 1.06357 - 1, or f1 = 6.357% The one-year forward rate, c1, on the corporate bond is: c1 = (1.1025)2 / 1.0850 = 1.12028 - 1, or c1 = 12.028% b. Using the current and forward one-year rates, calculate the marginal probability of repayment on the corporate bond in years 1 and 2, respectively.

The probability of repayment in year 1 is: p1 = 1.0465 / 1.085 = 0.9645 , or probability of default = 1 – 0.9645 = 5.35% The marginal probability of repayment in year 2 is: p2 = (1.06357) / 1.12028 = 0.9494 , or probability of default = 1 – 0.9494 = 5.06% c. Calculate the cumulative probability of default on the corporate bond over the next two years.

The probability of the borrower surviving—not defaulting at any time between now (time 0) and the end of year 2—is: p1 × p2 = (0.9645)(0.9494) = 0.9157. Thus, Cp = 1- [(0.9645)(0.9494)] = 0.843, or 8.43% 31.

Calculate the term structure of default probabilities over three years using the following spot rates from the Treasury strip and corporate bond (pure discount) yield curves. Be sure to calculate both the annual marginal and the cumulative default probabilities.

Treasury strips

Spot 1 Year 5.0%

Spot 2 Year 6.1% 13 © 2022

Spot 3 Year 7.0%

BBB-rated bonds

7.0

8.2

9.3

The notation used for implied forward rates on Treasuries is f1 = forward rate from period 1 to period 2 and on corporate bonds is c1 = forward rate from period 1 to period 2.

Treasury strips (1.061)2 = (1.05)(1 + f1)

BBB-rated debt (1.082)2 = (1.07)(1 + c1)

f1 = 7.21%

c1 = 9.41%

(1.07)3 = (1.061)2(1 + f2) f2 = 8.82%

(1.093)3 = (1.082)2(1 + c 2) c2 = 11.53%

Using the implied forward rates, estimate the annual marginal probability of repayment: p1(1.07) = 1.05 p2(1.0941) = 1.0721 p3 (1.1153) = 1.0882

=> p1 = 98.13 percent => p2 = 97.99 percent => p3 = 97.57 percent

Using marginal probabilities, estimate the cumulative probability of default: Cp2 Cp3

32.

= 1 - (p1)(p2) = 1 - (0.9813)(0.9799) = 3.84 percent = 1 - (p1)(p2)(p3) = 1 - (0.9813)(0.9799)(0.9757) = 6.18 percent

The bond equivalent yields for U.S. Treasury and A-rated corporate bonds with maturities of 93 and 175 days are given below: U.S. Treasury A-rated corporate Spread

93 Days 8.07% 8.42% 0.35%

175 Days 8.11% 8.66% 0.55%

a. What are the implied forward rates for both an 82-day Treasury and an 82-day A-rated bond beginning in 93 days? Use daily compounding on a 365-day year basis.

The forward rate, f, for the period 93 days to 175 days, or 82 days, for the Treasury is: (1 + 0.0811)175/365 = (1 + 0.0807)93/365 (1 + f)82/365

 f = 8.16 percent

The forward rate, c, for the corporate bond for the 82-day period is: 14 © 2022

(1 + 0.0866)175/365 = (1 + 0.0842)93/365 (1 + c)82/365

 c = 8.933%

b. What is the implied probability of default on A-rated bonds over the next 93 days?

Over 175 days?

The probability of repayment of the 93-day A-rated bond is:  p(1 + 0.0842)93/365 = (1 + 0.0807)93/365 p = 99.92 percent Therefore, the probability of default is (1 - p) = (1 - 0.9992) = 0.0008 or 0.08 percent.

The probability of repayment of the 175-day A-rated bond is:  p(1 + 0.0866)175/365 = (1 + 0.0811)175/365 p = 99.76 percent Therefore, the probability of default is (1 - p) = (1 - 0.9976) = 0.0024 or 0.24 percent. c. What is the implied default probability on an 82-day A-rated bond to be issued in 93 days?

The probability of repayment of the A-rated bond for the period 93 days to 175 days, p, is:  p = 0.9984, or 99.84 percent p (1.08933)82/365 = (1 + 0.0816)82/365 Therefore, the probability of default is (1 - p) or 0.0016 or 0.16 percent.

33.

What is the mortality rate of a bond or loan? What are some of the problems with using a mortality rate approach to determine the probability of default of a given bond issue?

Mortality rates reflect the historic default risk experience of a bond or a loan. One major problem is that the approach looks backward rather than forward in determining probabilities of default.

Further, the estimates are sensitive to the time period of the analysis, the number of bond issues, and the sizes of the issues.

34.

The following is a schedule of historical defaults (yearly and cumulative) experienced by an FI manager on a portfolio of commercial and mortgage loans.

Loan Type 1 Year Commercial: Annual default 0.00% Cumulative default Mortgage: 0.10% Annual default Cumulative default

Years after Issuance 2 Years 3 Years

4 Years

0.50% 0.10%

5 Years 0.30%

0.80%

0.25%

0.60%

0.80% 1.64%

a. Complete the blank spaces in the table.

15 © 2022

Commercial: Annual default 0.00%, 0.10%, 0.50%, 0.20%, and 0.30% Cumulative default: 0.00%, 0.10%, 0.60%, 0.80%, and 1.10% Mortgage: Annual default 0.10%, 0.25%, 0.60%, 0.70%, and 0.80% Cumulative default 0.10%, 0.35%, 0.95%, 1.64%, and 2.43% The annual survival rate is pt = 1 – annual default rate, and the cumulative default rate for: n = 3 of commercial loans is 1 – (p1 x p2 x p3) = 1 - (1 x 0.999 x 0.995) = 0.005995 = 0.60% n = 4 of commercial loans is 1 – (p1 x p2 x p3 x p4) = 1 - (1 x 0.999 x 0.995 x p4) = 0.008 => p4 = (1 – 0.008)/ (1 x 0.999 x 0.995) = 0.99798 => annual default rate = 1 - 0.99798 = 0.0020 = 0.20% n = 5 of commercial loans is 1 – (p1 x p2 x p3 x p4 x p5) = 1 - (1 x 0.999 x 0.995 x 0.99798 x 0.997) = 0.0110 = 1.10% n = 2 of mortgage loans is 1 – (p1 x p2) = 1 – (0.999 x 0.9975) = 0.0035 = 0.35% n = 3 of mortgage loans is = 1 – (p1 x p2 x p3) = 1 - (0.999 x 0.9975 x 0.9940) = 0.0095 = 0.95% n = 4 of mortgage loans is 1 – (p1 x p2 x p3 x p4) = 1 - (0.999 x 0.9975 x 0.9940 x p4) = 0.0164 => p4 = (1 – 0.0164)/ (0.999 x 0.9975 x 0.9940) = 0.9930 => annual default rate = 1 - 0.9930 = 0.0070 = 0.70% n = 5 of commercial loans is 1 – (p1 x p2 x p3 x p4 x p5) = 1 - (0.999 x 0.9975 x 0.9940 x 0.9930 x 0.992) = 0.0243 = 2.43% b. What are the probabilities that each type of loan will not be in default after five years?

The cumulative survival rate is = (1 - MMR1) x (1 - MMR2) x (1 - MMR3) x (1 - MMR4) x (1 - MMR5) where MMR = marginal mortality rate Commercial loan = (1 - 0.00) x (1 - 0.001) x (1 - 0.005) x (1 - 0.002) x (1 - 0.003) = 0.989 or 98.9%.

Mortgage loan = (1 - 0.001) x (1 - 0.0025) x (1 - 0.006) x (1 - 0.007) x (1 - 0.008) = 0.9757 or 97.57%. c. What is the measured difference between the cumulative default (mortality) rates for commercial and mortgage loans after four years?

Looking at the table, the cumulative rates of default in year 4 are 0.80% and 1.64%, respectively, for the commercial and mortgage loans. Another way of estimation is: Cumulative mortality rate (CMR) For commercial loan

= 1- (1 - MMR1)(1 - MMR2)(1 - MMR3)(1 - MMR4) = 1- (1 - 0.000)(1 - 0.0010)(1 - 0.0050)(1 - 0.0020) = 1- 0.9920 = 0.0080 or 0.80 percent.

For mortgage loan

= 1- (1 - 0.0010)(1 - 0.0025)(1 - 0.0060)(1 - 0.0070) = 1- 0.98359 = 0.01641 or 1.64 percent.

The difference in cumulative default rates is 1.64 - 0.80 = 0.84 percent.

16 © 2022

35.

The table below shows the dollar amounts of outstanding bonds and corresponding default amounts for every year over the past five years. Note that the default figures are in millions, while those outstanding are in billions. The outstanding figures reflect default amounts and bond redemptions.

Years after Issuance Loan Type 1 Year 2 Years 3 Years 4 Years 5 Years A-rated: Annual default (millions) 0 0 0 $1 $2 Outstanding (billions) $100 $95 $93 $91 $88 B-rated: Annual default (millions) Outstanding (billions)

0 $100

$1 $94

$2 $92

$3 $89

$4 $85

C-rated: Annual default (millions) Outstanding (billions)

$1 $100

$3 $97

$5 $90

$5 $85

$6 $79

a. What are the annual and cumulative default rates of the above bonds?

A-rated Bonds Millions Millions Annual Survival = Cumulative % Cumulative Year Default Balance Default 1 - An. Def. Default Rate Default Rate 1 0 100,000 0.000000 1.000000 0.000000 0.0000% 2 0 95,000 0.000000 1.000000 0.000000 0.0000% 3 0 93,000 0.000000 1.000000 0.000000 0.0000% 4 1 91,000 0.000011 0.999989 0.000011 0.0011% 5 2 88,000 0.000023 0.999977 0.000034 0.0034% Where cumulative default for nth year = 1 - product of survival rates to that year.

B-rated Bonds Millions Year Default 1 0 2 1 3 2 4 3 5 4

Millions Balance 100,000 94,000 92,000 89,000 85,000

Annual Survival = Cumulative % Cumulative Default 1 - An. Def. Default Rate Default Rate 0.000000 1.000000 0.000000 0.0000% 0.000011 0.999989 0.000011 0.0011% 0.000022 0.999978 0.000032 0.0032% 0.000034 0.999966 0.000066 0.0066% 0.000047 0.999953 0.000113 0.0113%

Millions Balance 100,000 97,000 90,000

Annual Survival = Cumulative % Cumulative Default 1 - An. Def. Default Rate Default Rate 0.000010 0.999990 0.000010 0.0010% 0.000031 0.999969 0.000041 0.0041% 0.000056 0.999944 0.000096 0.0096%

C-rated Bonds Millions Year Default 1 1 2 3 3 5

17 © 2022

4 5

5 6

85,000 79,000

0.000059 0.000076

0.999941 0.999924

0.000155 0.000231

0.0155% 0.0231%

Years after Issuance 2 Years 3 Years 4 Years 5 Years 0% 0% 0.0011% 0.0023% 0% 0% 0.0011% 0.0034%

Bond Type A-rated: Annual default Cumulative default

1 Year 0% 0%

B-rated: Annual default Cumulative default

0% 0%

0.0011% 0.0022% 0.0011% 0.0032%

0.0034% 0.0047% 0.0066% 0.0113%

C-rated: Annual default 0.0010% Cumulative default 0.0010%

0.0031% 0.0056% 0.0041% 0.0096%

0.0059% 0.0076% 0.0155% 0.0231%

Note: These percentage values seem very small. More reasonable values can be obtained by increasing the default dollar values by a factor of ten, or by decreasing the outstanding balance values by a factor of 0.10. Either case will give the same answers that are shown below. While the percentage numbers seem somewhat more reasonable, the true values of the problem are (a) that default rates are higher on lower rated assets, and (b) that the cumulative default rate involves more than the sum of the annual default rates.

36.

What is RAROC? How does this model use the concept of duration to measure the risk exposure of a loan? How is the expected change in the credit risk premium measured?

What precisely is LN in the RAROC equation?

RAROC is a measure of expected loan net income in the form of interest plus fees less cost of funding relative to some measure of asset risk. One version of the RAROC model uses the duration model to measure the change in the value of the loan for given changes or shocks in credit quality. The change in credit quality (R) is measured by finding the change in the spread in yields between Treasury bonds and corporate bonds of the same risk class on the loan. The actual value chosen is the highest change in yield spread for the same maturity or duration value assets. In this case, LN represents the change in loan value or the change in capital for the largest reasonable adverse changes in yield spreads. The actual equation for LN looks very similar to the duration equation.

RAROC =

Net Income

where LN = − DLN x LN x

Loan risk (or LN )

37.

R

where Risthechangein yield spread.

1+ R

An FI wants to evaluate the credit risk of a $5 million loan with a duration of 4.3 years to a AAA borrower. There are currently 500 publicly traded bonds in that class (i.e., bonds issued by firms with a AAA rating). The current average level of rates (R) on AAA bonds is 8 percent. The largest increase in credit risk premiums on AAA loans, the 99 percent 18 © 2022

worst-case scenario, over the last year was equal to 1.2 percent (i.e., only 6 bonds out of 500 had risk premium increases exceeding the 99 percent worst case). The projected (one-

19 © 2022

year) spread on the loan is 0.3 percent and the FI charges 0.25 percent of the face value of the loan in fees. Calculate the capital at risk and the RAROC on this loan.

The estimate of loan (or capital) risk is: ΔLN = -DLN x LN x (ΔR/(1 + R)) = -4.3 x $5m x (0.012/(1 + 0.08)) = $238,889 While the market value of the loan amount is $5 million, the risk amount, or change in the loan’s market value due to a decline in its credit quality, is $238,889. Thus, the denominator of the RAROC equation is this possible loss, or $238,889. To determine whether the loan is worth making, the estimated loan risk is compared with the loan’s income (spread over the FI’s cost of funds plus fees on the loan).

Spread = 0.003 x $5 million = $15,000 Fees = 0.0025 x $5 million = $12,500 $27,500 The loan’s RAROC is: RAROC = $27,500/238,889 = 11.51% 38.

A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects to charge a servicing fee of 50 basis points. The loan has a maturity of 8 years with a duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 percent. The bank has estimated the maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2 percent, based on two years of historical data. The current market interest rate for loans in this sector is 12 percent. a. Using the RAROC model, determine whether the bank should make the loan?

RAROC = Fees and interest earned on loan/Loan or capital risk Loan risk, or LN = -DLN x LN x (R/(1 + R)) = -7.5 x $5m x (0.042/1.12) = -$1,406,250 Expected interest = 0.12 x $5,000,000 = $600,000 Servicing fees = 0.0050 x $5,000,000 = $25,000 Less cost of funds = 0.10 x $5,000,000 = -$500,000 Net interest and fee income = $125,000 RAROC = $125,000/1,406,250 = 8.89 percent. Since RAROC is lower than the cost of funds to the bank, the bank should not make the loan. b. What should be the duration in order for this loan to be approved?

For RAROC to be 10 percent, loan risk should be: 20 © 2022

$125,000/LN = 0.10

 LN = 125,000 / 0.10 = $1,250,000  -DLN x LN x (R/(1 + R)) = 1,250,000

DLN = 1,250,000/(5,000,000 x (0.042/1.12)) = 6.67 years.

Thus, this loan can be made if the duration is reduced to 6.67 years from 7.5 years. c. Assuming that duration cannot be changed, how much additional interest and fee income will be necessary to make the loan acceptable?

Necessary RAROC = Income/Risk  Income = RAROC x Risk = $1,406,250 x 0.10 = $140,625 Therefore, additional income = $140,625 - $125,000 = $15,625, or $15,625/$5,000,000 = 0.003125 = 0.3125%.

Thus, this loan can be made if fees are increased from 50 basis points to 81.25 basis points. d. Given the proposed income stream and the negotiated duration, what adjustment in the loan rate would be necessary to make the loan acceptable?

Need an additional $15,625 => $15,625/$5,000,000 = 0.003125 or 0.3125% Expected interest = 0.123125 x $5,000,000 = $615,625 Servicing fees = 0.0050 x $5,000,000 = $25,000 Less cost of funds = 0.10 x $5,000,000 = -$500,000 Net interest and fee income = $140,625 RAROC = $140,625/1,406,250 = 10.00 percent = cost of funds to the bank. Thus, increasing the loan rate from 12% to 12.3125% will make the loan acceptable 39.

Calculate the value of and interest rate on a loan using the option model and the following information.

Face value of loan (B) = $500,000 Length of time remaining to loan maturity (τ) = 4 years Risk-free rate (i) = 4% Borrower’s leverage ratio (d) = 51% Standard deviation of the rate of change in the value of the underlying assets = 15%

Substituting these values into the equations for h1 and h2 and solving for the areas under the standardized normal distribution, we find that: h1 = -[0.5 x (0.15)2 x 4 - ln(0.51)]/(0.15)(4)1/2 = -2.39448 21 © 2022

h2 = -[0.5 x (0.15)2 x 4 + ln(0.51)]/(0.15)(4)1/2 = 2.09448 h -2.40 -2.35 -2.30 -2.25

N(h) 0.0082 0.0094 0.0107 0.0122

h 2.00 2.05 2.10 2.15

N(h) 0.9773 0.9798 0.9821 0.9842

Current market value of loan = L(τ) = Be-iτ [N(h1)1/d + N(h2)] = $500,000 e-0.04(4) [N(-2.39448) x 1.6667 + N(2.09448)] = $426,071.89[0.008332 x 1.6667 + 0.981846] = $424,254 The risk premium, ϕ = k(τ) – i = (-1/τ) ln[N(h2) + (1/d)N(h1)] = (-1/4)ln[0.981846 + 0.008332 x 1.6667] = 0.001069 = 0.1069% Thus, the risky loan rate k(τ) should be set at 4.1069 percent when the risk-free rate (i) is 4 percent.

40.

A firm is issuing a two-year loan in the amount of $200,000. The current market value of the borrower’s assets is $300,000. The risk-free rate is 4 percent and the standard deviation of the rate of change in the underlying assets of the borrower is 20 percent. Using an options framework, determine the following: a. The current market value of the loan. b. The risk premium to be charged on the loan.

The following need to be estimated first: d, h1 and h2 . d = Be-iτ /A = $200,000e-0.04(2)/300,000 = 0.6154 or 61.54 percent. h1 = -[0.5 x (0.20)2 x 2 - ln(0.6154)]/(0.20)(2)1/2 = -1.8578 h2 = -[0.5*(0.20)2 *2 + ln(0.6154)]/(0.20)(2)1/2 = 1.5750 Current market value of loan = L(τ) = Be-iτ [N(h1)1/d + N(h2)] = $184,623.27[N(-1.8578) x 1.62493 + N(1.5750)] = $184,623.27[0.031654 x 1.62493 + 0.94265] = $183,531 The risk premium, ϕ = k(τ) – i = (-1/τ) ln[N(h2) + (1/d)N(h1)] = (-½)ln[0.94265 + 1.62493 x 0.031654] = 0.002966 = 0.2966% 41.

A firm has assets of $200,000 and total debts of $175,000. With an option pricing model, the implied volatility of the value of the firm’s assets is estimated at $10,730. Under the Moody’s Analytics method, what is the expected default frequency (assuming a normal distribution for assets)?

22 © 2022

The firm will be in technical bankruptcy if the value of the assets falls below $175,000. If  = $10,730, then it takes 25,000/10,730 = 2.33 standard deviations for the assets to fall below this value. Under the assumption that the market value of the assets are normally distributed, then 2.33 represents a 1 percent probability that the firm will become bankrupt.

42.

Carman County Bank (CCB) has a $5 million face value outstanding adjustable-rate loan to a company that has a leverage ratio of 80 percent. The current risk-free rate is 6 percent and the time to maturity on the loan is exactly ½ year. The asset risk of the borrower, as measured by the standard deviation of the rate of change in the value of the underlying assets, is 12 percent. The normal density function values are given below. h -2.55 -2.60 -2.65 -2.70 -2.75

N(h) 0.0054 0.0047 0.0040 0.0035 0.0030

h 2.50 2.55 2.60 2.65 2.70

N(h) 0.9938 0.9946 0.9953 0.9960 0.9965

a. Use the Merton option valuation model to determine the market value of the loan.

The following need to be estimated first: d, h1 and h2 .

D = 0.80 h1 = -[0.5 x (0.12)2 x 0.5 - ln(0.8)]/(0.12)0.5 = -0.226744/0.084853 = -2.6722 h2 = -[0.5 x (0.12)2 x 0.5 + ln(0.8)]/(0.12)0.5 = 0.219544/0.084853 = 2.5873 Current market value of loan = L(τ) = Be-iτ [N(h1)1/d + N(h2)] = $4,852,227.67[N(-2.6722) x 1.25 + N(2.5873)] = $4,852,227.67 [0.003778 x 1.25 + 0.995123] = $4,851,478 b. What should be the interest rate for the last six months of the loan?

The risk premium k(τ) – i = (-1/τ) ln[N(h2) + (1/d)N(h1)] = (-1/0.5)ln[0.995123 + 1.25 x 0.003778] = 0.0003 The loan rate = risk-free rate plus risk premium = 0.06 + 0.0003 = 0.0603 or 6.03%.

The questions and problems that follow refer to Appendix 10A. 43. Suppose you are a loan officer at Carbondale Local Bank. Joan Doe listed the following information on her mortgage application.

Characteristic

Value 23 © 2022

Annual gross income $45,000 TDS 10% Relations with FI Checking account Major credit cards 5 Age 27 Residence Own/mortgage Length of residence 2½ years Job stability 5½ years Credit history Missed 2 payments 1 year ago

24 © 2022

Use the information below to determine whether or not Joan Doe should be approved for a mortgage from your bank.

Characteristic Annual gross income Score TDS

<$10,000

Characteristic Values and Weights $10,000-$25,000 $25,000-$50,000 $50,000-$100,000

0 >50%

10 35%-50%

Score Relations with FI Score Major credit cards Score Age

-10 None

0 Checking account

0 None

10 Between 1 and 4

10 5 or more

0 <25

20 25-60

10

Score Residence

5 Rent

Score Length of residence Score Job stability

5 <1 year

Score Credit history

0 No record

0 <1 year

20 15%-35% 20 Savings account

>$100,000

35

60

5%-15%

<5%

40

60 Both 20

>60

25 35 Own with mortgage Own outright 20 1-5 years

50 >5 years

25 1-5 years

40 >5 years

25 50 Missed a payment Met all payments in last 5 years Score 0 -15 40 The loan is automatically rejected if the applicant’s total score is less than or equal to 120; the loan is automatically approved if the total score is greater than or equal to 190. A score between 120 and 190 (noninclusive) is reviewed by a loan committee for a final decision.

21

Jane Doe=s credit score is calculated as follows: Characteristic Value Annual gross income $45,000 TDS 10% Relations with FI Checking account Major credit cards 5 Age 27 Residence Own/Mortgage Length of residence 2½years Job stability 5½ years Credit history Missed 2 payments 1 year ago Score

Score 20 40 10 10 25 20 25 50 -15 185

The loan request will go to the credit committee for review and decision.

44.

What are some of the special risks and considerations when lending to small businesses rather than large businesses?

Besides the obvious difference in the sizes of the borrowers, for a large business there is also a more well defined corporate structure and a clearer delineation of the corporate assets from the personal assets of the owners. The large business borrower is also more likely to have a track record to use as a basis for future performance. Small-business loans are also more complicated because the FI is frequently asked to assume the credit risk of an individual whose business cash flows require considerable analysis, often with incomplete accounting information available to the credit officer. The payoff for this analysis is also small, by definition, because loan principal amounts are usually small. A $50,000 loan with a 3 percent interest spread over the cost of funds provides only $1,500 of gross revenues before loan loss provisions, monitoring costs, and allocation of overheads. This low profitability has caused many FIs to build small business scoring models similar to, but more sophisticated than, those used for mortgages and consumer credit. These models often combine computer-based financial analysis of borrower financial statements with behavioral analysis of the owner of the small business.

45.

How does ratio analysis help to answer questions about the production, management, and marketing capabilities of a prospective borrower?

Although financial ratios are normally thought to represent financial health, they also demonstrate other aspects of the company’s health. Generally, a set of healthy ratios should reflect a well-managed company. A company with strong profits, an ability to pay off its debt, and an above average turnover of assets should be in a good position to meet future obligations.

More specifically, the profitability and asset management ratios reflect the production efficiency of management. Receivables turnover and days sales outstanding are indicators of the company’s credit policy and collection policies and are also indicative of the marketing efficiency of the company.

46.

Consider the following company balance sheet and income statement.

22

Balance Sheet: Assets Cash Accounts receivable Inventory Total current assets Fixed assets Total assets

Liabilities and Equity Accounts payable Notes payable Total current liabilities Long-term debt Equity Total liabilities and equity

$4,000 52,000 40,000 96,000 44,000 $140,000

$30,000 12,000 42,000 36,000 62,000 $140,000

Income Statement Sales (all on credit) Cost of goods sold Gross margin Selling and administrative expenses Depreciation EBIT Interest expense Earning before tax Taxes Net income

$200,000 130,000 70,000 20,000 8,000 42,000 4,800 37,200 11,160 $26,040

For this company, calculate the following: a. Current ratio.

96,000/42,000 = 2.2857X b. Number of days' sales in receivables.

52,000 x 365/200,000 = 94.90 days c. Sales to total assets.

200,000/140,000 = 1.4286X d. Number of days in inventory.

40,000 x 365/130,000 = 112.31 days e. Debt to assets ratio.

(42,000 + 36,000)/140,000 = .5571 = 55.71% f. Cash flow to debt ratio.

(42,000 + 8,000)/(42,000 + 36,000) = .6410 = 64.10% g. Return on assets.

26,040/140,000 = 0.1860 = 18.60% h. Return on equity.

26,040/62,000 = 0.4200 = 42.00% 47.

Industrial Corporation has an income to sales (profit margin) ratio of 0.03, a sales to assets (asset utilization) ratio of 1.5, and a debt to asset ratio of 0.66. What is Industrial’s return on equity?

ROE = NI/Equity = NI/Sales x Sales/Total assets x Total assets/Equity = PM  AU  EM = 0.03 x 1.5 x (1/(1 - 0.66)) = 0.1324 = 13.24%

23

Answer to Integrated Mini Case: Loan Analysis Loan: 1.

PD = -0.08(2.15) + 0.15(0.45) + 1.25(0.13) - 0.45(0.12) = 0.004 = 0.4% < 0.5% => accept the loan

2.

Z = 1.2((40m+120m+210m-55m-60m-70m)/1470m) + 1.4(200m/1470m) + 3.3((1250m930m) /1470m) + 0.6(2.2x735m/(55m+60m+70m+550m) + 1.0(1250m/1470m) = 0.1510 + 0.1905 + 0.7184 + 1.32 + 0.8503 = 3.2302 > 2.99 => accept the loan

3. Cumulative default probability = 0.595% < 1.25% => accept the loan 4.

LN = -4.5 x $2m x (0.055/1.10) = -$450,000 Expected interest = 0.10 x $2,000,000 Servicing fees = 0.0075 x $2,000,000 Less cost of funds = 0.08 x $2,000,000 Net interest and fee income

= $200,000 = $15,000 = -$160,000 = $ 55,000

RAROC = $55,000/450,000 = 12.22 percent. Since RAROC is greater than the cost of funds to the bank, 8%, the bank should make the loan.

The bank should accept all four of the loans.

24

Solution for End-of-Chapter Questions and Problems: Chapter Eleven 1.

How do loan portfolio risks differ from individual loan risks?

Loan portfolio risks refer to the risks of a portfolio of loans as opposed to the risks of a single loan. Inherent in the distinction is the elimination of some of the borrower-specific risks of individual loans because of benefits from diversification.

2.

What is migration analysis? How do FIs use it to measure credit risk concentration? What are its shortcomings?

Migration analysis uses information from the market to determine the credit risk of an individual loan or sectoral loans. With this method, FI managers track credit ratings, such as S&P and Moody’s ratings, of firms in particular sectors or ratings classes for unusual declines to determine whether firms in a particular sector are experiencing repayment problems. This information can be used to either curtail lending in that sector or to reduce maturity and/or increase interest rates. A problem with migration analysis is that the information may be too late, because ratings agencies usually downgrade issues only after the firm or industry has experienced a downturn.

3.

What does loan concentration risk mean?

Loan concentration risk refers to the extra risk borne by having too many loans concentrated with one firm, industry, or economic sector. To the extent that a portfolio of loans represents loans made to a diverse cross section of the economy, concentration risk is minimized.

4.

A manager decides not to lend to any firm in sectors that generate losses in excess of 5 percent of capital. a. If the average historical losses in the automobile sector total 8 percent, what is the maximum loan a manager can lend to firms in this sector as a percentage of total capital?

Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = 0.05 x 1/0.08 = 62.5 percent of capital is the maximum amount that can be lent to firms in the automobile sector. b. If the average historical losses in the mining sector total 15 percent, what is the maximum loan a manager can lend to firms in this sector as a percentage of total capital?

Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = 0.05 x 1/0.15 = 33.3 percent of capital is the maximum amount that can be lent to firms in the mining sector.

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5.

An FI has set a maximum loss of 2 percent of total capital as a basis for setting concentration limits on loans to individual firms. If it has set a concentration limit of 25 percent to a firm, what is the expected loss rate for that firm?

Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) 25 percent = 2 percent x 1/Loss rate => Loss rate = 0.02/0.25 = 8 percent 6.

Explain how modern portfolio theory can be applied to lower the credit risk of an FI’s portfolio.

The fundamental lesson of modern portfolio theory is that, to the extent that an FI manager holds widely traded loans and bonds as assets, or can calculate loan or bond returns, portfolio diversification models can be used to measure and control the FI’s aggregate credit risk exposure. By taking advantage of its size, an FI can diversify considerable amounts of credit risk as long as the returns on different assets are imperfectly correlated with respect to their default risk adjusted returns. By fully exploiting diversification potential with bonds or loans whose returns are negatively correlated or that have a low positive correlations with those in the existing portfolio, the FI manager can produce a set of efficient frontier portfolios, defined as those portfolios that provide the maximum returns for a given level of risk or the lowest risk for a given level of returns. By choosing portfolios on the efficient frontier, an FI manager may be able to reduce credit risk to the fullest extent. As shown in Figure 11-1, a manager’s selection of a particular portfolio on the efficient frontier is determined by the risk-return trade-off.

7.

Suppose that an FI holds two loans with the following characteristics: Loan i 1 2

Xi 0.55 0.45

Ri 8% 10

σi 8.55% 9.15

σi2 .

73.1025% 83.7225

ρ12 = 0.24 σ12 = 18.7758

Calculate the return and risk of the portfolio.

The return on the loan portfolio is: Rp = 0.55 (8%) + 0.45 (10%) = 8.90% The risk of the portfolio is: σp2 = (0.55)2 (73.1025%) + (0.45)2 (83722.5%) + 2 (0.55) (0.45) (18.7758%) = 48.36133% or

σp2 = (0.55)2 (73.1025%) + (0.45)2 (83722.5%) + 2 (0.55) (0.45) (0.24)(8.55%)(9.15%) =

48.36133% and σp = √ 48.36133% = 6.95% 2 © 2022 .

Notice that the risk (or standard deviation of returns) of the portfolio, σp (6.95 percent), is less than the risk of either individual asset (8.55 percent and 9.15 percent, respectively). The low correlation of the returns of the two loans (0.24) results in an overall reduction of risk when they are put together in an FI's portfolio.

8.

The Bank of Tinytown has two $20,000 loans with the following characteristics: Loan A has an expected return of 10 percent and a standard deviation of returns of 10 percent. The expected return and standard deviation of returns for loan B are 12 percent and 20 percent, respectively. a. If the correlation coefficient between the returns on loans A and B is 0.15, what are the expected return and standard deviation of this portfolio?

XA = XB = $20,000/$40,000 = 0.5 Expected return = 0.5(10%) + 0.5(12%) = 11 percent Standard deviation = [0.52(0.10)2 + 0.52(0.20)2 + 2(0.5)(0.5)(0.15)(0.10)(0.20)]½ = 11.83% b. What is the standard deviation of the portfolio if the correlation is -0.15?

Standard deviation = [0.52(0.10)2 + 0.52(0.20)2 + 2(0.5)(0.5)(-0.15)(0.10)(0.20)]½ = 10.49% c. What role does the covariance, or correlation, play in the risk reduction attributes of modern portfolio theory?

The risk of the portfolio as measured by the standard deviation is reduced when the covariance is reduced. If the correlation is less than +1.0, the standard deviation of the portfolio will always be less than the weighted average of the standard deviations of the individual assets.

9.

Why is it difficult for small banks and thrifts to measure credit risk using modern portfolio theory?

The basic premise behind modern portfolio theory is the ability to diversify and reduce risk by eliminating diversifiable risk. Small banks and thrifts may not have the ability to diversify their asset base, especially if the local markets which they serve have a limited number of industries.

The ability to diversify is even more acute if these loans cannot be traded easily.

10.

What is the minimum risk portfolio? Why is this portfolio usually not the portfolio chosen

by FIs to optimize the return-risk tradeoff?

The minimum risk portfolio is the combination of assets that reduces portfolio risk as measured by the standard deviation of returns to the lowest possible level. This portfolio usually is not the optimal portfolio choice because the returns on this portfolio are low relative to other alternative 3 © 2022 .

portfolio selections. By accepting some additional risk, portfolio managers are able to realize a higher level of return relative to the risk of the portfolio.

11.

The obvious benefit to holding a diversified portfolio of loans is to spread risk exposures so that a single event does not result in a great loss to an FI. Are there any benefits to not being diversified?

One benefit to not being diversified is that an FI that lends to a certain industrial or geographic sector is likely to gain expertise about that sector. Being diversified requires that the FI becomes familiar with many more areas of business. This may not always be possible, particularly for small FIs. 12.

A bank vice president is attempting to rank, in terms of the risk-reward trade-off, the loan portfolios of three loan officers. Information on the portfolios is noted below. How would you rank the three portfolios?

Expected Return 10% 12% 11%

Portfolio A B C

Standard Deviation 8% 9% 10%

Portfolio B dominates portfolio C because B has a higher expected return and a lower standard deviation. Thus, C is clearly inferior. A comparison of portfolios A and B represents a risk-return trade-off in that B has a higher expected return, but B also has higher risk. A crude comparison may use the coefficient of variation or the Sharpe measure, but a judgment regarding which portfolio is “better” would be based on the risk preference of the vice president.

13. Suppose that an FI holds two loans with the following characteristics.

Loan 1 2

Xi 0.45 0.55

Annual Spread between Loan Rate and FI’s Cost of Funds 5.5% 3.5

Annual Fees 2.25% 1.75

Loss to FI Given Default 30% 20

Expected Default Frequency 3.5% 1.0

Calculate of the return and risk on the two-asset portfolio using Moody’s Analytics Portfolio Manager.

The return and risk on loan 1 are: R1 = (0.055 + 0.0225) - [0.035 x 0.30] = 0.0670 or 6.70% σ1 = [0.035 x (1 - 0.035)]1/2 x 0.30 = 0.05513 or 5.513% The return and risk on loan 2 are: 4 © 2022 .

ρ12 = -0.15

R2 = (0.035 + 0.0175) - [0.01 x 0.20] = 0.0505 or 5.05% σ2 = [0.01 x (1 - 0.01)]1/2 x 0.20 = 0.01990 or 1.990% The return and risk of the portfolio is then: Rp = 0.45 (6.70%) + 0.55 (5.05%) = 5.7925% σp2 = (0.45)2 (5.513%)2 + (0.55)2 (1.990%)2 + 2 (0.45) (0.55)(-0.15)(5.513%)(1.990%) = 6.53876% and, σp = (6.53876%)1/2 = 2.56% 14.

CountrySide Bank uses Moody’s Analytics Portfolio Manager to evaluate the risk-return characteristics of the loans in its portfolio. A specific $10 million loan earns 2 percent per year in fees and the loan is priced at a 4 percent spread over the cost of funds for the bank.

Because of collateral considerations, the loss to the bank if the borrower defaults will be 20 percent of the loan’s face value. The expected probability of default is 3 percent. What is the anticipated return on this loan? What is the risk of the loan?

Expected return = AISi – E(Li) = (0.02 + 0.04) – (0.03 x 0.20) = 0.054 or 5.4 percent Risk of the loan = Di x LGDi = [0.03(0.97)]½ x 0.20 = 0.0341 or 3.41 percent 15.

Suppose that an FI holds two loans with the following characteristics.

Loan 1 2

Annual Spread between Loan Rate and FI’s Xi Cost of Funds ?

4.0% ?

2.5

Annual Fees 1.50% 1.15

Loss to FI Given Default ?% ?

Expected Default Frequency 4.0% 1.5

ρ12 = -0.10

The return on loan 1 is R1 = 6.25%, the risk on loan 2 is σ2 = 1.8233%, and the return of the portfolio is Rp = 4.555%. Calculate of the loss given default on loans 1 and 2, the proportions of loans 1 and 2 in the portfolio, and the risk of the portfolio, σp, using Moody’s Analytics Portfolio Manager.

R1 = 0.0625 = (0.04 + 0.015) - [0.040 x LGD1] => LGD1 = (0.0625 – (0.04 + 0.015))/(-0.04) = 0.1875 => σ1 = [0.04(1 - 0.04)]1/2 x 0.1875 = 0.03674 or 3.674% σ2 = 0.018233 = [(0.015(1 - 0.015)]1/2 x LGD2 => LGD2 = 0.018233/[(0.015(1 - 0.015)]1/2 = 0.15 => R2 = (0.025 + 0.0115) - [0.015 x 0.15] = 0.03425 or 3.425% => Rp = X1 (0.0625) + (1 – X1) (0.03425) = 0.04555 => X1 = (0.04555 - 0.03425)/(0.0625 - 0.03425) = 0.40 and X2 = 1 - 0.40 = 0.60 5 © 2022 .

σp2 = (0.40)2 (0.03674)2 + (0.60)2 (0.018233)2 + 2 (0.40)(0.60)(-0.10)(0.03674)(0.018233) = 0.000303523 Thus, σp = (0.000303523)1/2 = 0.0174 = 1.74%.

16.

What databases are available that contain loan information at national and regional levels?

How can they be used to analyze credit concentration risk?

Two publicly available databases are (a) the commercial bank Call Reports of the Federal Reserve Board which contain various information supplied by banks quarterly and (b) the Shared National Credit database, which provides information on loan volumes of FIs separated by twodigit SIC (Standard Industrial Classification) codes. Such data can be used as a benchmark to determine whether an FI’s asset allocation is significantly different from the national or regional average.

17.

Information concerning the allocation of loan portfolios to different market sectors is given below.

Allocation of Loan Portfolios in Different Sectors (%) .

Sectors National Bank A Bank B Commercial 30% 50% 10% Consumer 40 30 40 Real Estate 30 20 50 Bank A and Bank B would like to estimate how much their portfolios deviate from the national average. a. Which bank is further away from the national average?

Using Xs to represent portfolio holdings: (X1j - X1 )2 (X2j - X2 )2 (X3j - X3 )2 n



Bank A (0.50 - 0.30)2 = 0.0400 (0.30 - 0.40)2 = 0.0100

Bank B (0.10 - 0.30)2 = 0.0400 (0.40 - 0.40)2 = 0.0000

(0.20 - 0.30)2 = 0.0100

(0.50 - 0.30)2 = 0.0400

n =3

n =3

 = 0.0600

( X ij −X i ) 2

i −1

i =1

 = 0.0800 i =1

n

=

( X ij − X i )2

A = 14.14 percent n Bank B deviates from the national average more than Bank A. i =1

B = 16.33 percent

b. Is a large standard deviation necessarily bad for an FI using this model?

6 © 2022 .

No, a higher standard deviation is not necessarily bad for an FI because the FI could have comparative advantages that are not required or available to a national well-diversified bank. For example, an FI could generate high returns by serving specialized markets or product niches that are not well diversified. Further, an FI could specialize in only one product, such as mortgages, but be well-diversified within this product line by investing in several different types of mortgages that are distributed both nationally and internationally. This would still enable it to obtain portfolio diversification benefits that are similar to the national average.

18.

Assume that, on average, national banks engaged primarily in mortgage lending have their assets diversified in the following proportions: 60 percent residential, 15 percent commercial, 5 percent international, and 20 percent mortgage-backed securities. A local bank has the following distribution of mortgage loans: 50 percent residential, 30 percent commercial, and 20 percent international. How does the local bank differ from national banks?

Using Xs to represent portfolio holdings: (0.50 - 0.60)2 = 0.0100 (X1j - X1 )2 (0.30 - 0.15)2 = 0.0225 (X2j - X2 )2 (0.20 - 0.05)2 = 0.0225 (X3j - X3 )2 (0.00 - 0.20)2 = 0.0400 (X4j - X4 )2 n



n =4

 = 0.0950

( X ij −X i ) 2

i =1

i =1

n

=

( X ij − X i )2 i =1

n

 = 15.41 percent

The bank’s standard deviation in its loan portfolio allocation is 15.41 percent. This suggests that the bank is different from the national average. Whether it is significantly different cannot be stated without comparing it to other banks.

19.

Over the past 10 years, a bank has experienced the following loan losses on its C&I loans, consumer loans, and total loan portfolio.

Year

C&I Loans

Consumer Loans

Total Loans

2018 2017 2016 2015 2014

0.0080 0.0088 0.0100 0.0120 0.0104

0.0165 0.0183 0.0210 0.0255 0.0219

0.0075 0.0085 0.0100 0.0125 0.0105

7 © 2022 .

2013

0.0084

0.0174

8 © 2022 .

0.0080

2012 2011 2010 2009

0.0072 0.0080 0.0096 0.0144

0.0147 0.0165 0.0201 0.0309

0.0065 0.0075 0.0095 0.0155

Using regression analysis on these historical loan losses, the bank has estimated the following: XC = 0.002 + 0.8XL

and

Xh = 0.003 + 1.8XL

where XC = loss rate in the commercial sector, Xh = loss rate in the consumer (household) sector, and XL = loss rate for its total loan portfolio. a. If the bank’s total loan loss rates increase to 10 percent, what are the expected loss rate increases in the commercial and consumer sectors?

Commercial loan loss rates will increase to 0.002 + 0.8(0.10) = 8.20 percent.

Consumer loan loss rates will increase to 0.003 + 1.8(0.10) = 18.30 percent. b. In which sector should the bank limit its loans and why?

The bank should limit its loans to the consumer sector because the loss rates are systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the commercial sector. For a 10 percent loss rate in the total loan portfolio, the consumer loss rate is expected to be by 18.30 percent, as opposed to only 8.2 percent for the commercial sector.

20.

What reasons did the Federal Reserve Board offer for recommending the use of subjective evaluations of credit concentration risk instead of quantitative models? How did this change in 2006?

The Federal Reserve Board recommended a subjective evaluation of credit concentration risk instead of quantitative models because (a) current methods to identify credit concentrations were not reliable and (b) there was insufficient data to develop reliable quantitative models. This changed in June 2006 as the Bank for International Settlements released guidance on sound credit risk assessment and valuation for loans. The guidance addresses how common data and processes related to loans may be used for assessing credit risk, accounting for loan impairment and determining regulatory capital requirements and is structured around ten principles that fall within two broad categories: i) supervisory expectations concerning sound credit risk assessment and valuation for loans and ii) supervisory evaluation of credit risk assessment for loans, controls and capital adequacy.

21.

What rules on credit concentrations has the National Association of Insurance Commissioners enacted? How are they related to modern portfolio theory?

9 © 2022 .

The NAIC set a maximum limit of 3% that life insurers can hold in securities belonging to a single issuer. Similarly, the limit is 5% for property-casualty (PC) insurers. This forces life insurers to hold a minimum of 33 different securities and PC insurers to hold a minimum of 20 different securities. Modern portfolio theory shows that by holding well-diversified portfolios, investors can eliminate undiversifiable risk and be subject only to market risk. This enables investors to hold portfolios that provide either high returns for a given level of risk or low risks for a given level of returns.

22.

An FI is limited to holding no more than 8 percent of its assets in securities of a single issuer. What is the minimum number of securities it should hold to meet this requirement?

What if the requirements are 2 percent, 4 percent, and 7 percent?

If an FI is limited to holding a maximum of 8 percent of securities of a single issuer, it will be forced to hold 100/8 = 12.5, or 13 different securities.

For 2%, it will be 100/2, or 50 different securities.

For 4%, it will be 100/4, or 25 different securities.

For 7%, it will be 100/7, or 15 different securities.

The questions and problems that follow refer to Appendixes 11A and 11B. Refer to the information in Appendix 11A for problems 23 through 25. Refer to Appendix 11B for problem 26.

23.

From Table 11A-1, what is the probability of a loan upgrade? A loan downgrade?

The probability of an upgrade is 5.95% + 0.33% + 0.02% = 6.30%. The probability of a downgrade is 5.30% + 1.17% + 0.12% = 6.59%. a. What is the impact of a rating upgrade or downgrade?

The effect of a rating upgrade or downgrade will be reflected on the credit-risk spreads or premiums on loans and thus on the implied market value of the loan. A downgrade should cause this credit-risk spread to rise. b. How is the discount rate determined after a credit event has occurred?

The discount rate for each year in the future in which cash flows are expected to be received includes the forward rates from the current Treasury yield curve plus the annual credit spreads for loans of a particular rating class for each year. These credit spreads are determined by observing the spreads of the corporate bond market over Treasury securities. c. Why does the probability distribution of possible loan values have a negative skew?

The negative skew occurs because the probability distribution is non-normal. The potential downside change in a loan’s value is greater than the possible upside change in value.

10 © 2022 .

d. How do the capital requirements of the CreditMetrics approach differ from those of the BIS and Federal Reserve System?

The Fed and the BIS require the capital reserve to be a fixed percentage of the risk-weighted book value of the loan (e.g., 8 percent). Under CreditMetrics each loan is likely to have a different VAR and thus a different implied capital requirement. Further, this required capital is likely to be greater than 8 percent of the risk-weighted book value because of the non-normality of the probability distributions.

24

A five-year fixed-rate loan of $100 million carries a 7 percent annual interest rate. The borrower is rated BB. Based on hypothetical historical data, the probability distribution given below has been determined for various ratings upgrades, downgrades, status quo, and default possibilities over the next year. Information also is presented reflecting the forward rates of the current Treasury yield curve and the annual credit spreads of the various maturities of BBB bonds over Treasuries.

Rating AAA AA A BBB BB B CCC Default

New Loan Value plus Coupon $ $114.82m 114.60m 114.03m

Probability Distribution 0.01% 0.31 1.45 6.05 85.48 5.60 0.90 0.20

Forward Rate Spreads at Time t rt% ϕt% . t 1 3.00% 0.72% 2 3.40 0.96 3 3.75 1.16 4 4.00 1.30

108.55m 98.43m 86.82m 54.12m

a. What is the present value of the loan at the end of the one-year risk horizon for the case where the borrower has been upgraded from BB to BBB? PV =$7m +

$7m

+

1.0372

$7m

$7m

+ 2

(1.0436)

(1.0491)3

+

$107m

=$113.27 million

(1.0530) 4

b. What is the mean (expected) value of the loan at the end of year 1?

Year-end Rating AAA AA A BBB BB B

Probability 0.0001 0.0031 0.0145 0.0605 0.8548 0.056

Value (m of $) $114.82 114.60 114.03 113.27 108.55 98.43

Probability Deviation x Value $0.01 6.76 0.36 6.54 1.65 5.97 6.85 5.21 92.79 0.49 5.51 -9.63 11

© 2022 .

Probability x Deviation Squared 0.0046 0.1325 0.5162 1.6402 0.2025 5.1968

CCC Default

0.009 0.002 1.000

86.82 54.12 Mean =

0.78 -21.24 0.11 -53.94 $108.06m Variance = Standard Deviation = The solution table reveals a value of $108.06 million.

4.0615 5.8197 17.5740 $4.19m

c. What is the volatility of the loan value at the end of year 1?

The volatility or standard deviation of the loan value is $4.19 million. d. Calculate the 5 percent and 1 percent VARs for this loan assuming a normal distribution of values.

The 5 percent VAR is 1.65 x $4.19m = $6.91m.

The 1 percent VAR is 2.33 x $4.19m = $9.76m. e. Estimate the approximate 5 percent and 1 percent VARs using the actual distribution of loan values and probabilities.

5% VAR = 95% of actual distribution = $108.06m - $98.43m = $9.63m 1% VAR = 99% of actual distribution = $108.06m - $86.82m = $21.24m where:

5% VAR is approximated by 0.056 + 0.009 + 0.002 = 0.067 or 6.7 percent, and 1% VAR is approximated by 0.009 + 0.002 = 0.011 or 1.1 percent.

Using linear interpolation, the 5% VAR = $10.65 million and the 1% VAR = $19.31 million.

For the 1% VAR, $19.31m = (1 – 0.1/1.1) x $21.24m. f. How do the capital requirements of the 1 percent VARs calculated in parts (d) and (e) above compare with the capital requirements of the BIS and Federal Reserve System?

The Fed and BIS systems would require 8 percent of the loan value, or $8 million. The 1 percent VAR would require $19.31 million under the approximate method, and $9.76 million (2.33 x $4.19m) in capital under the normal distribution assumption. In each case, the amounts exceed the Fed/BIS amount.

25.

How does the Credit Risk+ model of Credit Suisse Financial Products differ from the CreditMetrics model of J.P. Morgan Chase?

CreditRisk+ attempts to estimate the expected loss of loans and the distribution of these losses with the focus on calculating the required capital reserves necessary to meet these losses. The method assumes that the probability of any individual loan defaulting is random and that the correlation between the defaults on any pair of loan defaults is zero. CreditMetrics focuses on estimating a complete VAR framework.

12 © 2022 .

26.

An FI has a loan portfolio of 10,000 loans of $10,000 each. The loans have a historical average default rate of 4 percent and the severity of loss is 40 cents per dollar. a. Over the next year, what are the probabilities of having default rates of 2, 3, 4, 5, and 8 percent? e−m mn (2.71828) −4 x42 = 0.018316x16 = = 0.1465 = 14.65% Pr obabilityof 2 defaults= n!

2 1x2 Pr obabilityof 3defaults =

e−mmn

=

(2.71828)−4 x43

n!

n Probability

2 14.65%

=

0.018316x16

1x2x3

3 19.54%

4 19.54%

= 0.1465 = 19.54%

6

5 15.63%

8 2.98%

.

b. What would be the dollar loss on the portfolios with default rates of 4 and 8 percent?

Dollar loss of 4 loans defaulting = 4 x 0.40 x $10,000 = $16,000 Dollar loss of 8 loans defaulting = 8 x 0.40 x $10,000 = $32,000 c. How much capital would need to be reserved to meet the 1 percent worst-case loss scenario? What proportion of the portfolio’s value would this capital reserve be?

The probability of 8 defaults is ~3 percent. The probability of 10 defaults is 0.00529 or rounded up to 1 percent. The dollar loss of 10 loans defaulting is $40,000. Thus, a 1 percent chance of losing $40,000 exists.

A capital reserve should be held to meet the difference between the unexpected 1 percent loss rate and the expected loss rate of 4 defaults. This difference is $40,000 minus $16,000 or $24,000. This amount is 0.024 percent of the total portfolio.

13 © 2022 .

Integrated Mini Case: Loan Portfolio Analysis As a senior loan officer at MC Financial Corp, you have a loan application from a firm in the biotech industry. While the loan has been approved on the basis of an individual loan, you must evaluate the loan based on its impact on the risk of the overall loan portfolio. The FI uses the following three methods to assess its loan portfolio risk.

1. Concentration Limits - The FI currently has lent an amount equal to 40 percent of its capital to the biotech industry and does not lend to a firm in any sector that generates losses in excess of 2 percent of capital. The average historical losses in the biotech industry total 5 percent.

Concentration limit = (Maximum loss as a percent of capital) x (1/Loss rate) = 0.02 x 1/0.05 = 40 percent of capital is the maximum amount that can be lent to firms in the biotech sector.

MC Financial already has 40 percent of its capital lent out to the biotech industry. To give out this new loan would put the FI over its concentration limit. Thus, MC Financial should not grant this loan.

2. Loan Volume-Based Model - National and MC Financial’s loan portfolio allocations are as follows.

Allocation of Loan Portfolios in Different Sectors (%) Sectors National MC Financial Commercial 30% 50% Real Estate 50% 35% Consumer 20% 15% MC Financial does not want to deviate from the national average by more than 14.72 percent.

Using Xs to represent portfolio holdings: (X1j - X1 )2 (0.50 - 0.30)2 = 0.0400 14 © 2022 .

(X2j - X2 )2 (X3j - X3 )2

(0.35 - 0.50)2 = 0.0225 (0.15 - 0.20)2 = 0.0025 n=3

n

 ( X ij −X i )

 = 0.0650

2

i =1

i=1 n

=

( X ij − X i )2 i =1

n

 = 14.72 percent

The FI’s standard deviation in its loan portfolio allocation is 14.72 percent. To issue another C&I loan would push MC Financial even further from the national average. Thus, the FI would not want to give out the loan 3. Loan Loss Ratio-Based Model - Based on regression analysis on historical loan losses, the FI estimates the following loan loss ratio models: XC&I = 0.001 + 0.85XL and Xcon = 0.003 + 0.65XL where XC&I = loss rate in the commercial sector, Xcon = loss rate in the consumer (household) sector, XL = loss rate for its total loan portfolio.

MC Financial’s total increase in the loan loss ratio is expected to be 12 percent next year.

Commercial loan loss rates will increase by 0.001 + 0.85(0.12) = 10.30 percent.

Consumer loan loss rates will increase by 0.003 + 0.65(0.12) = 8.10 percent.

MC Financial should limit its loans to the commercial sector because the loss rates are systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the consumer sector. For a 12 percent increase in the total losses in the loan portfolio, the commercial loss rate is expected to increase by 10.30 percent, as opposed to only 8.10 percent for the consumer sector. Thus, MC Financial should not issue this loan.

Should MC Financial Corp. grant this loan?

Even though the loan was approved on an individual loan basis, from an overall loan portfolio perspective, all three models suggest that MC Financial would not want to issue this loan to a firm in the biotech sector.

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Additional Example for Chapter 12 Allocation of Loan Portfolios in Different Sectors (%) National Bank A Bank B

Sectors Commercial Consumer Real Estate

20% 40% 40%

50% 20% 30%

30% 40% 30%

How different are Banks A and B from the national benchmark? When using this example, note that there is an implied assumption that Bank A and B belong to a certain size class or have some common denominator linking them to the national benchmark. If that is the case, then the solution is to estimate the standard deviation.

We use Xs to represent the portfolio concentrations. X1, X2 and X3 are the national benchmark percentages Bank A Bank B 2 2 (X1j - X1 ) (50 - 20) = 900 (30 - 20)2 = 100 (X2j - X2 )2 (20 - 40)2 = 400 (40 - 40)2 = 0 (X3j - X3 )2 (30 - 40)2 = 100 (30 - 40)2 = 100 n

 ( X ij −X i )

2

i =1

n=3

n=3

 =1,400

 = 200

 = 37.42 percent

 = 14.14 percent

i=1

i=1

n

=

( X ij − X i )2 i =1

n

Thus we can see here that Bank A is significantly different from the national benchmark

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Solutions for End-of-Chapter Questions and Problems: Chapter Twelve 1. How does the degree of liquidity risk differ for different types of financial institutions?

Due to the nature of their asset and liability contracts, depository institutions are the FIs most exposed to liquidity risk. Mutual funds, hedge funds, pension funds, and PC insurance companies are the least exposed. In the middle are life insurance companies.

2.

What are the two reasons liquidity risk arises? How does liquidity risk arising from the liability side of the balance sheet differ from liquidity risk arising from the asset side of the balance sheet? What is meant by fire-sale prices?

Liquidity risk occurs because of situations that develop from economic and financial transactions that are reflected on either the asset side of the balance sheet or the liability side of the balance sheet of an FI. Liability side liquidity risk arises from transactions whereby a creditor, depositor, or other claim holder demands cash in exchange for the claim. The withdrawal of funds from a bank is an example of such a transaction. Asset side risk arises from transactions that result in a transfer of cash to some other asset, such as the exercise of a loan commitment or a line of credit.

Another type of asset side liquidity risk arises from the FI’s investment portfolio. During a selloff, liquidity dries up and investment securities can be sold only at fire-sale prices. A fire-sale price refers to the price of an asset that is less than the normal market price because of the need or desire to sell the asset immediately under conditions of financial distress.

3.

What are core deposits? What role do core deposits play in predicting the probability distribution of net deposit drains?

Core deposits are those deposits that will stay with the DI over an extended period of time. These deposits are relatively stable sources of funds and consist mainly of demand, savings, and retail time deposits. Because of their stability, a higher level of core deposits will increase the predictability of forecasting net deposit drains from the DI. 4.

The probability distribution of the net deposit drains of a DI has been estimated to have a mean of 2 percent and a standard deviation of 1 percent. Is this DI increasing or decreasing in size? Explain.

This DI is decreasing in size because less core deposits are being added to the DI than are being withdrawn. On average, the rate of decrease of deposits is 2 percent. If the distribution is normal, we can state with 95 percent confidence that the rate of decrease of deposits will be between 0 percent and 4 percent (i.e., plus or minus two standard deviations).

5.

How is the DI's distribution pattern of net deposit drains affected by the following? a. The holiday season.

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The entire distribution shifts to the right (an increase in the expected amount of withdrawals) as individuals spend more. Moreover, the standard deviation decreases as the distribution narrows.

b. Summer vacations.

The entire distribution shifts to the right (an increase in the expected amount of withdrawals) as individuals spend more. Moreover, the standard deviation decreases as the distribution narrows. c. A severe economic recession.

The entire distribution shifts to the right and may have a positive mean value as withdrawals average more than deposits. However, as the opportunity cost of holding money declines, some depositors may increase their net deposits. The impact will be to widen the distribution. d. Double-digit inflation.

The entire distribution shifts to the right and may have a positive mean value as withdrawals average more than deposits. Inflation may cause a general flight from cash that will cause the distribution to narrow.

6.

What are two ways a DI can offset the liquidity effects of a net deposit drain of funds?

How do the two methods differ? What are the operational benefits and costs of each method?

If the DI has a net deposit drain, it needs to either increase its liabilities (by borrowing funds or issuing equity, i.e., purchased liquidity management) or reduce its assets (i.e., stored liquidity management). An institution can reduce its assets by drawing down on its cash reserves, selling securities, or calling back (or not renewing) its loans. It can increase liabilities by issuing more federal funds, long-term debt, or equity. If a DI offsets the drain by increasing liabilities, the size of the firm remains the same. However, if it offsets the drain by reducing its assets, the size of the firm is reduced. If it has a net negative deposit drain, then it needs to follow the opposite strategy.

The operational benefit of addressing a net deposit drain is to restore the financial stability and health of the DI. However, this process does not come without costs. On the asset side, liquidating assets may occur only at fire-sale prices that will result in realized losses of value.

Further, not renewing loans may result in the loss of profitable relationships that could have negative effects on profitability in the future. On the liability side, entering the borrowed funds market normally requires paying market interest rates that are above those rates that it had been paying on low interest deposits. Further, since most of these funds are not covered by deposit insurance, their availability may be limited should the depository institution incur insolvency difficulties.

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7.

What are two ways a DI can offset the effects of asset-side liquidity risk such as the drawing down of a loan commitment?

A DI can use either purchased liquidity management or stored liquidity management. Purchased liquidity management involves borrowing funds in the money/purchased funds market. Stored liquidity management involves selling cash-type assets, such as Treasury bills, or simply reducing excess cash reserves to the minimum level required to meet regulatory imposed reserve requirements.

8.

A DI with the following balance sheet (in millions) expects a net deposit drain of $15 million.

Assets Liabilities and Equity Cash $10 Deposits $68 Loans 50 Equity 7 Securities 15 Total assets $75 Total liabilities and equity $75 Show the DI's balance sheet if the following conditions occur: a. The DI purchases liabilities to offset this expected drain.

If the DI purchases liabilities, then the new balance sheet is: Cash $10 Deposits $53 Loans 50 Purchased liabilities 15 Securities 15 Equity 7 Total assets $75 Total liabilities and equity $75 b. The stored liquidity management method is used to meet the expected drain.

If the DI liquidates assets to meet the deposit withdrawals, a possible balance sheet may be: Loans $50 Deposits $53 Securities 10 Equity 7 Total assets $60 Total liabilities and equity $60 DIs will most likely use some combination of these two methods.

9.

AllStarBank has the following balance sheet (in millions): Assets Cash Loans Securities Total assets

$30 90 50 $170

Liabilities and Equity Deposits Borrowed funds Equity Total liabilities and equity

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$110 40 20 $170

AllStarBank’s largest customer decides to exercise a $15 million loan commitment. How will the new balance sheet appear if AllStar uses the following liquidity risk strategies? a. Stored liquidity management.

Assets Cash Loans Securities Total assets

$15 105 50 $170

Liabilities and Equity Deposits Borrowed funds Equity Total liabilities and equity

$110 40 20 $170

b. Purchased liquidity management.

Assets Cash Loans Securities Total assets

10.

$30 105 50 $185

Liabilities and Equity Deposits Borrowed funds Equity Total liabilities and equity

$110 55 20 $185

A DI has assets of $10 million consisting of $1 million in cash and $9 million in loans. The DI has core deposits of $6 million, subordinated debt of $2 million, and equity of $2 million. Increases in interest rates are expected to cause a net drain of $2 million in core deposits over the year? a. The average cost of deposits is 6 percent and the average yield on loans is 8 percent.

The DI decides to reduce its loan portfolio to offset this expected decline in deposits.

What will be the effect on net interest income and the size of the DI after the implementation of this strategy?

Assuming that the decrease in loans is offset by an equal decrease in deposits, the change in net interest income = (0.06 – 0.08) x $2 million = -$40,000. The average size of the firm will be $8 million after the drain. b. If the interest cost of issuing new short-term debt is expected to be 7.5 percent, what would be the effect on net interest income of offsetting the expected deposit drain with an increase in interest-bearing liabilities?

Change in net interest income = (0.06 – 0.075) x $2 million = -$30,000. c. What will be the size of the DI after the drain if the DI uses this strategy?

The size of the firm will be $10 million after the drain.

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d. What dynamic aspects of DI management would support a strategy of replacing the deposit drain with interest-bearing liabilities?

Purchasing interest-bearing liabilities may cost significantly more than the cost of replacing the deposits that are leaving the DI. However, using interest-bearing deposits protects the DI from decreasing asset size or changing the composition of the asset side of the balance sheet.

11.

Define each of the following four measures of liquidity risk. Explain how each measure would be implemented and utilized by a DI. a. Financing gap and financing requirement.

The financing gap can be defined as average loans minus average deposits, or alternatively, as negative liquid assets plus borrowed funds. A negative financing gap implies that the DI must borrow funds or rely on liquid assets to fund the non-liquid assets. Thus, the financing requirement can be expressed as the financing gap plus liquid assets. This relationship implies that some level of loans and core deposits as well as some amount of liquid assets determine the need for the DI to borrow or purchase funds. b. Sources and uses of liquidity.

This statement identifies the total sources of liquidity as the amount of cash-type assets that can be sold with little price risk and at low cost, the amount of funds the DI can borrow in the money/purchased funds market, and any excess cash reserves over the necessary reserve requirements. The statement also identifies the amount of each category the DI has utilized. The difference is the amount of liquidity available for the DI. This amount can be tracked on a dayto-day basis. c. Peer group ratio comparisons.

DIs can easily compare their liquidity with peer group institutions by looking at several easy to calculate ratios: borrowed funds to deposits, loans to deposits, core deposits to total assets, and commitments to lend to total assets. High levels of the loan to deposit and borrowed funds to total asset ratios will identify reliance on borrowed funds markets rather than core deposits to fund loans, while heavy amounts of loan commitments to assets may reflect a heavy amount of potential liquidity needs in the future. d. Liquidity index.

The liquidity index measures the amount of potential losses suffered by a DI from a fire-sale of assets compared to a fair market value established under the conditions of normal sale. The lower is the index, the less liquidity the DI has on its balance sheet. The index should always be a value between 0 and 1.

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12.

Plainbank has $10 million in cash and equivalents, $30 million in loans, and $15 in core deposits. a. Calculate the financing gap.

Financing gap = Average loans – Average deposits = $30 million - $15 million = $15 million b. What is the financing requirement?

Financing requirement = Financing gap + Liquid assets = $15 million + $10 million = $25 m c. How can the financing gap be used in the day-to-day liquidity management of the bank?

A rising financing gap on a daily basis over a period of time may indicate future liquidity problems due to increased deposit withdrawals and/or increased exercise of loan commitments.

Sophisticated lenders in the money markets may be concerned about these trends and they may react by imposing higher risk premiums for borrowed funds or stricter credit limits on the amount of funds lent.

13.

A DI has $10 million in T-bills, a $5 million line of credit to borrow in the repo market, and $5 million in excess cash reserves (above reserve requirements) with the Fed. The DI currently has borrowed $6 million in fed funds and $2 million from the Fed’s discount window to meet seasonal demands. a. What is the DI’s total available (sources of) liquidity?

The DI’s available sources of liquidity are $10m + $5m + $5m = $20 million. b. What is the DI’s current total uses of liquidity?

The DI’s current uses of liquidity are $6m + $2m = $8 million. c. What is the net liquidity of the DI? The DI’s net liquidity is $20m - $8m = $12 million. d. What conclusions can you derive from the result?

The net liquidity of $12 million suggests that the DI can withstand unexpected withdrawals of $12 million without having to reduce its less liquid assets at potential fire-sale prices.

14.

A DI has the following assets in its portfolio: $10 million in cash reserves with the Fed, $25 million in T-bills, and $65 million in mortgage loans. If the DI has to liquidate the assets today, it will receive only $98 per $100 of face value of the T-bills and $90 per $100 6 © 2022

of face value of the mortgage loans. Liquidation at the end of one month (closer to maturity) will produce $100 per $100 of face value of the T-bills and $97 per $100 of face value of the mortgage. Calculate the one-month liquidity index for this DI using the preceding information.

I = ($10m/$100m)(1.00/1.00) + ($25m/$100m)(0.98/1.00) + ($65m/$100m)(0.90/0.97) = 0.948 15.

A DI has the following assets in its portfolio: $20 million in cash reserves with the Fed, $20 million in T-bills, and $50 million in mortgage loans. If the assets need to be liquidated at short notice, the DI will receive only 99 percent of the fair market value of the T-bills and 90 percent of the fair market value of the mortgage loans. Liquidation at the end of one month (closer to maturity) will produce $100 per $100 of face value of the T-bills and the mortgage loans. Calculate the liquidity index using the above information.

I = ($20m/$90m)(1.00/1.00) + ($20m/$90m)(0.99/1.00) + ($50m/$90m)(0.90/1.00) = 0.942 16.

Conglomerate Corporation has acquired Acme Corporation. To help finance the takeover, Conglomerate will liquidate the overfunded portion of Acme’s pension fund. The face values and current and one-year future liquidation values of the assets that will be liquidated are given below: Liquidation Values Asset Face Value t=0 t = 1 year IBM stock $10,000 $9,900 $10,500 GE bonds 5,000 4,000 4,500 Treasury securities 15,000 13,000 14,000

Calculate the one-year liquidity index for these securities.

I = ($10,000/$30,000)($9,900/$10,500) + ($5,000/$30,000)($4,000/$4,500) + ($15,000/$30,000)($13,000/$14,000) = 0.927 17.

Central Bank has the following balance sheet (in millions of dollars).

Liquidity Assets level Cash $ 15 Level 1 Deposits at the Fed 30 Level 1 Treasury bonds 145 Level 1 Qualifying marketable securities 50 Level 1 GNMA bonds 60 Level 2A Loans to AA- corporations 540 Level 2A Mortgages 285 Premises 40 7 © 2022

Liabilities and Equity Stable retail deposits $190 Less stable retail deposits 70 CDs maturing in 6 months 100 Unsecured wholesale funding from: Stable small business deposits 125 Less stable small business deposits 100 Nonfinancial corporates 450 Equity 130

Run-off factor 3% 10 0 5 10 75

Total

$1,165

Total

$1,165

Cash inflows over the next 30 days from the bank’s performing assets are $7.5 million.

Calculate the LCR for Central Bank.

The liquidity coverage ratio for Central Bank is calculated as follows: Level 1 assets = $15 + $30 + $145 + $50 = Level 2A assets = ($60 + $540) x 0.85 = $510.00 Capped at 40% of high-quality liquid assets = $240 x 0.40 = Stock of high-quality liquid assets Cash outflows: Stable retail deposits Less stable retail deposits CDs maturing in 6 months Stable small business deposits Less stable small business deposits Non-financial corporates Total cash outflows over next 30 days

240 96 $336

$190 x 0.03 = $5.70 $70 x 0.10 = 7.00 $100 x 0.00 = 0.00 $125 x 0.05 = 6.25 $100 x 0.10 = 10.00 $450 x 0.75 = 337.50 $366.45

Total cash inflows over next 30 days Total net cash outflows over next 30 days

7.50 $358.95

Liquidity coverage ratio = $336m/$358.95m = 93.61%. The bank is not in compliance with liquidity requirements based on the LCR. 18.

WallsFarther Bank has the following balance sheet (in millions of dollars).

Assets Cash $ 12 Deposits at the Fed 19 Treasury securities 125 GNMA securities 94 Loans to AA rated corporations 138 Loans to BB rated corporations 106 Premises 20 Total $514

Liquidity level Level 1 Level 1 Level 1 Level 2A Level 2A Level 2B

Liabilities and Equity Stable retail deposits $ 55 Less stable retail deposits 20 Unsecured wholesale funding from: Stable small business deposits 80 Less stable small business deposits 49 Nonfinancial corporates 250 Equity 60 Total $514

Cash inflows over the next 30 days from the bank’s performing assets are $5.5 million.

Calculate the LCR for WallsFarther Bank.

The liquidity coverage ratio for WallsFarther Bank is calculated as follows: 8 © 2022

Run-off factor 3% 10 5 10 75

Level 1 assets = $12 + $19 + $125 = Level 2A assets = ($94 + $138) x 0.85 = $197.20 Capped at 40% of high-quality liquid assets = $156 x 0.40 = Stock of high-quality liquid assets Level 2B assets = $106 x 0.50 = $53.00 40% cap on Level 2 assets already met Stock of high-quality liquid assets Cash outflows: Stable retail deposits $55 x 0.03 = $ 1.65 Less stable retail deposits $20 x 0.10 = 2.00 Stable small business deposits $80 x 0.05 = 4.00 Less stable small business deposits $49 x 0.10 = 4.90 Non-financial corporates $250 x 0.75 = 187.50 Total cash outflows over next 30 days $200.05 Total cash inflows over next 30 days Total net cash outflows over next 30 days

156 62.4 $218.4 0.0 $218.4

5.50 $194.55

Liquidity coverage ratio = $218.4m/$194.55m = 112.26%. The bank is in compliance with liquidity requirements based on the LCR. 19.

FirstBank has the following balance sheet (in millions of dollars).

Required stable Available stable Funding funding Assets factor Liabilities and Equity factor Cash $ 12 0% Stable retail deposits $ 55 95% Deposits at the Fed 19 0 Less stable retail deposits 20 90 Treasury securities 125 5 Unsecured wholesale funding from: GNMA securities 94 15 Stable small business deposits 80 95 Loans to A rated corporations 138 65 Less stable small business deposits 49 90 (maturity > 1 year) Nonfinancial corporates 250 50 Loans to B rated corporations 106 50 Equity 60 100 (maturity < 1 year) Total $514 Premises 20 100 Total $514 Calculate the NSFR for FirstBank.

The net stable funding ratio for FirstBank is calculated as follows: Available amount of stable funding = $60 x 1.00 + ($55 + $80) x 0.95 + ($20 + $49) x 0.90 + $250 x 0.50 = $375.35m Required amount of stable funding = ($12 + $19) x 0.00 + $125 x 0.05 + $94 x 0.15 + $138 x 0.65 + $106 x 0.50 + $20 x 1.00 = $183.05m 9 © 2022

Net stable funding ratio = $375.35m/$183.05m = 205.05%. The bank is in compliance with liquidity requirements based on the NSFR. 20.

BancTwo has the following balance sheet (in millions of dollars).

Required stable Available stable funding funding Assets factor Liabilities and Equity factor Cash $ 20 0% Stable retail deposits $190 95% Deposits at the Fed 30 0 Less stable retail deposits 70 90 Treasury bonds 145 5 CDs maturing in 6 months 100 0 Qualifying marketable securities 50 0 Unsecured wholesale funding from: (maturity < 1 year) Stable small business deposits 125 95 FNMA bonds 60 15 Less stable small business deposits 100 90 Loans to AA- corporations 540 65 Nonfinancial corporates 450 50 (maturity > 1 year) Equity 130 100 Mortgages (unencumbered) 285 65 Total $1,165 Premises 35 100 Total $1,165 Calculate the NSFR for BancTwo. The net stable funding ratio for BancTwo is calculated as follows: Available amount of stable funding = $130 x 1.00 + ($190 + $125) x 0.95 + ($70 + $100) x 0.90 + $450 x 0.50 = $807.25m Required amount of stable funding = ($20 + $30) x 0.00 + $145 x 0.05 + $60 x 0.15 + ($540 + $285) x 0.65 + $35 x 1.00 = $587.50m Net stable funding ratio = $807.25m/$587.50m = 137.40%. The bank is in compliance with liquidity requirements based on the NSFR. 21.

How can an FI’s liquidity plan help reduce the effects of liquidity shortages? What are the components of a liquidity plan?

A liquidity plan requires forward planning so that an optimal mix of funding can be implemented to reduce costs and unforeseen withdrawals. In general, a plan could incorporate the following: (a)

Assigning a team that will take charge in the event of a liquidity crisis. Set the delineation of managerial details and responsibilities. Responsibilities are assigned to key management personnel should a liquidity crisis occur.

(b)

Identifying the account holders that will most likely withdraw funds in the event of a crisis.

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(c)

Estimating the size of the run-offs and the sources of borrowing to stem the run-offs.

(d)

Establishing maximum limits for borrowing by subsidiaries and affiliates, including interaffiliate loans, and the maximum risk premium to be paid during crisis borrowing.

(e)

Specifying the sequencing of asset disposal in the event of a crisis.

Planning will ensure an orderly procedure to stem the rush of withdrawals and avert a total breakdown during a crisis. This is very important for firms that rely on deposits or short-term funds as a source of borrowing because of the difficulty in rolling over debt in periods of crisis.

22.

What is a bank run? What are some possible withdrawal shocks that could initiate a bank run? What feature of the demand deposit contract provides deposit withdrawal momentum that can result in a bank run?

A bank run is a sudden and unexpected increase in deposit withdrawals from a DI. Bank runs can be triggered by several economic events including (a) concerns about solvency relative to other DIs, (b) failure of related DIs, and (c) sudden changes in investor preferences regarding the holding of nonbank financial assets. The first-come, first-serve (full pay or no pay) nature of a demand deposit contract encourages priority positions in any line for payment of deposit accounts. Thus, even though money may not be needed, customers have an incentive to withdraw their funds.

23.

The following is the balance sheet of a DI (in millions): Assets Cash $ 2 Loans 50 Premises and equipment 3 Total $55

Liabilities and Equity Demand deposits $50 Equity Total

5 $55

The asset-liability management committee has estimated that the loans, whose average interest rate is 6 percent and whose average life is three years, will have to be discounted at 10 percent if they are to be sold in less than two days. If they can be sold in four days, they will have to be discounted at 8 percent. If they can be sold later than a week, the DI will receive the full market value. Loans are not amortized; that is, principal is paid at maturity. a. What will be the price received by the DI for the loans if they have to be sold in two days. In four days?

Price of loan = PVAn=3,k=10($3m) + PVn=3, k=10($50m) = $45.03m if sold in two days.

Price of loan = PVAn=3,k=8($3m) + PVn=3, k=8($50m) = $47.42m if sold in four days.

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b. In a crisis, if depositors all demand payment on the first day, what amount will they receive? What will they receive if they demand to be paid within four days? Assume no deposit insurance.

If depositors demand to withdraw all their money on the first day, the DI will have to dispose of its loans at fire-sale prices of $45.03 million. With its $2 million in cash, it will be able to pay depositors on a first-come basis until $47.03 million has been withdrawn. The rest will have to wait until liquidation to share the remaining proceeds.

Similarly, if the run takes place over a four-day period, the DI may have more time to dispose of its assets. This could generate $47.42 million. With its $2 million in cash it would be able to satisfy on a first-come basis withdrawals up to $49.42 million.

24.

What government safeguards are in place to reduce liquidity risk for DIs?

Deposit insurance and the Federal Reserve’s discount window both help in the event of a liquidity drain and both help to prevent liquidity drains from occurring.

25.

What are the levels of defense against liquidity risk for a life insurance company? How does liquidity risk for a property-casualty insurer differ from that for a life insurance company?

In the normal course of business the amount of premium income and returns on the asset portfolio provide an adequate cushion against liquidity risk for life insurance companies. As additional policies are surrendered, the insurance company may need to sell some of the relatively liquid assets such as government bonds. In the case of extreme liquidity pressures, the company may need to begin to liquidate the less-liquid assets in the portfolio, possibly at distressed prices.

Property-casualty insurance covers short-term contingencies, and thus the assets of PC insurers generally are more short-term than for life insurance companies, and the policy premium adjustments come at shorter intervals. As a result, although the degree and timing of contingency payout is more uncertain for PC companies, the flexibility to deal with liquidity pressures is better.

26.

How is the liquidity problem faced by investment funds different from that faced by DIs and insurance companies? How does the liquidity risk of an open-end mutual fund compare with that of a closed-end fund?

In the case of a liquidity crisis in DIs and insurance firms, there are incentives for depositors and policyholders to withdraw their money or cash in their policies as early as possible. Latecomers will be penalized because the financial institution may have insufficient liquid assets to cover their cash needs. They will have to wait until the institution sells its assets at fire-sale prices, resulting in a lower payout. In the case of investment funds, the net asset value for all shareholders is lowered or raised as the market value of assets change, so that everybody will 12 © 2022

receive the same price if they decide to withdraw their funds. Hence, the incentive to engage in a run is minimized.

Closed-end funds issue a fixed number of shares as liabilities. Unless the issuing fund chooses to repurchase them, the number of outstanding shares does not change. Open-end funds issue an unlimited supply of shares to investors. Open-end funds must also stand ready to buy back previously issued shares from investors at the current market price for the fund’s shares. Thus, at a given market price, P, the supply of open-end fund shares is perfectly elastic.

27.

A mutual fund has the following assets in its portfolio: $40 million in fixed-income securities and $40 million in stocks at current market values. In the event of a liquidity crisis, the fund can sell the assets at a 96 percent of market value if they are disposed of in two days. The fund will receive 98 percent if the assets are disposed of in four days. Two shareholders, A and B, own 5 percent and 7 percent of equity (shares), respectively. a. Market uncertainty has caused shareholders to sell their shares back to the fund. What will the two shareholders receive if the mutual fund must sell all of the assets in two days? In four days?

Value of fixed-income securities if sold in two days $40m x 0.96 = $38.4m Value of stocks if sold in two days $40m x 0.96 = $38.4m Total $76.8m

Shareholder A will receive $76.8m x 0.05 = $3.84m down from the current value of $4.00m.

Shareholder B will receive $76.8m x 0.07 = $5.376m down from the current value of $5.60m.

Value of fixed-income securities if sold in four days $40m x 0.98 = $39.2m Value of stocks if sold in four days $40m x 0.98 = $39.2m Total $78.4m Shareholder A will receive $78.4m x 0.05 = $3.92m down from the current value of $4.00m.

Shareholder B will receive $78.4m x 0.07 = $5.488m down from the current value of $5.60m. b. How does this situation differ from a bank run? How have bank regulators mitigated the problem of bank runs?

This differs from a run on a bank in that in the mutual fund the claimants of the assets all receive the same amount, as a percentage of their investments. In the case of bank runs, the first to withdraw receives the full amount, leaving the likelihood that some depositors may not receive any money at all. One way of mitigating this problem is for regulators to offer deposit insurance such as that provided by the FDIC. This reduces the incentive to engage in runs.

28.

A mutual fund has $1 million in cash and $9 million invested in securities. It currently has 1 million shares outstanding.

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a. What is the net asset value (NAV) of this fund?

NAV= Market value of shares/number of shares = $10m/1m = $10 per share b. Assume that some of the shareholders decide to cash in their shares of the fund. How many shares at its current NAV can the fund take back without resorting to a sale of assets?

At the current NAV, it can absorb up to $1 million, or 100,000 shares ($1 million/$10 per share). c. As a result of anticipated heavy withdrawals, the fund sells 10,000 shares of IBM stock currently valued at $40. Unfortunately, it receives only $35 per share. What is the net asset value after the sale? What are the cash assets of the fund after the sale?

The loss by selling 10,000 shares of IBM at $35 instead of $40 = -$5 x 10,000 = -$50,000.

New NAV = $9,950,000 /1m = $9.95 Cash = $1 million + ($35 x 10,000) = $1.35 million and $8.60 million in securities. d. Assume that after the sale of IBM shares, 100,000 shares are sold back to the mutual fund. What is the current NAV? Is there a need to sell more securities to meet this redemption?

If 100,000 shares are redeemed, it needs to pay $9.95 x 100,000 = $995,000. Its NAV will remain the same, i.e., ($9,950,000 - $995,000)/900,000 = $9.95. The mutual fund does not need to sell any extra shares since it has $1.35 million in cash to pay the $995,000.

29. Go to J.P. Morgan Chase’s website (www.jpmorganchase.com) and find the latest Sources and Uses of Funds Statement. How have the sources and uses changed since March 2015 (as shown in Appendix 12A)?

To get the Sources and Uses of Funds Statements, use the following steps. Click on “INVESTOR RELATIONS,” then on “Financial Information.” Click on “SEC Filings” and then on “10-Q.” Click on the PDF symbol of the latest date and this will download a file that contains the Sources and Uses of Funds Statement (listed as the “Consolidated statements of cash flows”).

Changes in the sources and uses of funds since March 2015 will vary depending on the time frame used.

Integrated Mini Case: Measuring Liquidity Risk A depository institution (DI) has the following balance sheet (USD millions): Assets Cash

Liabilities & Equity 9 Equity 14 © 2022

5

Loans Securities Other assets Total

Deposits 90 Purchased funds 26 Other liabilities 10 Total 135

75 50 5 135

The DI’s securities portfolio includes $16 million in Treasury-bills (T-bills) and $10 million in GNMA securities (Government National Mortgage Association). The DI has a $20 million line of credit to borrow in the repo market and $5 million in excess cash reserves (above reserve requirements) with the Fed. The DI currently has borrowed $22 million in Fed funds and $18 million from the Fed discount window to meet seasonal demands.

1. What is the DI’s total sources of liquidity?

The DI’s available resources for liquidity purposes are $16 million + $10 million + $9 million + $20 million + $5 million = $60 million 2. What is the DI’s total uses of liquidity?

The DI’s current use of liquidity is $22 million + $18 million = $40 million 3. What is the net liquidity of the DI? The DI’s net liquidity is $60 million – $40 million = $20 million 4. What does the net liquidity figure imply?

The net liquidity implies that the DI can withstand $20 million unexpected withdrawals without having to resort to potential fire-sale prices of its less liquid assets.

5. Calculate the financing gap.

Financing gap = Average loans – Average deposits = $90 million - $75 million = $15 million 6. What is the financing requirement?

Financing requirement = Financing gap + Liquid assets Financing gap + Liquid assets = $15 + $9 + $26 = $50 million

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7. The DI expects a net deposit drain of $20 million. Show the DI's balance sheet if the following conditions occur: a) The DI purchases liabilities to offset this expected drain. b) The stored liquidity management method is used to meet the expected drain (the DI does not want the cash balance to fall below $5 million, and securities can be sold at their fair value). a. The DI purchases liabilities to offset this expected drain.

If the DI purchases liabilities, then the new balance sheet is: Assets Cash Loans Securities Other assets Total

Liabilities & Equity 9 90 26 10 135

Equity Deposits Purchased funds Other liabilities Total

5 55 70 5 135

b. The stored liquidity management method is used to meet the expected drain (the DI does not want the cash balance to fall below $5 million, and securities can be sold at their fair value).

If the DI uses reserve asset adjustment, a possible balance sheet may be: Assets Cash Loans Securities Other assets Total

5 90 10 10 115

Liabilities & Equity Equity Deposits Purchased funds Other liabilities Total

5 55 50 5 115

8. In the event of an unexpected and severe drain on deposits in the next 3 and 10 days, the DI will liquidate assets in the following manner:

Asset Cash T-bills GNMAs Loans

Liquidation Values ($ millions) Fair value t=3 9 9 16 14 10 8 90 60 16 © 2022

t = 10 9 15.5 9 70

Calculate the 3-day and 10-day liquidity index for the DI. I3-day = ($9/$130)($9/$9) + ($16/$130)($14/$16) + ($10/$130)($8/$10) + ($90/$130)($60/$90) = 0.700 I10-day = ($9/$130)($9/$9) + ($16/$130)($15.5/$16) + ($10/$130)($9/$10) + ($90/$130)($70/$90) = 0.796

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Solutions for End-of-Chapter Questions and Problems: Chapter Thirteen 1.

What are four FX risks faced by FIs?

Four risks include (1) trading in foreign securities, (2) making foreign currency loans, (3) issuing foreign currency-denominated debt, and (4) buying foreign currency-issued securities.

2.

What is the spot market for FX? What is the forward market for FX? What is the position of being net long in a currency?

The spot market for foreign exchange involves transactions for immediate settlement, or delivery, of a currency, while the forward market involves agreements to settle, or deliver, a currency at a later time for a price or exchange rate that is determined at the time the agreement is reached. The net exposure of a foreign currency is the net foreign asset position plus the net foreign currency position. Net long in a currency means that the amount of foreign assets exceeds the amount of foreign liabilities.

3. Refer to Table 13-1. a.

What was the spot exchange rate of Canadian dollars for U.S. dollars on June 15, 2015?

The spot exchange rate of Canadian dollars for U.S. dollars was 1.2327 on June 15, 2015. b.

What was the six-month forward exchange rate of Japanese yen for U.S. dollars on June 15, 2015?

The six-month forward exchange rate of Japanese yen for U.S. dollars was 123.3734 on June 15, 2015. c.

What was the three-month forward exchange rate of U.S. dollars for Swiss francs on June 15, 2015?

The three-month forward exchange rate of U.S. dollars for Swiss francs was 1.0799 on June 15, 2015.

4.

Refer to Table 13-1. a.

On May 15, 2015, you purchased a British pound-denominated CD by converting $1 million to pounds at a rate of 0.6435 pounds for U.S. dollars. It is now June 15, 2015. Has the U.S. dollar appreciated or depreciated in value relative to the pound?

The exchange rate of British pounds for U.S. dollars on June 15, 2015 was 0.6409. The U.S. dollar has depreciated in value relative to the pound. b.

Using the information in part (a), what is your gain or loss on the investment in the CD? Assume no interest was been paid on the CD. 1 © 2022

Initial investment was $1 million x 0.6435 = ₤643,500 pounds.

Exchanging the funds back to dollars on June 15, 2015 you will have ₤643,500 pounds / 0.6409 = $1,004,057 Your gain is $1,004,057 - $1,000,000 = $4,057.

5.

On May 15, 2015, the exchange rate of U.S. dollars for Canadian dollars was 0.8095. It is now June 15, 2015. A U.S. made Chevrolet Tahoe costs $65,000 over the entire period.

Has the U.S. dollar appreciated or depreciated in value relative to the pound? Is it cheaper or more costly for a Canadian citizen to buy the car (converting pounds into U.S. dollars) on June 15, 2015? What is the Canadian citizen’s C$ gain or loss on the purchase of the car if he waits to buy on June 15?

The exchange rate of Canadian pounds for U.S. dollars on June 15, 2015 was 0.8113. The U.S. dollar has depreciated in value relative to the pound.

Purchase price on May 15: the Canadian citizen must needs $65,000/0.8095 = C$80,296 to purchase the Tahoe.

Purchase price on June 15: the Canadian citizen must needs $65,000/0.8113 = C$80,118 to purchase the Tahoe.

As the dollar depreciates relative to the Canadian dollar, the U.S. made car has become cheaper for the Canadian citizen to buy. The gain from waiting (from the depreciation of the U.S. dollar relative to the Canadian dollar) is C$80,296 - C$80,118 = C$178 6.

On May 20, 2015, the exchange rate of U.S. dollars for Australian dollars was 0.7794. It is now June 15, 2015. A U.S. made big screen TV costs $3,500 over the entire period.

Has the U.S. dollar appreciated or depreciated in value relative to the Australian dollars?

Is it cheaper or more costly for an Australian citizen to buy the TV (converting Australian dollars into U.S. dollars) on June 15, 2015? What is the Australian citizen’s A$ gain or loss on the purchase of the TV if she waits to buy on June 15?

The exchange rate of Australian dollars for U.S. dollars on June 15, 2015 was 0.7766. The U.S. dollar has appreciated in value relative to the Australian dollar.

Purchase price on May 15: the Australian citizen must needs $3,500/0.7794 = A$4,491 to purchase the TV. Purchase price on June 15: the Australian citizen must needs $3,500/0.7766 = A$4,507 to purchase the TV. As the dollar appreciates relative to the Australian pound, the U.S. made TV has become more expensive for the Australian citizen to buy. The loss from waiting (from the appreciation of the U.S. dollar relative to the Australian dollar) is A$4,491 - A$4,507 = -A$16 7.

On June 15, 2015, you convert $500,000 U.S. dollars to Japanese yen in the spot foreign exchange market and purchase a one-month forward contract to convert yen into dollars.

2 © 2022

How much will you receive in U.S. dollars at the end of the month? Use the data in Table 13-1 for this problem.

At the beginning of the month you convert $500,000 to yen at a rate of 123.4100 yen per dollar, or you will have 500,000 x 123.4100 = ¥61,705,000.

The one-month forward rate for the U.S. dollar for Japanese yen on June 15, 2015 was 0.0081.

So, at the end of the month you will convert ¥61,705,000 to dollars at 123.4035 yen per dollar or you will have ¥61,705,000 / 123.4035 = $500,026.34 8.

X-IM Bank has ¥14 million in assets, ¥23 million in liabilities, and has sold ¥8 million in foreign currency trading. What is the net exposure for X-IM? For what type of exchange rate movement does this exposure put the bank at risk?

The net exposure would be ¥14 million – ¥23 million – ¥8 million = - ¥17 million. This negative exposure puts the bank at risk of an appreciation of the yen against the dollar. A stronger yen means that repayment of the net position would require more dollars.

9.

What two factors directly affect the profitability of an FI’s position in a foreign currency?

The profitability is a function of the size of the net exposure and the volatility of the foreign exchange rate.

10.

The following are the foreign currency positions of an FI, expressed in the foreign currency.

Currency Swiss franc (SFr) British pound (£) Japanese yen (¥)

Assets Liabilities SFr116,171 SFr46,468 £30,488 £13,415 ¥9,252,406 ¥3,700,962

FX Bought SFr9,294 £9,146 ¥1,480,385

FX Sold SFr13,941 £12,195 ¥10,856,156

The exchange rate of dollars per SFrs is 1.0760, of dollars per British pounds is 1.6400, and of dollars per yen is 0.0081060.

The following are the foreign currency positions converted to dollars.

Currency Swiss franc (SF) British pound (£) Japanese yen (¥)

Assets $125,000 $50,000 $75,000

Liabilities $50,000 $22,001 $30,000

FX Bought $10,000 $14,999 $12,000

FX Sold $15,000 $20,000 $88,000

a. What is the FI’s net exposure in Swiss francs stated in SFr and in $s?

Net exposure in stated in SFrs = SFr116,171 – SFr46,468 + SFr9,294 - SFr13,941 = SFr65,056 Net exposure in stated in $s = $125,000 - $50,000 + $10,000 - $15,000 = $70,000 3 © 2022

b. What is the FI’s net exposure in British pounds stated in £ and in $s?

Net exposure in £ = £30,488 - £13,415 + £9,146 - £12,195= £14,024 Net exposure in $ = $50,000 - $22,001 + $15,000 - $20,000 = $22,999 c. What is the FI’s net exposure in Japanese yen stated in ¥s and in $s?

Net exposure in ¥ = ¥9,252,406 - ¥3,700,962 + ¥1,480,385 - ¥10,856,156= - ¥3,824,328 Net exposure in $ = $75,000 - $30,000 + $12,000 - $88,000 = -$31,000 d. What is the expected loss or gain if the SF exchange rate appreciates by 1 percent?

State you answer in SFs and $s.

If assets are greater than liabilities, then an appreciation of the foreign exchange rates will generate a gain = SFr65,056 x 0.01 = SFr651, or $70,000 x 0.01 = $700. e. What is the expected loss or gain if the £ exchange rate appreciates by 1 percent? State you answer in £s and $s.

Gain = £14,024 x 0.01 = $140, or $22,999 x 0.01 = $230 f. What is the expected loss or gain if the ¥ exchange rate appreciates by 2 percent? State you answer in ¥s and $s.

Loss = - ¥3,824,328 x 0.02 = -$76,487 or -$31,000 x 0.02 = -$620 11.

On June 14, 2015, a U.S. FI has a net exposure to Swiss francs of SFr5,500,000. The exchange rate of U.S. dollars for Swiss francs was 1.0955. It is now June 15, 2015.

Calculate the FI’s dollar loss/gain for this shock to the US$/SFr exchange rate.

The exchange rate of Swiss francs for U.S. dollars on June 15, 2015 was 1.0761. The U.S. dollar has appreciated in value relative to the Swiss francs (or the Swiss francs as depreciated relative to the U.S. dollar).

The value of the FI’s Swiss francs position on June 14 is SFr5,500,000 x 1.0955 = $6,025,250.

The value of the FI’s Swiss francs position on June 15 is SFr5,500,000 x 1.0761 = $5,918,550.

Thus, the loss from the net long position in Swiss francs (and the depreciation of the Swiss francs relative to the U.S. dollar) is $5,918,550 - $6,025,250 = -$106,700.

Or, the U.S. FI’s dollar loss/gain in Swiss francs is: [SFr5,500,000] x (1.0761 - 1.0955) = -$106,700 12.

On June 14, 2015, a U.S. FI has a net exposure to Euros of -€7,500,000. The exchange rate of U.S. dollars for Euros was 1.1045. It is now June 15, 2015. Calculate the FI’s dollar loss/gain this shock to the US$/€ exchange rate.

4 © 2022

The exchange rate of Euros for U.S. dollars on June 15, 2015 was 1.1285. The U.S. dollar has depreciated in value relative to the Euro (or the Euro as appreciated relative to the U.S. dollar).

The U.S. dollar value of the FI’s Euro position on June 14 is -€7,500,000 x 1.1045 = -$8,283,750.

The U.S. dollar value of the FI’s Euro position on June 15 is -€7,500,000 x 1.1285 = -$8,463,750.

Thus, the loss from the net short position in Euros (and the appreciation of the Euro relative to the U.S. dollar) is -$8,463,750 – (-$8,283,750) = -$180,000.

Or, the U.S. FI’s dollar loss/gain in Euros is: [-€7,500,000] x (1.1285 - 1.1045) = -$180,000 13.

What are the four FX trading activities undertaken by FIs? How do FIs profit from these activities?

The four areas of FX activity undertaken by FIs are either for their customer’s accounts or for their own proprietary trading accounts. They involve the purchase and sale of FX in order to (a) complete international commercial transactions, (b) invest abroad in direct or portfolio investments, (c) hedge outstanding currency exposures, and (d) speculate against movements in currencies. Most FIs earn commissions on transactions made on behalf of their customers. If the FIs are market makers in currencies, they make their profits on the bid-ask spread.

14.

City Bank issued $200 million of one-year CDs in the United States at a rate of 6.50 percent. It invested part of this money, $100 million, in the purchase of a one-year bond issued by a U.S. firm at an annual rate of 7 percent. The remaining $100 million was invested in a one-year Brazilian government bond paying an annual interest rate of 8 percent. The exchange rate at the time of the transaction was Brazilian real 0.50/$1. a. What will be the net return on this $200 million investment in bonds if the exchange rate between the Brazilian real and the U.S. dollar remains the same?

Brazilian bonds issued in reals = $100m/0.50 = Real 200m Cost of funds

=

Return on U.S. loan = Return on Brazilian bond = Total interest earned

0.065 x $200 million

= $13,000,000

0.07 x $100 million (0.08 x Real 200m) x 0.50

= $ 7,000,000 = $ 8,000,000 = $15,000,000

Net return on investment = ($15 million - $13 million)/$200 million = 1.00 percent. b. What will be the net return on this $200 million investment if the exchange rate changes to real 0.4167/$1?

Cost of funds

=

0.065 x $200 million 5 © 2022

= $13,000,000

Return on U.S. loan = 0.07 x $100 million = $ 7,000,000 Return on Brazilian bond = (0.08 x Real 200m) x 0.4167 = $ 6,667,200 Total interest earned = $13,667,200 Net return on investment = $13,666,667 - $13,000,000/$200,000,000 = 0.33 percent.

Consideration should be given to the fact that the Brazilian bond was for Real200 million. Thus, at maturity the bond will be paid back for Real200 million x 0.4167 = $83,340,000. Therefore, the strengthening dollar will have caused a loss in capital ($16,660,000) that far exceeds the interest earned on the Brazilian bond. Including this capital loss, the net return on investment is: Net return on investment = ($13,666,667 - $13,000,000 - $16,666,667))/$200,000,000 = -8% c. What will be the net return on this $200 million investment if the exchange rate changes to real 0.625/$1?

Cost of funds

=

0.065 x $200 million

= $13,000,000

Return on U.S. loan = 0.07 x $100 million = $ 7,000,000 Return on Brazilian bond = (0.08 x Real 200m) x 0.625 = $10,000,000 Total interest earned = $17,000,000 Net return on investment = $17,000,000 - $13,000,000/$200,000,000 = 2.00 percent.

Consideration should be given to the fact that the Brazilian bond was for Real200 million. Thus, at maturity the bond will be paid back for Real200 million x 0.625 = $125,000,000. Therefore, the strengthening real will have caused a gain in capital of $25,000,000 in addition to the interest earned on the Brazilian bond. Including this capital loss, the net return on investment is: Net return on investment = ($17,000,000 - $13,000,000 + $25,000,000)/$200,000,000 = 14.50% 15.

Sun Bank USA purchased a €16 million one-year euro loan that pays 12 percent interest annually. The spot rate of U.S. dollars per euro is 1.25. Sun Bank has funded this loan by accepting a British pound-denominated deposit for the equivalent amount and maturity at an annual rate of 10 percent. The current spot rate of U.S. dollars per British pound is 1.60. a. What is the net interest income earned in dollars on this one-year transaction if the spot rates of U.S. dollars per euro and U.S. dollars per British pound at the end of the year are 1.35 and 1.70? What is the net return on the loan?

Loan amount = €16 million x 1.25 = $20.0 million Deposit amount = $20.0m/1.60 = £12,500,000 Interest income at the end of the year = €16m x 0.12 = €1.92m x 1.35 = $2,592,000 Interest expense at the end of the year = £12,500,000 x 0.10 = £1,250,000 x 1.70 = $2,125,000 Net interest income = $2,592,000 - $2,125,000 = $290,000 6 © 2022

Net return on loan = $290,000/$20,000,000 = 1.45% b. What should be the spot rate of U.S. dollars per British pound at the end of the year in order for the bank to earn a net return on the loan of 4 percent?

A net return on the loan of 4 percent would imply $20,000,000 x 0.04 = $800,000.

The net cost of deposits should be $2,592,000 - 800,000 = $1,792,000.

Pound rate = $1,792,000/£1,250,000 = $1.4336/£1.

Thus, the pound should be selling at $1.4336/£1 in order for the bank to earn 4 percent. c. Does your answer to part (b) imply that the dollar should appreciate or depreciate against the pound?

The dollar should appreciate against the pound. Each pound gives fewer dollars. d. What is the total effect on net interest income and principal of this transaction given the end-of-year spot rates in part (a)?

Interest income and loan principal at year-end = (€16m x 1.12) x 1.35 = $24,192,000 Interest expense and deposit principal at year-end = (£12.5m x 1.10) x 1.70 = $23,375,000 Total income = $24,192,000 - $23,375,000 = $817,000 16.

Bank USA just made a one-year $10 million loan that pays 10 percent interest annually.

The loan was funded with a Swiss franc-denominated one-year deposit at an annual rate of 6 percent. The current spot rate is SFr0.9500/$1. a. What will be the net interest income in dollars on the one-year loan if the spot rate at the end of the year is SFr0.9300/$1?

Swiss deposit account issued in SFr = $10m x 0.95 = SFr9.5m Interest income at year-end = $10m x 0.10 = $1,000,000 Interest expense at year-end = (SFr9,500,000 x 0.06)/0.93 = SFr570,000/0.93 = $612,903.23 Net interest income = $1,000,000 - $612,903.23 = $387,096.77 b. What will be the net return on the loan?

Net return on the loan = $387,096.77/$10,000,000 = 0.0387 or 3.87 percent. c. What is the total effect on net interest income and principal of this transaction given the end-of-year spot rates in part (a)?

Interest income and loan principal at year-end = $10m x 1.10 = $11,000,000.

Interest expense and deposit principal at year-end = (SFr9,500,000 x 1.06)/0.93 = SFr10,070,000/0.93 = $10,827,956.99 Total income = $11,000,000 - $10,827,956.99 = $172,043.01 7 © 2022

d. How far can the SFr/$ appreciate before the transaction will result in a loss for Bank USA? Interest expense and deposit principal at year-end = (SFr9,500,000 x 1.06)/SFr/$ = $11,000,000 => CHF/$ = CHF10,070,000/11,000,000 = 0.91545 17.

What motivates FIs to hedge foreign currency exposures? What are the limitations to hedging foreign currency exposures?

FIs hedge to manage their exposure to currency risks, not to eliminate it. As in the case of interest rate risk exposure, it is not necessarily an optimal strategy to completely hedge away all currency risk exposure. By its very definition, hedging reduces the FI's risk by reducing the volatility of possible future returns. This narrowing of the probability distribution of returns reduces possible losses, but also reduces possible gains (i.e., it shortens both tails of the distribution). A hedge would be undesirable, therefore, if the FI wants to take a speculative position in a currency in order to benefit from some information about future currency rate movements. The hedge would reduce possible gains from the speculative position.

18.

What are the two primary methods of hedging FX risk for an FI? What two conditions are necessary to achieve a perfect hedge through on-balance-sheet hedging? What are the advantages and disadvantages of off-balance-sheet hedging in comparison to on-balancesheet hedging?

The manager of an FI can hedge using on-balance-sheet techniques or off-balance-sheet techniques. On-balance-sheet hedging requires matching currency positions and durations of assets and liabilities. If the duration of foreign-currency-denominated fixed rate assets is greater than similar currency denominated fixed rate liabilities, the market value of the assets could decline more than the liabilities when market rates rise and therefore the hedge will not be perfect. Thus, in matching foreign currency assets and liabilities, not only do they have to be of the same currency, but also of the same duration in order to have a perfect hedge.

Advantages of off-balance-sheet FX hedging: The use of off-balance-sheet hedging devices, such as forward contracts, enables an FI to reduce or eliminate its FX risk exposure without forfeiting potentially lucrative transactions. Onbalance-sheet transactions result in immediate cash flows, whereas off-balance-sheet transactions result in contingent future cash flows. Therefore, the up-front cost of hedging using off-balancesheet instruments is lower than the cost of on-balance-sheet transactions. Moreover, since onbalance-sheet transactions are fully reflected in financial statements, there may be additional disclosure costs to hedging on the balance sheet.

Off-balance-sheet hedging instruments have been developed for many types of risk exposures.

For currency risk, forward contracts are available for the majority of currencies at a variety of delivery dates. Moreover, since the forward contract is negotiated over the counter, the counterparties have maximum flexibility to set terms and conditions.

Disadvantages of off-balance-sheet FX Hedging: 8 © 2022

There is some credit risk associated with off-balance-sheet hedging instruments since there is some possibility that the counterparty will default on its obligations. This credit risk exposure is exacerbated in negotiated markets such as the forward market, but mitigated for exchange-traded hedging instruments such as futures contracts.

19.

Suppose that a U.S. FI has the following assets and liabilities: Assets $100 million U.S. loans (one year) in dollars $100 million equivalent U.K. loans (one year) (loans made in pounds)

Liabilities $200 million U.S. CDs (one year) in dollars

The promised one-year U.S. CD rate is 5 percent, to be paid in dollars at the end of the year; the one-year, default risk–free loans are yielding 6 percent in the United States; and one-year, default risk–free loans are yielding 12 percent in the United Kingdom. The exchange rate of dollars for pounds at the beginning of the year is $1.60/£1. a. Calculate the dollar proceeds from the UK investment at the end of the year, the return on the FI’s investment portfolio, and the net return for the FI if the spot foreign exchange rate has not changed over the year.

At the beginning of the year, the FI sells $100 million for pounds on the spot currency markets at an exchange rate of $1.60 to £ => $100 million/1.60 = £62.5 million.

At the end of the year, pound revenue from these loans will be £62.5(1.12) = £70 million.

Then the dollar proceeds from the U.K. investment are: £70 million x $1.60/£1 = $112 million or as a return $112 million - $100 million = 12.00% $100 million Given this, the weighted return on the FI’s portfolio of investments would be: (0.5)(0.06) + (0.5)(0.12) = 0.09, or 9% This exceeds the cost of the FI’s CDs by 4 percent (9% - 5%). b. Calculate the dollar proceeds from the UK investment at the end of the year, the return on the FI’s investment portfolio, and the net return for the FI if the spot foreign exchange rate falls to $1.45/£1 over the year.

At the end of the year, pound revenue from these loans will be £62.5(1.12) = £70 million.

Then the dollar proceeds from the U.K. investment are: 9 © 2022

£70 million x $1.45/£1 = $101.5 million or as a return $101.5 million - $100 million = 1.50% $100 million Given this, the weighted return on the FI’s portfolio of investments would be: (0.5)(0.06) + (0.5)(0.0150) = 0.0375, or 3.75% In this case, the FI actually has a loss or a negative return (3.75% - 5% = -1.25%) on its balance sheet investments. c. Calculate the dollar proceeds from the UK investment at the end of the year, the return on the FI’s investment portfolio, and the net return for the FI if the spot foreign exchange rate rises to $1.70/£1 over the year.

At the end of the year, pound revenue from the loans will be £62.5(1.12) = £70 million.

Then the dollar proceeds from the U.K. investment are: £70 million x $1.70/£1 = $119 million or as a return $119 million - $100 million = 19.00% $100 million Given this, the weighted return on the FI’s portfolio of investments would be: (0.5)(0.06) + (0.5)(0.19) = 0.1250, or 12.50% This exceeds the cost of the FI’s CDs by 7.5 percent (12.5% - 5%).

20.

Suppose that instead of funding the $100 million investment in 12 percent British loans with U.S. CDs, the FI manager in problem 19 funds the British loans with $100 million equivalent one-year pound CDs at a rate of 8 percent. Now the balance sheet of the FI would be as follows: Assets $100 million U.S. loans (6%) $100 million U.K. loans (12%) (loans made in pounds)

Liabilities $100 million U.S. CDs (5%) $100 million U.K. CDs (8%) (deposits raised in pounds)

a. Calculate the return on the FI’s investment portfolio, the average cost of funds, and the net return for the FI if the spot foreign exchange rate falls to $1.45/£1 over the year.

As in part b in question 19, when the pound falls in value to $1.45/£1 at the end of the year, pound revenue from the British loans is be £62.5(1.12) = £70 million.

Then the dollar proceeds from the U.K. investment are: £70 million x $1.45/£1 = $101.5 million or as a return 10 © 2022

$101.5 million - $100 million = 1.50% $100 million and the weighted return on the FI’s portfolio of investments would be: (0.5)(0.06) + (0.5)(0.0150) = 0.0375, or 3.75% On the liability side of the balance sheet, at the beginning of the year, the FI borrows $100 million equivalent in pound CDs for one year at a promised interest rate of 11 percent. At an exchange rate of $1.60/£1, this is a pound equivalent amount of borrowing of $100 million/1.6 = £62.5 million.

At the end of the year, the FI must pay the pound CD holders their principal and interest, £62.5 million (1.08) = £67.50 million.

If the pound falls to $1.45/£1 over the year, the repayment in dollar terms would be £67.50 million x $1.45/£1 = $97.875 million or as a return $97.875 million - $100 million = -2.125% $100 million Thus, at the end of the year, Average cost of funds: (0.5)(0.05) + (0.5)(-0.02125) = 0.014375 = 1.4375% Net return: Average return on assets - Average cost of funds 3.75% - 1.4375% = 2.3125% b. Calculate the return on the FI’s investment portfolio, the average cost of funds, and the net return for the FI if the spot foreign exchange rate rises to $1.70/£1 over the year.

As in part c in question 19, when the pound rises in value to $1.70/£1 at the end of the year, pound revenue from the British loans is be £62.5(1.12) = £70 million.

Then the dollar proceeds from the U.K. investment are: £70 million x $1.70/£1 = $119 million or as a return $119 million - $100 million = 19.00% $100 million and the weighted return on the FI’s portfolio of investments would be: (0.5)(0.06) + (0.5)(0.19) = 0.1250, or 12.50% On the liability side of the balance sheet, at the beginning of the year, the FI borrows $100 million equivalent in pound CDs for one year at a promised interest rate of 11 percent. At an exchange rate of $1.60/£1, this is a pound equivalent amount of borrowing of $100 million/1.6 = £62.5 million.

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At the end of the year, the FI must pay the pound CD holders their principal and interest, £62.5 million (1.08) = £67.50 million.

If the pound increases to $1.70/£1 over the year, the repayment in dollar terms would be £67.50 million x $1.70/£1 = $114.75 million or as a return $114.75 million - $100 million = 14.75% $100 million Thus, at the end of the year, Average cost of funds: (0.5)(0.05) + (0.5)(0.1475) = 0.09875 = 9.875% Net return: Average return on assets - Average cost of funds 12.50% - 9.875% = 2.625% 21.

Suppose that instead of funding the $100 million investment in 12 percent British loans with CDs issued in the United Kingdom, the FI manager in problem 20 hedges the foreign exchange risk on the British loans by immediately selling its expected one-year pound loan proceeds in the forward FX market. The current forward one-year exchange rate between dollars and pounds is $1.53/£1. a. Calculate the return on the FI’s investment portfolio (including the hedge) and the net interest margin for the FI over the year.

The U.S. FI sells $100 million for pounds at the spot exchange rate today and receives $100 million/1.6 = £62.5 million. The FI then immediately lends the £62.5 million to a British customer at 12 percent for one year.

The FI also sells the expected principal and interest proceeds from the pound loan forward for dollars at today’s forward rate for one-year delivery.

This means that the forward buyer of pounds promises to pay: £62.5 million (1.12) x $1.53/£1 = £70 million x $1.53/£1 = $107.1 million to the FI (the forward seller) in one year when the FI delivers the £70 million proceeds of the loan to the forward buyer.

In one year, the British borrower repays the loan to the FI plus interest in pounds (£70 million).

The FI delivers the £70 million to the buyer of the one-year forward contract and receives the promised $107.1 million.

The FI knows from the very beginning of the investment period that it has locked in a guaranteed return on the British loan of: $107.10m - $100m = 0.0710 = 7.10% $100m 12 © 2022

Given this return on British loans, the overall expected return on the FI’s asset portfolio is: (0.5)(0.06) + (0.5)(0.0710) = 0.0655, or 6.55% Net return: Average return on assets - Average cost of funds 6.55% - 5.00% = 1.55% b. Will the net return be affected by changes in the dollar for pound spot foreign exchange rate at the end of the year?

The net return is fully hedged against any dollar for pound exchange rate changes over the oneyear holding period of the loan investment. By selling the expected proceeds on the pound loan forward, at a known (forward FX) exchange rate today, the FI removes the future spot exchange rate uncertainty and thus, the uncertainty relating to investment returns on the British loan.

22.

Suppose that a U.S. FI has the following assets and liabilities: Assets $300 million U.S. loans (one year) in dollars $200 million equivalent German loans (one year) (loans made in euros)

Liabilities $500 million U.S. CDs (one year) in dollars

The promised one-year U.S. CD rate is 4 percent, to be paid in dollars at the end of the year; the one-year, default risk–free loans are yielding 6 percent in the United States; and one-year, default risk–free loans are yielding 10 percent in Germany. The exchange rate of dollars for euros at the beginning of the year is $1.25/€1. a. Calculate the dollar proceeds from the German loan at the end of the year, the return on the FI’s investment portfolio, and the net return for the FI if the spot foreign exchange rate has not changed over the year.

At the beginning of the year, the FI sells $200 million for euros on the spot currency markets at an exchange rate of $1.25 to € => $200 million/1.25 = €160 million.

At the end of the year, euro revenue from these loans will be €160(1.10) = €176 million.

Then the dollar proceeds from the German loan are: €176 million x $1.25/€1 = $220 million or as a return $220 million - $200 million = 10% $200 million Given this, the weighted return on the FI’s portfolio of investments would be: 13 © 2022

(300m/500m)(0.06) + (200m/500m)(0.10) = 0.076, or 7.60% This exceeds the cost of the FI’s CDs by 3.6 percent (7.6% - 4%). b. Calculate the dollar proceeds from the German loan at the end of the year, the return on the FI’s investment portfolio, and the net return for the FI if the spot foreign exchange rate falls to $1.15/€1 over the year.

At the end of the year, euro revenue from these loans will be €160(1.10) = €176 million.

Then the dollar proceeds from the German loan are: €176 million x $1.15/€1 = $202.4 million or as a return $202.4 million - $200 million = 1.20% $200 million Given this, the weighted return on the FI’s portfolio of investments would be: (300m/500m)(0.06) + (200m/500m)(0.0120) = 0.0408, or 4.08% This exceeds the cost of the FI’s CDs by 0.08 percent (4.08% - 4% = 0.08%). c. Calculate the dollar proceeds from the German loan at the end of the year, the return on the FI’s investment portfolio, and the net return for the FI if the spot foreign exchange rate rises to $1.35/€1 over the year.

At the end of the year, euro revenue from the loans will be €160(1.10) = €176 million.

Then the dollar proceeds from the German loan are: €176 million x $1.35/€1 = $237.6 million or as a return $237.6 million - $200 million = 18.8% $200 million Given this, the weighted return on the FI’s portfolio of investments would be: (300m/500m)(0.06) + (200m/500m)(0.188) = 0.1112, or 11.12% This exceeds the cost of the FI’s CDs by 7.12 percent (11.12% - 4%).

23.

Suppose that instead of funding the $200 million investment in 10 percent German loans with U.S. CDs, the FI manager in problem 22 funds the German loans with $200 million equivalent one-year euro CDs at a rate of 7 percent. Now the balance sheet of the FI would be as follows: Assets $300 million U.S. loans (6%) $200 million German loans (10%)

Liabilities $300 million U.S. CDs (4%) $200 million German CDs (7%) 14 © 2022

(loans made in euros)

(deposits raised in euros)

a. Calculate the return on the FI’s investment portfolio, the average cost of funds, and the net return for the FI if the spot foreign exchange rate falls to $1.15/€1 over the year.

As in part b in question 22, when the euro falls in value to $1.15/€1 at the end of the year, euro revenue from the German loans is be €160(1.10) = €176 million.

Then the dollar proceeds from the German loan are: €176 million x $1.15/€1 = $202.4 million or as a return $202.4 million - $200 million = 1.20% $200 million and the weighted return on the FI’s portfolio of investments would be: (300m/500m)(0.06) + (200m/500m)(0.0120) = 0.0408, or 4.08% On the liability side of the balance sheet, at the beginning of the year, the FI borrows $200 million equivalent in euro CDs for one year at a promised interest rate of 7 percent. At an exchange rate of $1.25/€1, this is a euro equivalent amount of borrowing of $200 million/1.25 = €160 million.

At the end of the year, the FI must pay the pound CD holders their principal and interest, €160 million (1.07) = €171.20 million.

If the euro falls to $1.15/€1 over the year, the repayment in dollar terms would be €171.20 million x $1.15/€1 = $196.88 million or as a return $196.88 million - $200 million = -1.56% $200 million Thus, at the end of the year, Average cost of funds: (300m/500m)(0.04) + (200m/500m)(-0.0156) = 0.01776, or 1.776% Net return: Average return on assets - Average cost of funds 4.08% - 1.776% = 2.304% b. Calculate the return on the FI’s investment portfolio, the average cost of funds, and the net return for the FI if the spot foreign exchange rate rises to $1.35/€1 over the year.

As in part c in question 22, when the euro rises in value to $1.35/€1 at the end of the year, euro revenue from the German loans is be €160(1.10) = €176 million.

Then the dollar proceeds from the German loan are: €176 million x $1.35/€1 = $237.6 million or as a return $237.6 million - $200 million = 18.80% $200 million 15 © 2022

and the weighted return on the FI’s portfolio of investments would be: (300m/500m)(0.06) + (200m/500m)(0.188) = 0.112, or 11.20% On the liability side of the balance sheet, at the beginning of the year, the FI borrows $200 million equivalent in euro CDs for one year at a promised interest rate of 7 percent. At an exchange rate of $1.25/€1, this is a euro equivalent amount of borrowing of $200 million/1.25 = €160 million.

At the end of the year, the FI must pay the pound CD holders their principal and interest, €160 million (1.07) = €171.20 million.

If the euro increases to $1.35/€1 over the year, the repayment in dollar terms would be €171.20 million x $1.35/€1 = $231.12 million or as a return $231.12 million - $200 million = 15.56% $200 million Thus, at the end of the year, Average cost of funds: (300m/500m)(0.04) + (200m/500m)(0.1556) = 0.08624, or 8.624% Net return: Average return on assets - Average cost of funds 11.2% - 8.624% = 2.576% 24.

Suppose that instead of funding the $200 million investment in 10 percent German loans with CDs issued in Germany, the FI manager in problem 23 hedges the foreign exchange risk on the German loans by immediately selling its expected one-year euro loan proceeds in the forward FX market. The current forward one-year exchange rate between dollars and euros is $1.20/€1. a. Calculate the return on the FI’s investment portfolio (including the hedge) and the net return for the FI over the year.

The U.S. FI sells $200 million for pounds at the spot exchange rate today and receives $200 million/1.25 = €160 million. The FI then immediately lends the €160 million to a German customer at 10 percent for one year.

The FI also sells the expected principal and interest proceeds from the euro loan forward for dollars at today’s forward rate for one-year delivery.

This means that the forward buyer of euros promises to pay: €160 million (1.10) x $1.20/€1 = €176 million x $1.20/€1 = $211.2 million to the FI (the forward seller) in one year when the FI delivers the €176 million proceeds of the loan to the forward buyer.

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In one year, the German borrower repays the loan to the FI plus interest in euros (€176 million).

The FI delivers the €176 million to the buyer of the one-year forward contract and receives the promised $211.2 million.

The FI knows from the very beginning of the investment period that it has locked in a guaranteed return on the German loan of: $211.20m - $200m = 0.0560 = 5.60% $200m Given this return on British loans, the overall expected return on the FI’s asset portfolio is: (300m/500m)(0.06) + (200m/500m)(0.0560) = 0.0584, or 5.84% Net return: Average return on assets - Average cost of funds 5.84% - 4.00% = 1.84% b. Will the net return be affected by changes in the dollar for euro spot foreign exchange rate at the end of the year?

The net return is fully hedged against any dollar for euro exchange rate changes over the oneyear holding period of the loan investment. By selling the expected proceeds on the euro loan forward, at a known (forward FX) exchange rate today, the FI removes the future spot exchange rate uncertainty and thus, the uncertainty relating to investment returns on the German loan.

25.

North Bank has been borrowing in the U.S. markets and lending abroad, thus incurring foreign exchange risk. In a recent transaction, it issued a one-year, $2 million CD at 6 percent and funded a loan in euros at 8 percent. The spot rate for the euro was €1.45/$1 at the time of the transaction. a. Information received immediately after the transaction closing indicated that the euro for dollar exchange rate will change to €1.47/$1 by year-end. If the information is correct, what will be the net return on the loan inclusive of principal? What should have been the bank interest rate on the loan to maintain the 2 percent net return?

Amount of loan in € = $2 million x 1.45 = €2.9 million Interest and principal at year-end = €2.9m x 1.08 = €3.132m/1.47 = $2,130,612.24 Interest and principal of CDs = $2m x 1.06 = $2,120,000 Net interest income = $2,130,612.24 – $2,120,000 = $10,612.24 Net return = $10,612.24/2,000,000 = 0.0053 or 0.53 percent In order to maintain a 2 percent net return, the interest and principal earned at €1.47/$ should be: €2.9m(1 + x)/1.47 = $2.16m (Because ($2.16m - $2.12m)/$2.00m = 0.02, or 2%).

Therefore, (1 + x) = ($2.16m x 1.47)/ €2.9m = 1.0949, and x = 0.0949 or 9.49 percent, or the bank should have charged a rate of 9.49 percent on the loan.

17 © 2022

b. The bank had an opportunity to sell one-year forward euros at €1.46/$1. What would have been the net return on the loan if the bank had hedged forward its foreign exchange exposure? = €2.9m x 1.08 = €3.132m/1.46 = $2.1452m - $2.12m = $0.0252 million, or $25,205.48 Net return = $0.0252m/$2m = 0.0126, or 1.26 percent Net interest income if hedged

c. What would have been an appropriate change in loan rates to maintain the 2 percent net return if the bank intended to hedge its exposure using the forward contracts?

To maintain a 2 percent net return: €2.9m(1 + x)/1.46 = $2.16m => x = 8.74 percent The bank should increase the loan rate to 8.74 percent and hedge with the sale of forward €s to maintain a 2 percent net return.

26.

A bank purchases a six-month, $1 million Eurodollar deposit at an annual interest rate of 6.5 percent. It invests the funds in a six-month Swedish krona AA-rated bond paying 7.5 percent per year. The current spot rate is $0.18/Kr1. a. The six-month forward rate on the Swedish krona is being quoted at $0.1810/Kr1. What is the net return earned on this investment if the bank covers its foreign exchange exposure using the forward market?

Interest plus principal expense on six-month CD = $1m x (1 + 0.065/2) = $1,032,500 Principal of Swedish bond = $1,000,000/0.18 = Kr5,555,555.56 Interest and principle = Kr5,555,555.56 x (1 + 0.075/2) = Kr 5,763,888.89 Interest and principle in dollars if hedged: Kr 5,763,888.89 x 0.1810 = $1,043,263.89 Net return = $1,043,263.89 - 1,032,500 = $10,763.89/1 million = 0.010764 for 6 months, or 2.15 percent annually b. What forward rate will cause the net return to be only 1 percent per year?

In this case, net interest income should be = (0.01/2) x 1,000,000 = $5,000 Therefore, interest income should be = $1,043,263.86 - $5,000 = $1,038,263.86 Forward rate = $1,038,263.86/Kr5,763,888.89 = $0.18/Kr1 For the spread to be 1% the spot and the forward need to be equal. c. Explain how forward and spot rates will both change in response to the increased net return?

If FIs are able to earn higher net returns in other countries and guarantee these returns by using the forward markets, these are equivalent to risk-free investments (except for default risk). As a result, in part (a), there will be an increase in demand for the Swedish krona in the spot market and an increase in sales of the forward Swedish krona as more FIs engage in this kind of lending.

18 © 2022

This results in an appreciation of the spot krona rate and a depreciation of the forward krona rate until the spread is zero for securities of equal risk. d. Why will a bank still be able to earn a net return of 1 percent knowing that interest rate parity usually eliminates arbitrage opportunities created by differential rates?

In part (b), the FI is still able to earn a net return of one percent because the risks of the securities are not equal. The FI earns an extra one percent because it is lending to an AA-rated firm. The dollar-denominated deposits in the Eurocurrency markets are rated higher because these deposits usually are issued by large institutions. Thus, the one percent spread reflects credit or default risk. If the FI were to invest in securities of equal risk in Sweden, arbitrage would ensure that the spread is zero.

27.

What is economic integration? What impact does the extent of economic integration of international markets have on the investment opportunities for FIs?

If markets are not perfectly correlated, some barriers for free trade exist between the markets and, therefore, they are not fully integrated. When markets are fully integrated, opportunities for diversification are reduced. Also, real returns across countries are equal. Thus, diversification benefits occur only when nominal and real rates differ between countries. This happens when some formal or informal barriers exist to prevent the free flow of capital across countries.

28.

How does the lack of perfect correlation of economic returns between international financial markets affect the risk-return opportunities for FIs holding multicurrency assets and liabilities? Refer to Table 13-6. Which country pairings seem to have the highest correlation of stock returns and which have the lowest?

If financial markets are not perfectly correlated, they provide opportunities to diversify and reduce risk from mismatches in assets and liabilities in individual currencies. The benefits of diversification depend on the extent of the correlations. The lower the correlation, the greater the benefits. However, FIs that only hold one or two foreign assets and liabilities cannot take advantage of these benefits and have to hedge their individual portfolio exposures.

From Table 13-6 in order of rank the country pairs with the highest correlations are United Kingdom-Europe, United States-United Kingdom, United States-Europe, United KingdomAustralia, Brazil-Hong Kong, and Brazil-Canada. The country pairs with the lowest correlations before are China-Japan, China-India, China-United Kingdom, China-Europe, China-United States, and Japan-South Africa.

29.

What is the purchasing power parity theorem?

As relative inflation rates (and interest rates) change, foreign currency exchange rates that are not constrained by government regulation should adjust to account for relative differences in the price levels (inflation rates) between the two countries. According to purchasing power parity (PPP), foreign currency exchange rates between two countries adjust to reflect changes in each country’s price levels (or inflation rates and implicitly interest rates) as consumers and importers 19 © 2022

switch their demands for goods from relatively high inflation (interest) rate countries to low inflation (interest) rate countries. Specifically, the PPP theorem states that the change in the exchange rate between two countries’ currencies is proportional to the difference in the inflation rates in the two countries.

30.

Suppose that the current spot exchange rate of U.S. dollars for Australian dollars, SUSD/AUD,is 1.0277 (i.e., $1.0277 can be received for 1 Australian dollar). The price of Australian-produced goods increases by 5 percent (i.e., inflation in Australia, iA, is 5 percent), and the U.S. price index increases by 3 percent (i.e., inflation in the United States, iUS, is 3 percent). Calculate the new spot exchange rate of U.S. dollars for Australian dollars that should result from the differences in inflation rates.

According to PPP, the 5 percent rise in the price of Australian goods relative to the 3 percent rise in the price of U.S. goods results in a depreciation of the Australian dollar (by 2 percent).

Specifically, the exchange rate of Australian dollars to U.S. dollars should fall, so that: iUS - iA = ΔSUSD/AUD/SUSD/AUD Plugging in the inflation and exchange rates, we get: 0.03 - 0.05 = ΔSUSD/AUD/SUSD/AUD = ΔSUSD/AUD/ 1.0277 or:

-0.02 = ΔSUSD/AUD/1.0277

and:

ΔSUSD/AUD = -(0.02) × 1.0277 = -0.020554

Thus, it costs 2.0554 cents less to receive an Australian dollar (or $1.007146 ($1.0277 $0.020554), can be received for 1 Australian dollar). The Australian dollar depreciates in value by 2 percent against the U.S. dollar as a result of its higher inflation rate.

31.

Explain the concept of interest rate parity? What does this concept imply about the profit opportunities from investing in international markets? What market conditions must prevail for the concept to be valid?

Interest rate parity argues that the discounted spread between domestic and foreign interest rates is equal to the percentage spread between forward and spot exchange rates. If interest rate parity holds, then it is not possible for FIs to borrow and lend in different currencies to take advantage of the differences in interest rates between countries. This is because the spot and forward rates will adjust to ensure that no arbitrage can take place through cross-border investments. If a disparity exists, the sale and purchase of spot and forward currencies by arbitragers will ensure that in equilibrium interest rate parity is maintained.

32.

Assume that annual interest rates are 8 percent in the United States and 4 percent in Japan.

An FI can borrow (by issuing CDs) or lend (by purchasing CDs) at these rates. The spot rate is $0.0080/¥.

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a. If the forward rate is $0.0085/¥, how could the FI arbitrage using a sum of $1million?

What is the expected return?

Borrow $1,000,000 in U.S. by issuing CDs  Interest and principal at year-end = $1,000,000 x 1.08 = $1,080,000 Make a loan in Japan  Interest and principal = $1,000,000/0.0080 = ¥125m x 1.04 = ¥130.0m Purchase U.S. dollars at the forward rate of $0.0085 x 130.0m = $1,105,000 Return = $1,105,000 - $1,080,000 = $25,000/1,000,000 = 2.50% b. What forward rate will prevent an arbitrage opportunity?

The forward rate that will prevent any arbitrage is given by solving the following equation: Ft

=

(1 + rD ) ust

L )

(1 + r jpt

x

St

Ft = [(1 + 0.08) x 0.0080]/(1.04) = $0.00831/¥ 33.

What is the relationship between the real interest rate, the expected inflation rate, and the nominal interest rate on fixed-income securities in any particular country? What factors may be the reasons for the relatively high correlation coefficients?

The nominal interest rate is equal to the real interest rate plus the expected inflation rate on assets where default risk is not an issue. The strength of correlations among countries whose economies are considered to be the leaders of the industrialized nations is evidence that the world capital markets among these markets are reasonably well-integrated.

34.

An FI has $100,000 of net positions outstanding in British pounds (₤) and -$30,000 in Swiss francs (SFr). The standard deviation of the net positions as a result of exchange rate changes is 1 percent for the SFr and 1.3 percent for the ₤. The correlation coefficient between the changes in exchange rates of the ₤ and the SFr is 0.80. a. What is the risk exposure to the FI of fluctuations in the ₤/$ rate?

Since the FI has a positive ₤ position, an appreciation of the ₤ relative to the dollar will increase the value of its ₤-denominated assets more than its liabilities, providing a net gain. The opposite will occur if the ₤ depreciates. b. What is the risk exposure to the FI of fluctuations in the SFr/$ rate?

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Since the FI has a negative net position in SFrs, the value of its Swiss-denominated assets will increase in value, but not as much as the value of its liabilities. Hence, an appreciation of the SFr relative to the dollar will lead to a net loss. The opposite will occur if the currency depreciates. c. What is the risk exposure if both the ₤and the SFr positions are combined?

Use the formula:  p = (100 )2(1 )2 +(-30 )2(1.3 )2 + 2(1)(1.3)(100)(-30)(0.8)

= $72,671

The FI’s net position is actually $72,671. Without including correlation, the exposure is estimated at $100,000 - $30,000 = $70,000.

35.

A money market mutual fund manager is looking for some profitable investment opportunities and observes the following one-year interest rates on government securities and exchange rates: rUS = 12%, rUK = 9%, S = $1.50/£1, F = $1.60/£1, where S is the spot exchange rate and F is the forward exchange rate. Which of the two types of government securities would constitute a better investment?

The U.K. securities would yield a higher return. Compared to the 12 percent return in the U.S., a U.S. investor could convert $1,000,000 to £666,667 and invest it at 9 percent. In one year the expected return of principal and interest is £726,667. If these pounds are sold forward at $1.6/£1, the investor will lock in $1,162,667 for a 16.27 percent return.

Integrated Mini Case: Foreign Exchange Risk Exposure Suppose that a U.S. FI has the following assets and liabilities: Assets $500 million U.S. loans (one year) in dollars $300 million equivalent U.K. loans (one year) (loans made in pounds) $200 million equivalent Turkish loans (one year) (loans made in Turkish lira)

Liabilities $1,000 million U.S. CDs (one year) in dollars

The promised one-year U.S. CD rate is 4 percent, to be paid in dollars at the end of the year; the one-year, default risk–free loans are yielding 6 percent in the United States; one-year, default risk–free loans are yielding 8 percent in the United Kingdom; and one-year, default risk–free loans are yielding 10 percent in Turkey. The exchange rate of dollars for pounds at the beginning 22 © 2022

of the year is $1.6/£1, and the exchange rate of dollars for Turkish lira at the beginning of the year is $0.5533/TL1.

1. Calculate the dollar proceeds from the FI’s loan portfolio at the end of the year, the return on the FI’s loan portfolio, and the net return for the FI if the spot foreign exchange rate has not changed over the year.

At the beginning of the year, the FI sells $300 million for pounds on the spot currency markets at an exchange rate of $1.60 to £ => $300 million/1.60 = £187.5 million.

In addition, the FI sells $200 million for lira on the spot currency markets at an exchange rate of $0.5533 to TL => $200 million/0.5533 = TL361,467,558.

At the end of the year, pound revenue from these loans will be £187.5(1.08) = £202.5 million and lira revenue from these loans will be TL361,467,558 (1.10) = TL397,614,314.

Then the dollar proceeds from the U.K. loan are: £202.5 million x $1.60/£1 = $324 million or as a return $324 million - $300 million = 8.00% $300 million and the dollar proceeds from the Turkish loan are: TL397,614,314 x $0.5533/TL1 = $220 million or as a return $220 million - $200 million = 10.00% $200 million Given this, the weighted return on the FI’s loan portfolio would be: (0.5)(0.06) + (0.3)(0.08) + (0.2)(0.10) = 0.074, or 7.40% This exceeds the cost of the FI’s CDs by 3.4 percent (7.4% - 4%).

2. Calculate the dollar proceeds from the FI’s loan portfolio at the end of the year, the return on the FI’s loan portfolio, and the net return for the FI if the pound spot foreign exchange rate falls to $1.45/£1 and the lira spot foreign exchange rate falls to $0.52/TL1 over the year.

At the end of the year, pound revenue from these loans will be £187.5(1.08) = £202.5 million and lira revenue from these loans will be TL361,467,558 (1.10) = TL397,614,314.

Then the dollar proceeds from the U.K. loan are: £202.5 million x $1.45/£1 = $293.625 million or as a return $293.625 million - $300 million = -2.125% $300 million and the dollar proceeds from the Turkish loan are: TL397,614,314 x $0.52/TL1 = $206,759,443 or as a return $206,759,443 - $200 million = 3.38% $200 million

21

Given this, the weighted return on the FI’s loan portfolio would be: (0.5)(0.06) + (0.3)(-0.02125) + (0.2)(0.0338) = 0.0304, or 3.04% In this case, the FI actually has a loss or a negative return (3.04% - 4% = -0.96%) on its balance sheet investments.

3. Calculate the dollar proceeds from the FI’s loan portfolio at the end of the year, the return on the FI’s loan portfolio, and the net return for the FI if the pound spot foreign exchange rate rises to $1.70/£1 and the lira spot foreign exchange rate rises to $0.58/TL1 over the year.

At the end of the year, pound revenue from these loans will be £187.5(1.08) = £202.5 million and lira revenue from these loans will be TL361,467,558 (1.10) = TL397,614,314.

Then the dollar proceeds from the U.K. investment are: £202.5 million x $1.70/£1 = $344.25 million or as a return $344.25 million - $300 million = 14.75% $300 million and the dollar proceeds from the Turkish loan are: TL397,614,314 x $0.58/TL1 = $230,616,302 or as a return $230,616,302 - $200 million = 15.31% $200 million Given this, the weighted return on the FI’s loan portfolio would be: (0.5)(0.06) + (0.3)(0.1475) + (0.2)(0.1531) = 0.1049, or 10.49% This exceeds the cost of the FI’s CDs by 6.49 percent (10.49% - 4%).

4. Suppose that instead of funding the $300 million investment in 8 percent British loans with U.S. CDs, the FI manager funds the British loans with $300 million equivalent one-year pound CDs at a rate of 5 percent and that instead of funding the $200 million investment in 10 percent Turkish loans with U.S. CDs, the FI manager funds the Turkish loans with $200 million equivalent one-year Turkish lira CDs at a rate of 6 percent. What will the FI’s balance sheet look like after these changes have been made?

The balance sheet of the FI would be as follows: Assets $500 million U.S. loans (6%) $300 million U.K. loans (8%) (loans made in pounds) $200 million Turkish loans (10%)

Liabilities $500 million U.S. CDs (4%) $300 million U.K. CDs (5%) (deposits raised in pounds) $200 million Turkish CDs (6%)

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(loans made in Turkish lira)

(deposits raised in Turkish lira)

5. Using the information in part 4, calculate the return on the FI’s loan portfolio, the average cost of funds, and the net return for the FI if the pound spot foreign exchange rate falls to $1.45/£1 and the lira spot foreign exchange rate falls to $0.52/TL1 over the year.

As in part 2, when the pound falls in value to $1.45/£1 at the end of the year, pound revenue from the British loans is £187.5(1.08) = £202.5 million. When the lira falls in value to $0.52/TL1 at the end of the year, lira revenue from the Turkish loans is be TL361,467,558 (1.10) = TL397,614,314.

Then the dollar proceeds from the U.K. loan are: £202.5 million x $1.45/£1 = $293.625 million or as a return $293.625 million - $300 million = -2.125% $300 million and the dollar proceeds from the Turkish loan are: TL397,614,314 x $0.52/TL1 = $206,759,443 or as a return $206,759,443 - $200 million = 3.38% $200 million and the weighted return on the FI’s loan portfolio would be: (0.5)(0.06) + (0.3)(-0.02125) + (0.2)(0.0338) = 0.0304, or 3.04% On the liability side of the balance sheet, at the beginning of the year, the FI borrows $300 million equivalent in pound CDs for one year at a promised interest rate of 5 percent. At an exchange rate of $1.60/£1, this is a pound equivalent amount of borrowing of $300 million/1.6 = £187.5 million.

At the end of the year, the FI must pay the pound CD holders their principal and interest, £187.5 million (1.05) = £196.875 million.

If the pound falls to $1.45/£1 over the year, the repayment in dollar terms would be £196.875 million x $1.45/£1 = $285,468,750 or as a return $285,468,750 - $300 million = -4.844% $300 million Additionally, the FI borrows $200 million equivalent in Turkish lira CDs for one year at a promised interest rate of 6 percent. At an exchange rate of $0.5533/TL1, this is a lira equivalent amount of borrowing of $200 million/0.5533 = TL361,467,558.

At the end of the year, the FI must pay the lira CD holders their principal and interest, TL361,467,558 (1.06) = TL383,155,612.

If the lira falls to $0.52/TL1 over the year, the repayment in dollar terms would be TL383,155,612 x $0.52/TL1 = $199,240,918 or as a return

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$199,240,918 - $200 million = -0.38% $200 million Thus, at the end of the year, Average cost of funds: (0.5)(0.04) + (0.3)(-0.04847) + (0.2)(-0.0038) = 0.0047, or 0.47%

Net return: Average return on assets - Average cost of funds 3.04% - 0.47% = 2.57% 6. Using the information in part 4, calculate the return on the FI’s loan portfolio, the average cost of funds, and the net return for the FI if the pound spot foreign exchange rate rises to $1.70/£1 and the lira spot foreign exchange rate falls to $0.58/TL1 over the year.

As in part 3, when the pound rises in value to $1.70/£1 at the end of the year, pound revenue from the British loans is £187.5(1.08) = £202.5 million.

Then the dollar proceeds from the U.K. loan are: £202.5 million x $1.70/£1 = $344.25 million or as a return $344.25 million - $300 million = 14.75% $300 million When the lira rises in value to $0.58/TL1 at the end of the year, lira revenue from the Turkish loans is be TL361,467,558 (1.10) = TL397,614,314 and the dollar proceeds from the Turkish loan are: TL397,614,314 x $0.58/TL1 = $230,616,302 or as a return $230,616,302 - $200 million = 15.31% $200 million The weighted return on the FI’s loan portfolio would be: (0.5)(0.06) + (0.3)(0.1475) + (0.2)(0.1531) = 0.1049, or 10.49% On the liability side of the balance sheet, at the beginning of the year, the FI borrows $300 million equivalent in pound CDs for one year at a promised interest rate of 5 percent. At an exchange rate of $1.60/£1, this is a pound equivalent amount of borrowing of $300 million/1.6 = £187.5 million.

At the end of the year, the FI must pay the pound CD holders their principal and interest, £187.5 million (1.05) = £196.875 million.

If the pound rises to $1.70/£1 over the year, the repayment in dollar terms would be £196.875 million x $1.70/£1 = $334,687,200 or as a return $334,687,200 - $300 million = 11.5625% $300 million

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Additionally, the FI borrows $200 million equivalent in Turkish lira CDs for one year at a promised interest rate of 6 percent. At an exchange rate of $0.5533/TL1, this is a lira equivalent amount of borrowing of $200 million/0.5533 = TL361,467,558.

At the end of the year, the FI must pay the lira CD holders their principal and interest, TL361,467,558 (1.06) = TL383,155,612.

If the lira rises to $0.58/TL1 over the year, the repayment in dollar terms would be TL383,155,612 x $0.58/TL1 = $222,230,255 or as a return $222,230,255 - $200 million = 11.12% $200 million Thus, at the end of the year, Average cost of funds: (0.5)(0.04) + (0.3)(0.115625) + (0.2)(0.1112) = 0.0769, or 7.69% Net return: Average return on assets - Average cost of funds 10.49% - 7.69% = 2.80% 7. Suppose that instead of funding the $300 million investment in 8 percent British loans with CDs issued in the United Kingdom, the FI manager hedges the foreign exchange risk on the British loans by immediately selling its expected one-year pound loan proceeds in the forward FX market. The current forward one-year exchange rate between dollars and pounds is $1.53/£1. Additionally, instead of funding the $200 million investment in 10 percent Turkish loans with CDs issued in the Turkey, the FI manager hedges the foreign exchange risk on the Turkish loans by immediately selling its expected one-year lira loan proceeds in the forward FX market. The current forward one-year exchange rate between dollars and Turkish lira is $0.5486/TL1. Calculate the return on the FI’s investment portfolio (including the hedge) and the net return for the FI over the year.

The U.S. FI sells $300 million for pounds at the spot exchange rate today and receives $300 million/1.6 = £187.5 million. The FI then immediately lends the £187.5 million to a British customer at 8 percent for one year.

The FI also sells the expected principal and interest proceeds from the pound loan forward for dollars at today’s forward rate for one-year delivery.

This means that the forward buyer of pounds promises to pay: £187.5 million (1.08) x $1.53/£1 = £202.5 million x $1.53/£1 = $309.825 million to the FI (the forward seller) in one year when the FI delivers the £202.5 million proceeds of the loan to the forward buyer.

In one year, the British borrower repays the loan to the FI plus interest in pounds (£202.5 million).

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The FI delivers the £202.5 million to the buyer of the one-year forward contract and receives the promised $309.825 million.

The FI knows from the very beginning of the investment period that it has locked in a guaranteed return on the British loan of: $309.825m - $300m = 0.03275 = 3.275% $300m Additionally, the U.S. FI sells $200 million for Turkish lira at the spot exchange rate today and receives $200 million/0.5533 = TL361,467,558. The FI then immediately lends the TL361,467,558 to a Turkish customer at 10 percent for one year.

The FI also sells the expected principal and interest proceeds from the Turkish lira loan forward for dollars at today’s forward rate for one-year delivery.

This means that the forward buyer of lira promises to pay: TL361,467,558 (1.10) x $0.5486/TL1 = TL397,614,314 x $0.5486/TL1 = $218,131,213 to the FI (the forward seller) in one year when the FI delivers the TL397,614,314 proceeds of the loan to the forward buyer.

In one year, the Turkish borrower repays the loan to the FI plus interest in pounds TL397,614,314.

The FI delivers the TL397,614,314 to the buyer of the one-year forward contract and receives the promised $218,131,213.

The FI knows from the very beginning of the investment period that it has locked in a guaranteed return on the British loan of: $218,131,213 - $200m = 0.09066 = 9.066% $200m Given this return on British loans, the overall expected return on the FI’s asset portfolio is: (0.5)(0.06) + (0.3)(0.03275) + (0.2)(0.09066) = 0.0580, or 5.80% Net return: Average return on assets - Average cost of funds 5.80% - 4.00% = 1.80%

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Solutions for End-of-Chapter Questions and Problems: Chapter Fourteen 1.

What risks are incurred in making loans to borrowers based in foreign countries?

Explain.

When making loans to borrowers in foreign countries, two risks need to be considered.

First, the credit risk of the project needs to be examined to determine the ability of the borrower to repay the money. This analysis is based strictly on the economic viability of the project and is similar in all countries. Second, unlike domestic loans, creditors are exposed to sovereign risk. Sovereign risk is defined as the risk that repayments from foreign borrowers may be interrupted because of interference from foreign governments.

Thus, even though the borrowing firm has the resources to repay, it may not be able to do so because of actions beyond its control. Thus, creditors need to account for sovereign risk in their decision process when choosing to invest abroad.

2.

What is the difference between debt rescheduling and debt repudiation?

Debt repudiation refers to a situation of outright cancelation of all current and futures debt obligations of a borrower. In contrast, debt rescheduling refers to a change in the contractual terms of a loan, such as the temporary postponement of payments during which time new terms and conditions are agreed upon between the borrower and lenders.

In most cases, these new terms are structured to make it easier for the borrower to repay.

3.

Identify and explain at least four reasons that rescheduling debt in the form of loans is easier than rescheduling debt in the form of bonds.

The reasons that it is easier to reschedule debt in the form of bank loans than bonds include: a)

Loans usually are made by a small group (syndicate) of FIs as opposed to bonds that are held by individuals and institutions that are geographically dispersed. Even though bondholders usually appoint trustees to look after their interests, it has proven to be much more difficult to approve renegotiation agreements with bondholders in contrast to FI syndicates.

b)

The group of FIs that dominate lending in international markets is limited and hence able to form a cohesive group. This enables them to act in a unified manner against potential defaults by countries.

c)

Many international loans contain cross-default clauses, which make the cost of default very expensive to borrowers. Defaulting on a loan would trigger default clauses on all loans with such clauses, preventing borrowers from selectively defaulting on a few loans.

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d)

In the case of post-war loans, governments were reluctant to allow banks to fail.

This meant that they would also be actively involved in the rescheduling process by either directly providing subsidies to prevent repudiations or providing incentives to international agencies like the IMF and World Bank to provide other forms of grants and aid.

4.

What three country risk assessment models are available to investors? How is each model compiled?

The Euromoney Country Risk (ECR) index rates sovereign risk of over 180 countries based on the opinions of a global network of economists and policy analysts. The index is based on a large number of economic and political factors including a country’s economic characteristics, political characteristics, structural characteristics, access to capital and credit ratings, and debt indicators. ECR scores are scaled from 0 to 100 (0 = maximum risk, 100 = no risk) and are put into one of five tiers that are updated quarterly.

The Economist Intelligence Unit (EIU) combines economic and political risk to achieve a risk rating of a country. The measure is based on a 100 point scale with ratings of smaller risk being lower values.

The Institutional Investor Index is based on surveys of the loan officers of major multinational FIs who subjectively give estimates of the credit quality of given countries.

The scores range from 0 for certain default to 100 for no probability of default.

5.

What types of variables normally are used in a CRA Z-score model? Define the following ratios and explain how each is interpreted in assessing the probability of rescheduling.

The models typically use micro- and macroeconomic variables that are considered important in explaining the probability of a country’s credit rescheduling. a. Debt service ratio. The debt service ratio (DSR) divides interest plus amortization on debt by exports. Because interest and debt payments normally are paid in hard currencies generated by exports, a larger ratio is interpreted as a positive signal of a pending debt rescheduling possibility. b. Import ratio. The import ratio (IR) divides total imports by total foreign exchange reserves. A growing amount of imports relative to FX reserves indicates a greater probability of credit restructuring. Thus, this ratio is positively related to debt rescheduling. c. Investment ratio. The investment ratio (INVR) measures the investment in real or productive assets relative to gross national product. A larger investment ratio is considered a signal that the country will be less likely to require rescheduling in the future because of increased productivity; thus the relationship is negative.

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However, because the bargaining position of the country will be enhanced, some observers feel that the relationship is positive. That is, a stronger ratio gives the country more power to request, even demand, rescheduling to achieve even better terms on its debt. d. Variance of export revenue. Export revenues are subject to both quantity and price risk due to demand and supply factors in the international markets.

Increased variance is interpreted as a positive signal that rescheduling will occur because of the decreased certainty that debt payments will be made on schedule. e. Domestic money supply growth. Rapid domestic money supply growth indicates an increase in inflationary pressures that typically means a decrease in the value of the currency in international markets. Thus, real output often is negatively impacted, and the probability of rescheduling increases.

6.

An FI manager has calculated the following values and weights to assess the credit risk and likelihood of having to reschedule a loan. From the Z-score calculated using these weights and values, is the manager likely to approve the loan?

Validation tests of the Z-score model indicated that scores below 0.500 were likely to be nonreschedulers, while scores above 0.700 indicated a likelihood of rescheduling. Scores between 0.500 and 0.700 do not predict well.

Variable DSR IR INVR VAREX MG

Country Value 1.25 1.60 0.60 0.15 0.02

Weight 0.05 0.10 0.35 0.35 0.15

Z = 0.05DSR + 0.10IR + 0.35INVR + 0.35VAREX + 0.15MG = 0.05(1.25) + 0.10(1.60) + 0.35(0.60) + 0.35(0.15) + 0.15(0.02) = 0.488 This score classifies the borrower as a probable nonrescheduler.

7.

Countries A and B have exports of $2 billion and $6 billion, respectively. The total interest and amortization on foreign loans for both countries are $1 billion and $2 billion, respectively. a. What is the debt service ratio (DSR) for each country?

DSR = Interest Plus Amortization Total Exports 3 © 2022

DSRA = $1b/$2b = 0.50

DSRB = $2b/$6b = 0.33

b. Based only on this ratio, to which country should lenders charge a higher risk premium?

Based on the above information, lenders should charge a higher risk premium on loans to Country A because it has more interest and amortization payments due as a percentage of total exports. c. What are the shortcomings of using only these ratios to determine your answer in part (b)?

This is a very static model and such a preliminary conclusion could be misleading. It is also necessary to consider other factors which may be more favorable for Country A. Looking forward, it is also possible that Country A may be at its developing stage where imports and loans are needed to increase future exports. Historically, most of the industrialized countries were net importers of capital during their developing stages.

Without a comprehensive analysis of the fundamentals, it is not possible to judge the quality of the borrower.

8.

How do price and quantity risks affect the variability of a country’s export revenue?

Quantity risk means that the production of the raw commodities the country sells abroad—for example, coffee or sugar—is subject to periodic gluts and shortages. This is most likely to be found in agricultural products subject to favorable and unfavorable weather conditions. Price risk means that the international dollar prices at which the country can sell its exportable commodities are subject to high volatility as world demand for and supply of a commodity, such as copper, vary. The more volatile a country’s export earnings, the less certain creditors can be that at any time in the future it will be able to meet its repayment commitments.

9.

Explain the following relation: p = f (IR, INVR) +, + or p = Probability of rescheduling IR = Total imports/Total foreign exchange reserves INVR = Real investment/GNP

This relation states that the probability of a country’s rescheduling of its foreign debt is a positive function of IR, but it may be positively or negatively related to INVR: IR = Total imports/Total FX reserves. If imports as a percentage of FX reserves increase, it leaves less foreign exchange for payments of debt. As a result, there is a higher 4 © 2022

likelihood that the country may have to reschedule its debt.

INVR = Real investment/GNP. If a country has higher savings and higher investments, it should lead to higher growth, reducing the likelihood of rescheduling. This supports the negative sign of the relationship. On the other hand, it is possible that the higher growth puts the country in a stronger bargaining position with its lenders and, consequently, it may be less intimidated by the threat of default. This may make the likelihood of rescheduling higher, suggesting a positive relationship between p and INVR. 10. What shortcomings are introduced by using traditional CRA models and techniques? In each case, what adjustments are made in the estimation techniques to compensate for the problems?

The following six items often are listed as problems in using these statistical models.

First, measuring the variables accurately and in a timely manner often is difficult because of data accessibility. These errors are further impacted by normal forecast errors that occur with the use of statistical models.

Second, the choice of rescheduling or not rescheduling often is not a dichotomous situation. Analysts seek to find variables that distinguish between only two possible outcomes: reschedulers and nonreschedulers. In actuality, a finer distinction may be necessary—for example, a distinction between those countries announcing a moratorium on only interest payments and those announcing a moratorium on both interest and principal payments.

Third, political risk factors are extremely difficult to quantify. One attempt to quantify political risk is the Index of Economic Freedom that includes measures of various activities that are considered to be related to the lack of government constraint or restriction. The index has a value of 0 to 100, with 100 indicating the most economic freedom. An alternative measure is the Corruption Perceptions Index which provides a similar measure, and scale ranging from 0 to 100.

Fourth, the portfolio effects of lending to more than one country are not considered.

Thus, the true amount of systematic risk added to the portfolio may be less than estimated by evaluating the rescheduling probability of countries independently. If an economic variable has a small systematic risk component relative to the unsystematic portion, the variable may be considered of little importance since its impact can be diversified away.

Fifth, statistical models are ill-prepared or designed to evaluate the incentives of both the borrowers and the lenders to negotiate a rescheduling of the debt. Borrowers benefit by lowering the present value of future payments at the expense of reducing the openness of the market to future borrowing as well as withstanding potentially adverse effects on trade. Lenders benefit by avoiding a possible default, collecting additional fees, and perhaps realizing tax benefits. Lenders, however, may also be subject to greater scrutiny 5 © 2022

by regulatory authorities and may have permanent changes in the maturity structure of their asset portfolios.

Finally, many of the key variables suffer from the problem of stability. That is, predictive performance in the past may not be a good indicator of predictive performance in the future. This implies that CRA models continuously must be updated.

11. What is systematic risk in terms of sovereign risk? Which of the variables often used in statistical models tend to have high systematic risk? Which variables tend to have low systematic risk?

Systematic risk refers to the risk effects that cannot be diversified away by lending to more than one country. In effect, some international economic situations will affect the economies of less developed countries in a similar manner. Economic research indicates that the DSR and the VAREX both have high systematic risk elements. Money supply growth and the import ratio seem to have low systematic risk elements.

12. The average 2ER (or VAREX = variance of export revenue) of a group of countries has been estimated at 20 percent. The individual VAREXes of two countries in the group, the Netherlands and Singapore, have been estimated at 15 percent and 28 percent, respectively. The regression of individual country VAREX on average VAREX provides the following beta (coefficient) estimates: N = Beta of the Netherlands = 0.80 S = Beta of Singapore = 0.20. a. Based only on the VAREX estimates, which country should be charged a higher risk premium? Explain.

Based on the VAREX measure alone, risk premiums should be lower for loans made to the Netherlands because its VAREX is lower than Singapore’s. VAREX measures the volatility of the export revenues and is one measure of the ability of countries to repay foreign debt. b. If FIs include systematic risk in their estimation of risk premiums, how would your conclusions to part (a) be affected? Explain.

Since the systematic beta of Singapore is lower than that of the Netherlands, it will reduce the overall systematic risk of an FI’s portfolio of foreign loans. In this case, it benefits the FI to add Singapore to its list of countries because its unsystematic risk can be diversified away. Thus, if the industrialized countries, including the Netherlands, are experiencing a recession and a decline in export revenues, Singapore’s exports are likely to be unaffected as evidenced by the low beta. This implies that the debt repayments between these two countries are not highly correlated, helping to reduce the FI’s total 6 © 2022

risk.

13. What are the benefits and costs of rescheduling to the following? a. A borrower.

Benefits: By rescheduling its debt, the borrower lowers the present value of its future payments in hard currencies to outside lenders. This allows it to increase its consumption of foreign imports and/or increase the rate of its domestic investment.

Costs: By rescheduling now, the borrower may close itself out of the market for loans in the future. As a result, even if the borrower encounters high-growth investment opportunities in the future, it may be difficult or impossible to finance them. Further, rescheduling may result in significant interference with the borrower’s international trade since it would be difficult to gain access to instruments such as letters of credit, without which trade may be more costly. b. A lender.

Benefits: Once a loan has been made, a rescheduling is much better than a borrower default. With a rescheduling, the FI lender may anticipate some present value loss of principal and interest on the loan. With an outright default, the FI stands to lose all its principal and future interest repayments. Further, the FI can renegotiate fees and various other collateral and option features into a rescheduled loan. Finally, there may be tax benefits to an FI’s taking a recognized write-down or loss in value on a rescheduled LDC loan portfolio.

Costs: Through rescheduling, loans become similar to long-term bonds or even equity, and the FI often becomes locked into a particular loan portfolio structure. Further, those FIs with large amounts of rescheduled loans are subject to greater regulatory attention.

For example, in the United States, such FIs may be placed on the regulators’ problem list of FIs. 14. Who are the primary sellers of LDC and EM debt? Who are the buyers? Why are FIs often both sellers and buyers of LDC and EM debt in the secondary markets?

The primary sellers of LDC and EM debt include large FIs who are willing to accept write-downs of loans and small FIs who no longer wish to be involved with the LDC and EM market. Buyers tend to be wealthy investors, hedge funds, FIs, and corporations who wish to use debt-for-equity swaps to further investment goals. FIs that are both buyers and sellers often do so to readjust their balance sheets to meet corporate goals.

15. Identify and describe the three market segments of the secondary market for LDC And EM debt.

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Sovereign bonds constitute government issued debt. Sovereign issuance has historically been primarily issued in foreign currencies external debt, either U.S. dollars or euros.

LDC and EM sovereign debt tends to have lower credit ratings than other sovereign debt because of the increased economic and political risks. Where most developed countries are either AAA or AA-rated, most LDC and EM issuance is rated below investment grade, though a few countries that have seen significant improvements have been upgraded to BBB or A ratings, and a handful of lower income countries have reached ratings levels equivalent to more profligate developed countries. Accordingly, sovereign bonds require higher interest spreads. Under the doctrine of sovereign immunity, the repayment of sovereign debt cannot be forced by the creditors and it is thus subject to compulsory rescheduling, interest rate reduction, or even repudiation. The only protection available to the creditors is threat of the loss of credibility and lowering of the international standing (the sovereign debt rating of the country which may make it much more difficult to borrow in the future.

Performing loans are the original or restructured sovereign loans on which the originating country continues to remain current in the payment of interest and principal.

Nonperforming loans are traded in the secondary markets at deep discounts because of nonpayment situations.

The following questions and problems are based on material presented in Appendix 14A. 16. What are the risks to an investing company participating in a debt-for-equity swap?

Debt-for-equity swap investors often face long periods before they can repatriate dividends, often have large withholding tax restrictions, have the long-term problem of potential expropriation or nationalization of assets, and face significant foreign exchange currency risk.

17. Chase Bank holds a $200 million loan to Argentina. The loans are being traded at bid-offer prices of 91-93 per 100 in the London secondary market. a. If Chase has an opportunity to sell this loan to an investment bank at a 7 percent discount, what are the savings after taxes compared with the revenue from selling the loan in the secondary market? Assume the tax rate is 40 percent.

The price that Chase could obtain from the investment bank is $200m(1 – 0.07) = $186m.

The tax loss benefit is $14m x 0.40 = $5.6m, for a net price of $186m + $5.6m = $191.60m.

In the secondary market, Chase would have had to sell the loans at 91cents on the dollar or $182 million. The tax loss benefit is $18m x 0.40 = $7.2m for a net price of $189.20.

Therefore, the savings from selling the loans to the investment bank as opposed to the secondary market is $191.60m - $189.20m = $2.4 million.

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b. The investment bank in turn sells the debt at a 6 percent discount to a real estate company planning to build apartment complexes in Argentina. What is the profit after taxes to the investment bank?

The investment bank purchased the loan for $186 million, and it sells the loan for $188 million ($200m(1 – 0.06) = $188m). Thus, profit before taxes is $188m - $186m = $2 million and profit after taxes is $2m(1 - 0.40) = $1.20 million. c. The real estate company converts this loan into pesos under a debt-for-equity swap organized by the Argentinian government. The official rate for dollar to peso conversion is P1.05/$1. The free market rate is P1.09/$1. How much did the real estate company save by investing in Argentina through the debt-forequity swap program as opposed to directly investing $200 million using the free market rates?

If the real estate company had invested directly, it would have received $200m x 1.09 = 218 million pesos. By purchasing through the debt-for-equity swap, the company pays $188 million and receives $200m x 1.05 = 210 million pesos, for an equivalent rate of 210m/188m = P1.117/$. Thus, it still saves by purchasing through the debt-for-equity swap (P1.117/$ > P1.09/$). d. How much would Chase benefit from doing a local currency debt-for-equity swap itself? Why does the bank not do this swap?

Assuming the bank could convert the loan at $200 million in to pesos at P1.05/$, receiving $200m x 1.05 = 210 million pesos. The actual benefit was $191.6 million.

Thus, the bank would gain $18.4 million.

Chase is not allowed to participate in real equity purchases in other countries by Federal Reserve Regulation K, nor is it allowed to engage in commerce in other countries.

Further, a long-term pesos-denominated position on the balance sheet may create more credit, liquidity, and foreign exchange risk than the benefits are worth.

18. Zlick Company plans to invest $20 million in Chile to expand its subsidiary’s manufacturing output. Zlick has two options. It can convert the $20 million at the current exchange rate of 410 pesos to a dollar (i.e., P410/$1), or it can engage in a debt-for-equity swap with its bank, City Bank, by purchasing Chilean debt and then swapping that debt into Chilean equity investments. a. If City Bank quotes bid-offer prices of 94-96 for Chilean loans, what is the bank expecting to receive from Zlick Corporation (ignore taxes)? Why would City Bank want to dispose of this loan?

City Bank expects to receive 96 cents to the dollar since it is selling this loan, i.e. 0.96 x 9 © 2022

20m = $19.20 million. It may wish to sell this loan to reduce its portfolio of troubled or bad quality assets. As U.S. banks experienced problems with several of their foreign loans, their choices were limited to either writing off the loans or disposing of them. The development of an active secondary market has made it easier for FIs to sell them at a discount and rearrange their composition of loans. b. If Zlick decides to purchase the debt from City Bank and convert it to equity, it will have to exchange it at the official rate of P400/$1. Is this option better than investing directly in Chile at the free market rate of P410/$1?

If exchanged at market rates: $20m x P410 = P8,200 million, for an effective rate of P410/$. If exchanged through a debt-for-equity swap: $20m x P400 = P8,000 million, for an effective price of P8,000m/$19.20m = P416.67/$. Therefore, Zlick should choose the debt-for-equity swap option. c. What official exchange rate will cause Zlick to be indifferent between the two options?

For the options to be equal, the effective price must be: ($20m x X)/$19.20m = P410 => X = (P410 x $19.20m)/$20m = P393.60/$ The Chilean government could reduce the official rate to as low as P393.60/$ and the two options will still be equal. This is because the discount obtained from the secondary market is substantial.

19. What is concessionality in the process of rescheduling a loan?

Concessionality refers to the net cost to the FI in restructuring a loan. The amount of concessionality is determined by subtracting the present value of the restructured loan from the present value of the original loan.

20. Which variables typically are negotiation points in a multiyear restructuring agreement (MYRA)? How do changes in these variables provide benefits to the borrower and to the lender?

The five common elements typically found in the MYRA negotiation include: (a)

A fee charged by the FI to cover the cost of the restructuring.

(b)

The interest rate on the loan is usually lowered to allow easier repayment of the loan by the borrowing country.

(c)

A grace period may be created to allow the country to build a reserve of hard currency from which it can repay the loan.

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(d)

The maturity of the loan normally is lengthened. This process reduces the periodic payment stream for the borrower country.

(e)

Various option and guarantee features may allow the lender to choose the currency for repayment and/or to provide protection in the case of default.

21. How would the restructuring, such as rescheduling, of sovereign bonds affect the interest rate risk of the bonds? Is it possible that such restructuring would cause the FI’s cost of capital to not change? Explain.

To the extent that the bonds have longer maturities and lower interest rates, the duration of these bonds will increase. Thus, the interest rate risk will increase. While it is possible that the FI’s cost of capital will not change, an FI with a significant portion of its assets in LDC or EM debt that has been restructured will likely find an adverse adjustment in its cost of capital.

22. A bank is in the process of renegotiating a sovereign loan. The principal outstanding is $50 million and is to be paid back in two installments of $25 million each, plus interest of 8 percent. The new terms will stretch the loan out to five years with only interest payments of 6 percent, no principal payments, for the first three years. The principal will be paid in the last two years in payments of $25 million along with the interest. The cost of funds for the bank is 6 percent for both the old loan and the renegotiated loan. An up-front fee of 1 percent is to be included for the renegotiated loan. a. What is the present value of the existing loan for the bank?

The present value of the loan prior to rescheduling is: Payment in Year 1: Principal + Interest = $25m + 0.08 x $50m = $29m Payment in Year 2: Principal + Interest = $25m + 0.08 x $25m = $27m PV = PVn=1, k=6 ($29m) + PVn=2, k=6 ($27m) = $51.3884 million b. What is the present value of the rescheduled loan for the bank?

Interest payments in years 1, 2 and 3: 0.06 x $50 = $3m Payment in Year 4: Principal + Interest = $25m + 0.06 x $50m = $28m Payment in Year 5: Principal + Interest = $25m + 0.06 x $25m = $26.5m PV = PVAn=3, k=6 ($3m) + PVn=4, k=6 ($28m) + PVn=5, k=6 ($26.5m) = $50 million Up-front fee = 0.01 x $50m = $0.50 million PV (total) = $50.50 million c. Is the concessionality positive or negative for the bank?

Concessionality = PVo - PVR = PV of old loan - PV of rescheduled loan 11 © 2022

= $51.3884m - $50.50m = $0.884 million 23. A bank is in the process of renegotiating a three-year nonamortizing loan to Greece.

The principal outstanding is $20 million, and the interest rate is 8 percent. The new terms will extend the loan to 10 years at a new interest rate of 6 percent. The cost of funds for the bank is 7 percent for both the old loan and the renegotiated loan. An up-front fee of 50 basis points is to be included for the renegotiated loan. a. What is the present value of the existing loan for the bank?

PV of old loan = PVAn=3,k=7%($1.6m) + PVn=3,k=7%($20m) = $20.5249 million b. What is the present value of the rescheduled loan for the bank?

PV of new loan = PVAn=10,k=7%($1.2m) + PVn=10,k=7%($20m) + up-front fee of $0.10m = $18.5953 million + $0.10 million = $18.6953 million c. What is the concessionality for the bank?

Concessionality = $20.5249m - $18.6953m = $1.8296 million d. What should be the up-front fee to make the concessionality zero?

Concessionality = $20.5249m - $18.5953m - x = 0  x = $1.9296 million or 9.65 percent.

24. A $20 million loan outstanding to the Nigerian government is currently in arrears with City Bank. After extensive negotiations, City Bank agrees to reduce the interest rate from 10 percent to 6 percent and to lengthen the maturity of the loan to 10 years from the present 5 years remaining to maturity. The principal of the loan is to be paid at maturity. There will be no grace period and the first interest payment is expected at the end of the year. a. If the cost of funds is 5 percent for the bank, what is the present value of the loan prior to the rescheduling?

Interest payments in years 1 - 5: 0.10 x $20m = $2m PV = PVAn=5,k=5($2m) + PVn=5,k=5($20m) = $24.3295 million b. What is the present value of the rescheduled loan to the bank?

Interest payments in years 1 - 10: 0.06 x $20m = $1.2m PV = PVAn=10,k=5($1.2m) + PVn=10,k=5($20m) = $21.5443 million c. What is the concessionality of the rescheduled loan if the cost of funds remains at 5 percent and an up-front fee of 5 percent is charged?

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Up-front fee = 0.05 x $20m = $1 million PV (total) = $21.5443 million + $1 million = $22.5443 million Concessionality = PVo - PVR = PV of old loan - PV of rescheduled loan = $24.3259m - $22.5443m = $1.7852 million d. What up-front fee should the bank charge to make the concessionality equal zero?

The bank has to increase its up-front fees by $1.7852 for a total of $2.7852, or 13.93%.

25. A bank was expecting to receive $100,000 from a loan issued to the Spanish government. Since Spain has problems repaying the loan immediately, the bank extends the loan for another year at the same interest rate of 10 percent. However, in the rescheduling agreement, the bank reserves the right to exercise an option for receiving the payment in euros, equal to €87,813, converted at the current exchange rate of €0.7983/$. a. If the cost of funds to the bank is also assumed to be 10 percent, what is the value of this option built into the agreement if only two possible exchange rates are expected at the end of the year, €0.8467/$ or €0.7499/$, with equal probability?

Without the option, the amount expected at the end of the year = $110,000. If the euro depreciates to €0.8467/$, the amount received by the bank is the maximum of $110,000, or €87,813/0.8467 = $103,712.06. If the euro appreciates to €0.7499/$, the amount received by the bank is the maximum of $110,000, or €87,813/0.7499 = $117,099.61.

With the option, the expected amount received is 0.50($110,000) + 0.50($117,099.61) = $113,549.81. The present value of the option is $113,549.81 - $110,000 = $3,549.81/1.1 = $3,227.10 b. How would your answer differ, if the probability of the exchange rate being €0.8467/$ is 70 percent and that of €0.7499/$ is 30 percent?

With the option, the expected amount received is 0.70($110,000) + 0.30($117,099.61) = $112,129.98. The present value of the option = $112,129.88 - $110,000 = $2,129.88/1.1 = $1,936.25. c. Does the currency option have more or less value as the volatility of the exchange rate increases?

The option will have more value as the volatility of the exchange rate increases.

26. What are the major benefits and costs of loan sales to an FI? 13 © 2022

The benefits of loan sales to an FI: (a) They remove bad loans from the balance sheet, freeing resources for other investments as well as improving the FI’s portfolio composition. (b)

They may signal to market investors that the FI is in a position to bear losses. This hypothesis has been confirmed by empirical studies showing stock prices reacting favorably to news of FIs adding additional reserves to cover loan reserves.

(c)

Losses can be deducted, providing write-offs for the FI.

The costs of loan sales to an FI: (a) There is an actual loss equal to the tax adjusted difference between the face value of the loan and its market value at the time of sale. (b)

Secondary loan prices are very volatile and can fluctuate dramatically, making the planning of the optimal time to sell-off difficult.

27. What are the major costs and benefits of converting loans to bonds for an FI? The advantage of converting loans to bonds for an FI is the increased liquidity, which makes bonds an attractive instrument to hold. Because of the full or partial collateral backing, these bonds are also normally senior in status to any remaining loans or sovereign bonds of that country. A disadvantage is that bonds have much longer maturities and there is usually a loss entailed because the restructured value of the bond is usually lower than the present value of the loan.

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Solutions for End-of-Chapter Questions and Problems: Chapter Fifteen 1.

What is meant by market risk?

Market risk is the risk related to the uncertainty of an FI’s earnings on its trading portfolio.

Market risk is caused by changes in market conditions such as interest rate risk and foreign exchange risk. Market risk emphasizes the risks to FIs that actively trade assets and liabilities rather than hold them for longer term investment, funding, or hedging purposes.

2.

Why is the measurement of market risk important to the manager of a financial institution?

Measurement of market risk can help an FI manager in the following ways: a. Provide information on the risk positions taken by individual traders. b. Establish limit positions on each trader based on the market risk of their portfolios. c. Help allocate resources to departments with lower market risks and appropriate returns. d. Evaluate performance based on risks undertaken by traders in determining optimal bonuses. e. Help develop more efficient internal models so as to avoid using standardized regulatory models.

3.

What is meant by daily earnings at risk (DEAR)? What are the three measurable components? What is the price volatility component?

DEAR, or daily earnings at risk, is a measure of market risk over the next 24 hours. It is defined as the estimated potential loss of a portfolio's value over a one-day period as a result of adverse moves in market conditions, such as changes in interest rates, foreign exchange rates, and market volatility. DEAR is comprised of (a) the dollar value of the position, (b) the price sensitivity of the asset to changes in the risk factor, and (c) the adverse move in the yield. The product of the price sensitivity of the asset and the adverse move in the yield provides the price volatility component.

4.

Follow Bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent and the standard deviation is 12 basis points. a. What is the modified duration of the bond?

MD = D/(1 + R) = 5/(1.07) = 4.6729 years b. What is the maximum adverse daily yield move given that we desire no more than a 1 percent chance that yield changes will be greater than this maximum?

Potential adverse move in yield at 1 percent = 2.33 = 2.33 x 0.0012 = 0.002796 1 © 2022

c. What is the price volatility of this bond?

Price volatility = MD x potential adverse move in yield = 4.6729 x 0.002796 = 0.013065 or 1.3065 percent d. What is the daily earnings at risk for this bond?

DEAR = ($ market value of position) x (price volatility) = $1,000,000 x 0.013065 = $13,065 5.

How can DEAR be adjusted to account for potential losses over multiple days? What would be the VAR for the bond in problem 4 for a 10-day period? What statistical assumption is needed for this calculation? Could this treatment be critical?

The DEAR can be adjusted to account for losses over multiple days using the formula N-day VAR = DEAR x [N]½, where N is the number of days over which potential loss is estimated. Nday VAR is a more realistic measure when it requires a longer period for an FI to unwind a position, that is, if markets are less liquid. The value for the 10-day VAR in problem 4 above is $13,065 x [10]½ = $41,315.

According to the above formula, the relationship assumes that yield changes are independent and daily volatility is approximately constant. This means that losses incurred one day are not related to losses incurred the next day. Recent studies have indicated that this is not the case, but that shocks are autocorrelated in many markets over long periods of time.

6.

The DEAR for a bank is $8,500. What is the VAR for a 10-day period? A 20-day period?

Why is the VAR for a 20-day period not twice as much as that for a 10-day period?

For the 10-day period: VAR = 8,500 x [10]½ = 8,500 x 3.1623 = $26,879 For the 20-day period: VAR = 8,500 x [20]½ = 8,500 x 4.4721 = $38,013 The reason that 20-day VAR  (2 x 10-day VAR) is because [20]½  (2 x [10]½). The interpretation is that the daily effects of an adverse event become less as time moves farther away from the event.

7.

The mean change in the daily yields of a 15-year, zero-coupon bond has been five basis points (bp) over the past year with a standard deviation of 15 bp. Use these data and assume that the yield changes are normally distributed. a. What is the highest yield change expected if a 99 percent confidence limit is required; that is, adverse moves will not occur more than 1 day in 100?

2 © 2022

If yield changes are normally distributed, 98 percent of the area of a normal distribution will be 2.33 standard deviations (2.33) from the mean – that is, 2.33 – and 2 percent of the area under the normal distribution is found beyond ± 2.33 (1 percent under each tail, -2.33 and +2.33, respectively). Thus, for a one-tailed distribution, the 99 percent confidence level will represent adverse moves that not occur more than 1 day in 100. In this example, it means 2.33 x 15 bp = 34.95 bp. Thus, the maximum adverse yield change expected for this zero-coupon bond is an increase of 34.95 basis points, or 0.3495 percent, in interest rates. b. What is the highest yield change expected if a 95 percent confidence limit is required; adverse movers will not occur more than 1 day in 20?

If yield changes are normally distributed, 90 percent of the area of a normal distribution will be 1.65 standard deviations (1.65) from the mean – that is, 1.65 – and 10 percent of the area under the normal distribution is found beyond ± 1.65 (5 percent under each tail, -1.65 and +1.65, respectively). Thus, for a one-tailed distribution, the 95 percent confidence level will represent adverse moves that not occur more than 1 day in 20.Thus, the maximum adverse yield change expected for this zero-coupon bond is an increase of (1.65 x 15 =) 24.75 basis points, or 0.2475 percent, in interest rates.

8.

In what sense is duration a measure of market risk?

Market risk calculations are typically based on the trading portion of an FIs fixed-rate asset portfolio because these assets must reflect changes in value as market interest rates change. As such, duration or modified duration provides an easily measured and usable link between changes in the market interest rates and changes in the market value of fixed-income assets.

9.

Bank Alpha has an inventory of AAA-rated, 15-year zero-coupon bonds with a face value of $400 million. The bonds currently are yielding 9.5 percent in the over-the-counter market. a. What is the modified duration of these bonds?

MD = D/(1 + R) = 15/(1.095) = 13.6986 b. What is the price volatility if the potential adverse move in yields is 25 basis points?

Price volatility = (MD) x (potential adverse move in yield) = (13.6986) x (0.0025) = 0.03425 or 3.425 percent. c. What is the DEAR? Daily earnings at risk (DEAR) = ($ market value of position) x (Price volatility) Dollar value of position = $400m/(1 + 0.095)15 = $102,529,350. Therefore, DEAR = $102,529,350 x 0.03425 = $3,511,279.

3 © 2022

d. If the price volatility is based on a 99 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard deviation of daily yield changes?

The potential adverse move in yields = confidence limit value x standard deviation value.

Therefore, 25 basis points = 2.33 x , and  = 0.0025/2.33 = 0.001073 or 10.73 basis points.

10.

Bank Beta has an inventory of AAA-rated, zero-coupon bonds with a maturity of 13.42 years and a face value of $127,503,041. The modified duration of these bonds is 12.5 years, the DEAR is $2,150,000, and the potential adverse move in yields is 35 basis points. What is the market value of the bonds, the yield on the bonds, and the duration of the bonds?

Price volatility = (MD) x (potential adverse move in yield) = (12.5) x (0.0035) = 0.04375 or 4.375 percent DEAR = ($ market value of position) x (Price volatility) DEAR = $2,150,000 = ($ value of position) x 0.04375 = > ($ value of position) = $2,150,000/0.04375 = $49,142,857 = market value Dollar value of position = $127,503,041/(1 + yield)13.42 = $49,142,857. = > yield = ($127,503,041/$49,142,857)1/13.42 – 1 = 7.36% Therefore, the bonds currently are yielding 7.36 percent in the over-the-counter market.

MD = D/(1 + R) = 12.5 = D/(1.0736) = > D = 12.5 x 1.0736 = 13.42 years 11.

12.

Bank Two has a portfolio of bonds with a market value of $200 million. The bonds have an estimated price volatility of 0.95 percent. What are the DEAR and the 10-day VAR for these bonds?

DEAR

= ($ market value of position) x (Price volatility) = $200 million x 0.0095 = $1,900,000

10-day VAR

= DEAR x N = $1,900,000 x 10 = $1,900,000 x 3.1623 = $6,008,328

Suppose that an FI has a €1.6 million long trading position in spot euros at the close of business on a particular day. Looking back at the daily percentage changes in the exchange rate of the €/$ for the past year, the volatility or standard deviation (σ) of daily percentage changes in the €/$ spot exchange rate was 62.5 basis points (bp). Calculate the FI’s daily earnings at risk from this position (i.e., adverse moves in the FX markets with respect to the value of the euro against the dollar will not occur more than 1 percent of the time, or 1 day in every 100 days) if the spot exchange rate is €0.80/$1, or $1.25/€, at the daily close.

4 © 2022

The first step is to calculate the dollar-equivalent amount of the position.

Dollar equivalent value of position = FX position x ($ per unit of foreign currency) = €1.6 million x $1.25/€ = $2 million If changes in exchange rates are historically normally distributed, the exchange rate must change in the adverse direction by 2.33σ, or FX volatility = 2.33 x 62.5 bp = 145.625 bp or 1.45625% As a result, DEAR = Dollar value of position x FX volatility = $2 million x 0.0145625 = $29,125 This is the potential daily earnings at risk exposure to adverse euro to dollar exchange rate changes for the bank from the €1.6 million spot currency holding.

13.

14.

Bank of Southern Vermont has determined that its inventory of 20 million euros (€) and 25 million British pounds (£) is subject to market risk. The spot exchange rates are $1.20/€ and $1.60/£, respectively. The σ’s of the spot exchange rates of the € and £, based on the daily changes of spot rates over the past six months, are 65 bp and 45 bp, respectively.

Determine the bank’s 10-day VAR for both currencies. Use adverse rate changes in the 99th percentile.

FX position of € FX position of £

= €20m x 1.20 = $24 million = £25m x 1.60 = $40 million

FX volatility € FX volatility £

= 2.33 x 65bp = 151.45bp, or 1.5145% = 2.33 x 45bp = 104.85bp, or 1.0485%

DEAR

= ($ market value of position) x (Price volatility)

DEAR of € DEAR of £

= $24m x 0.015145 = $363,480 = $40m x 0.010485 = $419,400

10-day VAR of € 10-day VAR of £

= $363,480 x 10 = $363,480 x 3.1623 = $1,149,425 = $419,400 x 10 = $419,400 x 3.1623 = $1,326,259

Bank of Bentley has determined that its inventory of yen (¥) and Swiss franc (SFr) denominated securities is subject to market risk. The spot exchange rates are ¥120.00/$ and SFr0.9500/$, respectively. The σ’s of the spot exchange rates of the ¥ and SFr, based on the daily changes of spot rates over the past six months, are 75 bp and 55 bp, respectively.

Using adverse rate changes in the 99th percentile, the 10-day VARs for the two currencies,

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¥ and SFr, are $350,000 and $500,000, respectively. Calculate the yen and Swiss francdenominated value positions for Bank of Bentley.

10-day VAR = DEAR x N => 10-day VAR of ¥ = $350,000 = DEAR x 10 = > DEAR = $350,000/10 = $110,680 10-day VAR of SFr = $500,000 = DEAR x 10 = > DEAR = $500,000/10 = $158,114 FX volatility = 2.33 x daily changes of spot rates over the past six months => FX volatility ¥ = 2.33 x 75bp = 0.017475, or 1.7475% FX volatility SFr = 2.33 x 55bp = 0.012815, or 1.2815% DEAR = ($ market value of position) x (Price volatility) DEAR of ¥ = $110,680 = ($ market value of position) x 0.017475 => ($ value of position) = $110,680/0.017475 = $6,333,603 DEAR of SFr = $158,114 = ($ market value of position) x 0.012815 => ($ value of position) = $158,114/0.012815 = $12,338,188 FX position in ¥ = Yen position/120.00 = $6,333,603 = > Yen position = 120.00 x $6,333,603 = ¥760,032,399 FX position in SFr = SFr position/0.9500 = $12,338,188 = > SFr position = 0.9500 x $12,338,188 = SFr11,721,279 15.

Suppose that an FI holds a $15 million trading position in stocks that reflect the U.S. stock market index (e.g., the S&P 500). Over the last year, the σm of the daily returns on the stock market index was 156 bp. Calculate the DEAR for this portfolio of stocks using a 99 percent confidence limit.

Since the portfolio of stocks reflect the U.S. stock market index, the β = 1. Thus, the DEAR for equities is: DEAR = Dollar market value of position x Stock market return volatility = $15,000,000 x 2.33 σm The σm of the daily returns on the stock market index was 156 bp over the last year. So, Stock market return volatility = 2.33 x 1.56% = 3.6348% and DEAR = $15,000,000 x 0.036348 = $545,220 That is, the FI stands to lose at least $545,220 in value if adverse stock market returns materialize tomorrow.

16.

Bank of Alaska’s stock portfolio has a market value of $10 million. The beta of the 6 © 2022

portfolio approximates the market portfolio, whose standard deviation (m) has been estimated at 1.5 percent. What is the five-day VAR of this portfolio using adverse rate changes in the 99th percentile?

DEAR = ($ market value of portfolio) x (2.33 x m ) = $10m x (2.33 x 0.015) = $10m x 0.03495 = $349,500 5-day VAR = $349,500 x 5 = $349,500 x 2.2361 = $781,506 17.

Jeff Resnick, vice president of operations at Choice Bank, is estimating the aggregate daily DEAR of the bank’s portfolio of assets consisting of loans (L), foreign currencies (FX), and common stock (EQ). The individual DEARs are $300,700; $274,000; and $126,700 respectively. If the correlation coefficients (ij) between L and FX, L and EQ, and FX and EQ are 0.3, 0.7, and 0.0, respectively, what is the DEAR of the aggregate portfolio? (DEAR )2 + (DEAR )2 + (DEAR )2  L FX EQ  

0.5

DEAR portfolio =



+ (2 L,FX x DEARL x DEAR FX )



 

+ (2L,EQ x DEARL x DEAREQ )

 

 + (2FX,EQ x DEARFX x DEAREQ )

 0.5

2 2 2 = $300,700 +$274,000 + $126,700 + 2(0.3)($300,700)($274,000)  + 2(0.7)($300,700)($126,700) + 2(0.0)($274,000)($126,700)  

=$284,322,626,0000.5 =$533,219 18.

Calculate the DEAR for the following portfolio with the correlation coefficients and then with perfect positive correlation between various asset groups.

Assets Stocks (S) Foreign Exchange (FX) Bonds (B)

Estimated DEAR $300,000 200,000 250,000

(S,FX) -0.10

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(S,B) 0.75

(FX,B) 0.20

) + (DEAR ) + (DEAR )    (DEAR S FX B  2

2

2 0.5

+ (2S,FX x DEARS x DEARFX ) DEAR portfolio =  + (2S,B x DEARS x DEARB)   + (2FX,B x DEARFX x DEARB )

    0.5

= $300,000 + $200,000 +$250,000 + 2(−0.1)($300,000)($200,000)  + 2(0.75)($300,000)($250,000) + 2(0.20)($200,000)($250,000)   2

2

2

=$313,000,000,0000.5 =$559,464 What is the amount of risk reduction resulting from the lack of perfect positive correlation between the various assets groups?

DEAR portfolio(correlation coefficients = 1) = 0.5 2 2 2   $300,000 +$200,000 +$250,000 + 2(1.0)($300,000)($200,000) =  + 2(1.0)($300,000)($250,000) + 2(1.0)($200,000)($250,000)   =$562,500,000,0000.5 =$750,000 The DEAR for a portfolio with perfect correlation would be $750,000. Therefore, the risk reduction is $750,000 - $559,464 = $190,536.

19.

What are the advantages of using the back simulation approach to estimate market risk?

Explain how this approach would be implemented.

The advantages of the back simulation approach to estimating market risk are that (a) it is a simple process, (b) it does not require that asset returns be normally distributed, and (c) it does not require the calculation of correlations or standard deviations of returns. Implementation requires the calculation of the value of the current portfolio of assets based on the prices or yields that were in place on each of the preceding 500 days (or some large sample of days). These data are rank-ordered from worst to best case and percentile limits are determined. For example, the one percent worst case scenario provides an estimate with 99 percent confidence that the value of the portfolio will not fall more than this amount.

20.

Export Bank has a trading position in Japanese yen (¥) and Swiss francs (SFr). At the close of business on February 4, the bank had ¥450 million and SFr10 million. The exchange rates for the most recent six days are given below: 8 © 2022

Exchange Rates per U.S. Dollar at the Close of Business

9 © 2022

Japanese yen Swiss francs

2/4 120.13 0.9540

2/3 120.84 0.9575

2/2 120.14 0.9533

2/1 123.05 0.9617

1/29 124.35 0.9557

1/28 124.32 0.9523

a. What is the foreign exchange (FX) position in dollar equivalents using the FX rates on February 4?

Japanese yen: ¥450,000,000/¥120.13 = $3,745,942 Swiss francs: SFr10,000,000/SFr0.9540 = $10,482,180 b. What is the definition of delta as it relates to the FX position?

Delta measures the change in the dollar value of each FX position if the foreign currency depreciates by 1 percent against the dollar. c. What is the sensitivity of each FX position; that is, what is the value of delta for each currency on February 4?

Japanese yen:

1.01 x current exchange rate = 1.01 x ¥120.13 = ¥121.3313/$ Revalued position in $s = ¥450,000,000/121.3313 = $3,708,853 Delta of $ position to Yen = $3,708,853 - $3,745,942 = -$37,089

Swiss francs:

1.01 x current exchange rate = 1.01 x SFr0.9540 = SFr0.96354 Revalued position in $s = SFr10,000,000/0.96354 = $10,378,396 Delta of $ position to CHF = $10,378,396 - $10,482,180 = -$103,784

d. What is the daily percentage change in exchange rates for each currency over the fiveday period?

Day 2/4 2/3 2/2 2/1 1/29

Japanese yen: -0.58755 0.58265 -2.36489 -1.04544 0.02413

Swiss franc -0.36554 0.44057 -0.87345 0.62781 0.35703

% Change = (Ratet/Ratet-1) - 1 x 100

e. What is the total risk faced by the bank on each day? What is the worst-case day?

What is the best-case day?

Day 2/4 2/3

Delta -$37,089 -$37,089

Japanese yen % Rate  Risk -0.58755 $21,792 0.58265 -$21,610

Swiss francs Delta % Rate  Risk -$103,784 -0.36554 $37,937 -$103,784 0.44057 -$45,724 10

© 2022

Total Risk $59,729 -$67,334

2/2 2/1 1/29

-$37,089 -$37,089 -$37,089

-2.36489 $87,710 -1.04544 $38,774 0.02413 -$895

-$103,784 -$103,784 -$103,784

-0.87345 $90,650 0.62781 -$65,157 0.35703 -$37,054

$178,360 -$26,383 -$37,949

The worst-case day is February 3, and the best-case day is February 2. f. Assume that you have data for the 500 trading days preceding February 4. Explain how you would identify the worst-case scenario with a 99 percent degree of confidence?

The appropriate procedure would be to repeat the process illustrated in part (e) above for all 500 days. The 500 days would be ranked on the basis of total risk from the worst-case to the bestcase. The one percent from the absolute worst-case situation would be day 5 in the ranking. g. Explain how the 1 percent value at risk (VAR) position would be interpreted for business on February 5.

Management would expect with a confidence level of 99 percent that the total risk on February 5 would be no worse than the total risk value for the 5th worst day in the previous 500 days. This value represents the VAR for the portfolio. h. How would the simulation change at the end of the day on February 5? What variables and/or processes in the analysis may change? What variables and/or processes will not change?

The analysis can be upgraded at the end of the each day. The values for delta may change for each of the assets in the analysis. As such, the value for VAR may also change. Any historical data used in the analysis will not change.

21.

Export Bank has a trading position in euros and Australian dollars. At the close of business on October 20, the bank had €22 million and A$40 million. The exchange rates for the most recent six days are given below: Exchange Rates per U.S. Dollar at the Close of Business 10/20 10/19 10/18 10/17 10/16 10/15 Euros 0.8800 0.8770 0.8575 0.8675 0.8750 0.8915 Australian $s 1.2900 1.2750 1.3000 1.2855 1.2705 1.2660 a. What is the foreign exchange (FX) position in dollar equivalents using the FX rates on October 20?

Euros: Australian $s:

€22 million/€0.8800 = $25,000,000 A$40 million/A$1.2900 = $31,007,752

b. What is the sensitivity of each FX position; that is, what is the value of delta for each currency on October 20?

11 © 2022

Euros:

1.01 x current exchange rate = 1.01 x €0.8800 = €0.8888/$ Revalued position in $s = €22 million/€0.8888 = $24,752,475 Delta of $ position to € = $24,752,475 - $25,000,000 = -$247,525

Australian $s:

1.01 x current exchange rate = 1.01 x A$1.2900 = A$1.3029 Revalued position in $s = A$40 million/1.3029 = $30,700,744 Delta of $ position to A$ = $30,700,744 - $31,007,752 = -$307,007

c. What is the daily percentage change in exchange rates for each currency over the fiveday period?

Day 10/20 10/19 10/18 10/17 10/16

Euro: 0.34208 2.27405 -1.15274 -0.85714 -1.85081

Australian $s % Change = (Ratet/Ratet-1) - 1 * 100 1.17647 -1.92308 1.12797 1.18064 0.35545

d. What is the total risk faced by the bank on each day? What is the worst-case day?

What is the best-case day?

Day 10/20 10/19 10/18 10/17 10/16

Euro % Rate  Delta Risk -$247,525 0. 34208 -$84,672 -$247,525 2. 27405 -$562,884 -$247,525 -1.15274 $285,331 -$247,525 -0.85714 $212,164 -$247,525 -1.85081 $458,122

Australian $s Total % Rate  Delta Risk Risk -$307,007 1.17647 -$361,185 -$445,857 -$307,007 -1.92308 $590,399 $27,515 -$307,007 1.12797 -$346,294 -$60,963 -$307,007 1.18064 -$362,465 -$150,301 -$307,007 0.35545 -$109,126 $348,996

The worst-case day is October 20, and the best-case day is October 16.

22.

What is the primary disadvantage to the back simulation approach in measuring market risk? What effect does the inclusion of more observation days have as a remedy for this disadvantage? What other remedies can be used to deal with the disadvantage?

The primary disadvantage of the back simulation approach is the confidence level contained in the number of days over which the analysis is performed. One possible solution to the problem is to go back further in time and use more days and to estimate the 1 percent VAR inclusive of the extra daily observations. The problem is that as one goes back farther in time, past observations may become decreasingly relevant in predicting VAR in the future.

12 © 2022

23.

How is Monte Carlo simulation useful in addressing the disadvantages of back simulation?

What is the primary statistical assumption underlying its use?

Monte Carlo simulation can be used to generate additional observations that more closely capture the statistical characteristics of recent experience. The generating process is based on the historical variance-covariance matrix of value changes. The values in this matrix are multiplied by random numbers that produce results that pattern closely the actual observations of recent historic experience.

24.

What is the difference between VAR and expected shortfall (ES) as measure of market risk?

VAR corresponds to a specific point of loss on the probability distribution. It does not provide information about the potential size of the loss that exceeds it, i.e., VAR completely ignores the patterns and the severity of the losses in the extreme tail. Thus, VAR gives only partial information about the extent of possible losses, particularly when probability distributions are non-normal. The drawbacks of VAR became painfully evident during the financial crisis as asset returns plummeted into the “fat tail” region of non-normally shaped distributions. FIs managers and regulators were forced to recognize that VAR projections of possible losses far underestimated actual losses on extreme bad days. Expected shortfall (ES), also referred to as conditional VAR and expected tail loss, is a measure of market risk that estimates the expected value of losses beyond a given confidence level, i.e., it is the average of VARs beyond a given confidence level. ES, which incorporates points to the left of VAR, is larger when the probability distribution exhibits fat tail losses. Accordingly, ES provides more information about possible market risk losses than VAR. For situations in which probability distributions exhibit fat tail losses, VAR may look relatively small, but ES may be very large.

25.

Consider the following discrete probability distribution of payoffs for two securities, A and B, held in the trading portfolio of an FI: Probability 50.00% 49.00 1.00

A $80m 60m -740m

Probability 50.00% 49.00 0.40 0.60

B $80m 68m -740m -1,393m

Which of the two securities will add more market risk to the FI’s trading portfolio according to the VAR and ES measures?

The expected return on security A = 0.50($80m) + 0.49($60m) + 0.01(-$740m) = $62m The expected return on security B = 0.50($80m) + 0.49($68m) + 0.0040(-$740m) + 0.0060(-$1,393m) = $62m For a 99% confidence level, VARA = VARB = -$740m For a 99% confidence level, ESA = -$740m, while ESB = 0.40(-$740m) + 0.60(-$1,393m) = -$1,131.8m 13 © 2022

While the VAR is identical for both securities, the ES finds that security B has the potential to subject the FI to much greater losses than security A. Specifically, if tomorrow is a bad day, VAR finds that there is a 1 percent probability that the FI’s losses will exceed $740 million on either security. However, if tomorrow is a bad day, ES finds that there is a 1 percent probability that the FI’s losses will exceed $740 million if security A is in its trading portfolio, but losses will exceed $1,131.8 million if security B is in its trading portfolio.

26.

Consider the following discrete probability distribution of payoffs for two securities, A and B, held in the trading portfolio of an FI: Probability 55.00% 44.00 1.00

A $120m 95m -1,100m

Probability 55.00% 44.00 0.30 0.70

B $120m 100m -1,100m -1,414m

Which of the two securities will add more market risk to the FI’s trading portfolio according to the VAR and ES measures?

The expected return on security A = 0.55($120m) + 0.44($95m) + 0.01(-$1,100m) = $96.8m The expected return on security B = 0.55($120m) + 0.44($100m) + 0.0030(-$1,100m) + 0.0070(-$1,414m) = $96.8m For a 99% confidence level, VARA = VARB = -$1,100m For a 99% confidence level, ESA = -$1,100m, while ESB = 0.30(-$1,100m) + 0.70(-$1,414m) = -$1,319.8m Thus, while the VAR is identical for both securities, the ES finds that security B has the potential to subject the FI to much greater losses than security A. Specifically, if tomorrow is a bad day, VAR finds that there is a 1 percent probability that the FI’s losses will exceed $1,100 million on either security. However, if tomorrow is a bad day, ES finds that there is a 1 percent probability that the FI’s losses will exceed $1,100 million if security A is in its trading portfolio, but losses will exceed $1,319.8m if security B is in its trading portfolio.

27.

An FI has ₤5 million in its trading portfolio on the close of business on a particular day.

The current exchange rate of pounds for dollars is ₤0.6400/$, or dollars for pounds is $1.5625, at the daily close. The volatility, or standard deviation (σ), of daily percentage changes in the spot ₤/$ exchange rate over the past year was 58.5 bp. The FI is interested in adverse moves – bad moves that will not occur more than 1 percent of the time, or 1 day in every 100. Calculate the one-day VAR and ES from this position.

The first step is to calculate the dollar value position: Dollar value of position = pound value of position x dollar for pound exchange rate 14 © 2022

= ₤5 million x 1.5625 = $7,812,500 Using VAR, which assumes that changes in exchange rates are normally distributed, the exchange rate must change in the adverse direction by 2.33σ (2.33 x 58.5 bp) for this change to be viewed as likely to occur only 1 day in every 100 days: FX volatility = 2.33 x 58.5 bp = 136.305 bp In other words, using VAR during the last year the pound declined in value against the dollar by 136.305 bp 1 percent of the time. As a result, the one-day VAR is: VAR = $7,812,500 x 0.0136305 = $106,488 Using ES, which assumes that changes in exchange rates are normally distributed but with fat tails, the exchange rate must change in the adverse direction by 2.665σ (2.665 x 58.5 bp) for this change to be viewed as likely to occur only 1 day in every 100 days: FX volatility = 2.665 x 58.5 bp = 155.9025 bp In other words, using ES during the last year the pound declined in value against the dollar by 155.9025 bp 1 percent of the time. As a result, the one-day ES is: ES = $7,812,500 x 0.01559025 = $121,799 The potential loss exposure to adverse pound to dollar exchange rate changes for the FI from the ₤5 million spot currency holdings are higher using the ES measure of market risk. ES estimates potential losses that are $15,311 higher than VAR. This is because VAR focuses on the location of the extreme tail of the probability distribution. ES also considers the shape of the probability distribution once VAR is exceeded.

28.

An FI has ¥750 million in its trading portfolio on the close of business on a particular day.

The current exchange rate of yen for dollars is ¥120.00/$, or dollars for yen is $0.00833, at the daily close. The volatility, or standard deviation (σ), of daily percentage changes in the spot ¥/$ exchange rate over the past year was 121.6 bp. The FI is interested in adverse moves – bad moves that will not occur more than 1 percent of the time, or 1 day in every 100. Calculate the one-day VAR and ES from this position.

The first step is to calculate the dollar value position: Dollar value of position = yen value of position x dollar for pound exchange rate = ¥750 million / 120.00 = $6,250,000 Using VAR, which assumes that changes in exchange rates are normally distributed, the exchange rate must change in the adverse direction by 2.33σ (2.33 x 121.6 bp) for this change to be viewed as likely to occur only 1 day in every 100 days: 15 © 2022

FX volatility = 2.33 x 121.6 bp = 283.328 bp In other words, using VAR during the last year the yen declined in value against the dollar by 283.328 bp 1 percent of the time. As a result, the one-day VAR is: VAR = $6,250,000 x 0.0283328 = $177,080 Using ES, which assumes that changes in exchange rates are normally distributed but with fat tails, the exchange rate must change in the adverse direction by 2.665σ (2.665 x 121.6 bp) for this change to be viewed as likely to occur only 1 day in every 100 days: FX volatility = 2.665 x 121.6 bp = 324.064 bp In other words, using ES during the last year the yen declined in value against the dollar by 324.064 bp 1 percent of the time. As a result, the one-day ES is: ES = $6,250,000 x 0.0324064 = $202,540 The potential loss exposure to adverse yen to dollar exchange rate changes for the FI from the ¥750 million spot currency holdings are higher using the ES measure of market risk. ES estimates potential losses that are $25,460 higher than VAR. This is because VAR focuses on the location of the extreme tail of the probability distribution. ES also considers the shape of the probability distribution once VAR is exceeded.

29.

Bank of Hawaii’s stock portfolio has a market value of $250 million. The beta of the portfolio approximates the market portfolio, whose standard deviation (m) has been estimated at 2.25 percent. What are the five-day VAR and ES of this portfolio using adverse rate changes in the 99th percentile?

Daily VAR = ($ market value of portfolio) x (2.33 x m ) = $250m x (2.33 x 0.0225) = $250m x 0.052425 = $13,106,250 5-day VAR = $13,106,250 x 5 = $13,106,250 x 2.2361 = $29,306,466

30.

Daily ES

= ($ market value of portfolio) x (2.665 x m ) = $250m x (2.665 x 0.0225) = $250m x 0.0599625 = $14,990,625

5-day ES

= $14,990,625 x 5 = $14,990,625 x 2.2361 = $33,520,057

Despite the fact that market risk capital requirements have been imposed on FIs since the 1990s, huge losses in value were recorded during the financial crisis from losses incurred in FIs’ trading portfolios. Why did this happen? What changes to capital requirements did regulators propose to prevent such losses from reoccurring?

16 © 2022

During the financial crisis, losses due to market risk were significantly higher than the minimum market risk capital requirements under BIS Basel I and Basel II rules. The financial crisis exposed a number of shortcomings in the way market risk was being measured in accordance with Basel II rules. Although the crisis largely exposed problems with the large-bank internal models approach to measuring market risk, the BIS also identified shortcomings with the standardized approach. These included a lack of risk sensitivity, a very limited recognition of hedging and diversification benefits, and an inability to sufficiently capture risks associated with more complex instruments.

To address shortcomings of the standardized approach to measuring market risk, Basel III proposes a “partial risk factor” approach as a revised standardized approach. To address shortcomings in the internal models approach, in addition to the risk capital charge already in place, an incremental capital charge is assessed which includes a “stressed value at risk” capital requirement taking into account a one year observation period of significant financial stress relevant to the FI’s portfolio. The introduction of stressed VAR in Basel 2.5 is intended to reduce the cyclicality of the VAR measure and alleviate the problem of market stress periods dropping out of the data period used to calculate VAR after some time. Basel 2.5 requires the following process be followed by large FIs using internal models to calculate the market risk capital charge.

Basel III proposes to replace VAR models with those based on Extreme Value Theory and Expected Shortfall (ES) (discussed above). The ES measure analyzes the size and likelihood of losses above the 99th percentile in a crisis period for a traded asset and thus measures “tail risk” more precisely. Thus, ES is a risk measure that considers a more comprehensive set of potential outcomes than VAR. The BIS change to ES highlights the importance of maintaining sufficient regulatory capital not only in stable market conditions, but also in periods of significant financial stress. Indeed, it is precisely during periods of stress that capital is vital for absorbing losses and safeguarding the stability of the banking system. Accordingly, the Committee intends to move to a framework that is calibrated to a period of significant financial stress. Two methods of identifying the stress period and calculating capital requirements under the internal models are the direct method and the indirect method. The direct method is based on the approach used in the Basel 2.5 stressed VAR. The FI would search the entire historical period and identify the period which produces the highest ES result when all risk factors are included. However Basel III would require the FI to determine the stressed period on the basis of a reduced set of risk factors. Once the FI has identified the stressed period, it must then determine the ES for the full set of risk factors for the stress period. The indirect method identifies the relevant historical period of stress by using a reduced set of risk factors. However, instead of calculating the full ES model to that period the FI calculates a loss based on the reduced set of risk factors. This loss is then scaled using the ratio of the full ES model using current market data to the full ES model using the reduced set of risk factors using current market data.

31.

In its trading portfolio, an FI holds 2,000 shares of Under Armour at a share price of $84.50, 3,000 shares of BT Group (British telecommunication firm) at a price of $68.50, and 4,500 shares of AT&T at $34.40. The FI also has sold 5,000 Swatch Group (a Swiss 17 © 2022

watchmaker) at $19.00 and 2,500 of AT&T shares. Calculate the market risk capital charge on these securities.

Step 1: Offset equities in the same equity name Long and short notional positions in the same equity name are allowed offset each other. So, the 2,500 shares of AT&T sold by the FI are offset against the 4,500 shares long to leave 1,500 shares to be assigned to a bucket Step 2: Place the net position in each equity name into the relevant risk bucket Net notional positions in each equity name are then assigned to the appropriate equity bucket based on their observable characteristics, according to the following table:

Accordingly, the shares of Under Armour and Swatch Group will be assigned to bucket 5 and shares of AT&T and BT Group will fall in bucket 6. Using the BIS assigned risk weights to each notional position as follows:

So, the shares of Under Armour and Swatch Group will have a risk weight of 30%, AT&T and BT Group will have a risk weight of 35%. Further, the BIS has set these correlations for equity risk as follows:

18 © 2022

Thus, Under Armour (long position) and Swatch Group (short position) will have a correlation, 𝜌𝑖j, of 10% and AT&T (long position) and BT Group (long position) will have a correlation, 𝜌𝑖j, of 30%. And the risk exposure from the two bucket 5 securities and the two bucket 6 securities is calculated as: K5 = [(0.30)2 (2,000 x $84.50)2 + (0.30)2 (5,000 x $19.00)2 + 2(0.10)(0.30)(2,000 x $84.50) (0.30)(5,000 x $19.00)]1/2 = $60,594.80 K6 = [(0.35)2 (1,500 x $34.40)2 + (0.35)2 (3,000 x $68.50)2 + 2(0.30)(0.35)(1,500 x $34.40) (0.35)(3,000 x $68.50)]1/2 = $79,238.55 Step 3: Aggregate the buckets The risk exposures for each of the individual risk buckets are then aggregated to obtain the capital requirement for equity risk. The BIS has set the correlations between buckets as follows:

Thus, the Equity Risk Capital for this FI is: Equity Risk Capital = {[($60,594.80)2 + ($79,238.55)2 + 2(0.20)[(0.30)(2,000 x $84.50) + (0.30)(5,000 x $19.00)] [(0.35)(1,500 x $34.40) + (0.35)(3,000 x $68.50)]}1/2 = $113,142.40 32.

In its trading portfolio, an FI holds 5,000 shares of HSBC at a share price of $43.50, 4,000 shares of China Construction Bank at a price of $16.40, and 2,500 shares of Whirlpool at $170.00. The FI also has sold 3,000 McDonald’s at $96.75 and 1,500 of China Construction Bank. Calculate the market risk capital charge on these securities.

19 © 2022

Step 1: Offset equities in the same equity name Long and short notional positions in the same equity name are allowed offset each other. So, the 1,500 shares of China Construction Bank sold by the FI are offset against the 4,000 shares long to leave 2,500 shares to be assigned to a bucket Step 2: Place the net position in each equity name into the relevant risk bucket Net notional positions in each equity name are then assigned to the appropriate equity bucket based on their observable characteristics, according to the following table:

Accordingly, the shares of Whirlpool and McDonald’s will be assigned to bucket 5 and shares of HSBC and China Construction Bank will fall in bucket 8. Using the BIS assigned risk weights to each notional position as follows:

So, the shares of Whirlpool and McDonald’s will have a risk weight of 30%, HSBC and China Construction Bank will have a risk weight of 50%. Further, the BIS has set these correlations for equity risk as follows:

20 © 2022

Thus, Whirlpool (long position) and McDonald’s (short position) will have a correlation, 𝜌𝑖j, of 10% and HSBC (long position) and China Construction Bank (long position) will have a correlation, 𝜌𝑖j, of 35%. And the risk exposure from the two bucket 5 securities and the two bucket 6 securities is calculated as: K5 = [(0.30)2 (2,500 x $170.00)2 + (0.30)2 (3,000 x $96.75)2 + 2(0.10)(0.30)(2,500 x $170.00) (0.30)(3,000 x $96.75)]1/2 = $161,427.13 K8 = [(0.50)2 (2,500 x $16.40)2 + (0.50)2 (5,000 x $43.50)2 + 2(0.35)(0.50)(2,500 x $16.40) (0.50)(5,000 x $43.50)]1/2 = $117,504.79 Step 3: Aggregate the buckets The risk exposures for each of the individual risk buckets are then aggregated to obtain the capital requirement for equity risk. The BIS has set the correlations between buckets as follows:

Thus, the Equity Risk Capital for this FI is: Equity Risk Capital = {[($161,427.13)2 + ($117,504.79)2 + 2(0.20)[(0.30)(2,500 x $170.00) + (0.30)(3,000 x $96.75)] [(0.50)(2,500 x $16.40) + (0.50)(5,000 x $43.50)]}1/2 = $225,742.38 33.

Suppose an FI’s portfolio VAR for the previous 60 days was $3 million and stressed VAR for the previous 60 days was $8 million using the 1 percent worst case (or 99th percentile).

Calculate the minimum capital charge for market risk for this FI.

21 © 2022

Capital charge = ($3 million x √10 x 3) + ($8 million x √10 x 3) = $104.355 million

Integrated Mini Case: Calculating DEAR on an FI’s Trading Portfolio An FI wants to obtain the DEAR on its trading portfolio. The portfolio consists of the following securities.

Fixed-income securities: i) The FI has a $1 million position in a six-year, zero bonds with a face value of $1,543,302. The bond is trading at a yield to maturity of 7.50 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 22 basis points. ii) The FI also holds a 12-year, zero bond with a face value of $1,000,000. The bond is trading at a yield to maturity of 6.75 percent. The price volatility of the potential adverse move in yields is 65 basis points.

Foreign exchange contracts: The FI has a €2.0 million long trading position in spot euros at the close of business on a particular day. The exchange rate is €0.80/$1, or $1.25/€, at the daily close. Looking back at the daily 22 © 2022

percentage changes in the exchange rate of the euro to dollars for the past year, the FI finds that the volatility or standard deviation (σ) of the spot exchange rate was 55.5 basis points (bp).

Equities: The FI holds a $2.5 million trading position in stocks that reflect the U.S. stock market index (e.g., the S&P 500). The β = 1. Over the last year, the standard deviation of the stock market index was 175 basis points.

Correlations (ρij) among Assets

Six-Year, Zero-Coupon

Six-Year, Zero-Coupon -

12-Year, Zero-Coupon 0.75

€/$ -0.2

U.S. Stock Index 0.40

12-Year, Zero-Coupon

-

-

-0.3

0.45

€/$

-

-

-

0.25

U.S. Stock Index

-

-

-

-

1. Calculate the DEAR of this trading portfolio.

Fixed-income securities: i) MD = D/(1 + R) = 6/(1.075) = 5.581395 => Potential adverse move in yield at 1 percent = 2.33 = 2.33 x 0.0022 = 0.005126 => Price volatility = MD x potential adverse move in yield = 5.581395 x 0.005126 = 0.02861 or 2.861 percent and the daily earnings at risk for this bond is: DEAR = ($ value of position) x (price volatility) = $1,000,000 x 0.02861 = $28,610 ii) Dollar value of position = $1m./(1 + 0.0675)12 = $456,652. The modified duration of these bonds is: MD = D/(1 + R) = 12/(1.0675) = 11.24122 => Price volatility = (MD) x (potential adverse move in yield) = (11.24122) x (0.0065) = 0.073068 or 7.3068 percent. => DEAR = $456,652 x 0.073068 = $33,367 Foreign exchange contracts: Dollar equivalent value of € position = FX position x ($/€ spot exchange rate) = €2.0 million x $ per unit of foreign currency Dollar equivalent value of € position = €2.0 million x $1.25/€ = $2,500,000 FX volatility = 2.33 x 55.5 bp = 129.315 bp or 1.29315% 23 © 2022

=> DEAR = Dollar value of DM position x FX volatility = $2,500,000 x 0.0129315 = $32,329 Equities: Stock market return volatility = 2.33 σm = 2.33 x 175 bp = 0.040775 = 4.0775% => DEAR = Dollar market value of position x Stock market return volatility = $2,500,000 x 0.040775 = $101,937 Portfolio DEAR: Using the correlation matrix along with the individual asset DEARs the risk (or standard deviation) of the whole (four-asset) trading portfolio is: DEAR portfolio =[(DEARz6)2 + (DEARz12)2 + (DEAR€)2 + (DEARUS)2 + (2 x ρz6,z12 x DEARz6 x DEARz12) + (2 x ρz6€ x DEARz6 x DEAR€) + (2 x ρz6,US x DEARz6 x DEARUS) + (2 x ρz12€ x DEARz12 x DEAR€) + (2 x ρz12,US x DEARz12 x DEARUS)+ (2 x ρ€,US x DEAR€ x DEARUS)]2 = [(28,610)2 + (33,367)2 + (32,329)2 + (101,937)2 + 2(0.75)(28,610)(33,367) + 2(-0.2)(28,610)(32,329) + 2(0.4)(28,610)(101,937) + 2(-0.3)(33,367)(32,329) + 2(0.45)(33,367)(101,937) + 2(0.25)(32,329)(101,937)]2 = $144,309 2. If the correlation matrix changes as follows, what will the FI’s DEAR be? Explain the change in DEAR.

Six-year, zero-coupon

Six-year zero-coupon -

12-year zero-coupon 0.85

€/$ -0.1

U.S. stock index 0.50

12-year, zero-coupon

-

-

-0.2

0.55

€/$

-

-

-

0.35

U.S. stock index

-

-

-

-

DEAR portfolio = [(28,610)2 + (33,367)2 + (32,329)2 + (101,937)2 + 2(0.85)(28,610)(33,367) + 2(-0.1)(28,610)(32,329) + 2(0.5)(28,610)(101,937) + 2(-0.2)(33,367)(32,329) + 2(0.55)(33,367)(101,937) + 2(0.35)(32,329)(101,937)]2 = $152,772 The DEAR increases because the correlation coefficients all increased. Thus, less of the individual security risk was diversified through portfolio formation.

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3. If the standard deviation of the stock market index increases to 325 basis points, what will the FI’s DEAR be? Use the original correlation matrix. Explain the change in DEAR. Stock market return volatility = 2.33 σm = 2.33 x 325 bp = 0.075725 = 7.5725% => DEAR = Dollar market value of position x Stock market return volatility = $2,500,000 x 0.075725 = $189,312 Portfolio DEAR: Using the correlation matrix along with the individual asset DEARs the risk (or standard deviation) of the whole (four-asset) trading portfolio is: DEAR portfolio = [(28,610)2 + (33,367)2 + (32,329)2 + (189,312)2 + 2(0.75)(28,610)(33,367) + 2(-0.2)(28,610)(32,329) + 2(0.4)(28,610)(189,312) + 2(-0.3)(33,367)(32,329) + 2(0.45)(33,367)(189,312) + 2(0.25)(32,329)(189,312)]2 = $228,712 The DEAR increases because the risk of the equity portion of the portfolio increased.

4. If the FI’s FX position were changed to €4.0 million, what will the FI’s DEAR be? Explain the change in DEAR. Use the original correlation matrix and the original standard deviation of the stock market index.

Dollar equivalent value of € position = FX position x ($/€ spot exchange rate) = €4.0 million x $ per unit of foreign currency Dollar value of € position = €4.0 million x $1.25/€ = $5,000,000 FX volatility = 2.33 x 55.5 bp = 129.315 bp or 1.29315% => DEAR = Dollar value of DM position x FX volatility = $5,000,000 x 0.0129315 = $64,658 DEAR portfolio = [(28,610)2 + (33,367)2 + (64,658)2 + (101,937)2 + 2(0.75)(28,610)(33,367) + 2(-0.2)(28,610)(64,658) + 2(0.4)(28,610)(101,937) + 2(-0.3)(33,367)(64,658) + 2(0.45)(33,367)(101,937) + 2(0.25)(64,658)(101,937)]2 = $156,815 The DEAR increases because the risk of the FX portion of the portfolio increased.

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Solutions for End-of-Chapter Questions and Problems: Chapter Sixteen 1.

Classify the following items as (1) on-balance-sheet assets, (2) on-balance-sheet liabilities, (3) off-balance-sheet assets, (4) off-balance-sheet liabilities, (5) capital account, or (6) none of the above.

Classification a. Loan commitments.

3 b. Written option contract on interest rates.

4 c. Letter of credit.

4 d. Retained earnings 5 e. Purchased option contract on interest rates.

3 f. Loan sales without recourse.

None of the above. g. Loan sales with recourse.

4 h. Forward contracts to purchase.

3 I. Forward contracts to sell.

4 j. Swaps.

4 (for liability swaps) k. Loan participations.

1 l. Securities borrowed.

3 m. Securities lent.

4 n. Loss adjustment expense account (PC insurers).

2 o. Net policy reserves.

2

2.

How does one distinguish between an off-balance-sheet asset and an off-balance-sheet liability?

Off-balance-sheet activities or items are contingent claim contracts. An item is classified as an off-balance-sheet asset when the occurrence of the contingent event results in the creation of an on-balance-sheet asset. An example is a loan commitment. If the borrower decides to exercise the right to draw down on the loan, the FI will incur a new asset on its portfolio. Similarly, an item is an off-balance-sheet liability when the contingent event creates an on-balance-sheet liability. An example is a standby letter of credit (SLC). In the event that the original payer of the SLC defaults, then the FI is liable to pay the amount to the payee, incurring a liability on the right-hand-side of its balance sheet.

3.

Contingent Bank has the following balance sheet in market value terms (in millions of dollars): Assets Cash Mortgages Total assets

$20 220 $240

Liabilities and Equity Deposits Equity Total liabilities and equity

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$220 20 $240

In addition, the bank has contingent assets with $100 million market value and contingent liabilities with $80 million market value. What is the true stockholder net worth? What does the term contingent mean?

Net worth = ($240m - $220m) + ($100m - $80m) = $40 million. The term contingent means an event that may or may not happen. In financial economics, the term is used in conjunction with the result given that some event does occur.

4.

Why are contingent assets and liabilities like options? What is meant by the delta of an option? What is meant by the term notional value?

Contingent assets and liabilities may or may not become on-balance-sheet assets and liabilities in a manner similar to the exercise or non-exercise of an option. In each case, the realization of the event is contingent or dependent on the occurrence of some other event. The delta of an option is the sensitivity of an option’s value for a unit change in the price of the underlying security. The notional value represents the amount of value that will be placed in play if the contingent event occurs. The notional value of a contingent asset or liability is the face value amount of asset or liability that will appear on the balance sheet if the contingent event occurs.

5.

An FI has purchased options on bonds with a notional value of $500 million and has sold options on bonds with a notional value of $400 million. The purchased options have a delta of 0.25 and the sold options have a delta of 0.30. What is (a) the contingent asset value of this position, (b) the contingent liability value of this position, and (c) the contingent market value of net worth?

a.

The contingent asset value is $500 million x 0.25 = $125 million.

b.

The contingent liability value is $400 million x 0.30 = $120 million.

c.

The contingent market value of net worth is $125 million - $120 million = $5 million.

6.

What factors explain the growth of off-balance-sheet activities in the 1980s through the 2000s among U.S. FIs? What factors explain the decrease in off-balance-sheet activities in the 2010s?

The narrowing of spreads on on-balance-sheet lending in a highly competitive market and large loan losses by commercial banks gave impetus to seek other sources of income in the 1980s. Offbalance-sheet activities represented one avenue. In addition, off-balance-sheet assets and liabilities were not subject to capital requirements or reserve requirements, increasing the effective returns on these activities. In the 1990s and early 2000s, increased revenue from trading activities was a major impetus to the increases in OBS activities. For the first time ever, OBS activities fell in late 2008 with the fallout from the financial crisis. However, growth of OBS securities was quickly seen again in early 2009 through 2011 before falling back in 2015.

Part of the Wall Street Reform and Consumer Protection Act, passed in 2010 in response to the financial crisis, is the Volker Rule which prohibits U.S. depository institutions (DIs) from 2 © 2022

engaging in proprietary trading (i.e., trading as a principal for the trading account of the bank).

This includes any transaction to purchase or sell derivatives. Thus, only the investment banking arm of the business is allowed to conduct such trading. The Volcker Rule was implemented in April 2014 and banks had until July 21, 2015 to be in compliance. The result has been a reduction in derivative securities held off-balance-sheet by these financial institutions.

7.

What role does Schedule L play in reporting off-balance-sheet activities? Refer to Table 16-4. What was the annual growth rate over the 21-year period 1992-2015 in the notional value of off-balance-sheet items compared with on-balance-sheet items? Which contingencies have exhibited the most rapid growth?

Schedule L is a method for the Federal Reserve to track the types and amounts of off-balancesheet (OBS) activities of commercial banks and savings institutions. Most of the OBS activities mentioned in this chapter are reported in Schedule L of the quarterly Call Reports, although items associated with settlement risk and affiliate risk are not reported.

The following information from Table 16-4 reflects the most significant OBS items in terms of notional value: Annual Growth OBS Item Rate (%) Commitments to lend 6.59% Future and forward contracts on interest rates 12.54 Written option contracts on interest rates 13.34 Purchased option contracts on interest rates 13.40 Commitments to buy foreign exchange 7.45 Notional value of all outstanding swaps 17.57 Total OBS 13.45 Total assets (on-balance-sheet items)

6.17%

Clearly the off-balance-sheet items have grown at a much faster rate than the on-balance-sheet items for U.S. commercial banks, with swaps growing the most rapidly of all OBS activities.

Further, the dollar value of the notional OBS items was a multiple of 14.51 times as large as the dollar value of the on-balance-sheet items in the first quarter of 2015.

8.

What are the characteristics of a loan commitment that an FI may make to a customer? In what manner and to whom is the commitment an option? What are the various possible pieces of the option premium? When does the option or commitment become an onbalance-sheet item for the FI and the borrower?

A loan commitment is an agreement to lend a fixed maximum amount of money to a firm within some given amount of time. The interest rate or rate spread normally is determined at the time of the agreement, as is the length of time that the commitment is open. Because the borrower usually triggers the timing of the drawdown, which may be any portion of the total commitment, the commitment is an option to the borrower. If the loan is not needed, the option or drawdown 3 © 2022

will not be exercised. The premium for the commitment may include a fee of some percent times the total commitment and a fee of some percent times the amount of the unused commitment. Of course, the borrower must pay interest while any portion of the commitment is in use. The option becomes an on-balance-sheet item for both parties at the point in time that a drawdown occurs.

9.

A FI makes a loan commitment of $2.5 million with an up-front fee of 50 basis points and a back-end fee of 25 basis points on the unused portion of the loan. The takedown on the loan is 50 percent and takedown occurs at the beginning of the year. a. What total fees does the FI earn when the loan commitment is negotiated?

Up-front fee = $2,500,000 x 0.0050 = $12,500 b. What are the total fees earned by the FI at the end of the year, that is, in future value terms? Assume the cost of capital for the FI is 6 percent.

Note that adjustment has not been made for the fact that the up-front fee is usually collected at the beginning of the period. To adjust, a common treatment is to find the future value for this fee by multiplying by bank’s cost of capital. Thus, $2,500,000 x 0.0050 x (1 + 0.06) = $13,250, and the total fees are: Up-front fee Back-end fee Total 10.

= $2,500,000 x 0.0050 x 1.06 = $2,500,000 x 0.0025 x 0.50

= = =

$13,250 3,125 $16,375

Use the following information on a one-year loan commitment to calculate the return on the loan commitment.

BR = FI’s base interest rate on the loans = 8% Φ = Risk premium on loan commitment = 2.5% f1 = Up-front fee on the whole commitment = 25 basis points f2 = Back-end fee on the average unused portion of the commitment = 50 basis points b = Compensating balance on loans = 10% RR = Reserve requirements = 8% td = Expected (average) takedown rate on the loan commitment = 70%

The general formula for the promised return (1 + k) of the loan commitment is: f + f 2 (1 - td) + (BR + )td Using the formula: 1 + k = 1 + 1 td - b(td)(1 - RR) 1 + k = 1 + [(0.0025) + (0.0050)(1 - 0.70) + (0.08 + 0.025)(0.70)]/{0.70 - [0.10(0.70)(1 - 0.08) ]} 1 + k = 1.12193, or k = 12.193 percent.

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11.

A FI has issued a one-year loan commitment of $2 million for an up-front fee of 25 basis points. The back-end fee on the unused portion of the commitment is 10 basis points. The FI’s base rate on loans is 7.5 percent and loans to this customer carry a risk premium of 2.5 percent. The FI requires a compensating balance on loans of 5 percent in the form of demand deposits. Reserve requirements on demand deposits are 8 percent. The customer is expected to draw down 80 percent of the commitment at the beginning of the year. a. What is the expected return on the loan without taking future values into consideration?

f + f 2 (1 - td) + (BR + )td Using the formula: 1 + k = 1 + 1 td - b(td)(1- RR) 1 + k = 1 + [(0.0025) + (0.0010)(1 - 0.80) + (0.075 + 0.025)(0.80)]/{0.80 - [0.05(0.80)(1 - 0.08)]} 1 + k = 1.10836, or k = 10.836 percent.

Alternatively, using dollar values: Up-front fees Interest income Back-end fee Total

= 0.0025 x $2,000,000 = 0.10 x $2,000,000(.80) = 0.0010 x $$2,000,000(1 - .80)

= = = =

$ 5,000 160,000 400 $165,400

Funds committed = $2,000,000(0.80) - $80,000 (compensating balances = $2,000,000 x 0.80 x 0.05) + $6,400 (reserve requirements on demand deposits = $80,000 x 0.08) = $1,526,400.

Expected rate of return = $165,400/$1,526,400 = 10.836% b. What is the expected return using future values? That is, the net fee and interest income are evaluated at the end of the year when the loan is due?

Using the formula: 1+k = 1 + [(0.0025(1 + 0.06) + 0.0010(1 - 0.80) + (0.075 + 0.025)(0.80)]/{0.80 - [0.05(0.80)(1 0.08)]} => 1+k = 1.108556, or k = 10.8556 percent.

Using dollar values, the only difference is that the up-front fee is estimated at year-end, i.e., $5,000 x 1.06 = $5,300. Thus, expected return = $165,700/$1,526,400 = 10.8556%. c. How is the expected return in part (b) affected if the reserve requirements on demand deposits are zero?

Using the formula: 1 + k = 1 + [(0.0025(1 + 0.06) + 0.0010(1 - 0.80) + (0.075 + 0.025)(0.80)]/ {0.80 - [0.05(0.80)(1 – 0)]} => 1 + k = 1.1090, or k = 10.90 percent.

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Using dollar values, the amount of funds committed is reduced by the amount set for reserves, i.e., $6,400. Thus, expected return = $165,700/$1,520,000 = 10.90%. d. How is the expected return in part (b) affected if compensating balances are paid a nominal interest rate of 1.5 percent?

Using the formula: 1+k = 1+[(0.0025(1 + 0.06) + 0.0010(1 - 0.80) + (0.075 + 0.025)(0.80) - 0.05(0.015)(0.80)]/[0.80 - 0.05(0.80)(1 - 0.08)] => 1 + k = 1.107770, or k = 10.7770 percent.

Using dollar values, we need to subtract additional payments of interest on reserve requirements from the total fees and interest earned, i.e., 0.015 x $80,000 = $1,200.

Expected return = $164,500/1,526,400 = 10.7770% e. What is the expected return using future values, but with the compensating balance placed in certificates of deposit that have an interest rate of 2.0 percent and no reserve requirements, rather than in demand deposits?

Using the formula: 1 + k = 1 + [(0.0025(1 + 0.06) + 0.0010(1 - 0.80) + (0.075 + 0.025)(0.80) – 0.05)(0.020)(0.80)]/ {0.80 - [0.05(0.80)(1 – 0)]} => 1 + k = 1.107961, or k = 10.7961 percent.

Using dollar values, in this case the compensating balance is placed in certificates of deposits paying 2.0 percent and with no compensating balance requirement Thus, revenue in part (b) above is reduced by $80,000 x 0.020 = $1,600, and the expected return is $164,100/$1,520,000 = 10.7961 percent.

12.

Suburb Bank has issued a one-year loan commitment of $10 million for an up-front fee of 50 basis points. The back-end fee on the unused portion of the commitment is 20 basis points. The bank’s base rate on loans is 7 percent and loans to this customer carry a risk premium of 2 percent. The bank requires a compensating balance on loans of 10 percent to be placed in demand deposits and must maintain reserve requirements on demand deposits of 8 percent. The customer is expected to draw down 60 percent of the commitment at the beginning of the year. a. What is the expected return on this loan?

Using the formula: 1+ k = 1 +

f 1+ f 2 (1 - td)+(BR + m)td



td - b(td )(1 - RR) 6 © 2022



1 + k = 1 + [(0.0050) + (0.0020)(1 - 0.60) + (0.07 + 0.02)(0.60)]/{0.60 - [0.10(0.60)(1 - 0.08)]} 1 + k = 1.109765, or k = 10.9765 percent.

Alternatively, using dollar values: Up-front fee Interest income Back-end fee Total revenue

= 0.0050 x $10,000,000 = 0.0900 x $10,000,000(0.6) = 0.0020 x $10,000,000(1 - 0.6)

= = =

$50,000 540,000 $8,000 $598,000

Funds committed = $10,000,000(0.6) - $600,000 (compensating balance = $10,000,000(0.60)(0.1)) + $48,000 (reserve requirements on demand deposits = $10,000,000(0.60)(0.1)(0.08)) = $5,448,000.

Expected rate of return = $598,000/$5,448,000 = 10.9765 percent. b. What is the expected annual return on the loan if the draw-down on the commitment does not occur until at the end of six months?

In this case the fees remain the same, but the interest revenue will be only half as large since the loan is taken down for only six months.

Using the formula: 1 + k = 1 + 2[(0.0050) + (0.0020)(1 - 0.60) + (0.07 + 0.02)(6/12)(0.60)]/{0.60 - [0.10(0.60)(1 0.08)]} = > 1 + k = 1.120147, or k = 12.0147 percent.

Using dollar values, the interest revenue will be only half as large and the average balance outstanding will be only half as large. Thus, revenue will be $598,000 - $270,000 = $328,000, and the funds committed will be $5,448,000/2 = $2,724,000. The expected rate of return on an annual basis is 12.0411 percent. Note, the return is greater than the return calculated in part (a) because the fees are dollar sensitive, not time sensitive.

13.

How is an FI exposed to interest rate risk when it makes loan commitments? In what way can an FI control for this risk? How does basis risk affect the implementation of the control for interest rate risk?

When an FI makes a fixed-rate loan commitment, it faces the likelihood that interest rates may increase during the intervening period. This reduces its net interest income if the borrower decides to take down the loan. The FI can partially offset this loan by making variable rate loan commitments. However, this still does not protect it against basis risk, that is, if lending rates and the cost of funds of the FI do not increase proportionately.

14.

How is an FI exposed to credit risk when it makes loan commitments? How is credit risk related to interest rate risk? What control measure is available to an FI for the purpose of 7 © 2022

protecting against credit risk? What is the realistic opportunity to implement this control feature?

An FI is exposed to credit risk because the credit quality of a borrower could decline during the intervening period of the loan commitment. When an FI makes a loan commitment, it is obligated to deliver the loan. Although most loan commitments today contain a clause releasing an FI from its obligations in the event of a significant decline in credit quality, the FI may not be inclined to use it for fear of reputation concerns. Interest rate risk is related to credit risk because default risks are much higher during periods of increasing interest rates. When interest rates rise, firms have to generate higher rates of return. Thus, FIs making loan commitments are subject to both risks in periods of rising interest rates.

15.

How is an FI exposed to takedown risk and aggregate funding risk? How are these two contingent risks related?

An FI is exposed to takedown risk because not all loan commitments are fully taken down. As a result, an FI has to forecast its funding requirements in order not to keep funds at levels that are too high or too low. Maintaining low levels of funds may result in paying more to obtain funds on short notice. Maintaining high levels of funds may result in lower earnings.

Additionally, FIs are exposed to aggregate funding risk, i.e., all customers may choose to take down their loan commitments during a similar period, such as when interest rates are rising or credit availability is low. This could cause a severe liquidity problem for the FI. These two risks are related because takedowns usually occur when interest rates are rising or when credit availability is low. If all customers decide to increase their takedowns in these circumstances, it could put a severe strain on the FI. Similarly, when interest rates are falling or when credit availability is high, customers are likely to find cheaper financing elsewhere. Thus, FIs should take into account the interdependence of these two events when forecasting future funding need.

16.

Do the contingent risks of interest rate, takedown, credit, and aggregate funding tend to increase the insolvency risk of an FI? Why or why not?

These risk elements all can have adverse effects on the solvency of an FI. While they need not occur simultaneously, there is a fairly high degree of correlation between them. For example, if rates rise, funding will become shorter, takedowns will likely increase, credit quality of borrowers will become lower, and the value of the typical FI will shrink.

17.

What is a letter of credit? How is a letter of credit like an insurance contract?

Like most insurance contracts, a letter of credit is a guarantee. It essentially gives the holder the right to receive payment from the FI in the event that the original purchaser of the product defaults on the payment. Like the seller of any guarantee, the FI is obligated to pay the guarantee holder at the holder’s request.

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18.

A German bank issues a three-month letter of credit on behalf of its German customer who is planning to import $100,000 worth of goods from the United States. The bank charges an up-front fee of 100 basis points. a. What up-front fee does the bank earn? How is this fee recorded on the bank’s income statement?

Up-front fee earned = $100,000 x 0.0100 = $1,000. This fee will be recorded as noninterest income for the bank. b. If the U.S. exporter decides to discount this letter of credit after it has been accepted by the German bank, how much will the exporter receive, assuming that the interest rate currently is 5 percent and that 90 days remain before maturity? (Hint: To discount a security, use the time value of money formula, PV = FV [(1 – (interest rate x (days to maturity/365))].)

PV = (1 - (0.05 x 90/365) x $100,000 = $98,767.12 c. What risk does the German bank incur by issuing this letter of credit?

The German bank faces the risk that the importer may default on its payment and it will be obligated to make the payment at the end of 90 days. In such a case, it will incur an on-balancesheet liability of $100,000.

19.

How do standby letters of credit differ from commercial letters of credit? With what other types of FI products do SLCs compete? What types of FIs can issue SLCs?

Standby letters of credit usually are written for contingent situations that are less predictable and that have more severe consequences than the LCs written for standard commercial trade relationships. Often SLCs are used as performance guarantees for projects over extended periods of time, or they are used in the issuance of financial securities such as municipal bonds or commercial paper. Banks and property-casualty insurance companies are the primary issuers of SLCs. 20.

A corporation is planning to issue $1 million of 270-day commercial paper for an effective annual yield of 5 percent. The corporation expects to save 30 basis points on the interest rate by using either an SLC or a loan commitment as collateral for the issue. a. What are the net savings to the corporation if a bank agrees to provide a 270-day SLC for an up-front fee of 20 basis points (of the face value of the loan commitment) to back the commercial paper issue?

Cost of using SLC = -(0.0020) x $1,000,000 Savings by using SLC as collateral = 0.0030 x (270/365) x $1,000,000) 9 © 2022

= -$2,000.00 = 2,219.18

Net savings

= $ 219.18

b. What are the net savings to the corporation if a bank agrees to provide a 270-day loan commitment to back the issue? The bank will charge 10 basis points for an up-front fee and 10 basis points for a back-end fee for any unused portion of the loan. Assume the loan is not needed and that the fees are on the face value of the loan commitment.

Up-front fee of loan commitment = -(0.0010) x $1,000,000 Back-end fee (assuming no usage) = -(0.0010) x $1,000,000 Cost of loan commitment Savings by using loan commitments as collateral = 0.0030 x (270/365 x $1,000,000) Net savings

= -$1,000.00 = -1,000.00 = -$2,000.00 = $2,219.18 = $ 219.18

c. Should the corporation be indifferent to the two alternative collateral methods at the time the commercial paper is issued?

Not necessarily. If some of the loan commitment is drawn down, the back-end fee will be less and the savings will be greater.

21.

Explain how the use of derivative contracts such as forwards, futures, swaps, and options creates contingent credit risk for an FI. Why do OTC contracts carry more contingent credit risk than do exchange-traded contracts? How is the default risk of OTC contracts related to the time to maturity and the price and rate volatilities of the underlying assets?

Credit risk occurs because of the potential for the counterparty to default on payment obligations, a situation that would require the FI to replace the contract at current market prices and rates.

OTC contracts typically are non-standardized or unique contracts that do not have external guarantees from an organized exchange. Defaults on these contracts usually will occur when the FI stands to gain and the counterparty stands to lose, i.e., when the contract is hedging the risk exactly as the FI hoped. Thus, default risk is higher when the volatility of the underlying asset is higher.

22.

What is meant by when-issued trading? Explain how forward purchases of when-issued government T-Bills can expose FIs to contingent interest rate risk.

The purchase or sale of a security before it is issued is called when-issued trading. For example, when an FI purchases T-bills on behalf of a customer prior to the actual weekly auctioning of securities, it incurs the risk of underpricing the security. On the day the T-bills are allotted, it is possible that because of high demand, the prices may be much higher than what the FI has forecasted. It then may be forced to purchase the securities at higher prices, which means lower interest rates.

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23.

Distinguish between loan sales with and without recourse. Why would FIs want to sell loans with recourse? Explain how loan sales can leave FIs exposed to contingent interest rate risks.

When FIs sell loans without recourse, the buyers of the loans accept the risk of non-repayment by the borrower. In other words, the loans are completely off the books of the FI. In the case of loans sold with recourse, FIs are still legally responsible for the payment of the loans to the seller in the event the borrower defaults. FIs are willing to sell such loans because they obtain better prices and also because it allows them to remove the assets from their balance sheets. FIs are more likely to sell such loans with recourse if the borrower of the loan is of good credit standing.

When interest rates increase, there is a higher likelihood of loan defaults and a higher probability that the FI will have to buy back some of the loans. This may be the case even for sales of loans without recourse because FIs are reluctant not to take back loans for reputation concerns.

24.

The manager of Shakey Bank sends a $2 million funds transfer payment message via CHIPS to the Trust Bank at 10 AM. Trust Bank sends a $2 million funds transfer message via CHIPS to Hope Bank later that same day. What type of risk is inherent in this transaction? How will the risk become reality?

This is an example of settlement risk. If the funds sent by Shakey Bank do not reach Trust Bank in time, then Trust Bank may not have sufficient funds to cover its promised payment to Hope Bank.

25.

Explain how settlement risk is incurred in the interbank payment mechanism and how it is another form of off-balance-sheet risk.

Settlement risk occurs when FIs transfer and receive funds from other FIs through the FedWire system or CHIPS (Clearing House Interbank Payment System). Since all settlements are netted out at the end of the day, FIs can engage in overdrafts during the day. This means that if an FI defaults during the middle of the day, several FIs may be caught short-ended because they may not receive their scheduled payments. This may also cause their payments made to other FIs to be denied. The risks of such intra-day overdrafts can be solved by real-time transfers. The essential feature of settlement risk is that an FI is exposed to a within-day, or intraday, credit risk that does not appear on its balance sheet. The balance sheet at best summarizes only the end-ofday closing position or book of an FI. Thus, intraday settlement risk is an additional form of OBS risk that FIs participating on private wholesale wire transfer system networks face.

26.

What is the difference between a one-bank holding company and a multibank holding company? How does the principle of corporate separateness ensure that a bank is safe from the failure of its affiliates?

A one-bank holding company (OBHC) is a holding company that has among its several subsidiaries only one bank. In contrast, a multibank holding company (MBHC) owns several banks. The principle of corporate separateness ensures that the affiliates are all structured as separate entities so that the failure of one will not have a negative impact on either the holding 11 © 2022

company or the other affiliates. This is accomplished by ensuring that each affiliate is run as a separate entity with its own financial resources and capital.

27.

Discuss how the failure of an affiliate can affect the holding company or its affiliates even if the affiliates are structured separately.

First, creditors of the failed affiliate may claim that it is not a truly separate firm under the “estoppel argument” because they could not distinguish between affiliates of the holding company with similar names. Second, regulators themselves have tried to challenge the principle of corporate separateness by asking the holding company or the other banks of the multibank holding company to bail out the failed unit. Although not yet approved by the courts, a future favorable ruling could undermine the separateness of the affiliates.

28.

Defend the statement that although off-balance-sheet activities expose FIs to several forms of risks, they also can alleviate the risks of FIs.

Although an FI is exposed to interest rate, foreign exchange, credit, liquidity, and other risks, it also can use these risks to help alleviate its overall risk, if used judiciously. For example, the use of options and futures can reduce the volatility of earnings if hedged with the appropriate amount. Such hedging can be incorporated in an FI’s overall portfolio so that both trading and hedging activities can be pursued independently while still reducing the total exposure of the FI. It is also possible to offset the exposures of on- and off-balance-sheet activities. For example, it is possible that decreases in interest rates could lead to increased exposures for some assets (reinvestment risks), but they could be offset by off-balance-sheet liabilities. Thus, regulation of off-balance-sheet activities should recognize the positive effects of these instruments in helping ameliorate the total exposure of the FI.

Integrated Mini Case: Calculating Income on Off-Balance-Sheet Activities Dudley National has issued the following off-balance-sheet items: •

A one-year loan commitment of $1 million with an up-front fee of 40 basis points. The back-end fee on the unused portion of the commitment is 55 basis points. The bank’s base rate on loans is 8 percent and loans to this customer carry a risk premium of 2 percent. The bank requires a compensating balance on this loan of 10 percent to be placed in demand deposits and must maintain reserve requirements on demand deposits of 8 percent. The customer is expected to draw down 75 percent of the commitment at the beginning of the year.

•

A one-year loan commitment of $500,000 with an up-front fee of 25 basis points. The back-end fee on the unused portion of the commitment is 30 basis points. Loans to this customer carry a risk premium of 2.5 percent. The bank will not require a compensating 12 © 2022

balance on this loan. The customer is expected to draw down 90 percent of the commitment at the beginning of the year.

•

A three-month commercial letter of credit on behalf of one of its AA-rated customers who is planning to import $400,000 worth of goods from the Germany. The bank charges an upfront fee of 75 basis points on commercial letters of credit to AA-rated customers.

•

A standby letter of credit to one its A-rated customers who is planning to issue $5 million of 270-day commercial paper for an effective yield of 5 percent. The corporation expects to save 50 basis points on the interest rate by using the SLC. The bank charges an up-front fee of 40 basis points on SLCs to A-rated customers to back the commercial paper issue. a. What up-front fees does the bank earn on each of these?

Up-front fee on $1m loan commitment

= 0.0040 x $1,000,000 =

$4,000

Up-front fees on $500,000 loan commitment = 0.0025 x $500,000 =

1,250

Up-front fee on commercial letter of credit

= 0.0075 x $400,000 =

3,000

Up-front fee on standby letter of credit

= 0.0040 x $5,000,000 =

20,000

Total up-front fees

$28,250

b. What other income does the bank earn on these off-balance-sheet activities? $1m loan commitment Interest income Back-end fee

= (0.08 + 0.02) x $1,000,000(0.75) = 0.0055 x $1,000,000(1 - 0.75)

$500,000 loan commitment Interest income = (0.08 + 0.025) x $500,000(0.9) Back-end fee = 0.0030 x $500,000(1 - 0.9)

= =

$75,000 1,375

= =

$47,250 150

No other income is earned on the letters of credit. c. Calculate the returns on each of the off-balance-sheet activities assuming that the takedowns on the loan commitments are at the expected percentage and the customers holding the letters of credit do not default on their obligations. $1m loan commitment Up-front fee Interest income Back-end fee Total revenue

= $4,000 = 75,000 = 1,375 $80,375 13 © 2022

Funds committed = $1,000,000(0.75) - $75,000 (compensating balances = $1,000,000 x 0.75 x 0.10) + $6,000 (reserve requirements on demand deposits = $75,000 x 0.08) = $681,000.

Expected rate of return = $80,375/$681,000 = 11.80% $500,000 loan commitment Up-front fee = $1,250 Interest income = 47,250 Back-end fee = 150 Total revenue $48,650 Funds committed = $500,000(0.90) = $450,000.

Expected rate of return = $48,650/$450,000 = 10.81%

No investment is made by the bank for the guarantees offered through the letters of credit. Thus, bank invests no funds, yet makes $3,000 on the commercial letter of credit and $20,000 on the standby letter of credit.

14 © 2022

Solutions for End-of-Chapter Questions and Problems: Chapter Seventeen 1.

Explain how technological improvements can increase an FI’s interest and noninterest income and reduce interest and noninterest expenses. Use some specific examples.

Technological improvements in the services provided by financial intermediaries help increase income and reduce costs in several ways: (a)

Interest income: By making it easier to draw down on loans directly via computers, as well as by processing loan applications faster.

(b)

Interest expense: By enabling banks to access lower cost funds that are available directly from brokers and dealers through computers and screen-based trading.

(c)

Noninterest income: By making more nonloan products available to customers through computers to customers such as letters of credit, commercial paper, and derivatives.

(d) Noninterest expense: By reducing processing and settlement fees, an area that has changed drastically for most FIs, especially in trading activities and in the use of automated teller machines (ATMs) and home banking capabilities.

2.

Table 17-1 shows data on earnings, expenses, and assets for all insured banks. Calculate the annual growth rates in the various income, expense, earnings, and asset categories from 1991 to 2014. If part of the growth rates in assets, earnings, and expenses can be attributed to technological change, in what areas of operating performance has technological change appeared to have the greatest impact? What growth rates are more likely to be caused by economy-wide economic activity?

Growth rates through the end of 2014: Category Interest income Interest expense Net interest income Provision for Loan Loss Noninterest income Noninterest expenses Net earnings Total assets

Twenty-Year Growth Rate 1.67% -5.70% 4.96% -1.17% 5.74% 4.88% 8.94% 6.19%

The high growth rate in noninterest income reflects in part, the additional fees for technology oriented products such as mobile banking and other services. The smaller growth in noninterest expense reflects a lower growth in personnel expenses that further supports the transition toward more technology. The relatively small growth rates in interest income and decrease in interest expense reflect the low interest rate environment of the economy that was prevalent during the 1 © 2022

2000s. The growth in net earnings, which is larger than the growth in assets, is fueled by all of the above.

3.

Compare the effects of technology on an FI’s wholesale operations with the effects of technology on an FI’s retail operations. Give some specific examples.

Generally, the wholesale efforts have centered on the FIs’ ability to improve the management of cash management or working capital services and technological operating efficiency for large corporate customers. These efforts include services dealing with lockboxes, electronic billing, treasury management software, cloud computing, etc. The effect on retail services primarily has been to make it easier for individuals to obtain banking services as exemplified by ATMs, pointof-sales debit cards, and web-based home banking products.

4.

What are some of the risks inherent in being the first to introduce a financial innovation?

One risk is that product innovations may fail to attract sufficient business relative to the initial cash outlay and the future costs related to these investments once they are in place. In the terminology of finance, a number of technologically based product innovations may turn out to be negative net present value projects because of uncertainties over revenues and costs and how quickly rivals will mimic or copy any innovation. Another factor is agency conflicts, in which managers undertake growth-oriented investments to increase an FI’s size. Such investments may be inconsistent with stockholders’ value-maximizing objectives. As a result, losses on technological innovations and new technology can weaken an FI because scarce capital resources are invested in value-decreasing products.

5.

The operations department of a major FI is planning to reorganize several of its back-office functions. Its current operating expense is $1.5 million, of which $1 million is for staff expenses. The FI uses a 12 percent cost of capital to evaluate cost-saving projects. a. One way of reorganizing is to outsource a portion of its data entry functions. This will require an initial investment of approximately $500,000 after taxes. The FI expects to save $150,000 in annual operating expenses after taxes for the next seven years. Should it undertake this project?

This is a traditional capital budgeting problem. Investments = $500,000, and annual cost savings = $150,000. NPV = CF x PVAk=12%, n=7 – Investment, where k = FI’s cost of capital and CF = cash flows or cost savings. NPV = $150,000 x PVAk=12%, n=7 -500,000 = $684,563.48 - $500,000 = $184,563.48. Yes, the FI should undertake this project. b. Another option is to automate the entire process by installing new state-of-the-art computers and software. The FI expects to realize more than $500,000 per year in aftertax savings, but the initial investment will be approximately $3 million. In addition, the life of this project is limited to seven years, at which time new computers and software will need to be installed. Using this seven-year planning horizon, should the FI invest in 2 © 2022

this project? What level of after-tax savings would be necessary to make this plan comparable in value creation to the plan in part (a)?

NPV = $500,000 x PVAk=12%, n=7 - $3,000,000 = -$718,121.73. No, the FI should not undertake the project under these terms. The level of after-tax savings necessary to make the plan comparable to part (a) is NPV = Savings x PVAk=12%, n=7 - $3,000,000 = $184,563.48, => Annual savings = $697,794.34 over the seven-year period.

6.

City Bank upgrades its computer equipment every five years to keep up with changes in technology. Its next upgrade is two years from today and is budgeted to cost $1 million.

Management is considering moving up the date by two years to install some new computers with breakthrough software that could generate significant cost savings. The cost for this new equipment also is $1 million. What should be the savings per year to justify moving up the planned update by two years? Assume a cost of capital of 10 percent

The equivalent annual cost for the planned 5 years is $1,000,000/PVAk=10%, n=5 = $263,797.48.

Since the cost of the planned improvement is the same as the original investment, the savings generated should be the present value of $263,797.48 in years 1 and 2, or a total of $457,830.34.

7.

Identify and discuss three benefits of technology in generating revenue for FIs?

Technology (1) allows for more efficient cross-marketing of new and old products; (2) encourages an increase in the rate of innovation of new products; and (3) supports improvements in service quality and convenience. Many FIs use high-tech efforts to determine how they can reach more customers with more products. As marketing lines are identified and defined, new product ideas emerge that further the usefulness of FI products to customers.

8.

Distinguish between economies of scale and economies of scope.

Economies of scale refer to the average cost of production falling as output of a firm increases, and thus reflect the benefits of a single product firm getting larger. Economies of scope refer to the average cost of production falling through the use of joint inputs to produce multiple products, and thus reflect the benefits of a single-product firm becoming a multi-product firm.

9.

What information on the operating costs of FIs does the measurement of economies of scale provide? If economies of scale exist, what implications do they have for regulators?

Economies of scale provide a measure of the average costs of producing a unit of output and usually are measured as total costs over on- and off-balance-sheet total assets, total loans, or total deposits. If average costs decline as the size of the firm increases, large FIs will be able to offer more competitive rates than their smaller counterparts and possibly drive them out of business.

The long-run implication of economies of scale on the FI sector is that the larger and most costefficient FIs will drive out smaller FIs, leading to increased large-firm dominance and concentration in financial services production. Such an implication is reinforced if time-related operating or technological improvements increasingly benefit larger FIs more than smaller FIs. 3 © 2022

Regulators have to be concerned about economies of scale, because, if it is true that larger firms have lower operating costs, policies on restricting mergers may be counterproductive, since social benefits may outweigh the social costs of mergers.

10.

What are diseconomies of scale? What are the risks of large-scale technological investments, especially to large FIs? Why are small FIs willing to outsource production to large FIs against which they are competing? Why are large FIs willing to accept outsourced production from smaller FI competition?

Diseconomies of scale occur when the average cost of production increases as the amount of production increases. The risks of large-scale technological investments have to do with whether the uncertain future cash flows will be sufficient to cover the fixed costs of development and installation of the systems. The costs of excess capacity and cost overruns due to integration problems can easily absorb the expected benefits from the expansions. As a result, large FIs will accept production from smaller competitor FIs if such acceptance will assure that the desired cost benefits are obtained. At the same time, small FIs are willing to outsource production in an attempt to gain the benefits of lower production expenses that may be unattainable through their own technology upgrades.

11.

What information on the operating costs of FIs is provided by the measurement of economies of scope?

Economies of scope measure the synergistic cost savings to FIs that offer multiple products or services. For example, if an FI offers both banking and insurance services and offers them at lower costs than a bank and an insurance company offering them separately, economies of scope are said to exist.

12.

Buy Bank had $130 million in assets and $20 million in expenses before the acquisition of Sell Bank, which had assets of $50 million and expenses of $10 million. After the merger, the bank had $180 million in assets and $35 million in expenses. Did this acquisition generate either economies of scale or economies of scope for Buy Bank?

Neither. The costs as a percentage of assets have increased from 15.38 percent ($20m/$130m) to 19.44 ($35m/$180m) percent for the bank. This represents diseconomies of scale.

13.

A commercial bank with assets of $2 billion and expenses of $200 million has acquired an investment banking firm subsidiary with assets of $40 million and expenses of $15 million.

After the acquisition, the expenses of the bank are $180 million and the expenses of the subsidiary are $20 million. Does the resulting merger reflect economies of scale or economies of scope?

This situation would represent economies of scope since different but joint operations are involved. The average cost of the separate firms was $215 million/$2.04 billion or 10.54 percent.

After the merger, the average costs are $200 million/$2.04 billion or 9.8 percent.

4 © 2022

14.

What are diseconomies of scope? How could diseconomies of scope occur?

Diseconomies of scope arise when the average cost of production is higher from the joint production of services than the average costs from the previous independent production of the services. This situation can occur if the technology used in the production of a portion of the services is not sufficiently efficient for the production of the remaining services.

15.

A survey of a local market has provided the following average cost data. Mortgage Bank A (MBA) has assets of $3 million and an average cost of 20 percent. Life Insurance Company B (LICB) has assets of $4 million and an average cost of 30 percent. Corporate Pension Fund C (CPFC) has assets of $4 million and an average cost of 25 percent. For each firm, average costs are measured as a proportion of assets. MBA is planning to acquire LICB and CPFC with the expectation of reducing overall average costs by eliminating the duplication of services. a. What should be the average cost after acquisition for MBA to justify this merger?

Average cost: Bank A = 0.20 x $3,000,000 Insurance Company B = 0.30 x $4,000,000 Pension Fund C = 0.25 x $4,000,000 Total costs

= $ 600,000 = 1,200,000 = 1,000,000 = $2,800,000

The average cost after merger should be no more than 25.45 percent (= 2,800,000 / 11,000,000).

If Bank A can lower its average costs to less than 25.45 percent, it should go ahead with the merger. b. If MBA plans to reduce operating costs by $500,000 after the merger, what will be the average cost of the new firm?

If Bank A lowers its operating costs by $500,000, the average cost of the new firm will be $2,300,000/$11,000,000 = 20.91 percent.

16.

Why does the United States lag behind most other industrialized countries in the proportion of annual electronic noncash transactions per capita? What factors probably will be important in causing the gap to decrease?

To some extent, the United States is only now starting to catch up with other countries in its use of electronic payment method. Part of the reason for this involves culture and tradition in the United States. For example, checks have been obsolete in Germany for some time, but in the United States many people still prefer to write checks. As a result, U.S. FIs have been slow in adopting and using online banking and electronic payment methods extensively. While decreasing, the speed with which this electronic payments gap will be closed will in large part depend on two factors: the speed with which the trend toward consolidation and automated banking continues and the degree and speed of technological innovation.

5 © 2022

17.

What are the differences between the Fedwire and CHIPS payment systems?

Fedwire and CHIPS both are electronic payments systems that transfer various transactions between FIs. Fedwire is comprised of domestic FIs linked with the Federal Reserve System, and CHIPS is a private consortium of the largest domestic and international FIs. When FIs engage in overdrafts while using the Fedwire system, the counterparty is safe even if the FI fails because the Federal Reserve guarantees any payments made over the wire. However, in the case of CHIPS, the transactions are only tentative and are confirmed only at the end of the day. In the event of an FI failure, the receipts and payments from all FIs dealing with the failed FI are tabulated again and new debits and credits are posted. Consequently, there is a danger that a systemic default can be triggered in the event of a single failure.

18.

What is a daylight overdraft? How do an FI’s overdraft risks incurred during the day differ for each of the two competing electronic payment systems, Fedwire and CHIPS? What provision has been taken by the members of CHIPS to introduce an element of insurance against the settlement risk problem?

A daylight overdraft occurs at the Federal Reserve Bank when a bank, in the continuing process of transferring in money and transferring out money from its account, has transferred out more money than is currently in the account. This is similar to the retail transaction of depositing a check and withdrawing cash before the funds from the initial check have cleared into the account. Under the Fedwire system, the Federal Reserve System guarantees all wire transfer messages, while the private CHIPS system will unwind transactions in the event that funds are not sufficient to cover the wire messages. To reduce the potential of a serious system-wide financial crisis, the members of CHIPS have created an escrow fund to cover message commitments of a failed bank.

19.

How does Regulation F of the 1991 FDICIA reduce the problem of daylight overdraft risk?

Regulation F requires banks, thrifts, and foreign institutions to implement procedures to reduce their daylight overdraft exposures. As of December 1992, banks are limited from keeping overdraft positions with a correspondent bank to no more than 25 percent of the correspondent bank’s capital. If a bank is adequately capitalized, then it can have exposures of up to 50 percent of the correspondent bank’s capital. For well-capitalized banks, there is no limit.

20.

Why do FIs in the United States face a higher degree of international technology risk than do the FIs in other countries?

In recent years the United States has been at the forefront in making technology investments and financial service innovations in the payments system. Indeed, the world looks to American innovation and entrepreneurship in building new banking technology and service (two areas in which the U.S. leads the world) to attract new customers. This suggests that U.S. financial service firms have often been unable to transfer profitably their domestic technological innovations to international markets to gain competitive advantage, at least in the short term. In 6 © 2022

contrast, foreign financial service firms entering the U.S. market gain direct access to, and knowledge of, U.S. technology–based products at a very low cost. For example, since the passage of the International Banking Act in 1978, foreign banks have had direct access to U.S. Fedwire.

21.

What has been the impact of rapid technological improvements in the electronic payment systems on crime and fraud risk?

The massive increase in the use of electronic payment mechanisms has greatly increased the level of sophistication required to commit unauthorized transfers by accessing computers illegally. However, knowledge of specialized technical information has created a new type of white-collared crime and thus security problems.

22.

What are usury ceilings? How does technology create regulatory risk?

Usury ceilings are state government imposed limits that FIs may charge on certain types of lending activities, such as consumer loans and credit cards. Because many product transactions rely heavily on electronic technology, financial products often can be marketed from locations without severe regulatory constraints. This activity in effect circumvents the regulatory effects desired in the constrained environments.

23.

How has technology altered the competition risk of FIs?

Competition in the financial services industry has increased because of the entrance of nontraditional financial service providers, such as industrial loan corporations (ILCs), through the use of technology. Thus, the franchise values of traditional service providers, such as banks, savings institutions, etc., are under increasing pressures from the new, technology-based, nontraditional providers.

26.

What actions has the BIS taken to protect depository institutions from insolvency due to operational risk?

In 1999 the Basle Committee (of the BIS) on Banking Supervision said that operational risks “are sufficiently important for banks to devote necessary resources to quantify the level of such risks and to incorporate them (along with market and credit risk) into their assessment of their overall capital adequacy.” In its follow up consultative document released in January 2001 and April 2003, the Basle Committee proposed three specific methods by which depository institutions (DIs) would hold capital to protect against operational risk. These methods were implemented in 2006.

7 © 2022

Solutions for End-of-Chapter Questions and Problems: Chapter Eighteen 1.

What are the benefits and costs to an FI of holding large amounts of liquid assets? Why are Treasury securities considered good examples of liquid assets?

A major benefit to an FI of holding a large amount of liquid assets is that it can offset any unexpected and large withdrawals without reverting to asset sales or emergency funding. If assets have to be sold at short notice, FIs may not be able to obtain a fair market value. It is more prudent to anticipate withdrawals and keep liquid assets to meet the demand. On the other hand, liquid assets provide lower yields, so the opportunity cost for holding a large amount of liquid assets is high. FIs taking conservative positions by holding large amounts of liquid assets will therefore have lower profits.

Treasury securities are considered good examples of liquid assets because they can be converted into cash quickly with very little loss of value from current market levels.

2.

How is an FI’s liability and liquidity risk management problem related to the maturity of its assets relative to its liabilities?

For most FIs, the maturity of assets is greater than the maturity of liabilities. As the difference in the average maturity between the assets and liabilities increases, liquidity risk increases. In the event that liabilities begin to leave the FI or are not reinvested by investors at maturity, the FI may need to liquidate some of its assets at fire-sale prices. These prices would tend to deviate further from their market value as the maturity of the assets increase. Thus, the FI may sustain larger losses.

3.

Consider the assets (in millions) of two banks, A and B. Both banks are funded by $120 million in deposits and $20 million in equity. Which bank has a stronger liquidity position?

Which bank probably has a higher profit?

Bank A Assets Cash Treasury securities Commercial loans Total assets

$10 40 90 $140

Bank B Assets Cash $20 Consumer loans 30 Commercial loans 90 Total assets $140

Bank A is more liquid because it has more liquid assets than Bank B. Although it has less cash, Bank A has $40 million in Treasury securities, which are highly liquid assets. Bank B probably earns a higher profit because the return on consumer loans should be greater than the return on Treasury securities. However, comparing the loan portfolios is difficult because it is impossible to evaluate the credit risk contained in each portfolio using just the information provided.

4.

What concerns motivate regulators to require DIs to hold minimum amounts of liquid assets?

1 © 2022

Regulators prefer DIs to hold more liquid assets because this ensures that they are able to withstand unexpected and sudden withdrawals. In addition, regulators are able to conduct monetary policy by influencing the money supply through liquid assets held by DIs. Finally, reserves held at the Fed by financial institutions also are a source of funds to regulators, since they pay little interest on these deposits. That is, a minimum required liquid asset reserve requirement is an indirect way for governments to raise additional “taxes” from DIs. While these reserves are not official government taxes, having DIs hold cash in the vault or cash reserves at the central bank (when there is only a small interest rate compensation paid) requires DIs to transfer a resource to the central bank.

5.

How do liquid asset reserve requirements enhance the implementation of monetary policy?

How are reserve requirements a tax on DIs?

In the case of DIs, reserve requirements on net transaction deposits allow regulators to increase or decrease the money supply in an economy. The reserve requirement against these deposits limits the ability of DIs to expand lending activity. Further, reserves represent a form of tax that regulators can impose on DIs. By raising the reserve requirements, regulators cause DIs to transfer more balances into non-earning assets. This tax effect is even larger in cases where inflation is stronger.

6.

Rank these financial assets according to their liquidity: cash, corporate bonds, NYSEtraded stocks, and T-bills.

The liquidity ranking from most liquid to least liquid would be cash, T-bills, NYSE-traded stocks, and corporate bonds.

7.

Define the reserve computation period, the reserve maintenance period, and the lagged reserve accounting system.

The reserve computation period is a two-week period beginning every other Tuesday and ending on a Monday over which the required reserves are calculated. The actual reserve calculation is accomplished by multiplying the average daily net transaction accounts balance over this 14-day period times the required reserve ratio. The exact amount of this reserve calculation is not known with certainty until the end of the computation period.

The reserve maintenance period is the 14-day period over which the average level of reserves must equal or exceed the required reserve target.

The lagged reserve accounting system occurs when the reserve maintenance period begins after the reserve computation period is completed. As long as these two periods do not overlap, the DI should have little uncertainty regarding the amount of reserves necessary to be in compliance with regulatory guidelines.

8.

The average daily net transaction accounts deposit balance of a local bank during the most recent reserve computation period is $325 million. The amount of average daily reserves at 2 © 2022

the Fed during the reserve maintenance period is $24.6 million and the average daily vault cash corresponding to the maintenance period is $4.3 million. a. What is the average daily reserve balance required to be held by the bank during the maintenance period?

Reserve requirements = (0 x $14.5m) + ($103.6m - $14.5m)(0.03) + ($325m - $103.6m) (0.10) = 0 + $2.673m + $22.140m = $24.813 million After subtracting the average daily balance of vault cash of $4.3 million, the bank needs to maintain a target daily average of $20.513 million ($24.813 million - $4.3 million) during the maintenance period. b. Is the bank in compliance with the reserve requirements?

Yes. The bank has average reserves of $22.6 million. This amount exceeds the required amount by $2.087 million. c. What amount of reserves can be carried over to the next maintenance period either as excess or shortfall?

A maximum of 4 percent of the gross required reserves can be carried over to the next maintenance period. Thus, 0.04 x $24.813 million = $0.9925 million can be carried over to the next maintenance period. The bank has deposited $1.0945 million ($2.087m - $0.9925m) in low interest paying accounts at the Fed that cannot be counted towards next period’s required reserves. d. If the local bank has an opportunity cost of 6 percent and deposits at the Fed pay 0.5 percent, what is the effect on the income statement from this reserve period?

A total of $1.0945 million has an opportunity cost of no earnings at the 6 percent rate. Thus, the loss would be $1.0945m(0.060 - 0.005)(14/365) = $2,308.95.

9.

The following net transaction accounts and cash reserves at the Fed have been documented by a bank for computation of its reserve requirements (in millions) under lagged reserve accounting.

Monday Tuesday Wednesday Thursday Friday April 10th 11th 12th 13th 14th Net transaction accounts $200 $300 $250 $280 $260 Reserves at Fed 20 22 21 18 27 Monday 17th

Tuesday 18th

Wednesday 19th

Net transaction 3 © 2022

Thursday 20th

Friday 21th

accounts Reserves at Fed

$280 20

$300 35

$270 21

$260 18

$250 28

Monday 24th

Tuesday 25th

Wednesday 26th

Thursday 27th

Friday 28th

$240 19

$230 19

$250 21

$260 19

$270 24

Monday 1st

Tuesday 2nd

Wednesday 3rd

Thursday 4th

Friday 5th

$200 20

$300 22

$250 21

$280 18

$260 27

Monday 8th

Tuesday 9th

Wednesday 10th

Thursday 11th

Friday 12th

$280 20

$300 35

$270 21

$260 18

$250 27

Monday 15th

Tuesday 16th

Wednesday 17th

Thursday 18th

Friday 19th

$240 20

$230 35

$250 21

$260 18

$270 28

Monday 22th

Tuesday 23th

Wednesday 24th

Thursday 25th

Friday 26th

$300 19

$250 21

$280 19

$260 24

Net transaction accounts Reserves at Fed

May Net transaction accounts Reserves at Fed

Net transaction accounts Reserves at Fed

Net transaction accounts Reserves at Fed

Net transaction accounts Reserves at Fed

$200 19

The average vault cash for the computation period has been estimated to be $1 million per day. a.

What level of average daily reserves is required to be held by the bank during the maintenance period, May 11 - 24?

Average daily net transaction accounts deposits = $300m + $250m + $280m + $260m + $260m + $260m + $280m + $300m + $270m + $260m + $250m + $250m + $250m + $240m = $3,710m/14 = $265m Reserve requirement = ($14.5m - $0)(0) + ($103.6m – $14.5m)(0.03) + ($265m – $103.6m)(0.10) = $0 + $2.673m + $16.140m = $18.813m 4 © 2022

After subtracting the average daily balance of vault cash of $1 million, the bank needs to maintain a target daily average of $17.813 million ($18.813 million - $1 million) during the maintenance period. b. Is the bank in compliance with the requirements?

The maintenance period begins on Thursday, May 11th.

Average Reserves at Fed = $18m + $27m + $27m + $27m + $20m + $35m + $21m + $18m + $28m + $28m + $28m + $19m + $19m + $21m = $336m/14 = $24m.

Excess over required reserves = $24m - $17.813 = $6.187m c. What amount of required reserves can be carried over to the following computation period?

Excess that can be carried over = 0.04 x $18.813 million = $0.7525 million. d. If the average cost of funds to the bank is 8 percent per year and deposits at the Fed pay 0.5 percent, what is the effect on the income statement for this bank for this reserve period?

Loss = (6.187m - 0.7525m) x (0.080 - 0.005)(14/365) = $15,6933.49.

10.

City Bank has estimated that its average daily net transaction accounts balance over the recent 14-day reserve computation period was $225 million. The average daily balance with the Fed over the 14-day maintenance period was $9 million, and the average daily balance of vault cash over the two-week computation period was $7.5 million. a. Under the rules effective in 2015, what is the amount of average daily reserves required to be held during the reserve maintenance period for these net transaction accounts balances?

Reserve requirements = (0 x $14.5m) + ($103.6m - $14.5m)(0.03) + ($225m - $103.6m) (0.10) = 0 + $2.673m + $12.140m = $14.813 million After subtracting the average daily balance of vault cash of $7.5 million, the bank needs to maintain a daily average of $7.313 million ($14.813 million - $7.5 million) during the maintenance period. b. What is the average daily balance of reserves held by the bank over the maintenance period? By what amount were the average reserves held higher or lower than the required reserves?

The average daily balance over the maintenance period was $7 million. Therefore, average reserves held were short $0.313 million.

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c. If the bank had transferred $20 million of its deposits every Friday over the two-week computation period to one of its offshore facilities, what would be the revised average daily reserve requirement?

For the 14-day period, the sum of its daily average is = $225m x 14 = $3,150m. If $20 million is transferred on Friday, the total reduction is $120 million over two weekends ($20m x 3 days x 2 weekends), and the total 14-day balance is $3,030m. The average daily deposits will be $216.4286 million.

Reserve requirements = (0 x $14.5m) + ($103.6m - $14.5m)(0.03) + ($216.4286m - $103.6m) (0.10) = 0 + $2.673m + $11.283m = $13.956 million. City Bank needs to maintain average reserves of $6.456 million ($13.956 million - $7.5 million) during the maintenance period. Since it had $7 million of reserves, extra reserves of $0.544m per day can be carried forward to the next reserve maintenance period.

11.

Assume that the 14-day reserve computation period for problem (10) above extended from May 18 through May 31. a. What is the corresponding reserve maintenance period under the rules effective in 2015?

The reserve maintenance period would extend from June 17 through June 30. The period begins 30 days after the beginning of the reserve computation period. This makes it easier for bank managers to meet their reserve requirements. By beginning two weeks and two days after the end of the computation period, managers can more easily make up for any errors in their forecast of reserve requirements. b. Given your answers to parts (a) and (b) of problem (10), what would the average required reserves need to be for the maintenance period for the bank to be in reserve compliance? What are the minimum and maximum reserves that may be maintained by the bank to be in reserve compliance?

The average required reserves necessary to be in compliance is $7.313 million and they could be as low as $6.720m ($7.313m - $14.813m(0.04)) or as high as $7.906m ($7.313m + $14.813m(0.04)).

12.

A bank has an average balance of transactions accounts, July 14 to 27, of $850.55 million.

The average balance in the cash account is $20.150 million over this period. The bank is carrying forward a deficit of $1.756 million from the last reserve period. Calculate the net reserve requirement for the reserve maintenance period from August 13 to 26. Calculate the minimum reserves that may be maintained and the maximum reserves that will count toward the next reserve maintenance period, August 27 to September 9.

Average balance of transactions accounts, July 14-27 = 850.55m 6 © 2022

14.5m at 0% $103.6m - $14.5m at 3% $850.55m - $103.6m at 10% Gross reserve requirement Daily average vault cash Aug 10-23 Net reserve requirement Reserve carry forward from last period daily average amount = 1.756m Reserves to be maintained with Fed

1.756m $58.974m

target reserves

Minimum reserves to be maintained -.04(77.368m) = -3.095m

$55.879m

minimum reserves

Maximum reserves to be maintained +.04(77.368m) = +3.095m

$62.069m

maximum reserves

13.

$

0 2.673m 74.695m 77.368m 20.150m $57.218m

If over the first 12 days of the current reserve maintenance period the average daily reserves held by the bank in problem (12) were $56 million (or 12 x $56m = $672 m cumulative total over the 12 days), what does the bank need to hold as reserves over the last two days to (1) exactly meet the reserve requirement, (2) meet the minimum reserve, and (3) meet the maximum reserve?

1. To meet the reserve requirement: Over the first 12 days the bank should have held a cumulative reserve of $58.974m x 12 = $707.688m. The bank is running a shortfall of $707.688m - $672 m = $35.688 m. Thus, the cumulative balance over the last two days, August 25 and 26, needs to be: $58.974m + 58.974m + $35.688m = $153.636 m 2. To hit the minimum cumulative balance: Over the first 12 days the bank should have held a cumulative reserve of $55.879m x 12 = $670.548 m. The bank is running a surplus of $670.548m - $672m = -$1.452 m. Thus, the cumulative balance over the last two days, August 25 and 26, needs to be: $55.879m + $55.879m - $1.452m = $110.306m 3. To hit the maximum cumulative balance: Over the first 12 days the bank should have held a cumulative reserve of $62.069m x 12 = $744.828 m. The bank is running a shortfall of $744.828m - $672m = $72.828m. Thus, the cumulative balance over the last two days, August 25 and 26, needs to be: $62.069m + $62.069m + $72.828m = $196.966m 7 © 2022

Or the bank must run a reserve balance between $110.306 million and $196.966 million over the two days, August 25 and 26.

14.

In July of 1998 the lagged reserve accounting (LRA) system replaced a contemporaneous reserve accounting (CRA) system as the method of reserve calculation for DIs. a. Contrast a contemporaneous reserve accounting (CRA) system with a lagged reserve accounting (LRA) system.

Under LRA, the DI holds reserves against the amount of deposits that had been in the DI 30 days prior. The DI knows its required reserves on every day of the reserve maintenance period. Since reserve requirements are stated in the form of average daily balances, the DI can adjust its reserves over the maintenance period to exactly equal the average reserve requirement. Under CRA, the two-week reserve maintenance period for meeting the reserve target began only two days after the start of the computation period. Thus, CRA resulted in only a two-day window during which required reserves were know with certainty. b. Under which accounting system, CRA or LRA, are DI reserves higher? Why? Ceteris paribus, one would expect reserves to be higher under the CRA than under the LRA, because under the LRA the DI knows its reserve requirement exactly on every day of the reserve maintenance period. There is no need for the DI to hold excess reserves as a cushion against an unforeseen increase in reserve requirements. DIs are able to keep their reserves to the minimum required level. Under CRA, the DI does not know its reserve requirement until the last two days of the reserve maintenance period. Since those are the days during which Fed fund rates are most volatile, DIs attempt to avoid large reserve shortages late in the reserve maintenance period.

They will therefore tend to hold excess reserves early in the maintenance period that may be reduced on the last two days of the settlement week. c. Under which accounting system, CRA or LRA, is DI uncertainty higher? Why? Since information is complete during the entire settlement week under LRA, but complete under CRA only during the last two days of the maintenance period, there is more uncertainty about reserve requirements under the CRA than under the LRA. 15.

What is the “weekend game”? Contrast a DI's ability and incentive to play the weekend game under LRA as opposed to CRA.

Since Friday balances are carried over the weekend and are counted for Saturday and Sunday, they carry more weight in the reserve computations. Thus, DIs developed a strategy to send deposits offshore on Friday, thereby reducing their Friday closing deposit balances. When these deposits were bought back on Monday, average daily deposit balances were reduced, thereby decreasing reserve requirements. Although the ratio of weekends to total days in the reserve computation period is the same under LRA as under CRA (2/7 or 4/14), there is greater 8 © 2022

flexibility for DIs to play the weekend game under LRA. That is because the DI has complete information about reserve requirements on each day of the maintenance period. However, because of the uncertainty under CRA, there is greater incentive for DIs to play the weekend game under CRA than under LRA. 16.

Under CRA, when is the uncertainty about the reserve requirement resolved? Discuss the feasibility of making large reserve adjustments during this period of complete information.

Under CRA, the uncertainty regarding reserve requirements is resolved on the last two days of the reserve maintenance period (on the last Tuesday and Wednesday of the 14 day period).

However, since these are also the days of greatest volatility in the fed funds rate, it could be very costly for the reserve manager to make large reserve adjustments or corrections during this twoday period. Moreover, since the fed funds market is comprised of active traders that deal daily with one another, a large reserve imbalance would lead to abnormal fed funds transactions and would be quickly detected and exploited (to the detriment of the original DI) by other DI traders.

17.

What is the relationship between funding cost and funding or withdrawal risk?

Liabilities that have a low cost often have the highest risk of withdrawal. Thus, a DI that chooses to attract low cost deposits may have high withdrawal risk.

18.

An FI has estimated the following annual costs for its demand deposits: management cost per account = $140, average account size = $1,500, average number of checks processed per account per month = 75, cost of clearing a check = $0.10, fees charged to customer per check = $0.05, and average fee charged per customer per month = $8. a. What is the implicit interest cost of demand deposits for the FI? Cost of clearing checks = $0.10 x 75 x 12 Cost of managing each account Per check fee per account = $0.05 x 75 x 12 Fee received per account = $8 x 12 Total cost per account

= $90.00 = $140.00 = -$45.00 = -$96.00 = $89.00

The average (imputed) interest cost of demand deposits = $89.00/1,500 = 5.93 percent. b. If the FI has to keep an average of 8 percent of demand deposits as required reserves with the Fed paying no interest, what is the implicit interest cost of demand deposits for the FI? If the bank has to keep 8 percent as reserves, its use of funds is limited to 0.92 x $1,500 per account, or $1,380. The average (imputed) interest cost = $89/$1,380 = 6.45 percent. c. What should be the per-check fee charged to customers to reduce the implicit interest costs to 3 percent? Ignore the reserve requirements.

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For an average imputed interest cost of 3 percent, the total cost per account = 1,500 x 0.03 = $45.

This means that the total cost per account should be decreased by $44 ($89 - $45) and the percheck fee charged to customers should be increased to $89 ($45 + $44). Thus, the fee per-check should be raised to $89/(75 x 12) = $0.0989 per check.

19.

A NOW account requires a minimum balance of $750 for interest to be earned at an annual rate of 4 percent. An account holder has maintained an average balance of $500 for the first six months and $1,000 for the remaining six months. The account holder writes an average of 60 checks per month and pays $0.02 per check, although it costs the bank $0.05 to clear a check. a. What average return does the account holder earn on the account?

Gross interest return = Explicit interest return + Implicit interest return Interest earned by account holder ($500 x 0.00 x 6/12) + ($1,000 x 0.04 x 6/12) = $20.00 Implicit fee earned on checks ($0.05-$0.02) x 60 x 12 = $21.60 Average deposit maintained during the year (6/12 x 500) + (6/12 x 1,000) = $750.00 Average interest earned = ($20.00 + $21.60)/750 = 5.55 percent b. What is the average return if the bank lowers the minimum balance to $400?

If the minimum balance requirement is lowered to $400, the account holder earns an extra $500 x 0.04 x 6/12 = $10 in interest. The average interest earned = $51.60/750 = 6.88 percent. c. What is the average return if the bank pays interest only on the amount in excess of $400? Assume that the minimum required balance is $400.

If the bank only pays interest on balances in excess of $400, the explicit interest earned = ($100 x 0.04 x 6/12) + ($600 x 0.04 x 6/12) = $2 + $12 = $14. The implicit fee earned on checks = $21.60, and the average interest earned = $35.60/$750 = 4.75% d. How much should the bank increase its check fee to the account holder to ensure that the average interest it pays on this account is 5 percent? Assume that the minimum required balance is $750.

Interest earned (both explicit and implicit) = $750 x 0.05 = $37.50. Fees to be earned through check clearing = $37.50 - $20 = $17.50. Fee subsidy per check = 17.50/(60 x 12) = $0.0243. So, the bank should charge $0.05 - $0.0243 = $0.0257 per check.

20. Rank the following liabilities, with respect, first, to funding risk and second to funding cost: 10 © 2022

a. Money market deposit account. b. Demand deposits. c. Certificates of deposit. d. Federal funds. e. Bankers’ acceptances. f. NOW accounts. g. Wholesale CDs. h. Passbook savings. i. Repos. j. Commercial paper.

Funding Risk 7 10 6 4 2 9 5 8 3 1

Funding Cost 4 1 5 7 9 2 6 3 8 10

The rankings above are not meant to be definitively precise, but are made to illustrate that the funding cost and the funding risk are inversely related. For example, demand deposits usually are considered to be the least-cost source of funding, but they also are easily withdrawn from the FI. On the other hand, repos, wholesale CDs, and fed funds are not liquid during their term, but can be extremely liquid at maturity if the FI has any kind of financial distress. The cost of each of these types of funds is directly linked to money market conditions. The contrast between funding risk and funding cost for several of the liabilities is discussed below: Demand deposits have low funding costs, but technically have high amounts of funding risk since they can be withdrawn at any time. However, in practical terms, demand deposits are often quite stable and may behave like long-term core deposits.

Certificates of deposit have high funding costs (because of reserve requirements and risk premiums on negotiable CDs), but they have low funding risk since they can be withdrawn only upon payment of interest penalties.

Federal funds have relatively low funding costs (although these costs are higher than those for demand deposits) because of their overnight maturity, but they can have high funding risk if the FI is distressed or not an active participant in the Fed funds market. However, for major money center banks, the funding risk on fed funds is quite low.

21.

How is the withdrawal risk different for federal funds and repurchase agreements?

Withdrawal risk is lower for repurchase agreements (RPs) because they are collateralized usually by government securities. Since RPs are collateralized, they require a lower risk premium but they require time to process because of the need to post collateral. In every other respect, the transaction of an RP is similar to federal funds.

22.

How does the cash balance, or liquidity, of an FI determine the types of repurchase agreements into which it will enter?

If the FI has surplus cash, it would buy securities with the understanding that the seller would repurchase them later. In this case, the repurchase agreement is an asset for the firm that bought 11 © 2022

the securities. If an FI is low on cash, it would sell securities for cash with the understanding that it would repurchase the securities later. Here the repo is a liability.

23.

How does the cost of MMMFs differ from the cost of MMDAs? How is the spread useful in managing the withdrawal risk of MMDAs?

MMMFs earn rates of return that are directly related to the money market conditions for the assets held by the funds. MMDAs can be priced to reflect these conditions, but they do not necessarily need to be priced in this manner. Since the two products compete for investor funds, FIs can control the rate of withdrawal of funds from the MMDAs by raising or lowering the explicit interest rate paid to depositors. Allowing the MMDA-MMMF spread to become increasingly negative will increase the rate of withdrawal from the MMDA accounts.

24.

Why do wholesale CDs have minimal withdrawal risk to the issuing FI?

Wholesale CDs are negotiable instruments that can be sold (discounted) in the secondary market.

Thus, if the initial investor needs funds before the CDs mature, the CDs can be liquidated at money market rates by the investor without withdrawing the funds from the issuing bank.

25.

What characteristics of fed funds may constrain a DI’s ability to use fed funds to expand its liquidity quickly?

Fed funds are uncollateralized loans. As such, DIs selling fed funds often will limit the amount of funds they will provide to any one borrowing institution. Further, fed funds do have risk of non-rollover at maturity.

26.

What does a low fed funds rate indicate about the level of DI reserves? Why does the fed funds rate have higher-than-normal variability around the last two days in the reserve maintenance period?

A low fed funds rate would indicate low levels of DI borrowing and an ample or at least adequate supply of reserves among DIs. Whether the general level of the fed funds rate is low or high, the variability of the rate around the last two days in the reserve maintenance period will accelerate as DIs attempt to meet the required reserve levels.

27.

What trends have been observed between 1960 and 2015 in regard to liquidity and liability structures of commercial banks? What changes have occurred in the management of assets that may cause the measured trends to be overstated?

From Table 18-5, it is clear that commercial banks have reduced their composition of liquid assets to illiquid assets from 44 percent to 26.62 percent (liquid assets = cash and government and agency securities). However, this may be overstated because the illiquid assets, such as commercial and mortgage loans, are significantly different today from prior years because they can be securitized and sold in the secondary markets. As a result, they are not as illiquid as they were in the past, which may be one reason why banks held more liquid assets in prior years.

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Table 18-6 also shows that there has been a shift away from transaction accounts to time accounts, CDs, and borrowed funds. Although this reduces withdrawal risk, these funds are more expensive for commercial banks.

28.

What are the primary methods that insurance companies can use to reduce their exposure to liquidity risk?

Insurance companies can reduce their exposure by diversifying the distribution of risk in the contracts they write. In addition, insurance companies can meet liquidity needs by holding relatively marketable assets to cover claim payments.

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Solutions for End-of-Chapter Questions and Problems: Chapter Nineteen 1.

What is a contagious run? What are some of the potentially serious adverse social welfare effects of a contagious run? Do all types of FIs face the same risk of contagious runs?

A contagious run is an unjustified panic condition in which liability holders withdraw funds from an FI without first determining whether the institution is at risk. This action usually occurs at a time that a similar run is occurring at a different institution that is at risk. The contagious run may have an adverse effect on the level of savings that may affect wealth transfers, the supply of credit, and control of the money supply. Depository institutions and insurance companies face the most serious risk of contagious runs.

2.

How does federal deposit insurance help mitigate the problem of bank runs. What other elements of the safety net are available to DIs in the United States?

Bank runs are costly to society since they create liquidity problems and can have a contagion effect. Because of the first-come, first-serve nature of deposit liabilities, DI depositors have incentives to run on the DI if they are concerned about solvency. As a result of the external cost of runs on the safety and soundness of the entire banking system, the Federal Reserve has put into place a safety net to remove the incentives to undertake DI runs. The primary pieces of this safety net are deposit insurance and other guaranty programs that provide assurance that funds are safe even in cases when the FI is in financial distress. Other elements of the federal safety net are access to the lender of last resort (discount window borrowing), reserve requirements, and minimum capital guidelines.

3.

What major changes did the Financial Institutions Reform, Recovery, and Enforcement Act of 1989 make to the FDIC and the FSLIC?

The FIRREA Act of 1989 closed down the FSLIC, the agency that used to provide deposit insurance to savings associations. The responsibility of providing insurance to these DIs was transferred to the FDIC, which manages it through the Deposit Insurance Fund.

4.

Contrast the two views on, or reasons why, depository institution insurance funds can become insolvent.

One view is that insolvency can be explained by external events in the financial environment such as the rise in interest rates and oil prices that took place in the early 1980s or the crash of the housing market in the 2000s. The other view is that deposit insurance brings about the types of behavior that lead to eventual insolvency. In particular, deposit insurance contributes to the moral hazard problem whereby DI owners and managers are induced to take on risky projects because the presence of deposit insurance substantially reduces the adverse consequences to the depositors of such behavior.

5. What is moral hazard? How did the fixed-rate deposit insurance program of the FDIC contribute to the moral hazard problem of the depository institution industry?

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Moral hazard occurs in the depository institution industry when the provision of deposit insurance or other liability guarantees encourages the institution to accept asset risks that are greater than the risks that would have been accepted without such liability insurance.

The fixed-rate deposit insurance administered by the FDIC created a moral hazard problem because it did not differentiate between the activities of risky and conservative lending institutions. From 1933 until January 1, 1993, regulators based deposit insurance premiums on a DI’s deposit size rather than on its risk, and the deposit insurance scheme implemented in 1993 did not impose a fee that fully covered a DI’s risk. Further, the 1980s and (to some extent) 2000s were periods of deregulation, increased risk taking, and capital adequacy forbearance rather than stringent activity regulation and tough capital requirements. Moreover, for the FSLIC, the number of bank examinations and examiners actually fell between 1981 and 1984. Finally, prompt corrective action and closure for severely undercapitalized banks did not begin until the end of 1992.The combination of excessive risk-taking together with a forbearance policy followed by the regulators contributed to the moral hazard problems in the depository institutions industry.

6.

How does a risk-based deposit insurance program solve the moral hazard problem of excessive risk taking by DIs? Is an actuarially fair premium for deposit insurance always consistent with a competitive banking system?

A risk-based deposit insurance program should deter FIs from engaging in excessive risk-taking as long as it is priced in an actuarially fair manner, meaning that insurance pricing is based on the perceived risk of the insured institution. Such pricing currently is being practiced by insurance firms in the property-casualty sector. However, since the failure of commercial banks can have significant social costs, regulators have a special responsibility towards maintaining their solvency, even providing them with some form of subsidies. In a completely free market system, it is possible that DIs located in sparsely populated areas may have to pay extremely high premiums to compensate for a lack of diversification or investment opportunities. These DIs may have to close down unless subsidized by the regulators. Thus, a strictly risk-based insurance system may not be compatible with a truly competitive banking system.

This suggests that, ideally, regulators should design the deposit insurance contract with the tradeoff between moral hazard risk and DI panic or run risk in mind. For example, by providing 100 percent coverage of all depositors and reducing the probability of runs to zero, the insurer may be encouraging certain DIs to take a significant degree of moral hazard risk-taking behavior. On the other hand, a very limited degree of deposit insurance coverage might encourage runs and panics, although moral hazard behavior itself would be less evident.

7.

What are three suggested ways a deposit insurance contract could be structured to reduce moral hazard behavior?

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Deposit insurance contracts could be structured to reduce moral hazard behavior by (1) increasing stockholder discipline, (2) increasing depositor discipline, and (3) increasing regulator discipline.

8.

What is capital forbearance? How does a policy of forbearance potentially increase the costs of financial distress to the deposit insurance fund as well as the stockholders?

Capital forbearance refers to regulators’ permitting an FI with depleted capital to continue to operate. The primary advantage occurs in the short run through the savings of liquidation costs.

In the long run, the likely cost is that the poorly managed FI will become larger, more risky, but no more solvent. Eventually even larger liquidation costs must be incurred.

9.

What are some ways of imposing stockholder discipline to prevent FI managers from engaging in excessive risk taking?

Two ways of imposing stockholder discipline to prevent excessive risk taking are (a) through a risk-based deposit insurance program and (b) through increased capital requirements and stricter closure rules.

Risk-based deposit insurance premiums ensure that DIs engaging in riskier activities will have to pay higher premiums. One reason for the savings institution crisis was the fixed-rate deposit insurance premiums that did not differentiate between risky and conservative DIs. As a result, stockholders of DIs in financial difficulties had nothing to lose by investing in projects that had high payoffs because depositors were protected by the FDIC insurance program.

Stockholder discipline also is increased if DIs are required to hold more capital and regulators stopped the practice of capital forbearance and followed a more prompt corrective action program. The more capital a DI has, the less likely the failure of a DI in the event of a decline in the market value of assets. This protects not only the depositors but also the FDIC, which provides the insurance. Further, while in the short term, forbearance may save the insurance fund some liquidation costs, in the long run, owners of bad banks or thrifts have continuing incentives to grow and take additional risks in the hope of a large payoff that could turn the institution around. This strategy potentially adds to the future liabilities of the insurance fund and to the costs of DI liquidation. Using a prompt corrective action program, riskier activities are met with progressively harsher mandatory actions being taken by regulators as capital ratios fall. Under this carrot-and-stick approach, a bank or thrift is placed into receivership within 90 days of the time when its capital falls below some positive book value level, that is, when it is critically undercapitalized (currently 2 percent of assets for DIs). To the extent that the book value of capital approximates true net worth or the market value of capital, this enhances stockholder discipline by imposing additional costs on DI owners for risk taking. It also increases the degree of coinsurance, in regard to risks taken, between DI owners and regulators such as the FDIC.

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10.

How is the provision of deposit insurance by the FDIC similar to the FDIC’s writing a put option on the assets of a DI that buys the insurance? What two factors drive the premium of the option?

As long as a DI is profitable, the owners of the DI benefit by maintaining a positive market value of equity. If the DI’s performance falters to the point that net worth becomes negative, the owners can put the assets back to the FDIC who will pay off the insured depositors and sell the assets. The premium on this put option, or deposit insurance, is positively related to the level of risk of the assets and to the amount of leverage maintained by the DI. 11.

What four factors were provided by FDICIA as guidelines to assist the FDIC in the establishment of risk-based deposit insurance premiums? What happened to the level of deposit insurance premiums in the late 1990s and early 2000s? Why?

The FDIC must base deposit insurance premiums on (1) different categories and concentrations of assets, (2) different categories and concentrations of liabilities, (3) other factors that affect the probability of loss, and (4) the revenue needs of the insurer. In most cases, the ranking of an institution is based on regulators’ judgments regarding asset quality, loan underwriting standards, and other operating risks.

Initially, the best DIs, those that were well capitalized and healthy, paid an annual insurance premium of 23 cents per $100 of deposits, while the worst DIs paid 31 cents. Although the 8cent differential in insurance premiums between the safest and the riskiest DIs was a first step in risk-based pricing, it was widely considered so small that it did not effectively price insurance according to DI risk exposures. In the mid-1990s, as the industry risk profile improved and the revenue needs of the FDIC insurance funds decreased and the amount of the minimum risk premium fell to zero for most banks. At the time, regulations restricted the FDIC form charging premiums to well-capitalized and highly rated DIs as long as the insurance fund reserves were above 1.25 percent of insured deposits. As a result over 90 percent of all insured DIs did not pay deposit insurance premiums in the late 1990s and early 2000s.

In the early 2000s, the FDIC identified several weaknesses with the existing system of deposit insurance that it felt needed to be corrected. Among these was that the system did not effectively price risk. The FDIC argued that it should charge regular premiums for risk regardless of the reserve levels of the fund. Beginning in 2009, the FDIC began calculating deposit insurance premiums based on a more aggressively risk-based system. Under this scheme, the lowest risk DIs paid a minimum of 5 cents per $100 of deposits for deposit insurance, while the highest risk DIs paid 43 cents per $100 of deposits. Under the FDIC Reform Act, if the reserve ratio drops below 1.15 percent─or the FDIC expects it to do so within six months─the FDIC must, within 90 days, establish and implement a plan to restore the DIF to 1.15 percent within five years. Such was the case in March 2008 when the FDIC reserve ratio dropped to 1.19 percent. At this point the FDIC was certain that the reserve ratio would drop below 1.15 by the end of the next quarter.

Accordingly, the FDIC developed and implemented (on April 1, 2009) a restoration plan for the DIF. The plan was revised in 2011 such that the safest DIs pay 0.05 percent and the riskiest Dis pay 0.45 percent of their average total assets less average tangible equity. The plan was revised 4 © 2022

again in 2015 to account for a reduction in assessment rates as the FDIC reserve ratio approached 1.15 percent.

12.

Under what conditions may the implementation of minimum capital guidelines, either riskbased or non-risk-based, fail to impose stockholder discipline as desired by the regulators?

The implementation of minimum capital guidelines would fail to impose stockholder discipline as desired by the regulators if regulators are unwilling to enforce immediately corrective action provisions against DIs that violate the minimum capital guidelines.

13.

Why did the fixed-rate deposit insurance system fail to induce insured and uninsured depositors to impose discipline on risky DIs in the United States in the 1980s?

The fixed-rate deposit insurance system understandably provided no incentives to depositors to discipline the actions of DIs since they were completely insured for deposits of up to $100,000 per account per DI. Uninsured depositors also had few incentives to monitor the activities of DIs because regulators had been reluctant to close down failing DIs, especially larger DIs. This is because of the anticipated widespread social implications. As a result, both insured and uninsured depositors were usually protected against DI losses, reducing the incentives to monitor the actions of DIs. a. How is it possible to structure deposits in a DI to reduce the effects of the insured ceiling?

Deposits are insured by the FDIC up to $250,000 per person account per DI. Therefore, individual depositors could expand coverage beyond $250,000 by placing deposits as joint accounts and by having accounts in many DIs at the same time. b. What are brokered deposits? Why are brokered deposits considered more risky than nonbrokered deposits by DI regulators?

Individuals and companies who wish to place more than $250,000 of deposits in DIs often will hire brokers to place these deposits in blocks of $250,000 in DIs that pay the highest interest rates. This activity is considered risky by regulators for two reasons. First, DIs willing to pay the highest rates often have the highest need for deposits from a liquidity standpoint. Second, when the deposits mature, the risk of withdrawal may force the DI to pay even higher rates to keep the deposits. As a result, this higher cost of funds may force the DI to engage in even riskier lending activities. c. What trade-offs were weighed in the decision to leave the deposit insurance ceiling at $100,000 in 2005 and then increase the ceiling to $250,000?

The 2005 decision was based on the idea that maintaining the $100,000 the deposit insurance ceiling potentially would give depositors the incentive to better monitor the risk of DIs. However, such monitoring may also allow these depositors to run from DIs that became too 5 © 2022

risky. Such action would perhaps cause more DIs to fail that would put increased solvency pressure on the insurance fund. Raising the coverage cap would decrease the incentives of depositors to monitor and run from more risky DIs, it would also decrease the number of DI failures and the probability of panics. Thus, the losses to the FDIC from covering a larger dollar amount of deposits per head were weighed against the possibility of fewer failures, with their attendant liquidation costs. Regulators decided in favor of maintaining the $100,000 coverage cap.

During the financial crisis of 2008-2009, in an attempt to provide stability to the U.S. banking system, the FDIC increased the deposit insurance limit to $250,000 from $100,000 per person per institution. At this time, the FDIC was more concerned about the possibility of contagious runs as a few major DIs (e.g., Washington Mutual) failed or nearly failed. The FDIC wanted to instill confidence in the banking system and made the change to avoid massive depositor runs from many of the troubled (and even safer) DIs, more DI failures, and an even larger collapse of the financial system.

14.

What changes did the Federal Deposit Insurance Reform Act of 2005 make to the deposit insurance cap?

The Federal Deposit Insurance Reform Act of 2005 left the deposit insurance cap at $100,000 per person per account. The Act also increased deposit insurance coverage for retirement accounts from $100,000 to $250,000. During the financial crisis of 2008-2009, in an attempt to provide stability to the U.S. banking system, the TARP called for the FDIC to increase the deposit insurance limit to $250,000 from $100,000 per person per institution.

15.

What is the too-big-to-fail doctrine? What factors caused regulators to act in a way that caused this doctrine to evolve?

Large DIs are not generally allowed to fail because of the draining effects on the resources of the insurance funds and the fear of contagious or systemic runs spreading to other large DIs. Thus, the fear of significant negative effects on the financial system usually meant that both large and small depositors in large DIs are protected. Indeed, during the financial crisis of 2008-2009, the Federal Reserve’s rescue of FIs such as Bear Stearns, AIG, and Citigroup and the $200 billion invested in over 640 banks through the Treasury Department’s Capital Purchase Program demonstrated that the TBTF bailouts reached much further than anyone would have predicted.

16.

What are some of the essential features of the FDICIA of 1991 with regard to the resolution of failing DIs?

The FDICIA of 1991 made it very difficult for regulators to delay the closing of failing DIs unless the danger of a systemic risk can be shown. They are expected to use the least cost resolution (LCR) strategy to close down DIs, and shareholders and uninsured depositors are expected to bear the brunt of the loss. Unlike in prior years, the FDIC only subsidizes if the liquidated assets are not sufficient to cover the insured deposits. The General Accounting Office 6 © 2022

has also been authorized to audit failure resolutions used by regulators to ensure that the least cost strategy has been adopted. a. What is the least-cost resolution (LCR) strategy?

The LCR requires the cost of each failure resolution alternative to be evaluated on a present value basis. b. When can the systemic risk exemption be used as an exception to the LCR policy of DI closure methods?

The systemic risk exemption can be used only when it can be shown that the closure of a large DI will cause a significant threat to the entire financial system. c. What procedural steps must be taken to gain approval for using the systemic risk exemption?

Use of the systemic risk exemption requires the approval of two thirds of the Federal Reserve Board members and the FDIC board as well as the recommendation of the Secretary of Treasury and the President of the United States. d. What are the implications to the other DIs in the economy of the implementation of this exemption?

The net cost of the bailout of a large DI will be shared by all other DIs by charging them an additional deposit insurance premium based on their size as measured by average total assets minus average tangible equity.

17.

What is the primary goal of the FDIC when employing the LCR strategy?

The purpose for implementing this strategy is to pass more of the failure resolution cost to uninsured depositors, thereby enhancing their incentives to monitor DIs and to control risk through requiring higher deposit rates and/or through their deposit placement decisions. a. How is the insured depositor transfer method implemented in the process of failure resolution?

Under the insured depositor transfer (or ‘haircut”) method of resolution, the insured deposits of a closed DI are usually transferred in full to another local DI in the community to conduct a direct payoff of the depositors for the FDIC. By contrast, uninsured depositors must file a claim against the receiver of the failed DI and share with the FDIC in any receivership distributions from the liquidation of the closed DI’s assets. This usually results in a loss for uninsured depositors (a socalled haircut).

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b. Why does this method of failure resolution encourage uninsured depositors to more closely monitor the strategies of DI managers?

Uninsured depositors will monitor DI managers more closely because uninsured depositors assume losses. Thus, they have a much stronger incentive to monitor and control the actions of DI owners.

18.

The following is a balance sheet of a commercial bank (in millions of dollars).

Assets Cash Loans

$5 40

Total assets

$45

Liabilities and Equity Insured deposits Uninsured deposits Equity Total liabilities and equity

$30 10 5 $45

The bank experiences a run on its deposits after it declares it will write off $10 million of its loans as a result of nonpayment. The bank has the option of meeting the withdrawals by first drawing down its cash and then selling off its loans. A fire sale of the remaining loans in one day can be accomplished at a 10 percent discount. They can be sold at a 5 percent discount if sold in two days. The full market value will be obtained if they are sold after two days. a. What is the amount of loss to the insured depositors if a run on the bank occurs on the first day? On the second day?

Insured depositors will not lose any money because even if the bank does not make the payment, they will be paid by the FDIC. Further, the value of the loans on the first day is 0.90 x $30 = $27m and their value on the second day is 0.95 x $30 = $28.5m. With its cash reserves, it has a more than adequate amount to pay the insured depositors as long as the uninsured depositors are not given the opportunity to cash in their deposits first. b. What amount do the uninsured depositors lose if the FDIC uses the insured depositor transfer method to close the bank immediately? The assets will be sold in two days.

The value of the loans on the second day is 0.95 x $30 = $28.5m. With its cash reserves of $5 million, the bank has a total of $33.5 million to pay the depositors. The first $30 million goes to the insured depositors. So, the uninsured depositors will receive the remaining $3.5 million, and thus they will lose $6.5 million out of their $10 million. The equity holders will lose all of their capital.

19.

A bank with insured deposits of $55 million and uninsured deposits of $45 million has assets valued at only $75 million. What is the cost of failure resolution to insured depositors, uninsured depositors, and the FDIC if an insured depositor transfer method is used?

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Neither the insured depositors nor the FDIC lose under the insured depositor transfer method.

Uninsured depositors receive $20 million (= $75m - $55m) equal to the cash (received from the sale of the bank’s assets) remaining after insured depositors have been paid in full. This results in a loss of $25 million (= $45m - $20m) for the uninsured depositors 20.

A commercial bank has $150 million in assets at book value. The insured and uninsured deposits are valued at $75 million and $50 million, respectively, and the book value of equity is $25 million. As a result of loan defaults, the market value of the assets decreases to $120 million. What is the cost of failure resolution to insured depositors, uninsured depositors, shareholders, and the FDIC if an insured depositor transfer method is used?

Under the insured depositor transfer method, all losses will be borne by shareholders, followed by uninsured depositors, before the FDIC takes any loss. Thus, in this example, neither the insured depositors nor the FDIC lose under the insured depositor transfer method. Uninsured depositors receive $45 million (= $120m - $75m) equal to the cash (received from the sale of the bank’s assets) remaining after insured depositors have been paid in full. This results in a loss of $5 million (= $50m - $45m) for the uninsured depositors. Shareholders will lose $25 million.

21.

In what ways did FDICIA enhance the regulatory discipline to help reduce moral hazard behavior? What has the operational impact of these directives been?

FDICIA approached the moral hazard problem in the separate areas of examinations and capital forbearance. In the area of examinations, FDICIA (1) required improved accounting standards that focused on market valuation, (2) required annual on-site examination of every DI, and (3) allowed private accountants a greater role in the auditing of DIs. FDICIA also clarified immediacy and degree of actions in cases where DI capital fell into different rating zones. The effect of these policies is to reduce discretion in the treatment of DIs that are in financial distress.

22.

Match the following policies with their intended consequences: Policies: a. Lower FDIC insurance levels b. Stricter reporting standards c. Risk-based deposit insurance Consequences: 1. Increased stockholder discipline 2. Increased depositor discipline 3. Increased regulator discipline

Answer: a-2, b-3, c-1 23.

How does the Federal Reserve’s discount window serve as an alternative to deposit insurance as a lender of last resort facility to financial institutions? What changes occurred in 2008 that expanded the scope of coverage for the Fed’s discount window?

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Traditionally, the Fed has provided a discount window facility to meet the short-term, nonpermanent liquidity needs of DIs. For example, suppose a DI has an unexpected deposit drain close to the end of a reserve requirement period and cannot meet its reserve target. It can seek to borrow from the Fed’s discount window facility. However, in January 2003, the Fed implemented changes to its discount window lending that increased the cost of borrowing but eased the terms. Specifically, three lending programs are now offered through the Feds discount window. Primary credit is available to generally sound depository institutions on a very shortterm basis, typically overnight, at a rate above the Federal Open Market Committee's (FOMC) target rate for federal funds. Primary credit may be used for any purpose, including financing the sale of fed funds. Primary credit may be extended for periods of up to a few weeks to depository institutions in generally sound financial condition that cannot obtain temporary funds in the financial markets at reasonable terms. Secondary credit is available to depository institutions that are not eligible for primary credit. It is extended on a very short-term basis, typically overnight, at a rate that is above the primary credit rate. Secondary credit is available to meet backup liquidity needs when its use is consistent with a timely return to a reliance on market sources of funding or the orderly resolution of a troubled institution. Secondary credit may not be used to fund an expansion of the borrower’s assets. The Federal Reserve's seasonal credit program is designed to assist small depository institutions in managing significant seasonal swings in their loans and deposits. Seasonal credit is available to depository institutions that can demonstrate a clear pattern of recurring intra-yearly swings in funding needs. Eligible institutions are usually located in agricultural or tourist areas. Under the seasonal program, borrowers may obtain longer term funds from the discount window during periods of seasonal need so that they can carry fewer liquid assets during the rest of the year and make more funds available for local lending.

With the change, discount window loans to healthy banks would be priced at 1 percent above (rather than below) the fed funds rate. Loans to troubled banks would cost 1.5 percent above the fed funds rate. The changes were not intended to change the Fed’s use of the discount window to implement monetary policy, but significantly increase the discount rate while making it easier to get a discount window loan. By increasing banks’ use of the discount window as a source of funding, the Fed hopes to reduce volatility in the fed funds market as well. The change also allows healthy banks to borrow from the Fed regardless of the availability of private funds.

Previously, the Fed required borrowers to prove they could not get funds from the private sector, which put a stigma on discount window borrowing. With the changes, the Fed will lend to all banks, but the subsidy will be gone.

The Fed took additional unprecedented steps, expanding the usual function of the discount window, to address the financial crisis. While the discount window had traditionally been available to DIs, in the spring of 2008 (as Bear Stearns nearly failed) investment banks gained access to the discount window through the Primary Dealer Credit Facility (PDCF). In the first three days, securities firms borrowed an average of $31.3 billion per day from the Fed. The largest expansion of the discount window’s availability to all FIs occurred in the wake of the Lehman Brothers failure, as a series of actions were taken in response to the increasingly fragile state of financial markets. After March, several new broad-based lending programs were implemented, providing funding to a wide array of new parties, including U.S. money market 10 © 2022

mutual funds, commercial paper issuers, insurance companies, and others. These programs rapidly expanded the current lending programs offered via the Fed. Over the next 18 months, in response to a weakening economy and a growing financial crisis, the Fed significantly reduced the level of short-term interest rates by lowering its target federal funds rate to near zero. The overall reduction in the target federal funds rate since late 2007 was been dramatic, going from 5.26 percent in September 2007 to a range of 0 percent to 0.25 percent as of December 2008. It also significantly reduced the spread (premium) between the discount rate and the federal funds target to just a quarter of a point, bringing the discount rate down to a half percent. With lower rates at the Fed's discount window and liquidity scarce as many lenders cut back their lending, more financial institutions chose to borrow at the window. The magnitude and diversity of nontraditional lending programs and initiatives developed during the crisis were unprecedented in Federal Reserve history. The lending programs were all designed to "unfreeze" and stabilize various parts of the credit markets, with the overall goal that parties receiving credit via these new Fed programs would, in turn, provide funding to creditworthy individuals and firms.

24.

Why is access to the discount window of the Fed less of a deterrent to bank runs than deposit insurance?

Although banks have access to the discount window in the event of DI runs, this is less effective than deposit insurance because: a.

DIs have to put up collateral in order to borrow from the discount window, and collateral may not be available during DI runs.

b.

Access is by no means guaranteed. Loans may be denied by the Fed if it is clear that the DI is insolvent.

c.

FDICIA of 1991 has limited the Fed’s ability to lend to undercapitalized DIs to only 60 days in any 120-day period. Extensions require approval by both the FDIC and the primary regulator of the DI to certify that the DI is viable.

d.

If the DI ultimately fails, the Fed will have to compensate the FDIC for incremental losses.

25.

How do insurance guaranty funds differ from deposit insurance? What impact do these differences have on the incentive for insurance policyholders to engage in a contagious run on an insurance company?

Insurance companies are regulated at the state level. As such, the state guaranty fund programs are administered by the private insurance companies. Further, there is no permanent guaranty reserve fund for the entire industry, and the amount of the required contributions required of surviving insurers to protect policyholders varies widely across the different states. Finally, small policyholders often must wait for an extended period of time before receiving benefits from the guaranty funds. As a result of these reasonable inefficiencies, the incentive for insurance 11 © 2022

policyholders to engage in a run on the companies is quite strong as compared to the banking industry.

26.

What was the purpose of the establishment of the Pension Benefit Guaranty Corporation (PBGC)?

PBGC was established to protect pension benefits from the underfunding of pension plans by corporations. a. How does the PBGC differ from the FDIC in its ability to control risk?

First, the premium is based on the number of participants, not on the amount of pension contributions or benefits covered. However, the Pension Protection Act of 2006, enacted in August 2006, made the PBGC’s variable-rate premium payable by all underfunded plans, reformed the pension funding rules, imposed benefit restrictions on underfunded plans, established new limits on PBGC’s guarantee, provided funding relief to certain companies (particularly those in the airline industry), and imposed new reporting and disclosure requirements. Nevertheless, despite these improvements, the PBGC has no monitoring power and thus cannot restrict the risk-taking of plan managers in the administration of the portfolios. b. How were the 1994 Retirement Protection Act and the Deficit Reduction Act of 2005 expected to reduce the deficits experienced by the PBGC? Although the PBGC has no way of monitoring the pension funds it insures, it was charging $19 per participant for funded plans and $72 for unfunded plans, the maximum allowed by law. The 1994 law phased out this ceiling by 1997 so that unfunded plans could pay more in premiums.

The Deficit Reduction Act of 2005 increased the PBGC’s premium of 2006 to $30 per participant for single-employer plans and $8 per participant for multi-employer plans. The Act also called for the 2007 premium for single employers to increase to $31 per participant and for multi-employer plans to remain at $8 participants. By 2016, the inflation adjusted fees were $64 for single employer plans and $26 for multi-employer plans.

Despite these changes, the numerous bankruptcies during the financial crisis took a further toll on the PBGC. By September 2009, the fund’s deficit stood at $21.95 billion, up from $11.15 billlion in September 2008. The agency assumed pension liabilities from collapsed investment bank Lehman Brothers, retailer Circuit City, plastics company Milacron, and auto supplier Delphi Corp. (where it assumed $6.2 billion in pension liabilities, the second largest amount ever behind United Airlines’s $7.5 billion in 2005). However, the PBGC stated that despite the deficit the agency had sufficient funds to meet its obligations for many years because benefits are paid out over the benficiaries’ lifetime and not in one lump sum. The PBGC also recognized that over the long term, the deficit needed to be addressed. However, by year-end 2014 the deficit had grown to $61.8 billion.

The following questions and problems are based on material in Appendix 19A to the chapter.

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27.

What changes did the Federal Deposit Insurance Reform Act of 2005 make to the deposit insurance assessment scheme for DIs?

The Federal Deposit Insurance Reform Act of 2005 instituted a deposit insurance premium scheme, effective January 1, 2007 and revised in April 2009, April 2011, and September 2015, that combined examination ratings, financial ratios. The new rules consolidate the existing nine risk categories into four, named Risk Categories I through IV. Risk Category I contains all wellcapitalized institutions in Supervisory Group A (generally those with CAMELS composite ratings of 1 or 2). Risk Category II contains all institutions in Supervisory Groups A and B (generally those with CAMELS composite ratings of 1, 2 or 3), except those in Risk Category I and undercapitalized institutions. Risk Category III contains all undercapitalized institutions in Supervisory Groups A and B, and institutions in Supervisory Group C (generally those with CAMELS composite ratings of 4 or 5) that are not undercapitalized. Risk Category IV contains all undercapitalized institutions in Supervisory Group C. The assessment rates are set by the FDIC and are a function of the size of the FDIC reserve ratio. For example, if the reserve ratio reaches 1.15 percent, but is less than 2 percent, Risk Category I institutions pay between 3 and 7 basis points on the assessment base.

28.

Under the Federal Deposit Insurance Reform Act of 2005, how is a Category I deposit insurance premium determined?

Within Risk Category I, the final rule combines CAMELS component ratings with financial ratios to determine an institution’s assessment rate. For Risk Category I institutions, each of eight financial ratios component ratings is multiplied by a corresponding pricing multiplier, as listed in Table 19A-2. The eight financial ratios are: Tier 1 leverage ratio; nonperforming loans and leases/gross assets; net income before taxes/risk-weighted assets; other real estate owned/gross assets, core deposits/total assets, one year asset growth, loan mix index, and the weighted-average CAMELS component rating. The loan mix index is a measure of the extent to which a bank’s total assets include higher-risk categories of loans. Each category of loan in a bank’s loan portfolio is divided by the bank’s total assets to determine the percentage of the bank’s assets represented by that category of loan. Each percentage is then multiplied by that category of loan’s historical weighted average industrywide charge-off rate since 2001. The products are then summed to determine the loan mix index value for that bank. Table 19A-3 lists the weighted average charge-off rate for each category of loan, as calculated by the FDIC through the end of 2014. The weighted average of CAMELS component ratings is created by multiplying each component by a stated percentage and adding the products. The sum of these products will be added to or subtracted from a uniform amount, set at 19.376 as of September 11, 2015. The resulting sum will equal an institution’s initial assessment rate. The assessment rate is then multiplied by the institution’s assessment base, defined as average total assets less average tangible equity. The changes instituted in September 2015 would take effect beginning the assessment period after the DIF reserve ratio first meets or exceeds 1.15 percent. As of March 2015, the reserve ratio was 1.03. The rates will remain in effect unless and until the reserve ratio meets or exceeds 2 percent.

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Large and highly complex institutions have a slightly different numeric used to calculate the assessment rates. The score card for these institutions focus more on the risk of the institution and differentiates risk during periods of good economic conditions and during periods of stress and downturns. The models also better take into account the losses the FDIC may incur if a large institution fails. Large institution is an institution with assets of at least $10 billion as of December 2006 and not classified as a highly complex institution (approximately 50 of the over 6,400 institutions in 2015). A highly complex institution (approximately 40 institutions in 2015) is defined by the FDIC as: (1) an insured depository institution (excluding a credit card bank) with greater than $50 billion in total assets that is wholly owned by a parent company with more than $500 billion in total assets, or wholly owned by one or more intermediate parent companies that are wholly owned by a holding company with more than $500 billion in assets; or (2) a processing bank and trust company with greater than $10 billion in total assets, provided that the information required to calculate assessment rates as a highly complex institution is readily available to the FDIC. After applying all possible adjustments and using a DIF reserve ration between 1.15 percent and 2 percent, minimum and maximum total base assessment rates for each risk category are set as listed in Table 19A-5. The unsecured debt adjustment is determined by multiplying an institution’s long term unsecured debt as a percent of domestic deposits. The base assessment may also increase depending on its ratio of securied liabilities to domestic deposits (secured liability adjustment). Finally, for institutions in Categories II, III, and IV the assessment rate may increase based on the amount of brokered deposits to domestic deposits.

29.

Webb Bank has a composite CAMELS rating of 2, a total risk-based capital ratio of 10.2 percent, a Tier I risk-based capital ratio of 6.2 percent, a CET1 capital ratio of 5.0 percent, and a Tier I leverage ratio of 4.8 percent. What deposit insurance risk category does the bank fall into, and assuming the DIF reserve ratio is currently 1.20 percent, what is the bank’s deposit insurance assessment rate?

With this CAMELS rating and capital ratios, Webb Bank falls into the Category II risk category and has a deposit insurance assessment rate of 12 basis points times the bank’s average total assets less average Tier I equity.

30.

Million Bank has a composite CAMELS rating of 2, a total risk-based capital ratio of 9.8 percent, a Tier I risk-based capital ratio of 6.8 percent, a CET1 capital ratio of 6.0 percent, and a Tier I leverage ratio of 4.9 percent. The average total assets of the bank equal $500 million and average Tier I equity equal $24.5 million. What deposit insurance risk category does the bank fall into? What is the bank’s deposit insurance assessment rate and assuming the DIF reserve ratio is currently 1.18 percent, the dollar value of deposit insurance premiums?

With this CAMELS rating and capital ratios, Million Bank falls into the Category II risk category. The deposit insurance assessment rate of 14 basis points times the bank’s average total assets less average Tier I equity. The dollar value of the insurance premiums is $570,600 (($500m - $24.5m) x 0.0012).

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31.

Two depository institutions have composite CAMELS ratings of 1 or 2 and are “well capitalized.” Thus, each institution falls into the FDIC Risk Category I deposit insurance assessment scheme. Further, the institutions have the following financial ratios and CAMELS ratings: Institution A

Institution B

8.25

7.58

2.15

1.85

Tier I leverage ratio (%) Net Income before taxes/risk-weighted assets (%) Nonperforming loans and leases/gross assets (%) Other real estate owned /gross assets (%) Core deposits/total assets (%) One year asset growth

0.25

0.55

0.54 84.56 5.66

0.75 79.68 7.75

Loans as a Percent of Total Assets: Construction & Development Commercial & Industrial Leases Other Consumer Loans to Foreign Government Real Estate Loans Residual Multifamily Residential Nonfarm Nonresidential 1–4 Family Residential Loans to Depository Banks Agricultural Real Estate Agricultural

0.00 11.35 0.45 16.50 0.00 0.00 0.50 0.00 38.85 0.00 4.55 7.40

0.00 15.66 1.05 16.80 0.60 0.00 1.25 0.00 40.15 2.80 0.00 0.00

1 2 1 2 1 2

1 2 2 3 1 1

CAMELS Components: C A M E L S

The DIF reserve ratio is currently 1.30 percent. Calculate the initial deposit insurance assessment for each institution.

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To determine the deposit insurance assessment for each institution, we set up the following tables: CAMELS Components: C 1 x 0.25 = 0.25 A 2 x 0.20 = 0.40 M 1 x 0.25 = 0.25 E 2 x 0.10 = 0.20 L 1 x 0.10 = 0.10 S 2 x 0.10 = 0.20 Weighted Average CAMELS Component 1.40 Loans Mix Index: (1)

1 x 0.25 = 0.25 2 x 0.20 = 0.40 2 x 0.25 = 0.50 3 x 0.10 = 0.30 1 x 0.10 = 0.10 1 x 0.10 = 0.10 .

1.65

(2)

(3) (4) (5) (6) Institution A Institution B Weighted Loan Product Loan Product charge-off rate category of two category of two percent as a percent columns as a percent columns of total assets of total assets Construction & Development 4.4965840 0.00 0.00 0.00 0.00 Commercial & Industrial 1.5984506 11.35 18.14 15.66 25.03 Leases 1.4974551 0.45 0.67 1.05 1.57 Other Consumer 1.4559717 16.50 24.02 16.80 24.46 Loans to Foreign Government 1.3384093 0.00 0.00 0.60 0.80 Real Estate Loans Residual 1.0169338 0.00 0.00 0.00 0.00 Multifamily Residential 0.8847597 0.50 0.44 1.25 1.11 Nonfarm Nonresidential 0.7286274 0.00 0.00 0.00 0.00 1–4 Family Residential 0.6973778 38.85 27.09 40.15 28.00 Loans to Depository Banks 0.5760532 0.00 0.00 2.80 1.61 Agricultural Real Estate 0.2376712 4.55 1.08 0.00 0.00 Agricultural 0.2432737 7.40 1.80 0.00 0.00 SUM (Loan Mix Index)

(1)

Uniform Amount

73.26

82.59

Base Assessment Rates for Two Institutions (2) (3) (4) (5) (6) Institution A Institution B Contribution Contribution Risk to Risk to Pricing Measure Assessment Measure Assessment Multiplier Value Rate Value Rate 19.376 19.376 16 © 2022

Tier I leverage ratio (%)

(1.337)

8.25

(11.030)

7.58

(10.135)

Net income before taxes/risk-weighted assets (%)

(0.652)

2.15

(1.402)

1.85

(1.206)

Nonperforming loans and leases/gross assets (%)

0.924

0.25

0.231

0.55

0.508

Other real estate owned /gross assets (%)

0.620

0.54

0.335

0.75

0.465

Core deposits/total assets (%)

(0.139)

84.56

(11.754)

79.68

(11.075)

One year asset growth (%)

0.043

5.66

0.243

7.75

0.333

Loan mix index

0.066

73.26

4.835

82.59

5.451

Weighted average CAMELS component ratings Sum of contributions Initial assessment rate

1.731

1.40

2.4237 3.258 3.258

1.65

2.856 6.573 6.573

32.

Two depository institutions have composite CAMELS ratings of 1 or 2 and are “well capitalized.” Thus, each institution falls into the FDIC Risk Category I deposit insurance assessment scheme. Institution A has average total assets of $750 million and average Tier I equity of $75 million. Institution B has average total assets of $1 billion and average Tier I equity of $110 million. Institution A has no unsecured debt or brokered deposits.

Institution B has no unsecured debt and an asset growth rate over the last four years of 8 percent. Further, the institutions have the following financial ratios and CAMELS ratings:

Tier I leverage ratio (%) Net Income before taxes/risk-weighted assets (%) Nonperforming loans and leases/gross assets (%) Other real estate owned

Institution A

Institution B

8.55

8.25

2.00

1.65

0.35

0.90

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/gross assets (%) Core deposits/total assets (%) One year asset growth

0.42 82.20 4.35

0.90 76.50 6.80

Loans as a Percent of Total Assets: Construction & Development Commercial & Industrial Leases Other Consumer Loans to Foreign Government Real Estate Loans Residual Multifamily Residential Nonfarm Nonresidential 1–4 Family Residential Loans to Depository Banks Agricultural Real Estate Agricultural

0.00 10.56 0.65 17.55 0.00 0.00 0.00 0.00 41.10 0.00 1.10 0.40

0.00 18.68 2.15 18.95 0.60 0.00 1.10 0.00 33.54 0.50 0.35 0.40

1 1 1 2 1 2

2 1 1 1 3 3

CAMELS Components: C A M E L S

The DIF reserve ratio is currently 1.30 percent. Calculate the deposit insurance assessment and the dollar value of the deposit insurance premium for each institution.

To determine the deposit insurance assessment for each institution, we set up the following tables: CAMELS Components: C 1 x 0.25 = 0.25 A 1 x 0.20 = 0.20 M 1 x 0.25 = 0.25 E 2 x 0.10 = 0.20 L 1 x 0.10 = 0.10 S 2 x 0.10 = 0.20 Weighted Average CAMELS Component 1.20 Loans Mix Index: (1)

(2)

2 x 0.25 = 0.50 1 x 0.20 = 0.20 1 x 0.25 = 0.25 1 x 0.10 = 0.10 3 x 0.10 = 0.30 3 x 0.10 = 0.30 .

1.65

(3) (4) Institution A 18 © 2022

(5) (6) Institution B

Weighted Loan Product Loan Product charge-off rate category of two category of two as a percent columns as a percent columns percent of total assets of total assets Construction & Development 4.4965840 0.00 0.00 0.00 0.00 Commercial & Industrial 1.5984506 10.56 16.88 18.68 29.86 Leases 1.4974551 0.65 0.97 2.15 3.22 Other Consumer 1.4559717 17.55 25.55 18.95 27.59 Loans to Foreign Government 1.3384093 0.00 0.00 0.60 0.80 Real Estate Loans Residual 1.0169338 0.00 0.00 0.00 0.00 Multifamily Residential 0.8847597 0.00 0.00 1.10 0.97 Nonfarm Nonresidential 0.7286274 0.00 0.00 0.00 0.00 1–4 Family Residential 0.6973778 41.10 28.66 33.54 23.39 Loans to Depository Banks 0.5760532 0.00 0.00 0.50 0.29 Agricultural Real Estate 0.2376712 1.10 0.26 0.35 0.08 Agricultural 0.2432737 0.40 0.10 0.40 0.10 SUM (Loan Mix Index)

72.43

86.30

Uniform Amount

Base Assessment Rates for Two Institutions (2) (3) (4) (5) (6) Institution A Institution B Contribution Contribution Risk to Risk to Pricing Measure Assessment Measure Assessment Multiplier Value Rate Value Rate 19.376 19.376

Tier I leverage ratio (%)

(1.337)

8.55

(11.431)

8.25

(11.030)

Net income before taxes/risk-weighted assets (%)

(0.652)

2.00

(1.304)

1.65

(1.076)

Nonperforming loans and leases/gross assets (%)

0.924

0.35

0.323

0.90

0.832

Other real estate owned /gross assets (%)

0.620

0.42

0.260

0.90

0.558

Core deposits/total assets (%)

(0.139)

82.20

(11.426)

76.50

(10.634)

(1)

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One year asset growth (%)

0.043

4.35

0.187

6.80

0..292

Loan mix index

0.066

72.43

4.780

86.30

5.696

Weighted average CAMELS component ratings Sum of contributions Initial assessment rate

1.731

1.20

2.077 2.843 3.000

1.65

2.856 6.871 6.871

For Institution A, the sum is 2.843. However, the minimum assessment rate for Category I banks is 3 basis points. The dollar value of the deposit insurance premium for Institution A is $202,500 (0.0003 x ($750m - $75m)) and for Institution B is $611,519 (0.0006871 x ($1b - $110m)).

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Solutions for End-of-Chapter Questions and Problems: Chapter Twenty 1.

Identify and briefly discuss the importance of the five functions of an FI’s capital?

First, the primary means of protection against the risk of insolvency and failure is an FI’s capital.

Capital is used to absorb unanticipated losses with enough margin to inspire confidence and enable the FI to continue as a going concern. Second FIs need to hold enough capital to provide confidence to uninsured creditors that they can withstand reasonable shocks to the value of their assets. Thus, capital protects uninsured depositors, bondholders, and creditors in the event of insolvency, and liquidation. Third, the FDIC, which guarantees deposits, is concerned that sufficient capital is held so that their funds are protected, because they are responsible for paying insured depositors in the event of a failure. Thus, the capital of an FI offers protection to insurance funds and ultimately the taxpayers who bear the cost of insurance fund insolvency.

Fourth, by holding capital and reducing the risk of insolvency, an FI protects the industry from larger insurance premiums. Such premiums are paid out of the net profits of the FI. Thus, capital protects the FI owners against increases in insurance premiums. Finally, capital also serves as a source of financing to purchase and invest in assets necessary to provide financial services.

2.

Why are regulators concerned with the levels of capital held by an FI compared with those held by a nonfinancial institution?

Regulators are concerned with the levels of capital held by an FI because of its special role in society. A failure of an FI can have severe repercussions to the local and/or national economy unlike non-financial institutions. Such externalities impose a burden on regulators to ensure that these failures do not impose major negative externalities on the economy. Higher capital levels will reduce the probability of such failures.

Part of the TARP program of 2008-09 was the Capital Purchase Program to encourage U.S. financial institutions to build capital to increase the flow of financing to U.S. businesses and consumers and to support the U.S. economy. Under the program, the Treasury purchased over $200 billion. The senior preferred shares qualify as Tier 1 capital and rank senior to common stock. Financial institutions had to meet certain standards, including: (1) ensuring that incentive compensation for senior executives does not encourage unnecessary and excessive risks that threaten the value of the financial institution; (2) required payback of any bonus or incentive compensation paid to a senior executive based on statements of earnings, gains or other criteria that are later proven to be materially inaccurate; (3) prohibition on the financial institution from making any golden parachute payment to a senior executive based on the Internal Revenue Code provision; and (4) agreement not to deduct for tax purposes executive compensation in excess of $500,000 for each senior executive. In addition to capital injections received as part of the Capital Purchase Program TARP provided additional emergency funding to Citigroup ($25 billion) and Bank of America ($20 billion).

3.

What is the difference between the economic definition of capital and the book value definition of capital?

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The book value definition of capital is the value of assets minus liabilities as found on the balance sheet. This amount often is referred to as accounting net worth. The economic definition of capital is the difference between the market value of assets and the market value of liabilities. a. How does economic value accounting recognize the adverse effects of credit risk?

The loss in value caused by credit risk is borne first by the equity holders, and then by the liability holders. With market value accounting, the adjustments to equity value are made simultaneously as the losses due to this risk element occur. Thus, economic insolvency may be revealed before accounting value insolvency occurs. b. How does book value accounting recognize the adverse effects of credit risk?

Because book value accounting recognizes the value of assets and liabilities at the time they were placed on the books or incurred by the firm, losses are not recognized until the assets are sold or regulatory requirements force the firm to make balance sheet accounting adjustments. In the case of credit risk, these adjustments usually occur after all attempts to collect or restructure the loans have occurred.

4.

Why is the market value of equity a better measure of an FI's ability to absorb losses than book value of equity?

The market value of equity is more relevant than book value because in the event of a bankruptcy, the liquidation (market) values determine the FI's ability to pay various claimants.

5.

State Bank has the following year-end balance sheet (in millions): Assets Cash Loans Total assets

$10 90 $100

Liabilities and Equity Deposits Equity Total liabilities and equity

$90 10 $100

The loans primarily are fixed-rate, medium-term loans, while the deposits are either shortterm or variable-rate deposits. Rising interest rates have caused the failure of a key industrial company, and as a result, 3 percent of the loans are considered uncollectable and thus have no economic value. One-third of these uncollectable loans will be charged off.

Further, the increase in interest rates has caused a 5 percent decrease in the market value of the remaining loans. What is the impact on the balance sheet after the necessary adjustments are made according to book value accounting? According to market value accounting?

Under book value accounting, the only adjustment is to charge off 1% (0.03 x 1/3) percent of the loans. Thus, the loan portfolio will decrease by $0.90million ($90m x 0.03 x 1/3) and a corresponding adjustment will occur in the equity account. The new book value of equity will be $9.10 million. We assume no tax affects.

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Under market value accounting, the 3 percent decrease in loan value will be recognized, as will the 5 percent decrease in market value of the remaining loans. Thus, equity will decrease by 0.03 x $90m + 0.05 x $90m(1 – 0.03) = $7.065 million. The new market value of equity will be $2.935 million.

6.

What are the arguments for and against the use of market value accounting for DIs?

Market values produce a more accurate picture of the FI’s current financial position for both stockholders and regulators. Stockholders can more easily see the effects of credit risk on the FI’s equity, and they can evaluate more clearly the liquidation value of a distressed FI. Among the arguments against market value accounting are that market values sometimes are difficult to estimate, particularly for small FIs with non-traded assets. This argument is countered by the increasing use of asset securitization as a means to determine value of even thinly traded assets.

In addition, some argue that market value accounting can produce higher volatility in the earnings of FIs. A significant issue in this regard is that regulators may close an FI too quickly under the prompt corrective action requirements of FDICIA. The third argument against market value accounting is that FIs are less willing to accept longer-term asset exposures, such as mortgage loans and C&I loans, if these assets have to be continuously marked to market to reflect changing credit quality and interest rates. The concern is that market value accounting may interfere with FIs’ special functions as lenders and monitors and may even result in (or accentuate) a major credit crunch.

7.

What is the significance of prompt corrective action as specified by the FDICIA legislation?

Since December 18, 1992, under the FDICIA legislation, regulators must take specific actions−prompt corrective action (PCA)−when a DI falls outside the zone 1, or well capitalized, category. Table 20-4 summarizes these regulatory actions. Importantly, the prompt corrective action provision requires regulators to appoint a receiver for the DI when the leverage ratio falls below 2 percent. Thus, even though the DI is not technically insolvent in terms of book value of equity, the institution can be placed into receivership. The idea behind the mandatory and discretionary set of actions to be taken by regulators for each of the five capital adequacy zones is to enforce minimum capital requirements and limit the ability of regulators to show forbearance to the worst capitalized DIs. 8.

What is the Basel Agreement?

The Basel Agreement identifies risk-based capital ratios agreed upon by the member countries of the Bank for International Settlements. The ratios are to be implemented for all DIs under their jurisdiction. Further, most countries in the world now have accepted the guidelines of this agreement for measuring capital adequacy.

9.

What are the major features of the Basel III capital requirements?

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The goal of Basel III is to raise the quality, consistency, and transparency of the capital base of banks and to strengthen the risk coverage of the capital framework. Specifically, Pillar I of Basel III calls for enhancements to both the Standardized Approach, discussed below, and IRB Approach to calculating adequate capital. Changes to Pillar 1 include a greater focus on common equity, the inclusion of new capital conservation and countercyclical buffers to the minimum level of capital, significantly higher capital requirements for trading and derivatives activities, and a substantial strengthening of counterparty credit risk calculations in determining required minimum capital. Pillar 2 calls for enhanced bank-wide governance and risk management to be put in place, such as enhanced incentives for banks to better manage risk and returns over the long term, more stress testing, and implementation of sound compensation practices. Pillar 3 calls for the enhanced disclosure of risks, such as those relating to securitization exposures and sponsorship of off-balance-sheet vehicles.

Basel III is applicable to all U.S. national banks, state member and nonmember banks, state and federal savings associations, all U.S. bank holding companies except those with less than $500 million in total consolidated assets (although the rules apply to the subsidiary banks of these small holding companies), and all U.S. savings association holding companies. Advanced (IRB) approaches may be used by institutions with consolidated assets of $250 billion or more, or with consolidated onbalance-sheet foreign exposures of $10 billion or more (approximately 20 of the largest U.S. banking organizations). All other depository institutions use the Standardized Approach for calculating capital adequacy. Under Basel III, depository institutions must calculate and monitor four capital ratios: common equity Tier I (CET1) risk-based capital ratio, Tier I risk-based capital ratio, total risk-based capital ratio, and Tier I leverage ratio.

10.

What are the definitional differences between CET1, Tier I, and Tier II capital?

CET1 is primary or core capital of the DI. CET1capital is closely linked to a DI’s book value of equity, reflecting the concept of the core capital contribution of a DI’s owners. CET1 capital consists of the equity funds available to absorb losses. Basically, it includes the book value of common equity plus minority equity interests held by the DI in subsidiaries minus goodwill.

Goodwill is an accounting item that reflects the amount a DI pays above market value when it purchases or acquires other DIs or subsidiaries.

Tier I capital is the primary capital of the DI plus additional capital elements. Tier I capital is the sum of CET1 capital and additional Tier I capital. Included in additional Tier I capital are other options available to absorb losses of the bank beyond common equity. These consist of instruments with no maturity dates or incentives to redeem, e.g., noncumulative perpetual preferred stock. These instruments may be callable by the issuer after 5 years only if they are replaced with “better” capital.

Tier II capital is supplementary capital. Tier II capital is a broad array of secondary “equity like” capital resources. It includes a DI’s loan loss reserves assets plus various convertible and subordinated debt instruments with maximum caps.

11.

Under Basel III, what four capital ratios must DIs calculate and monitor?

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Under Basel III, depository institutions must calculate and monitor four capital ratios: common equity Tier I (CET1) risk-based capital ratio, Tier I risk-based capital ratio, total risk-based capital ratio, and Tier I leverage ratio. i) Common equity Tier I risk-based capital ratio = Common equity Tier I capital/credit risk-adjusted assets ii) Tier I risk-based capital ratio = Tier I capital (Common equity Tier I capital + additional Tier I capital)/credit risk-adjusted assets iii) Total risk-based capital ratio = Total capital (Tier I + Tier II)/credit risk-adjusted assets, and iv) Tier I leverage ratio = tier I capital / total exposure.

12. What are the credit risk-adjusted assets in the denominator of the common equity Tier I (CET1) risk-based capital ratio, the Tier I risk-based capital ratio, and the total risk-based capital ratio?

Under Basel III capital adequacy rules, risk-adjusted assets represent the denominator of the riskbased capital ratios. Two components make up credit risk-adjusted assets: (1) credit risk-adjusted on-balance-sheet assets and (2) credit risk-adjusted off-balance-sheet assets.

13.

How is the leverage ratio for an DI defined?

The Basel III leverage ratio is defined as the ratio of Tier 1 capital to a combination of on- and off-balance-sheet assets (total exposure). Total exposure is equal to the DI’s total assets plus offbalance-sheet exposure. For derivative securities, off-balance-sheet exposure is current exposure plus potential exposure as described above. For off-balance-sheet credit (loan) commitments a conversion factor of 100 percent is applied unless the commitments are immediately cancelable.

In this case, a conversion factor of 10 percent is used. Once Basel III is fully phased in, to be to be adequately capitalized, a DI must hold a minimum leverage ratio of 4.5 percent.

14.

Identify the five zones of capital adequacy and explain the mandatory regulatory actions corresponding to each zone.

Zone 1: Well capitalized. The CET1 risk-based capital (RBC) ratio exceeds 6.5 percent, Tier I RBC ratio exceeds 8 percent, total RBC ratio exceeds 10 percent, and leverage ratio exceeds 5 percent. No regulatory action is required.

Zone 2: Adequately capitalized. The CET1 RBC ratio exceeds 4.5 percent, Tier I RBC ratio exceeds 6 percent, total RBC ratio exceeds 8 percent, and leverage ratio exceeds 4 percent. Institutions may not use brokered deposits except with the permission of the FDIC. Zone 3: Undercapitalized. The CET1 RBC ratio is less than 4.5 percent, Tier I RBC ratio is less than 6 percent, total RBC ratio is less than 8 percent, or leverage ratio is less than 4 percent. Requires a capital restoration plan, restricts asset growth, requires approval for 5 © 2022

acquisitions, branching, and new activities, disallows the use of brokered deposits, and suspends dividends and management fees.

Zone 4: Significantly undercapitalized. The CET1 RBC ratio is less than 3 percent, Tier I RBC ratio is less than 4 percent, total RBC ratio is less than 6 percent, or leverage ratio is less than 3 percent. Same as zone 3 plus recapitalization is mandatory, places restrictions on deposit interest rates, interaffiliate transactions, and the pay level of officers.

Zone 5: Critically undercapitalized. Tangible equity to total assets is less than or equal to 2 percent. Places the bank in receivership within 90 days, suspends payment on subordinated debt, and restricts other activities at the discretion of the regulator.

The mandatory provisions for each of the zones described above include the penalties for any of the zones prior to the specific zone.

15.

Explain the process of calculating credit risk-adjusted on-balance-sheet assets.

Balance sheet assets are assigned to one of several categories of credit risk exposure. The dollar amount of assets in each category is multiplied by an appropriate weight, e.g., 0 percent, 20 percent, 50 percent, 100 percent, or 150 percent. The weighted dollar amounts of each category are added together to get the total credit risk-adjusted on-balance-sheet assets.

16.

Under Basel III, how are residential 1-4 family mortgages assigned to a credit risk class?

Residential 1-4 family mortgages would be separated into two risk categories (“category 1 residential mortgage exposures” and “category 2 residential mortgage exposures”). Category 1 residential mortgages include traditional, first-lien, prudently underwritten mortgage loans.

Category 2 residential mortgages include junior liens and non-traditional mortgage products. The risk weight assigned to the residential mortgage exposure then depends on the mortgage’s loanto-value ratio. For example, category 1 mortgages with a loan-to-value ratio of less than 60 percent have a risk weight of 35 percent; category 2 mortgages with a loan-to-value ratio of greater than 90 percent have a risk weight of 200 percent. Mortgages over 90 days past due are assigned a risk weight of 150 percent.

17.

Under Basel III, how are risk weights for sovereign exposures are determined?

Risk weights for sovereign exposures are determined using OECD Country Risk Classifications (CRCs). A sovereign is a central government (including the U.S. government) or an agency, department, ministry, or central bank of a central government. The OECD’s CRCs assess a country’s credit risk using two basic components: the country risk assessment model (CRAM)− an econometric model that produces a quantitative assessment of country credit risk−and the qualitative assessment of the CRAM results−which integrates political risk and other risk factors not fully captured by the CRAM. The two components are combined and classified into one of eight risk categories (0-7). Countries assigned to categories 0-1 have the lowest possible risk 6 © 2022

assessment and are assigned a risk weight of 0 percent, while countries assigned to category 7 having the highest possible risk assessment and are assigned a risk weight of 150 percent. The OECD provides CRCs for more than 150 countries. Assessments are publicly available on the OECD website. Countries with no CRC assessments are assigned a credit risk weight of 100 percent. A 150 percent risk weight is assigned to sovereign exposures immediately upon determining that an event of sovereign default has occurred or if a sovereign default has occurred during the previous five years.

18.

National Bank has the following balance sheet (in millions) and has no off-balance-sheet activities.

Assets Liabilities and Equity Cash $20 Deposits $960 Treasury bills 40 Subordinated debentures 25 Residential mortgages Common stock 45 (category 1; loan-to-value Retained earnings 40 ratio = 70%) 600 Total liabilities and equity $1,090 Business loans 430 Total assets $1,090 a. What is the CET1 risk-based ratio?

Risk-adjusted assets = $20x0.0 + $40x0.0 + $600x0.5 + $430x1.0 = $730 The CET1 risk-based ratio is ($45 + $40)/$730 = 0.11644 or 11.644 percent. b. What is the Tier I risk-based capital ratio?

Risk-adjusted assets = $20x0.0 + $40x0.0 + $600x0.5 + $430x1.0 = $730 Tier I capital ratio = ($45 + $40)/$730 = 0.11644 or 11.644 pe8rcent. c. What is the total risk-based capital ratio?

The total risk-based capital ratio = ($45 + $40 + $25)/$730 = 0.15068 or 15.068 percent. d. What is the leverage ratio?

The leverage ratio is ($45 + $40)/$1,090 = 0.07798 or 7.798 percent. e. In what capital risk category would the bank be placed?

The bank would be place in the well-capitalized category.

19.

What is the capital conservation buffer? How would this buffer affect your answers to question 18?

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Basel III introduced a capital conservation buffer designed to ensure that DIs build up a capital surplus, or buffer, outside periods of financial stress which can be drawn down as losses are incurred during periods of financial stress. The buffer requirements provide incentives for DIs to build up a capital surplus (e.g., by reducing discretionary distributions of earnings (reduced dividends, share buy-backs and staff bonuses)) to reduce the risk that their capital levels would fall below the minimum requirements during periods of stress. The capital conservation buffer must be composed of CET1 capital and are held separately from the minimum risk-based capital requirements. Under Basel III, a DI would need to hold a capital conservation buffer of greater than 2.5 percent of total risk-weighted assets to avoid being subject to limitations on capital distributions and discretionary bonus payments to executive officers.

To have no limitations on the bank’s payout ratio, the CET1 ratio must be > 7%, the Tier I ratio must be > 8.5%, and the total capital ratio must be > 10.5%. In problem 18, all three of these conditions are met. So, the bank has no limitations on its payout ratio.

20.

What is the countercylical capital buffer? If the home country set a countercyclical capital buffer of 2.5 percent, how would this buffer affect your answers to question 18?

Basel III also introduced a countercyclical capital buffer which may be declared by any country which is experiencing excess aggregate credit growth. The countercyclical buffer can vary between 0 percent and 2.5 percent of risk-weighted assets. This buffer must be met with CET1 capital and DIs are given 12 months to adjust to the buffer level. Like the capital conservation buffer, if a DI’s capital levels fall below the set countercyclical capital buffer, restrictions on earnings payouts are applied. The countercyclical capital buffer aims to protect the banking system and reduce systemic exposures to economic downturns. Losses can be particularly large when a downturn is preceded by a period of excess credit growth. The accumulation of a capital buffer during an expansionary phase would increase the ability of the banking system to remain healthy during periods of declining asset prices and losses from weakening credit conditions. By assessing a countercyclical buffer when credit markets are overheated, accumulated capital buffers can absorb any abnormal losses that a DI might experience when the credit cycle turns.

Consequently, even after these losses are realized, DIs would remain healthy and able to access funding, meet obligations, and continue to serve as credit intermediaries.

To have no limitations on the bank’s payout ratio with a 2.5% buffer, the CET1 ratio must be > 9.5%, the Tier I ratio must be > 11.0%, and the total capital ratio must be > 13.0%. In problem 18, the bank’s CET1 is 11.644%, the Tier I ratio is 11.644%, and the total capital ratio is > 15.068%. So, the bank has no limitations on its payout ratio.

21.

Onshore Bank has $20 million in assets, with risk-adjusted assets of $10 million. CET1 capital is $500,000, additional Tier I capital is $50,000, and Tier II capital is $400,000.

How will each of the following transactions affect the value of the CET1, Tier I, and total capital ratios? What will the new value of each ratio be?

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The current value of the CET1 ratio is 5 percent ($500,000/$10m), of the Tier I ratio is 5.5 percent (($500,000 + $50,000)/$10m), and the total capital ratio is 9.5 percent (($500,000 + $50,000 + $400,000)/$10m). a. The bank repurchases $100,000 of common stock with cash.

CET1 capital decreases to $400,000, Tier I capital decreases to $450,000 and total capital decreases to $850,000. Cash has a 0 risk weight so risk-weighted assets do not change. Thus, the CET1 ratio decreases to 4 percent, the Tier I ratio decreases to 4.5 percent and the total capital ratio decreases to 8.5 percent. b. The bank issues $2 million of CDs and uses the proceeds to issue category 1 mortgage loans with a loan-to-value ratio of 80 percent.

The risk weight for category 1 mortgages with a loan-to-value ratio of 80 percent is 50 percent.

Thus, risk-weighted assets increase to $10 million + $2 million (0.5) = $11 million. The CET1 ratio decreases to $500,000/$11 million = 4.54 percent, the Tier I ratio decreases to $550,000/$11 million = 5 percent and the total capital ratio decreases to $950,000/$11 million = 8.64 percent. c. The bank receives $500,000 in deposits and invests them in T-bills.

T-bills have a 0 risk weight so risk-weighted assets remain unchanged. Thus, all three ratios remain unchanged. d. The bank issues $800,000 in common stock and lends it to help finance a new shopping mall.

CET1 equity increases to $1.3 million, Tier I equity increases to $1.35 million, and total capital increases to $1.75 million. The business loan’s risk weight is 100 percent. Thus, risk-weighted assets increase to $10 million + $800,000 (1) = $10.8 million. The CET1 ratio, increases to $1.3m/$10.8m = 12.03 percent, the Tier I ratio increases to $1.35m/$10.8m = 12.50 percent, and the total capital ratio increases to $1.75m/$10.8m = 16.20 percent. e. The bank issues $1 million in nonqualifying perpetual preferred stock and purchases general obligation municipal bonds.

CET1 and Tier I capital are unchanged. Total capital increases to $1.95 million. General obligation municipal bonds fall into the 20 percent risk category. So, risk-weighted assets increase to $10 million + $1 million (0.2) = $10.2 million. Thus, the CET1 ratio decreases to $500,000/$10.2 million = 4.90 percent, the Tier I ratio decreases to $550,000/$10.2 million = 5.39 percent, and the total capital ratio increases to 19.12 percent. f. Homeowners pay back $4 million of category 1 mortgages with loan-to-value ratios of 40 percent and the bank uses the proceeds to build new ATMs. 9 © 2022

The category 1 mortgage loans with loan-to-value ratios of 40 percent have a risk weight of 35 percent. The ATMs are 100 percent risk weighted. Thus, risk-weighted assets increase to $10 million - $4 million (0.35) + $4 million (1.0) = $12.6 million. The CET1 capital ratio decreases to $500,000/$12.6m = 3.97 percent, the Tier I capital ratio decreases to $550,000/$12.6m = 4.37 percent, and the total capital ratio decreases to $950,000/$12.6m = 7.54 percent.

22.

Explain the process of calculating risk-adjusted off-balance-sheet contingent guaranty contracts?

The first step is to convert the off-balance-sheet items to credit equivalent amounts of an onbalance-sheet item by multiplying the notional amounts by an appropriate conversion factor as given in Table 20-9. The converted amounts are then multiplied by the appropriate risk weights as if they were on-balance-sheet items. a. What is the basis for the use of the credit equivalent amounts of contingent guaranty contracts rather than the face value of these contracts?

These OBS activities represent contingent rather than actual claims against depository institutions. Thus, regulations require that capital be held not against the full face value of these items, but against an amount equivalent to any eventual on-balance-sheet credit risk these securities might create for a depository institution. b. On what basis are the risk weights for the credit equivalent amounts differentiated?

Under Basel III, risk weights assigned to OBS contingent guaranty contracts are the same as if the DI had entered into the transactions as a principal. Thus, the credit ratings used to assign a credit risk weight for on-balance-sheet assets are also used to assign credit risk weights on these OBS activities.

23.

Explain how off-balance-sheet market contracts, or derivative instruments, differ from contingent guaranty contracts.

Off-balance-sheet contingent guaranty contracts in effect are forms of insurance that FIs sell to assist customers in the financial management of the customers’ businesses. FI management typically uses market contracts, or derivative instruments, to assist in the management of the FI’s asset and liability risks. For example, a loan commitment or a standby letter of credit may be provided to help a customer with another source of financing, while an over-the-counter interest rate swap likely would be used by the FI to help manage interest rate risk. a. What is counterparty credit risk?

Counterparty credit risk is the risk that the other party in a contract may default on their payment obligations.

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b. Why do exchange-traded derivative security contracts have no capital requirements?

Counterparty obligations of exchange-traded contracts are guaranteed by the exchange on which they are traded. Thus, there is no counterparty risk to the DI. c. What is the difference between the potential exposure and the current exposure of overthe-counter derivative contracts?

The potential exposure is the portion of the credit equivalent amount that would be at risk if the counterparty to the contract defaulted in the future. The current exposure is the cost of replacing the contract if the counterparty defaulted today. d. Why do credit conversion factors for the potential exposure of differ for various derivative security contracts?

The potential exposure component reflects the risk if the counterparty to the contract defaults in the future. The probability of such an occurrence depends on the future volatility of interest rates for an interest rate contract, credit risk for a credit contract, or exchange rates for an exchange rate contract. Thus, the potential exposure conversion factors are larger for credit contracts than for interest rate contracts. Also, note the larger potential exposure risk for longer-term contracts of both types. e. Why do regulators not allow DIs to benefit from positive current exposure values?

Regulators fear that allowing DIs to gain from a counterparty default would create risk-taking incentives that would not be in the best interests of the DI or the financial services industry.

24.

What are G-SIBs? How do capital ratio requirements differ for these FIs?

As part of Basel III, the BIS imposed an additional common equity Tier I surcharge (“loss absorbency requirement”) on G-SIBs: banking groups whose distress or disorderly failure would cause significant disruption to the wider financial system and economic activity. The surcharge ranges from 1 percent to 3.5 percent to be held over and above the 7 percent minimum CET1 plus conservation buffer requirement. The surcharge may be larger under exceptional circumstances. For example, in 2015 J.P. Morgan Chase was required to hold a surcharge of 4.5 percent because of its extreme size, complexity, and entanglements with other big financial institutions. The purpose of the additional capital requirement is twofold: i) to reduce the probability of failure of a G-SIB by increasing their going-concern loss absorbency and ii) to reduce the extent or impact of the failure of a G-SIB on the financial system by improving global recovery and resolution frameworks.

G-SIBs are identified using a methodology developed by the BIS based on an indicator measurement approach that identifies factors that cause international contagion. The indicators were selected to capture the systemic impact of a bank’s failure, rather than the probability that the bank will fail. The indicators include bank size, interconnectedness, cross-jurisdictional (global) activity, the lack of substitutes for their services, and complexity to rank their global 11 © 2022

systemic importance. Using this methodology on an initial sample of 73 of the world’s largest banks and year-end 2009 data for each indicator, the BIS designated 27 banks as G-SIBs. Three additional banks were added to this initial list based on the home supervisor’s judgment, resulting in 30 G-SIBs headquartered in 12 countries. The number of G-SIBs can change over time reflecting changes in the systemic importance of banks. The sample of banks to be assessed will be reviewed every three years and the BIS also anticipates eventually expanding the surcharge to a wider group of financial institutions, including insurance companies and other nonbank financial institutions. The exact amount of the surcharge depends on a bank’s placement in one of five “buckets” (requiring a 1%, 1.5%, 2%, 2.5% and 3.5% surcharge, respectively) based on the bank’s score from the indicator measurement approach and may be met with CET1 capital only.

25.

Identify and discuss the problems in the risk-based capital approach to measuring capital adequacy.

First, the risk weights may not be true representations of the correct or necessary weights, or they may not be in the correct proportion to each other. For example, does a weight of 100 percent imply twice as much risk as a weight of 50 percent? Further, under Basel III all business loans are given a single 100 percent risk weight regardless of the risk of the business. Thus, loans made to AAA rated companies are assigned a credit risk weight of 1, as are loans made to CCC rated companies. That is, within a broad risk weight class, such as commercial loans, credit risk quality differences are not recognized. This may create perverse incentives for DIs to pursue lower quality customers thereby increasing the risk of the DI. Second, the risk weights may not accurately measure the relative risk exposures of individual borrowers. While the change to the use of OECD country risk classifications (CRC) in Basel III removed the problems associated with the use of a non-commercial entity (e.g., S&P) to assign credit risk to sovereign loans and foreign bank loans, OECD country risk ratings have problems of their own. However, as they were developed, in 1999, CRC ratings were not intended to reflect the probability of sovereign defaults. Rather, CRCs were intended to measure the minimum risk premiums for use in the market for export credits. They are not sovereign ratings such as those described in Chapter 14. Individual CRCs are estimated by economists using a quantitative country risk assessment model, as well as qualitative input. Countries that are classified with a zero CRC rating are not subject to the quantitative model and review. Instead, OECD rules state that in these circumstances, pricing on export credits should not be less than the risk premium available in the wider market. Thus, when a country has a CRC rating of zero, it does not mean the country should have zero country risk premiums.

Third, the RBC ratio does not consider the effects of portfolio risk diversification. In effect, RBC assumes the correlation between assets is one. When returns on assets have negative or less than perfectly positive correlations, a DI may lower its portfolio risk through diversification. As constructed, Basel III (standardized model) capital adequacy plans are essentially linear risk measures that ignore correlations or covariances among assets and asset group credit risks—such as between residential mortgages and commercial loans. That is, the DI manager weights each asset separately by the appropriate risk weight and then sums those numbers to get an overall 12 © 2022

measure of credit risk. No account is taken of the covariances among asset risks between different counterparties (or risk weights).

Fourth, Basel III greatly raises the cost of regulation by adding new levels of complexity to the calculation of adequate capital. The cost of developing and implementing new risk management systems will clearly be significant, and the benefits may turn out to be small. Indeed, Andrew Haldane, executive director for financial stability at the Bank of England, pointed out that risk models have grown so complex that to have statistical confidence that a given set of formulas have captured true risks, you need 400 to 1,000 years of data.

Fifth, Basel III places a great reliance on the loan-to-value ratio for residential mortgages. During the financial crisis, property values used by DIs were inflated by real estate appraisers. If this were to happen again, insufficient capital would be held against these mortgages.

Sixth, Pillar 2 of Basel III requires lots of very sensitive judgment calls from regulators (such as the determination of the adequacy of internal bank models) who may be ill-equipped to make them. This will particularly be a problem for developing-country regulators. If Pillar 2 is taken seriously, supervisors may be exposed to a lot of criticism that most would rather avoid.

Finally, reducing bank leverage levels (through increased capital) will reduce DIs’ ROEs and make it harder for them to generate additional capital. Indeed, rather than earning traditional ROEs of more than 15 percent, many DIs will see ROEs in the range of 8 to 10 percent post– Basel III. When added to the two new liquidity ratios introduced under Basel III that force DIs to more closely match maturities of assets and liabilities rather than “borrowing short” and “lending long” as has traditionally been a special feature of DIs, the special features of banking discussed in Chapter 1 will be reduced.

26.

What is the contribution to the credit risk-adjusted asset base of the following items under Basel III requirements?

Risk weight

a. $10 million cash. b. $50 million 91-day U.S. Treasury bills. c. $25 million cash items in the process of collection. d. $5 million U.K. government bonds, OECD CRC rated 1. e. $5 million French short-term government bonds, OECD CRC rated 2. f. $1 million general obligation municipal bonds. g. $40 million repurchase agreements (backed with U.S. Treasuries). h. $2 million loan to foreign bank, OECD CRC rated 3. i. $500 million 1-4 family home mortgages, category 1, loan-to-value ratio 80%.

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0% 0

$0 $0

20

$5 million

0

$0

20 20

$1 million $200,000

20 50 50

$8 million $1 million $250 million

j. $10 million 1-4 family home mortgages, category 2, loan-to-value ratio 95%. k. $5 million 1-4 family home mortgages, 100 days past due. l. $500 million commercial and industrial loans, AAA rated. m. $500 million commercial and industrial loans, B- rated.

200

$20 million

150

$7.5 million

100

$500 million

100

$500 million

50

100

$50,000

50

20

$10,000

20

20

$280,000

50

0

$0

20

100

$1,600,000

50

100

$8.5 million

20

100

$3.4 million

100

$30 million

100

$20,000

500,000 100

$800,000

credit equivalent amount

n. $100,000 performance-related standby letters of credit to an AAA rated corporation. o. $100,000 performance-related standby letters of credit to a municipality issuing general obligation bonds. p. $7 million commercial letter of credit to a foreign bank, OECD CRC rated 2. q. $3 million five-year loan commitment to a foreign government, OECD CRC rated 1. r. $8 million bankers’ acceptance conveyed to a U.S., AA rated corporation. s. $17 million three-year loan commitment to a private firm.. t. $17 million three-month loan commitment to a private firm. u. $30 million standby letter of credit to back an A rated corporate issue of commercial paper v. $4 million five-year interest rate swap with no current exposure w. $6 million two-year currency swap with $500,000 current exposure 27.

100

potential exposure

current exposure

5%

$0

5

How does the leverage ratio test impact the stringency of regulatory monitoring of DI capital positions?

One of the features of the financial crisis of 2008-2009 was the accumulation of extreme on- and off-balance sheet leverage throughout the banking system. During the worst of the crisis, DIs were forced by the market to reduce leverage to an extent that intensified falling asset prices, and intensified DI losses, declines in DI capital, and the reduction in credit availability. To prevent this cycle from reoccurring, Basel III introduced a leverage ratio requirement that is intended to discourage the use of excess leverage and to act as a backstop to the risk-based capital requirements described above.

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28.

Third Bank has the following balance sheet (in millions), with the risk weights in parentheses.

Assets Cash (0%) $21 OECD interbank deposits (20%) 25 Mortgage loans (50%) 70 Consumer loans (100%) 70 Reserve for loan losses (1) Total assets $185

Liabilities and Equity Deposits Subordinated debt (5 years) Cumulative preferred stock Equity

$176 2 2 5

Total liabilities and equity

$185

The cumulative preferred stock is qualifying and perpetual. In addition, the bank has $30 million in performance-related standby letters of credit (SLCs) to a public corporation, $40 million in two-year forward FX contracts that are currently in the money by $1 million, and $300 million in six-year interest rate swaps that are currently out of the money by $2 million. Credit conversion factors follow: Performance-related standby LCs 1- to 5-year foreign exchange contracts 1- to 5-year interest rate swaps 5- to 10-year interest rate swaps

50% 5% 0.5% 1.5%

a. What are the risk-adjusted on-balance-sheet assets of the bank as defined under the Basel Accord?

Risk-adjusted assets: Cash OECD interbank deposits Mortgage loans Consumer loans Total risk-adjusted assets

0 x 21 0.20 x 25 0.50 x 70 1.00 x 70

= = = = =

$0 $5 $35 $70 $110

= $110

b. To be adequately capitalized, what are the CET1, Tier I, and total capital required for both off- and on-balance-sheet assets?

Standby LCs: $30 x 0.50 x 1.0 Foreign exchange contracts: Potential exposure $40 x 0.05 Current exposure in the money Interest rate swaps: Potential exposure $300 x 0.015 Current exposure Out-of-the money

=

$15

= =

$2 $0

= = = Total risk-adjusted on- and off-balance-sheet assets 15 © 2022

$4.5 $2 $8.5 x

= $15

1.0

= $8.5 = $133.50 x 0.045

CET1 capital required

$6.0075

Tier I capital required

x 0.06 $8.01

Total capital required

x 0.08 = $10.68

c. Disregarding the capital conservation buffer, does the bank have enough capital to meet the Basel requirements? If not, what minimum CET1, additional Tier 1, or total capital does it need to meet the requirement?

No, the bank does not have sufficient total capital to meet the Basel requirements. It needs CET1 capital of $6.0075 million, Tier I capital of $8.01 million, and total capital of $10.68 million. The bank has $5 million of CET1 capital, $7 million of Tier I capital ($5 million CET1 capital and $2 million of additional Tier I capital), and $10 million of total capital ($3 million ($2 million in subordinate debt and $1 million in reserve for loan losses) of Tier II capital).

If the bank issues $1.0075 million in CET1 capital, it will need $0.0025 million in additional Tier I capital, and no Tier II capital. With these additions the bank will have $6.0075 million of CET1 capital, $8.01 million of Tier I capital, and $11.01million of total capital.

A new balance sheet after the issuance of the new required equity is shown below. You will note that the total capital exceeds the minimum of $10.68 million.

New balance sheet: Cash OECD interbank deposits Mortgage loans Consumer loans Reserve for loan losses Total d.

$22.01 25 70 70 (1) $186.01

Deposits $176 Subordinated debt (over 5 years) 2 Cumulative preferred stock 2.0025 Equity 6.0075 $186.01

Does the bank have enough capital to meet the Basel requirements, including the capital conservation buffer requirement? If not, what minimum CET1, additional Tier 1, or total capital does it need to meet the requirement?

Total risk-adjusted on- and off-balance-sheet assets CET1 capital required including capital conservation buffer

= $133.50 x 0.070 $9.345

Tier I capital required including capital conservation buffer

x 0.085 $11.3475 x 0.105

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Total capital required

= $14.0175

No, the bank does not have sufficient total capital to meet the Basel requirements. It needs CET1 capital of $9.345 million, Tier I capital of $11.3475 million, and total capital of $14.0175 million. The bank has $5 million of CET1 capital, $7 million of Tier I capital, and $10 million of total capital.

If the bank issues $4.345 million in CET1 capital, it will need $0.0025 million in additional Tier I capital, and no Tier II capital. With these additions the banks will have $9.345 million of CET1 capital, $11.345 million of Tier I capital, and $14.345 million of total capital.

A new balance sheet after the issuance of the new required equity is shown below. You will note that the total capital exceeds the minimum of $14.0175 million.

New balance sheet: Cash OECD interbank deposits Mortgage loans Consumer loans Reserve for loan losses Total 29.

$25.3475 25 70 70 (1) $189.3475

Deposits $176 Subordinated debt (over 5 years) 2 Cumulative preferred stock 2.0025 Equity 9.345 $189.3475

Third Fifth Bank has the following balance sheet (in millions), with the risk weights in parentheses.

Assets Cash (0%) Mortgage loans (50%) Consumer loans (100%) Reserve for loan losses Total assets

$21 50 70 (1) $140

Liabilities and Equity Deposits Subordinated debt (> 5 years) Equity

$133 1 6

Total Liabilities and equity

$140

In addition, the bank has $20 million in commercial direct-credit substitute standby letters of credit to a public corporation and $40 million in 10-year FX forward contracts that are in the money by $1 million. a. What are the risk-adjusted on-balance-sheet assets of the bank as defined under the Basel III? Risk-adjusted on-balance-sheet assets:

$21 x 0 $50 x 0.50 $70 x 1.00 Total

= = = =

$0 25 70 $95

b. What is the CET1, Tier I, and total capital required for both off- and on-balance-sheet 17 © 2022

assets?

Standby LCs: Foreign exchange contracts: Potential exposure Current exposure

$20 x 1.0

=

$40 x 0.075 in the money

= = = Total risk-adjusted on- and off-balance-sheet assets

$20 x 1.0 = $20

CET1 capital required

$3 $0 $3 x 1.0 = $ 3 = $118 x 0.045 $5.31

Tier I capital required

x 0.06 $7.08

Total capital required

x 0.08 = $9.44

c. Disregarding the capital conservation buffer, does the bank have sufficient capital to meet the Basel requirements? How much in excess? How much short?

No, the bank does not have sufficient total capital to meet the Basel requirements. It needs CET1 capital of $5.31 million, Tier I capital of $7.08 million, and total capital of $9.44 million. The bank has $6 million of CET1 capital and Tier I capital, and $8 million of total capital. Thus, the bank has sufficient CET1 capital, but insufficient additional Tier I and Tier II capital.

If the bank issues $1.08 million in CET1 (or additional Tier I) capital, it will need $0.36 million in additional Tier II capital. With these additions the bank will have $7.08 million of CET1 capital, $7.08 million of Tier I capital, and $9.44 million of total capital.

A new balance sheet after the issuance of the new required equity is shown below.

Assets Cash (0%) Mortgage loans (50%) Consumer loans (100%) Reserve for loan losses Total assets

Liabilities and Equity Deposits Subordinated debt (> 5 years) Equity

$22.44 50 70 (1) $141.44

Total Liabilities and equity

$133 1.36 7.08 $141.44

d. Does the bank have enough capital to meet the Basel requirements, including the capital conservation buffer requirement? If not, what minimum CET1, additional Tier 1, or total capital does it need to meet the requirement?

Total risk-adjusted on- and off-balance-sheet assets CET1 capital required including capital conservation buffer 18 © 2022

= $118 x 0.070 $8.26

Tier I capital required including capital conservation buffer

x 0.085 $10.03

Total capital required

x 0.105 = $12.39

No, the bank does not have sufficient total capital to meet the Basel requirements. It needs CET1 capital of $8.26 million, Tier I capital of $10.03 million, and total capital of $12.39 million. The bank has $6 million of CET1 capital and Tier I capital, and $8 million of total capital.

Capital conservation buffer must be met with CET1 capital. Thus, if the bank issues $4.03 million in CET1 capital, it will need $0.36 million in Tier II capital. With these additions the bank will have $10.03 million of CET1 and Tier I capital, and $12.39 million of total capital.

A new balance sheet after the issuance of the new required equity is shown below.

Assets Cash (0%) Mortgage loans (50%) Consumer loans (100%) Reserve for loan losses Total assets 30.

Liabilities and Equity Deposits Subordinated debt (> 5 years) Equity

$25.39 50 70 (1) $144.39

Total Liabilities and equity

$133 1.36 10.03 $144.39

According to SEC Rule 15C 3-1, what adjustments must securities firms make in the calculation of the book value of net worth?

Specifically, broker-dealers must maintain aggregate indebtedness to net capital of no more than 1500 percent. Aggregate indebtedness consists of the total liabilities arising from any transaction. This includes, among other things, money borrowed, money payable against securities lent, the market value of securities borrowed, customers' and non-customers' free credit balances, credit balances in customers' and non-customers' accounts having short positions in securities, equities in customers' and non-customers' future commodities accounts, and credit balances in customers' and non-customers' commodities accounts. Net capital is the net worth adjusted for unrealized profit or loss, deferred tax provisions, and certain liabilities.

In addition to this capital ratio, the 2013 amendment introduced an additional ‘net capital rule’ that is a net liquid assets test. Broker-dealers must calculate the market value for their highly liquid assets on a day-to-day basis and ensure that the market value of these assets exceed the value of their liabilities. This standard is designed to allow a broker-dealer the flexibility to engage in activities that are part of conducting a securities business (e.g., taking securities into inventory), but in a manner that places the firm in the position of holding more than one dollar of highly liquid assets for each dollar of unsubordinated liabilities (e.g., money owed to customers, counterparties, and creditors) at all times. For example, Rule 15c3-1 allows securities positions to count as allowable net capital. The rule, however, does not permit most unsecured receivables to count as allowable net capital. This aspect of the rule severely limits the ability of broker19 © 2022

dealers to engage in activities that generate unsecured receivables (e.g., lending money without obtaining collateral). The rule also does not permit fixed assets or other illiquid assets to count as allowable net capital. This creates disincentives for broker-dealers to own real estate and other fixed assets that cannot be readily converted into cash. For these reasons, Rule 15c3-1 incentivizes broker-dealers to confine their business activities and devote capital to activities such as underwriting, market making, and advising on and facilitating customer securities transactions.

31.

A securities firm has the following balance sheet (in millions): Assets Cash Debt securities Equity securities Other assets Total assets

$40 300 500 60 $900

Liabilities and Equity Five-day commercial paper Bonds Debentures Equity Total liabilities and equity

$20 550 270 60 $900

The debt securities have a coupon rate of 6 percent, 20 years remaining until maturity, and trade at a yield of 8 percent. The equity securities have a market value equal to book value, and the other assets represent building and equipment which was recently appraised at $80 million. The company has 1 million shares of stock outstanding and its price is $62 per share. Is this company in compliance with SEC Rule 15C 3-1?

The firm’s aggregate indebtedness to net capital is ($20 + $550 + $270)/62 = 1355% < 1500%.

Also, the market value of the bonds held by the firm is ($60 x PVAn=20,i=8 + $1,000 x PVn=20,i=8) x 300,000 = $241,091,115.56. Thus, the market value of the highly liquid assets is ($40m + $241m + $500m + $80m) = $861 million.

The net capital rule states that the value of the firm’s highly liquid assets must exceed the value of their liabilities. For this firm, the highly liquid assets to liabilities ratio is $861m/$840m = 1.025 = 102.50%. Therefore, the company is in compliance with SEC Rule 15C 3-1.

32.

An investment bank specializing in fixed-income assets has the following balance sheet (in millions). Amounts are in market values and all interest rates are annual unless indicated otherwise.

Assets Cash 8% 10-year Treasury-notes semiannual (par = $16.0) Total assets

$0.5 15.0 $15.5

Liabilities and Equity 5% 1-year Eurodollar deposits 6% 2-year subordinated debt (par = $9.5) Equity Total liabilities and equity

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$5.0 9.5 1.0 $15.5

a. Does the investment bank have sufficient liquid assets per the net capital rule? Is the investment bank in compliance with SEC Rule 15C 3-1?

The net capital rule states that the value of the firm’s highly liquid assets must exceed the value of their liabilities. For this firm, the highly liquid assets to liabilities ratio is ($0.5m + $15.0)/ $14.5m = 1.06897 = 106.897%. Further, the firm’s aggregate indebtedness to net capital is ($5.0m + $9.5m)/1.0m = 1450% < 1500%. Therefore, the company is in compliance with SEC Rule 15C 3-1. b. Assume that the rates on all assets rise 15 basis points and on all liabilities rise 25 basis points (per year). Will the FI be in compliance with SEC Rule 15C 3-1?

Change in the value of the assets: For 15 basis point change $15m = PVAn=20,k=?($0.64m) + PVn=20,k=?($16m)  k = 4.4796 x 2 = 8.9593 percent. If k =8.9593 + 0.15 = 9.1093/2 = 4.5546 percent,  the PV of the notes will be: PVAn=20,k=4.5546($0.64m) + PVn=20,k=4.5546($16m) = $14,851,114.01 And the decrease in value is $14,851,114.01 - $15.0m = - $148,885.99 Change in the value of deposits: $5m = PVAn=1,k=?($0.25m) + PVn=1,k=?($5m)  k = 5 percent. If k = 5.0 + 0.25 = 5.25%, the value of the notes will be: PVA n=1,k=5.25($0.25m) + PVn=1,k=5.25($5m) = $4,988,123.52.

And the market value will decrease by $4,988,123.52 - $5m = -11,876.49.

Change in the value of debt: $9.5m = PVAn=2,k=?($0.57m) + PVn=2,k=?($9.5m)  k = 6 percent. If k = 6 + 0.25 = 6.25%, the value of the notes will be: PVAn=2,k=6.25($0.57m) + PVn=2,k=6.25($9.5m) = $9,456,609.00.

And the decrease in value will be $9,456,609.00 - $10m = -$43,391.00.

The decline in the value of equity = $148,885.99 - $11,876.49 - $43,391.00 = $93,618.50, or the value of equity after these changes will be $1,000,000 - $93,618.50 = $906,381.50.

For this firm, the highly liquid assets to liabilities ratio is ($500,000 + $14,851,114.01)/ ($4,988,123.52 + $9,456,609.00) = 0.94096 = 94.06%. Further, the firm’s aggregate indebtedness to net capital is ($4,988,123.52 + $9,456,609.00)/ $906,381.50 = 1694% > 1500%.

Therefore, the company is no longer in compliance with SEC Rule 15C 3-1. c. How does the net capital rule for investment banks differ from the capital requirements imposed on commercial banks and other depository institutions?

Unlike the book value capital rules employed by bank and thrift regulators, the capital requirements for broker–dealers set by the SEC’s Rule 15C 3–1 in 1975 and amended in 2013 are close to a market value accounting rule.

33.

Identify and define the five risk categories incorporated into the life insurance risk-based capital model.

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a.

Asset risk–affiliate is the risk of default of assets for affiliated investments.

b.

Asset risk – investments reflects the riskiness of the asset portfolio. The category is split into common stock risk (C1cs) and other investment risk (C1o). It is calculated on an assetrisk-weighted basis similar to the risk-adjusted asset calculation for banks.

c.

Insurance risk measures the risk of mortality (risk of death) and morbidity (risk of ill health).

d.

Interest rate, credit, and market risk measures the liquidity of liabilities and their probability or ease of withdrawal as interest rates, credit risk, or market risk change. This measure is calculated on a risk-adjusted basis after classifying liabilities into three risk classes: interest rate risk (C3a), credit risk (C3b), and market risk (C3c).

e.

Business risk deals with the cost of insurer insolvencies. The category is split into business risk (C4a) and administrative expense risk (C4b).

34.

A life insurance company has estimated capital requirements for each of the following risk classes: asset risk-affiliate (C0) = $2 million, asset risk-common stock (C1cs) = $5 million, asset risk-other investments (C1o) = $1.5 million, insurance risk (C2) = $4 million, interest rate risk (C3a) = 3.5, credit risk (C3b) = 2.5, and market risk (C3c) = $1 million, and business risk (C4a) = $3 million, and administrative expense risk (C4b) = 0.5 million. a. What is the required risk-based capital for the life insurance company?

RBC = C0 + C4a +

=> RBC = $2m + $3m + ($1.5m + $3.5m )2 + ($5m + $1m)2 + ($4m)2 + ($2.5m)2 + ($0.5m)2 = $14.138 million b. If the total surplus and capital held by the company is $12.45 million, does it meet the minimum requirements?

No. Total capital and surplus is not sufficient since (Total capital + Surplus)/RBC < 1: $12.45m/14.138m = 0.8806 = 88.06% c. How much capital must be raised to meet the minimum requirements?

The life insurer needs to raise its total capital and surplus to $14.138 million, or a total additional amount of $1.688 million.

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35.

How do the risk categories in the risk-based capital model for property-casualty insurance companies differ from those of life insurance companies? What are the assumed relationships between the risk categories in the model?

The risk-based capital requirements model for property-casualty companies contains eight risk categories including three categories for asset risk. One of the asset risk factors, the credit risk factor, the two underwriting risk factors and the two catastrophe risk factors are assumed to be independent of each other. Further, the investment risk in PC affiliates and off-balance-sheet items is assumed to be perfectly correlated with the net amount of the other seven risk categories.

36.

A property-casualty insurance company has estimated the following required charges for its various risk classes (in millions): Risk R0 R1 R2 R3 R4 R5 R4 R5 Total

Description Affiliated P/C Fixed income Common stock Reinsurance Loss adjustment expense Written premiums Loss adjustment expense Written premiums

RBC Charge $1 2 4 3 2 3 3 2 $20

a. What is the RBC charge as per the model recommended by the NAIC? RBC = R0 + = $1m + ($2m)2 + ($4m)2 + ($3m)2 + ($2m)2 + ($3m)2 + ($3m)2 + ($2m)2 = $1m + $7.4162m = $9.4162 million b. If the firm currently has $8 million in capital, what should be its surplus to meet the minimum capital requirement?

It needs to hold a minimum surplus of $1.4162 million.

Integrated Mini Case: Calculating Capital Requirements A bank’s balance sheet information is shown below (in $000).

Used for answers to 1-4 Face Value Weight Value $121,600 0% $0 5,400 0% $0

On Balance Sheet Items Cash Short-term government securities (<92 days.)

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Long-term government securities (>92 days) Federal Reserve stock Repos secured by federal agencies Claims on U.S. depository institutions Loans to foreign banks, OECD CRC rated 2 General obligations municipals Claims on or guaranteed by federal agencies Municipal revenue bonds Residential mortgages, category 1, loan-to-value ratio 75% Commercial loans Loans to sovereigns, OECD CRC rated 3.

Premises and equipment

Off Balance Sheet Items: U.S. Government Counterparty Loan commitments: < 1 year 1-5 year Standby letters of credit: Performance-related Direct-credit substitute

Conversion Factor

0% 0% 20% 20% 20% 20% 20% 50%

$0 $0 $31,800 $187,580 $328,000 $34,000 $5,300 $56,450

5,000,000 4,667,669 11,600 455,000

50% 100% 50% 100%

$2,500,000 $4,667,669 $5,800 $455,000

Face Credit-Equivalent Risk-Adjusted Value Amount Asset Value

20% 50%

$300 1,140

$60 570

$0 0

50% 100%

200 100

100 100

0 0

100 3,000

20 1,500

4 300

200 56,400 400

100 56,400 80

20 11,280 16

100

50

25

135,400

67,700

33,850

3,212,400 3,046,278

642,480 1,523,139

642,480 1,523,139

U.S. Depository Institutions Counterparty Loan commitments: < 1 year.

20% > 1 year 50% Standby letters of credit: Performance-related 50% Direct-credit substitute 100% Commercial letters of credit: 20% State and Local Government Counterparty (revenue municipals) Loan commitments: >1 year 50% Standby letters of credit: Performance-related 50% Corporate Customer Counterparty Loan commitments: < 1 year >1 year

414,400 9,800 159,000 937,900 1,640,000 170,000 26,500 112,900

20% 50% 24 © 2022

Standby letters of credit: Performance-related Direct-credit substitute Commercial letters of credit:

50% 100% 20%

101,543 490,900 78,978

50,772 490,900 15,796

50,772 490,900 15,796

Sovereign Counterparty Loan commitments, OECD CRC rated 1: < 1 year >1 year

20% 50%

110,500 1,225,400

22,100 612,700

0 0

Sovereign Counterparty Loan commitments, OECD CRC rated 2: < 1 year >1 year

20% 50%

85,000 115,500

17,000 57,750

3,400 11,550

Sovereign Counterparty Loan commitments, OECD CRC rated 7: >1 year.

50%

30,000

15,000

22,500

Interest rate market contracts: (current exposure assumed to be zero.) < 1 year (notional amount) 0% > 1-5 year (notional amount) 0.5%

2,000 5,000

0 25

0 25

1.

What is the bank's risk-adjusted asset base under Basel III?

The risk-adjusted asset base under Basel III is: On-balance-sheet risk-adjusted asset base Off-balance-sheet risk-adjusted asset base Total risk-adjusted asset base 2.

$8,271,599 $2,806,057 $11,077,656

To be adequately capitalized, what are the bank's CET1, Tier I, and total risk-based capital requirements under Basel III?

Under Basel III: CET1 = 4.5% capital requirement x $11,077,656 = 498,492 Tier I = 6% capital requirement x $11,077,656 = $664,656 Tier II = 8% capital requirement x $11,077,656 = $886,208 3.

Using the leverage ratio requirement, what is the minimum regulatory capital required to keep the bank in the adequately-capitalized zone?

The bank has $13,731,769 in total on-balance-sheet assets, $8,693,839 in off-balance sheet lending commitments, and $25 in credit equivalent amounts of derivative securities. Thus, total exposure is $22,425,633. The minimum regulatory Tier I capital at 4% is $897,025.

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4.

Disregarding the capital conservation buffer, what is the bank's capital adequacy level (under Basel III) if the par value of its equity is $225,000, surplus value of equity is $200,000, retained earnings is $565,545, qualifying perpetual preferred stock is $50,000, subordinate debt is $50,000, and loan loss reserve is $85,000? Does the bank meet Basel (CET1, Tier I, total, and leverage) adequate capital standards? Does the bank comply with the well-capitalized leverage ratio requirement?

CET1 capital = $225,000 + $200,000 + $565,545 = $990,545; Tier I capital = $990,545 + $50,000 = 1,040,545; and total capital = 1,040,545 + $50,000 + $85,000 = $1,175,545. Yes, the bank meets the Basel III standards for adequate capital because CET1 capital ratio is above 4.5% ($990,545/$11,077,656 = 8.94%), Tier I capital ratio is above 6% ($1,040,545/$11,077,656 = 9.39%), total capital ratio is above 8% ($1,175,545/$11,077,656 = 10.61%), and leverage ratio is above 4% ($1,040,545/$22,425,633 = 4.64%). The bank does not comply with the wellcapitalized: the CET1 capital is above 6.5%, Tier I capital is above 8%, total capital is above 10%, and leverage ratio is above 5%. While the CET1, Tier I and total capital ratios meet the well-capitalized levels, the leverage ratio does not. All four of the capital ratios must meet the minimum standards for well-capitalized.

5.

Does the bank have enough capital to meet the Basel requirements, including the capital conservation buffer requirement?

The bank does have sufficient capital to meet the capital conservation buffer: the CET1 capital is above 7.0%, Tier I capital is above 8.5%, and total capital is above 10.5%. The capital conservation buffer does not consider the leverage ratio.

6.

The bank’s various lines of business produced the following gross income: Retail banking Commercial banking Payment and settlement Trading and sales Asset management

$40,000 50,000 15,000 5,000 10,000

What is the add-on to capital for operational risk? Does the bank have sufficient capital to cover this add-on and remain adequately capitalized, while meeting the capital conservation buffer?

The add-on capital requirement for operational risk is: [($40,000 x 0.12) + ($50,000 x 0.15) + ($15,000 x 0.18) + ($5,000 x 0.18) + ($10,000 x 0.12)] x 0.12 = $17,100 x 0.12 = $2,052 To cover this add-on and remain adequately capitalized while meeting the capital conservation buffer: CET1 = (7% capital requirement x $11,077,656) + $2,052 = 777,488 26 © 2022

Tier I = (8.5% capital requirement x $11,077,656) + $2,052 = $943,653 Tier II = (10.5% capital requirement x $11,077,656) + $2,052 = $1,165,206 The bank has more than these amounts, so does remain adequately capitalized.

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Solutions for End-of-Chapter Questions and Problems: Chapter Twenty-One 1.

How does product segmentation reduce the profitability and risk of FIs?

Historically, many U.S. financial service firms have faced return and risk problems due to constraints on product diversification. Arguably, product expansion restrictions have affected commercial banks the most. For example, to the extent that regulations have limited the franchise of banks to traditional areas such as deposit taking and commercial lending, banks have been increasingly susceptible to nonbank or shadow bank competition on both the liability and asset sides of their balance sheets. Specifically, the growth of money market mutual funds (MMMFs) that offer checking account–like deposit services with high liquidity, stability of value, and an attractive return has proven to be very strong competition for bank deposit and transaction account products. From virtually no assets in 1972, MMMFs had grown to more than $2.7 trillion by June 2015, compared to money market deposit accounts of $4.6 trillion in commercial banks. In addition, until recently banks have been threatened by the growth of annuities offered by the life insurance industry. Annuities are a savings product that have many of the same features as bank CDs. In 2015, fixed and variable annuities held in U.S. retirement funds totaled $2.0 trillion.

On the asset side of the balance sheet, the commercial and industrial (C&I) loans of banks have faced increased competition from the dynamic growth of the commercial paper market as an alternative source of short-term financing for large- and middle-sized corporations. For example, in January 1988, C&I loans outstanding were $565 billion versus $380 billion of commercial paper; in June 2015, C&I loans were $1.69 trillion versus $1.06 trillion of commercial paper outstanding. In addition, relatively unregulated finance companies are taking an increasing share of the business credit market. In June 2015, the ratio of finance company business credit to bank C&I loans was approximately 25 percent. These trends mean that the economic value of narrowly defined bank franchises has declined. In particular, product line restrictions inhibit the ability of an FI to optimize the set of financial services it can offer, potentially forcing it to adopt a more risky set of activities than it would adopt if it could fully diversify. Product restrictions also limit the ability of FI managers to adjust flexibly to shifts in the demand for financial products by consumers and to shifts in costs due to technology and related innovations 2.

What general prohibition regarding the activities of commercial banking and investment banking did the Glass-Steagall Act impose?

The Glass-Steagall Act specifically prohibited banks from engaging in the underwriting, issuing, and distributing of stocks, bonds, and other securities, while specifically prohibiting investment banks from taking deposits and making commercial loans.

3.

What restrictions were placed on Section 20 subsidiaries of U.S. commercial banks that made investment banking activities other than those permitted by the Glass-Steagall Act less attractive? How did this differ from banking activities in other countries?

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Although banks were allowed to engage in otherwise ineligible investment banking activities by creating Section 20 subsidiaries, the revenue from these ineligible activities could not exceed more than 50 percent of the revenues they generated. Consequently, only the largest banks with businesses in activities permitted under the Glass-Steagall Act, such as trading U.S. Treasuries or general obligation municipal bonds were able to undertake the ineligible activities. In addition, stringent firewalls between Section 20 subsidiaries and the commercial banks made it difficult for banks to exploit economies of scale and diversification benefits. In most countries (except for Japan) both commercial and investment banking activities were undertaken under one roof, allowing full flexibility and benefits of integrated operations.

4.

Explain in general terms what impact the Financial Services Modernization Act of 1999 should have on the strategic implementation of Section 20 activities.

The Financial Services Modernization Act of 1999 allows the creation of financial services holding companies that can engage in banking activities and securities activities. The securities activities are allowed through the creation of Section 4(k)(4)(E) subsidiaries that replace the Section 20 subsidiaries. Thus, banks are able to underwrite securities providing that the activity is placed in a subsidiary under the regulation of the Office of the Comptroller of the Currency.

Thus, full service financial institutions in the U.S. are able to compete with those of many other countries in the world.

5.

What types of insurance products were commercial banks permitted to offer before 1999?

How did the Financial Services Modernization Act of 1999 change this? How have nonbanks managed to exploit the loophole in the Bank Holding Company Act of 1956 and engage in banking activities? What law closed this loophole? How did insurance companies circumvent this law?

Commercial banks were prohibited from offering almost all insurance products with the exception of annuities, life, health, and accident insurance related to credit products, and some forms of employment related insurance. The Bank Holding Company Act of 1956 legally defined a bank as an organization that accepts demand deposits and makes commercial and industrial loans. By acquiring banks and subsequently divesting off either their deposits or their loans, nonbanks and commercial firms gained control over banking institutions, essentially exploiting a loophole. The 1987 Competitive Equality Banking Act redefined a bank as any institution that accepts deposit insurance, thereby closing this loophole. The Financial Services Modernization Act of 1999 allowed bank holding companies to open affiliates to underwrite insurance and to sell insurance under the same regulations as the insurance industry.

6.

The Financial Services Modernization Act of 1999 allows banks to own controlling interests in nonfinancial companies. What are the two restrictions on such ownership?

First, the investment cannot be made for an indefinite period of time, although the act did not specify a definition for the word “indefinite.” Second, the bank cannot become actively involved in the management of the corporation in which it invests.

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7.

What is shadow banking? How does the shadow banking system differ from the traditional banking system?

Activities of nonfinancial service firms that perform banking services has been termed shadow banking. Shadow banks include finance companies, money market deposit funds, structured investment vehicles (SIVs), asset-backed paper vehicles, credit hedge funds, asset-backed commercial paper (ABCP) conduits, limited-purpose finance companies, and credit hedge funds.

As of 2015, worldwide total assets managed by the shadow banking system totaled $75 trillion.

In the shadow banking system savers place their funds with money market mutual and similar funds, which invest these funds in the liabilities of shadow banks. Borrowers get loans and leases from shadow banks such as finance companies rather than from banks. Like the traditional banking system, the shadow banking system intermediates the flow of funds between net savers and net borrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, or shadow bank, that intermediates. Further, unlike the traditional banking system, where the complete credit intermediation is performed by a single bank, in the shadow banking system it is performed through a series of steps involving many nonbank financial service firms. For example, the lending process might involve (1) loan origination performed by a finance company, (2) loan warehousing conducted by single and multiple sellers funded through asset-backed commercial paper (ABCP), (3) ABS issuance conducted by broker-dealers, (4) ABS warehousing funded with repurchase agreements, (5) ABS collateralized debt obligation (CDO) issuance conducted by broker-dealers, and (6) ABS intermediation performed by limited purpose finance companies. Each step is performed by a specific type of shadow bank and through a specific funding vehicle. Thus, the shadow banking system decomposes the traditional process of deposit-funded, hold-to-maturity lending conducted by banks, into a more complex, wholesale-funded, securitization-based lending process that involves multiple shadow banks which are not regulated or monitored by a regulatory body.

Because of the specialized nature involved in the credit intermediation process as performed shadow banks, these nonbank financial service firms can perform the process more cost efficiently than traditional banks. Further, because of the lower costs and lack of regulatory oversight, shadow banks can take on risks that traditional banks either cannot or are unwilling to take. Thus, the shadow banking system allows credit to be available for individuals or businesses that might not otherwise have access to credit through the traditional banking system. However, shadow banks can increase the risk inherent in the financial system. Shadow banks fund their activities mainly with short-term, checking account like deposit services. They are, for the most part, highly levered financial institutions. They do not take deposits, so they are not subject to regulations to the extent seen by traditional banks. However, unlike traditional banks, since shadow banks do not have deposit insurance like traditional banks, a sudden loss of confidence in the asset quality of these nonbank financial institutions can lead to funding runs. Because commercial banks and shadow banks are interrelated through the credit intermediation system, problems that arise in the shadow banking system can quickly spread to the traditional banking system. Indeed, by transforming the way the credit intermediation process works—from the traditional banking method to the multilayered process used by shadow banks—shadow banks fuelled the unprecedented growth in the real estate markets in the mid-2000s that eventually crashed and led to the financial crisis.

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What are the differences in the risk implications of a firm commitment securities offering versus a best-efforts offering?

In a best-efforts offering, the underwriting firm serves as a placement agent with the promise to do the best job possible. The firm has very little risk of loss in this situation. In a firm commitment offering, the investment bank actually buys the securities from the issuing firm and then must resell them to the public in the market. The investment firm faces two risks in this process. First, the securities cannot be sold at any price different from the negotiated price in effect during the offering window or period. Second, if adverse events occur during this window, the investment firm may be unable to sell the securities and will either hold the securities in inventory or sell them at a reduced price after the offering period. In either case, the underwriting firm is at risk to suffer a loss.

9.

An FI is underwriting the sale of 1 million shares of Ultrasonics, Inc., and is quoting a bidask price of $6.00-$6.50. a. What are the fees earned by the FI if a firm commitment method is used to underwrite the securities?

Firm commitment: ($6.50 - $6.00) x 1 million = $500,000 b. What are the fees if the FI uses the best-efforts method and a commission of 50 basis points is charged?

Best efforts: 0.005 x $6.50 x 1 million = $ 32,500 c. How would your answer be affected if the FI manages to sell the shares only at $5.50 using the firm commitment method? The commission for best efforts is still 50 basis points.

Firm commitment: ($5.50 - $6.00) x 1 million = -$500,000 Best efforts: 0.005 x $5.50 x 1 million = $27,500 10.

An investment bank subsidiary of a financial services holding company agrees to underwrite a debt issue for one of its clients. It has suggested a firm commitment offering for issuing 100,000 shares of stock. The FI quotes a bid-ask spread of $97-$97.50 to its customer on the issue date. a. What are the total underwriting fees generated if all the issue is sold? If only 60 percent is sold?

If all shares are sold, underwriting fees = 100,000 x $0.50 = $50,000. If only 60 percent are sold, the fee will depend on what price the remaining 40 percent are sold. Most likely the affiliate will keep the shares in inventory and try to sell them at a later date when the price for these shares has 4 © 2022

stabilized. If none of the shares are sold, the minimum fees will be 100,000 x $0.50 x 0.6 = $30,000 b. Instead of taking a chance that only 60 percent of the shares will be sold on the issue date, the FI suggests a price of $95 to the issuing firm. The FI quotes a bid-ask spread of $95-$95.40 and sells 100 percent of the issue. From the FI’s perspective, which price is better if it expects to sell the remaining 40 percent at the bid price of $97 under the first quote?

If the price quoted is $95.00-$95.40, the underwriting fees = 100,000 x $0.40 = $40,000. If 60 percent is sold at $97.50, the underwriting fees = 60,000 x 0.50 = $30,000, and if the remaining 40 percent are sold at $97, the underwriting fee is $0 for that portion. Thus, the total fees generated = $30,000 + $0. Clearly, the FI is better off recommending an issue price of $95 rather than $97.

11.

What are three ways that the failure of a securities affiliate in a holding company organizational form could negatively affect a bank affiliate? How has the Fed attempted to prevent a breakdown of the firewalls between bank and nonbank affiliates in these situations?

An FI could be affected negatively in three ways if its securities affiliate fails. First, the holding company could upstream resources by increasing dividend and other fee payments from the bank to the holding company. The holding company could then downstream these funds to protect the failing securities affiliate from insolvency. As a result, the bank would be weakened at the expense (or because) of the securities affiliate.

Second, a holding company could compel the bank to make interaffiliate loans to its loss-making unit. The Federal Reserve Act prevents banks from making loans to their affiliates in excess of 15 percent of their capital.

Third, a securities affiliate that incurs losses may induce depositors to engage in a run on the bank even though the Fed requires strict separation between the bank and nonbank affiliates.

This is even more likely if the two affiliates bear a common name, such as Bank of America and Bank of America Securities. Such contagion effects cannot be controlled by the Fed except through publicizing the information on the soundness of the firewall between the institutions.

Recognizing that allowing banking organizations to expand their securities activities may lead to more risk in the banking system, the FSMA of 1999 explicitly incorporated provisions regarding the way the new financial services holding companies would be regulated. For example, the act streamlines bank holding company supervisions by clarifying the regulatory roles of the Federal Reserve as the umbrella holding company supervisor and of the state and federal financial regulators that “functionally” regulate various affiliates. It provides for federal bank regulators to prescribe prudential safeguards for bank organizations engaging in new financial activities. It provides for state regulation of insurance, subject to a standard that no state may discriminate against persons affiliated with a bank. Finally, the Act prohibits FDIC assistance to affiliates and 5 © 2022

subsidiaries of banks and savings institutions. However, FDIC “bailouts” to failing bank holding companies during the financial crisis provided indirect assistance to their affiliates and subsidiaries. The Wall Street Reform and Consumer Protection Act of 2010 calls for the Federal Reserve to receive new oversight powers and to impose conditions designed to discourage any type of financial institution from posing extensive risk to the overall financial system. For example, the Act requires the largest, systemically important financial institutions (SIFIs) to implement “living wills.” Specifically, bank holding companies with total consolidated assets of $50 billion or more, and certain nonbank financial companies (that the Financial Stability Oversight Council (FSOC) designates as systemic), must develop, maintain, and periodically submit resolution plans that are credible and that would enable these entities to be resolved under the Bankruptcy Code.

12.

What role does bank activity diversification play in the ability of a bank to exploit economies of scale and scope? What remains as the limitation to creating potentially greater benefits?

As financial firms become larger, the potential scale can lower an FI’s average costs of financial service production. Thus, larger financial services holding companies may have an economy of scale advantage over smaller financial firms. Further, financial services holding companies’ abilities to generate synergistic cost savings through joint use of inputs in producing multiple financial products create economies of scope. Most studies find cost-based economies of scope are negligible, although revenue-based economies of scope may arise for the largest FIs. Arguably, the pre-1997 restrictions between banks and their Section 20 investment banking affiliates covering finance, management and cross-marketing severely limited economies of scope and related revenue and cost synergies. Post-1997 and, more so, post-1999 U.S. financial service firms may realize greater economies of scope as restrictions were removed and the FSHCs became more universal in product scope.

13.

What six conflicts of interest have been identified as potential roadblocks to the expansion of banking powers into the financial services area?

The six conflicts of interest are (1) the incentive interest of the salesperson to sell rather than to just provide dispassionate advice, (2) the opportunity to sell unwanted securities in a firm commitment underwriting to trust department accounts within the bank, (3) the ability to encourage a creditor to issue bonds and to use the proceeds to pay down the bank loan under conditions where the creditor’s bankruptcy risk has increased, (4) the incentive to lend to thirdparty investors for the purpose of buying securities that are offered by the investment affiliate, (5) the opportunity to tie lending availability to the use of the investment affiliate products for securities’ needs, and (6) the opportunity to misuse inside information.

14.

Under what circumstances could the existence of deposit insurance provide an advantage to banks in competing with other traditional securities firms?

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affiliates have received explicit benefits. However, since the FSMA allowed other financial service firms to establish banks that offer deposit insurance coverage, this explicit subsidy advantage has been lessened.

15.

In what ways does the current regulatory structure argue against providing additional securities powers to the banking industry? Does this issue concern only banks?

The regulatory structure for most banks is multilayered and complex. The efficiency of the overlapping structure is questionable from a public policy perspective because of the waste of monitoring and surveillance resources as well as the inherent coordination problems. Further, these problems may become magnified in times of financial distress regardless of the source, causing potentially serious negative effects to occur for shareholders, customers, and the general financial system.

The Fed’s role as the supervisor of a bank holding company is to review and assess the consolidated organization’s operations, risk management systems, and capital adequacy to ensure that the holding company and its nonbank subsidiaries do not threaten the financial stability of the company’s depository institutions. In this role, the Fed serves as the umbrella supervisor of the consolidated organization. In fulfilling this role, the Fed relies to the fullest extent possible on information and analysis provided by the appropriate supervisory authority of the company’s bank, securities, or insurance subsidiaries.

The Wall Street Reform and Consumer Protection Act of 2010 calls for the Federal Reserve to receive new oversight powers. The proposals put the Federal Reserve in charge of monitoring the country’s biggest financial firms—those considered critical to the health of the system as a whole. Those firms would also face new, stiffer requirements on how much capital and liquidity they keep in reserve. The overhaul also provides unprecedented powers to the Fed to step into any financial institutions—such as insurance giant AIG (whose main regulators include the New York State Department of Insurance and the Office of Thrift Supervision)—that are facing imminent collapse, in order to force an orderly bankruptcy that would protect the wider economy.

16.

How do limitations on domestic geographic diversification affect an FI’s profitability?

Limitations on domestic geographic diversification increase FI profitability by creating locally uncompetitive markets. FIs in these markets earn monopoly rents that are protected by limitations on domestic geographic expansion by potential competitors. Limitations on geographic diversification reduce FI profitability by preventing the FI from exploiting any economies of scale and/or scope or revenue synergies that may be available.

17.

How are insurance companies able to offer services in states beyond their state of incorporation?

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Insurance companies are state-regulated firms that are not prohibited from establishing subsidiaries and offices in other states. Further, the capital requirements are kept low by state regulators.

18.

In what way did the Garn-St. Germain Act and FIRREA provide incentives for the expansion of interstate branching?

Both legislative acts provided for sound banks and thrifts to acquire failing banks and thrifts across state lines. These acquisitions could be operated either as separate subsidiaries or as branches of the acquiring institution.

19.

What is an interstate banking pact?

An interstate banking pact is an agreement between states defining the conditions under which out-of-state banks can acquire in-state subsidiaries. A major feature of these pacts normally was the reciprocity conditions awarded each state involved.

20.

How did the provisions of the Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994 allow for full interstate banking? What are the expected profit performance effects of interstate banking? What has been the impact on the structure of the banking and financial services industry?

The main feature of the Riegle-Neal Act of 1994 is the removal of barriers to interstate banking.

Bank holding companies were allowed to acquire banks in other states. In 1997, banks were allowed to convert out-of-state subsidiaries into branches of a single interstate bank. The act has resulted in significant consolidations and acquisitions, with the emergence of very large banks with branches all over the country, as currently practiced in the rest of the world. The law, as of now, does not allow the establishment of de novo branches unless allowed by the individual states.

21.

What cost synergies may be obtained by an FI from domestic geographic expansion?

Annual cost savings from geographic expansion can be achieved by consolidating certain operations and eliminating redundant costs, including the elimination of overlapping positions, cutting duplicate back-office operations. Larger banks can also take more advantage of outsourcing operations locally or abroad.

22.

What are the three revenue synergies that may be obtained by an FI from domestic geographic expansion?

The three revenue synergies that an FI may obtain by expanding geographically are: (a) Opportunities to increase revenue because of growing market share.

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(b) Different credit risk, interest rate risk, and other risks that allow for diversification benefits and the stabilization of revenues. (c) Expansion into less-than-competitive markets, which provides opportunities to reap some economic rents that may not be available in competitive markets.

23.

What is the Herfindahl-Hirschman Index? How is it calculated and interpreted?

The Herfindahl-Hirschman Index (HHI) is a measure of market concentration whose value can be 0 to 10,000. The index is measured by adding the squares of the percentage market share of the individual firms in the market. An index value greater than 2,500 indicates a highly concentrated market, a value between 1,500 and 2,500 indicates a moderately concentrated market, and an unconcentrated market would have a value less than 1,500.

24.

City Bank currently has a 60 percent market share in banking services, followed by NationsBank with 20 percent and State Bank with 20 percent. a. What is the concentration ratio as measured by the Herfindahl-Hirschman Index (HHI)?

HHI = (60)2 + (20)2 + (20)2 = 4,400 b. If City Bank acquires State Bank, what will be the new HHI? HHI = (80)2 + (20)2 = 6,800 c. Assume the Justice Department will allow mergers as long as the changes in HHI do not exceed 1,400. What is the minimum amount of assets that City Bank will have to divest after it merges with State Bank?

For City Bank to complete the merger, its maximum HHI should be such that when it disposes of part of its assets, the HHI will be X2 + Y2 + Z2 = 5,800. Since Z = 20 percent, we need to solve the following: X2 + Y2 = 5,400; that is, 5,800 less the share of Z2 which is 202 or 400.

If the merger stands with no adjustment, then X = 80 and Y = 0. But some portion of X must be liquidated. Therefore, we need to solve the equation (80 – Q)2 + Q2 = 5,400 where Q is the amount of disinvestment. This requires solving the quadratic equation of the form: Q2 + (80 Q)2 = 5,400 which expands and simplifies to 2Q2 – 160Q + 1,000 = 0.

- b  (b2 - 4ac)1/2 Using the formula: Q =

, we get Q = 73.1662 percent, which means

2a

City Bank has to dispose of 6.8338 percent of total banking assets. To verify, we can check the total relationship: (73.1662)2 + (6.8338)2 + (20)2 = 5,800.

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25.

The Justice Department has been asked to review a merger request for a market with the following four FI's: Bank Assets A $12 million B 25 million C 102 million D 3 million a. What is the HHI for the existing market?

Bank A B C D

Assets $12 m $25 m $102 m $3 m

Market Share 8.45% 17.61% 71.83% 2.11% 100.00%

The HHI = (8.45)2 + (17.61)2 + (71.83)2 + (2.11)2 = 5,545.5 b. If bank A acquires bank D, what will be the impact on the market's level of concentration?

Bank A B C

Assets $15 m $25 m $102 m

Market Share 10.56% 17.61% 71.83% 100.00%

The HHI = (10.56)2 + (17.61)2 + (71.83)2 = 5,581 c. If bank C acquires bank D, what will be the impact on the market's level of concentration?

Bank A B C

Assets $12 m $25 m $105 m

Market Share 8.45 % 17.61% 73.94% 100.00%

The HHI = (8.45)2 + (17.61)2 + (73.94)2 + (2.11)2 = 5,848.6 d. What is likely to be the Justice Department's response to the two merger applications?

The Justice Department may challenge Bank C’s application to acquire Bank D since it significantly increases market concentration (HHI = 5,848.6 vs 5,545.5, an increase of 303.1).

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On the other hand, the Justice Department would most likely approve Bank A's application since the merger causes only a small increase in market concentration (HHI = 5,581 vs 5,545.5, an increase of 35.5).

26.

What factors other than market concentration does the Justice Department consider in determining the acceptability of a merger?

Other factors considered by the Justice Department include ease of entry, the nature of the product, the terms of sale of the product, market information about specific transactions, buyer market characteristics, conduct of firms in the market, and market performance.

27.

What are some plausible reasons for the percentage of assets of small and intermediatesized banks decreasing and the percentage of assets of large banks increasing since 1984?

One reason for the decreasing share of small and intermediate-sized bank assets is the wave of mergers that has taken place over the period. If two small banks merge, the merged bank may have assets that move it into the next higher asset category. The changes in the interstate banking laws have encouraged this wave of mergers. However, even though the degree of concentration of assets among the largest banks has increased, the percentage share exhibited by the largest U.S. banks is still well below the shares attained by the largest Canadian and European banks in their domestic markets. Thus, mergers involving the largest U.S. banks will likely continue to be approved by the Department of Justice as well as other regulatory bodies.

28.

What are some of the benefits for banks engaging in geographic expansion?

The benefits to geographic diversification are: (a) Economies of scale: If there are efficiency gains to growth, geographic diversification can reduce costs and increase profitability. (b) Risk reduction: Overall risk reduction via diversification. (c) Survival: As nonbank financial firms have increasingly eroded banks’ market share, banks’ campaign to expand geographically can be viewed as a competitive response. That is, as global FIs dominate the financial environment, larger institutions with presence in many regions may better position the FI to compete.

29.

How did the Overseas Direct Investment Control Act of 1964 assist in the growth of global banking activities? How much growth in foreign assets occurred from 1980 to 2015?

The Overseas Direct Investment Control Act of 1964 restricted the ability of U.S. banks to lend to U.S. corporations that wanted to make foreign investments. Although later repealed, the law created incentives for U.S. banks to establish offices offshore to serve the financial needs of their U.S. corporate clients. From 1980 to 2015, foreign assets of U.S. banks grew from $353.8 billion to $1,1,581.9 in 2012 before falling back to $1,497.0 in 2015. Further, as a percent of these banks’ total assets, assets in foreign offices fell from 32.4 percent in 1980 to 16.2 percent in 11 © 2022

2012. As a percent of total assets, assets in foreign offices continued to fall, down to 10.2 percent of total bank assets by 2015.

30.

Identify and explain the impact of at least four factors that have encouraged global U.S. bank expansion.

First, the growth of international trade with the dollar as the primary medium of exchange has encouraged the use of U.S. foreign bank subsidiaries to assist in these trade-related transactions.

Second, the U.S. banks in strategic locations, such as the Cayman Islands and the Bahamas, have become preferred depositories for funds that are flowing out of politically sensitive and risky countries. Third, the Federal Reserve Bank often allows U.S. banks to participate in activities that are permitted in foreign countries, even though those same activities may not be permitted in the U.S. Finally, the technological improvements in communications, and the development of an international payment system (CHIPS) provide banks with the control of overseas operations at a decreasing rate.

31.

What is the expected impact of the implementation of Basel III risk-based capital requirements on the international activities of some major U.S. banks?

Several large banks may find it necessary to increase capital because under Basel III, risk weights for sovereign exposures are determined using OECD Country Risk Classifications (CRCs), which assigns countries to one of eight risk categories (0-7). Countries assigned to categories 0-1 have the lowest possible risk assessment and are assigned a risk weight of 0 percent, while countries assigned to category 7 having the highest possible risk assessment and are assigned a risk weight of 150 percent.

32.

What effect have the problems of emerging market economies in the late 1990s and 2000s had on the global expansion of traditional banking activities by U.S. banks?

Many U.S. banks have become more cautious in expanding outside the traditional overseas markets even though the regulatory environment seems more favorable.

33.

What is the European Community (EC) Second Banking Directive? What impact has the Second Banking Directive had on the competitive banking environment of Europe?

The EC Second Banking Directive created a single banking market in Europe wherein banks could branch and acquire banks throughout the entire European Community. As a result, there has been a cross-border merger wave among European banks that has paralleled the U.S. domestic merger and acquisition wave that followed the dismantling of interstate branching restrictions after the passage and implementation of the Riegle-Neal Act in 1994. In addition, a number of European banks have formed strategic alliances that enable retail bank customers to open new accounts, access account information, and make payments to third parties through any of the branches of the member banks in the alliance. This greater consolidation in European banking has created more intense competition for U.S. and other foreign banks in European wholesale markets and has made it more difficult for them to penetrate European retail markets.

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34.

What factors affected the proportion of U.S. banking assets that were controlled by foreign banks during the 1990s through 2015?

In 1980 foreign banks had $166.7 billion in assets held in the U.S. (10.8 percent of the size of total U.S. bank assets). This activity grew through 1992, when foreign banks had $514.3 billion in assets (16.4 percent of the size of U.S. assets). In the mid-1990s, there was a modest retrenchment in the asset share of foreign banks in the United States. In 1994, their U.S. assets totaled $471.1 billion (13.8 percent of the size of U.S. assets). This retrenchment reflected a number of factors, including the highly competitive market for wholesale banking in the United States, a decline in average U.S. loan quality, capital constraints on Japanese banks at home, and their poor lending performance at home, and the introduction of the Foreign Bank Supervision and Enhancement Act (FBSEA) of 1991, which tightened regulations on foreign banks in the United States (discussed below). However, as foreign banks adjusted to these developments and because of the strong U.S. economy in the late 1990s, activity of foreign banks in the United States grew, reaching 16.1 percent in 2000. The worldwide economic recession in the early 2000s again depressed the level of international activity in the United States. As the economic situation improved, the level of international activity in the United States accelerated. In September 2009 (late in the financial crisis) foreign bank assets in the U.S. were 13.2 percent the size of domestic bank assets. At year-end 2010 they were 14.8 percent the size of domestic assets and, most recently, in August 2015, foreign bank assets in the U.S. were 18.3 percent the size of domestic assets.

35.

What was the fundamental philosophical focus of the International Banking Act (IBA) of 1978?

The IBA of 1978 (and the Foreign Bank Supervision Enhancement Act of 1991) brought the regulation of foreign banks under the control of federal regulators with the intent of treating them under the same guidelines as domestic national banks.

36.

What events led to the passage of the Foreign Bank Supervision Enhancement Act (FBSEA) of 1991? What was the main objective of this legislation?

The primary objective of FBSEA was to extend federal regulatory authority over foreign banking organizations in the United States. The three events that served as the catalyst for this legislation were the failure of the Bank of Credit and Commerce International (BCCI), the issuance of more than $1 billion of unauthorized letters of credit to Iraq by the Atlanta branch of Banca Nazionale del Lavoro, and the unauthorized use of deposit funds by the U.S. representative office of the Greek National Mortgage Bank of New York.

37.

What were the main features of FBSEA? How did FBSEA encourage cooperation with the home country regulator? What was the effect of the FBSEA on the Federal Reserve and on the foreign banks?

The five main features of FBSEA are identified and discussed below: 13 © 2022

Entry. The Fed must approve the establishment of a subsidiary, branch, agency, or representative office in the United States. The two mandatory standards are (a) the comprehensive supervision of the foreign bank on a consolidated basis by a home country regulator, and (b) the provision by the home country regulator of all of the necessary information needed by the Fed to evaluate the application.

Closure. The Fed has the power to close the foreign bank if (a) the home country supervision is inadequate, (b) the bank has violated U.S. laws, and (c) the bank is engaged in unsound and unsafe banking practices.

Examination. The Fed has the power to examine each office of a foreign bank, and must examine at least annually each branch or agency.

Deposit taking. Only foreign subsidiaries with access to FDIC insurance are allowed to take deposits under $250,000.

Activity powers. Effective December 19, 1992, state-licensed branches and agencies of foreign banks could not engage in any activity not permitted to a federal branch.

Clearly the authority of the Federal Reserve over the foreign banks was increased. Further, the regulatory burden and the costs of entry by foreign banks into the United States also increased.

38.

What are the major advantages of international expansion to FIs? Explain how each advantage can affect the operating performance of FIs?

First, an FI can benefit from significant risk diversification, especially if the economies of the world are not perfectly integrated, or if different countries allow different banking activities.

Second, an FI may benefit from economies of scale. Third, the returns from new product innovations may be larger if the market is international rather than just domestic. Fourth, the risk and cost of sources of funds both should be reduced. Fifth, FIs should be able to maintain contact with, and thus provide better service to, their international customers. Sixth, an FI may be able to reduce its regulatory burden by selectively finding those countries that have lower regulatory restrictions.

39.

What are the difficulties of expanding globally? How can each of these difficulties create negative effects on the operating performance of FIs?

First, the difficulties of international expansion include the higher cost of information collection and monitoring in many countries. Because the level of customer specific information may not be as readily available as in the U.S., the absolute level of lending risk may be higher. Also, coordinating different regulatory rules and guidelines will increase the cost of regulation.

Second, the political risk of nationalization or expropriation may increase the costs to an FI from the loss of fixed assets to the legal recovery of deposits in U.S. courts from such action. Third, the establishment of foreign offices may have large fixed costs.

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Solutions for End-of-Chapter Questions and Problems: Chapter Twenty-Two 1.

What are derivative contracts? What is the value of derivative contracts to the managers of FIs? Which type of derivative contracts had the highest notional value outstanding among all U.S. banks as of 2015?

Derivatives are financial assets whose value is determined by the value of some underlying asset.

As such, derivative contracts are instruments that provide the opportunity to take some action at a later date based on an agreement to do so at the current time. Although the contracts differ, the price, timing, and extent of the later actions are usually agreed upon at the time the contracts are arranged. Normally, the contract values depend on the activity of the underlying asset.

Derivative contracts have value to managers of FIs because of their ability to help in managing the various types of risk prevalent in the institutions. As of 2015 the largest category of derivatives in use by commercial banks was swaps, followed by futures and forwards, and then options.

2.

What are some of the major differences between futures and forward contracts? How do these contracts differ from spot contracts?

A spot contract is an exchange of cash, or immediate payment, for financial assets, or any other type of assets, at the time the agreement to transact business is made, i.e., at time 0. Futures and forward contracts both are agreements between a buyer and a seller at time 0 to exchange the asset for cash (or some other type of payment) at a later time in the future. The specific grade and quantity of asset is identified at time 0, as is the specific price paid and time the transaction will eventually occur.

One of the differences between futures and forward contracts is that futures contracts are marked to market daily by the exchange and the exchange guarantees the performance of the contract to both parties. Forward contracts are not. This means the future contract’s price is adjusted each day as the futures price for the contract changes. Therefore, actual daily cash settlements occur between the buyer and seller in response to this marking-to-market process. This can be compared to a forward contract, where the whole cash payment from buyer to seller occurs at the end of the contract period. A second difference between futures and forward contracts is that forwards are tailor-made contracts that are negotiated between two parties, while futures contracts are standardized because they are offered by and traded on an exchange. Third, as exchange-traded securities, the exchange itself guarantees the performance of the futures contract. Thus, the risk of default by either party is minimized since the exchange will step in and take over the defaulting counter-party’s position. No such guarantee exists for a forward contract. Finally, delivery of the asset almost always occurs for forward contracts, but seldom occurs for futures contracts. Instead, an offsetting or reverse transaction occurs through the exchange prior to the maturity of the contract.

3.

What is a naive hedge? How does a naive hedge protect an FI from risk?

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A hedge involves protecting the price of or return on an asset from adverse changes in price or return in the market. A naive hedge usually involves the use of a derivative instrument that has the same underlying asset as the asset being hedged. Thus, if a change in the price of the cash asset results in a gain, the same change in market value will cause the derivative instrument to generate a loss that offsets the gain in the cash asset.

4.

An FI holds a 15-year, $10 million par value bond that is priced at 104 with a yield to maturity of 7 percent. The bond has a duration of eight years and the FI plans to sell it after two months. The FI’s market analyst predicts that interest rates will be 8 percent at the time of the desired sale. Because most other analysts are predicting no change in rates, twomonth forward contracts for 15-year bonds are available at 104. The FI would like to hedge against the expected change in interest rates with an appropriate position in a forward contract. What will this position be? Show that if rates rise 1 percent as forecast, the hedge will protect the FI from loss.

The expected change in the spot position is –8 x $10,400,000 x (0.01/1.07) = -$777,570. This would mean a price change from 104 to 96.2243 per $100 face value of bonds. By entering into a two-month forward contract to sell $10,000,000 of 15-year bonds at 104, the FI will have hedged its spot position. If rates rise by 1 percent, and the bond value falls by $777,570, the FI can close out its forward position by receiving 104 for bonds that are now worth 96.2243 per $100 face value. The profit on the forward position will offset the loss in the spot market.

The actual transaction to close the forward contract may involve buying the bonds in the market at 96.2243 and selling the bonds to the counterparty at 104 under the terms of the forward contract. Note that if a futures contract were used, closing the hedge position would involve buying a futures contract through the exchange with the same maturity date and dollar amount as the initial opening hedge contract.

5.

Contrast the position of being short with that of being long in futures contracts.

To be short in futures contracts means that you have agreed to sell the underlying asset at a future time, while being long means that you have agreed to buy the asset at a later time. In each case, the price and the time of the future transaction are agreed upon when the contracts are initially negotiated.

6.

Suppose an FI purchases a Treasury bond futures contract at 95. a. What is the FI’s obligation at the time the futures contract is purchased?

The FI is obligated to take delivery of a $100,000 face value 20-year Treasury bond at a price of $95,000 at some predetermined later date. b. If an FI purchases this contract, in what kind of hedge is it engaged?

This is a long hedge undertaken to protect the FI from falling interest rates.

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c. Assume that the Treasury bond futures price falls to 94. What is the loss or gain?

The FI will lose $1,000 since the FI must pay $95,000 for bonds that have a market value of only $94,000. d. Assume that the Treasury bond futures price rises to 97. Mark to market the position.

In this case the FI gains $2,000 since the FI pays only $95,000 for bonds that have a market value of $97,000.

7.

Long Bank has assets that consist mostly of 30-year mortgages and liabilities that are shortterm demand and time deposits. Will an interest rate futures contract the bank buys add to or subtract from the bank’s risk?

The purchase of an interest rate futures contract will add to the risk of the bank. If rates increase in the market, the value of the bank’s assets will decrease more than the value of the liabilities. In addition, the value of the futures contract also will decrease. Thus, the bank will suffer decreases in value both on and off the balance sheet. If the bank sells the futures contract, the increase in rates would results in the futures position producing a gain that would offset (at least partially) the loss in value on the balance sheet.

8.

In each of the following cases, indicate whether it would be appropriate for an FI to buy or sell a forward contract to hedge the appropriate risk. a. A commercial bank holds three-month CDs in its liability portfolio.

The bank should buy a forward contract to protect against a decrease in interest rates. b. An insurance company plans to buy bonds in two months.

The insurance company should buy a forward contract to protect against a decrease in interest rates. c. A savings bank is going to sell Treasury securities it holds in its investment portfolio next month.

The savings bank should sell a forward contract to protect against an increase in interest rates. d. A U.S. bank lends to a French company. The loan is payable in euros.

The bank should sell euros forward to protect against a decrease in the value of the euro, or an increase in the value of the dollar.

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e. A finance company has assets with a duration of six years and liabilities with a duration of 13 years.

The finance company should buy a forward contract to protect against decreasing interest rates that would cause the value of liabilities to increase more than the value of assets, thus causing a decrease in equity value.

9.

The duration of a 20-year, 8 percent coupon Treasury bond selling at par is 10.292 years.

The bond’s interest is paid semiannually and the bond qualifies for delivery against the Treasury bond futures contract. a. What is the impact on the Treasury bond price if market interest rates increase 50 basis points?

P = -D(R/(1+R/2))$100,000 = -10.292 x (0.005/(1+0.08/2)) x $100,000 = -$4,948.08. c. If you sold a Treasury bond futures contract at 95 and interest rates rose 50 basis points, what would be the change in the value of your futures position? ΔF = - D(R/(1 + R/2))P = - 10.292(0.005/(1 + 0.08/2))$95,000 = - $4,700.67

d. If you purchased the bond at par and sold the futures contract, what would be the net value of your hedge after the increase in interest rates?

Decrease in market value of the bond purchase Gain in value from the sale of futures contract Net gain or loss from hedge 10.

-$4,948.08 $4,700.67 -$247.41

What are the differences between a microhedge and a macrohedge for an FI? Why is it generally more efficient for FIs to employ a macrohedge than a series of microhedges?

A microhedge uses a derivative contract such as a forward or futures contract to hedge the risk exposure of a specific transaction, while a macrohedge is a hedge of the duration gap of the entire balance sheet. FIs that attempt to manage their risk exposure by hedging each balance sheet position will find that hedging is excessively costly, because the use of a series of microhedges ignores the FI’s internal hedges that are already on the balance sheet. That is, if a long-term fixed-rate asset position is exposed to interest rate increases, there may be a matching long-term fixed-rate liability position that also is exposed to interest rate decreases. Putting on two microhedges to reduce the risk exposures of each of these positions fails to recognize that the FI has already hedged much of its risk by taking matched balance sheet positions. The efficiency of the macrohedge is that it focuses only on those mismatched positions that are candidates for off-balance-sheet hedging activities.

11.

What are the reasons why an FI may choose to hedge selectively its portfolio?

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Selective hedging involves an explicit attempt to not minimize the risk on the balance sheet. An FI may choose to hedge selectively in an attempt to improve profit performance by accepting some risk on the balance sheet, or to arbitrage profits between a spot asset’s price movements and the price movements of the futures price. This latter situation often occurs because of differential changes in interest rates caused in part by cross-hedging. For example, an FI manager may generate expectations regarding future interest rates before deciding on a futures position.

As a result, the manager may selectively hedge only a proportion of its balance sheet position.

Alternatively, the FI manager may decide to remain unhedged or even to overhedge by selling more futures than required by the cash position, although regulators may view this as speculative. Thus, the fully hedged position—and the minimum risk portfolio—becomes one of several choices depending, in part, on managerial interest rate expectations, managerial objectives, and the nature of the return-risk trade-off from hedging. Finally, an FI may selectively hedge in an attempt to arbitrage profits between a spot asset’s price movements and movements in a futures price.

12.

Hedge Row Bank has the following balance sheet (in millions): Assets

$150

Total

$150

Liabilities Equity Total

$135 15 $150

The duration of the assets is six years and the duration of the liabilities is four years. The interest rate on both the assets and the liabilities is 10 percent. The bank is expecting interest rates to fall from 10 percent to 9 percent over the next year. a. What is the duration gap for Hedge Row Bank?

DGAP = DA – kDL = 6 – (0.9)(4) = 6 – 3.6 = 2.4 years b. What is the expected change in net worth for Hedge Row Bank if the forecast is accurate? E = -DGAP[R/(1 + R)]A = -2.4(-0.01/1.10)$150m = $3.272 million c. What will be the effect on net worth if interest rates increase 110 basis points? E = -DGAP[R/(1 + R)]A = -2.4(0.011/1.10)$150 = -$3.6 million. d. If the existing interest rate on the liabilities is 6 percent, what will be the effect on net worth of a 1 percent increase in interest rates?

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Solving for the impact on the change in equity under this assumption involves finding the impact of the change in interest rates on each side of the balance sheet, and then determining the difference in these values. The analysis is based on the equation: Expected E = A - L A = -DA[RA/(1 + RA)]A = -6[0.01/1.10]$150m = -$8.1818 million and L = -DL[RL/(1 + RL)]L = -4[0.01/1.06]$135m = -$5.0943 million Therefore, E = A - L = -$8.1818m – (-$5.0943m) = - $3.0875 million 13.

For a given change in interest rates, why is the sensitivity of the price of a Treasury bond futures contract greater than the sensitivity of the price of a Treasury bill futures contract?

The price sensitivity of a futures contract depends on the duration of the asset underlying the contract. In the case of a T-bill contract, the duration is 0.25 years. In the case of a T-bond contract, the duration is much longer.

14.

What is the meaning of the Treasury bond futures price quote 101-130?

A quote of 101 - 130 = $101 13/32 per $100 face value. Since Treasury bond futures contracts are for $100,000 face value, the quoted price is $101,406.25.

15.

What is meant by fully hedging the balance sheet of an FI?

Fully hedging the balance sheet involves using a sufficient number of futures contracts so that any loss (or gain) of net worth on the balance sheet is just offset by the gain (or loss) from the off-balance-sheet use of futures contracts for given changes in interest rates. In this case, the FI reduces its interest rate or other risk exposure to the lowest possible level by selling sufficient futures to offset the interest rate risk exposure of its whole balance sheet or cash positions in each asset and liability.

16.

Tree Row Bank has assets of $150 million, liabilities of $135 million, and equity of $15 million. The asset duration is six years and the duration of the liabilities is four years.

Market interest rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with Eurodollar futures contracts, which currently have a price quote of $96 per $100 face value for the benchmark three-month Eurodollar CD underlying the contract. The current rate on three-month Eurodollar CDs is 4.0 percent and the duration of these contracts is 0.25 years. a. Should the bank go short or long on the futures contracts to establish the correct macrohedge?

The bank should sell futures contracts since an increase in interest rates would cause the value of the equity and the futures contracts to decrease. But the bank could buy back the futures contracts to realize a gain to offset the decreased value of the equity.

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b. Assuming no basis risk, how many contracts are necessary to fully hedge the bank?

The number of contracts to hedge the bank is: NF =

− (DA − kDL )A DF x PF

=

− (6 −(0.9)4)$150m = −1,500 contracts 0.25 x 0.96x$1,000,000

c. Verify that the change in the futures position will offset the change in the cash balance sheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points.

For an increase in rates of 100 basis points, the change in the cash balance sheet position is: E = -DGAP[R/(1 + R)]A = -2.4(0.01/1.10)$150m = -$3,272,727.27.

Since there is no basis risk, [R/(1 + R)] = [RF/(1 + RF)], the change in the value of the $1,000,000 face value futures contract is: R   F = −DF  NF  PF = -0.25 x (-1,500) x 0.96 x $1,000,000 x (0.01/1.10) F 1+RF

= $3,272,727.27

For a decrease in rates of 50 basis points, the change in the cash balance sheet position is: E = -DGAP[R/(1 + R)]A = -2.4(-0.005/1.10)$150m = $1,636,363.64.

The change in the value of the futures contract is: R   F = −DF  NF  PF = -0.25 x (-1,500) x 0.96 x $1,000,000 x (-0.005/1.10) F 1+RF

= -$1,636,363.64

d. If the bank had hedged with Treasury bond futures contracts that had a market value of $95 per $100 of face value, a yield of 8.5295 percent, and a duration of 10.3725 years, how many futures contracts would have been necessary to fully hedge the balance sheet? Assume no basis risk.

If Treasury bond futures contracts are used, the face value of the contract is $100,000, and the number of contracts necessary to hedge the bank is: NF =

− (DA −kDL )A − (6 −(0.9)4)$150m − $360,000,000 = = = − 365.338509contracts 10.3725x $95,000 $985,387.5 DF x PF 7 © 2022

e. What additional issues should be considered by the bank in choosing between Eurodollar or T-bond futures contracts?

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In cases where a large number of Treasury bonds are necessary to hedge the balance sheet with a macrohedge, the FI may need to consider whether a sufficient number of deliverable Treasury bonds are available. The number of Eurodollar contracts necessary to hedge the balance sheet is greater than the number of Treasury bonds. Further, the Eurodollar market is much deeper and the availability of sufficient deliverable securities should be less of a problem.

17.

What is basis risk? What are the sources of basis risk?

Basis risk is the lack of perfect correlation between changes in the yields of the on-balance-sheet assets or liabilities and changes in interest rates on the futures contracts. Basis risk occurs for two reasons. First, the balance sheet asset or liability being hedged is not the same as the underlying security on the futures contract. For instance, an FI may hedge interest rate changes on the FI’s entire balance sheet with T-bond futures contracts written on 20-year maturity bonds with a duration of 9.5 years. The interest rates on the various assets and liabilities on the FI’s balance sheet and the interest rates on 20-year T-bonds do not move in a perfectly correlated (or one-toone) manner. The second source of basis risk comes from the difference in movements in spot rates versus futures rates. Because spot securities (e.g., government bonds) and futures contracts (e.g., on the same bonds) are traded in different markets, the shift in spot rates may differ from the shift in futures rates (i.e., they are not perfectly correlated).

18.

How would your answer for part (b) in problem 16 change if the relationship of the price sensitivity of futures contracts to the price sensitivity of underlying bonds were br = 0.92?

The number of contracts to hedge the bank is: NF =

− (DA − kDL )A D F x PF x br

=

− (6 − (0.9)4)$150m

= −1,630.434783 contracts

0.25 x 0.96x$1,000,000x0.92

The number of contracts necessary to hedge the bank would increase to 1,630.434783 contracts.

19.

Reconsider Tree Row Bank in problem 16 but assume that the cost rate on the liabilities is 6 percent. On-balance-sheet rates are expected to increase by 100 basis points. Further, assume there is basis risk such that rates on three-month Eurodollar CDs are expected to change by 0.10 times the rate change on assets and liabilities. That is, RF = 0.10 x R. a. How many contracts are necessary to fully hedge the bank?

In this case, the bank faces different average interest rates on both sides of the balance sheet.

Further, the yield on the Eurodollar CDs underlying the futures contracts is a third interest rate.

Thus, the hedge also has the effects of basis risk. Determining the number of futures contracts necessary to hedge this balance sheet must consider separately the effect of a change in rates on each side of the balance sheet, and then consider the combined effect on equity. Estimating the 9 © 2022

number of contracts can be determined with the modified general equation:

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Modified Equation Model: F + E = 0 F + A − L = 0   R R RF x L =  − D (N xP )x = −  − D x x A− − D x  L  F F F A (1+ R ) (1+ RL ) (1+ RF )  A  R −DA x (1+ RA NF =

)

RL x A − DL x (1+ R ) x L 

A

DF x PF x

A

R

=

F

(1+ RF ) 0.01 6x x150,000,000 − 4x x135,000,000 1.10 1.06 = −( ) 0.10x0.01 0.25x0.96x1,000,000x 1.04 − ( $8,181,8183.18 −$5,094,339.63 ) = $230.7692308 − $3,087,478.56 = $230.7692308 = − 13,379.07376 contracts 0.01

b. Verify that the change in the futures position will offset the change in the balance sheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points.

For an increase in rates of 100 basis points, E = -[6 x (0.01/1.01) x $150 m – 4 x (0.01/1.06) x $135 m] = -$3,087,478.56.

The change in the value of the futures contract is: R   F = −DF  NF  PF F 1+RF

= -0.25 x (-13,379.07376) x 0.96 x $1,000,000 x (0.10 x 0.01/1.04) = $3,087,478.56 For a decrease in rates of 50 basis points, E = -[6 x (-0.005/1.10) x $150 m – 4 x (-0.005/1.06) x $135 m] = = $1,543,739.28.

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The change in the value of the futures contract is:

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R  F = −DF  NF  PF F 1+RF

= -0.25 x (-13,379.07376) x 0.96 x $1,000,000 x (0.10 x (-0.005)/1.04) = -$1,543,739.28 c.

If the bank had hedged with Treasury bond futures contracts that had a market value of $95 per $100 of face value, a yield to maturity of 8.5295 percent, and a duration of 10.3725 years, how many futures contracts would have been necessary to fully hedge the balance sheet? Assume there is basis risk such that rates on T-bonds are expected to change by 0.75 times the rate change on assets and liabilities. That is, RF = 0.75 x R.

Estimating the number of contracts can be determined with the modified general equation: Modified Equation Model: F+ E = 0 F+ A − L = 0   − DF (N F * PF )* RF = −  − D * R * A − − D * R * L = A (1+ R ) L (1+ R ) (1+ R ) L  A  F R −DA x (1+ RA NF =

A

xA − D x RL xL  L (1+ R ) ) A

R

=

F DFxPFx (1+ RF ) 0.01 0.01 6x x150,000,000 − 4x x135,000,000 1.10 1.06 = −( 0.75x0.01 10.3725x0.95x100,000x 1.085295 − ( $8,181,8183.18 −$5,094,339.63 ) = 6,809.582878 − $3,087,478.56 = 6,809.582878 = − 453.402009 contracts

20.

)

A mutual fund plans to purchase $500,000 of 30-year Treasury bonds in four months.

These bonds have a duration of 12 years and are priced at 96.25 (percent of face value).

The mutual fund is concerned about interest rates changing over the next four months and is considering a hedge with T-bond futures contracts that mature in six months. The T-bond 13 © 2022

futures contracts are selling for 98-24 (32nds) and have a duration of 8.5 years.

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a. If interest rate changes in the spot market exactly match those in the futures market, what type of futures position should the mutual fund create?

The mutual fund needs to buy futures contracts, thus entering into a contract to buy Treasury bonds at 98-24 in four months. The fund manager fears a fall in interest rates (meaning the Tbond’s price will increase) and by buying a futures contract, the profit from a fall in rates will offset a loss in the spot market from having to pay more for the securities. b. How many contracts should be used?

The number of contracts can be determined by using the following equation: D  P 12  $481,250 N = = = 6.88 contracts F D F  PF 8.5  $98,750 c. If the implied rate on the deliverable bond in the futures market moves 12 percent more than the change in the discounted spot rate (i.e., br = 1.12), how many futures contracts should be used to hedge the portfolio?

In this case the value of br = 1.12, and the number of contracts is 6.88/1.12 = 6.14 contracts. d. What causes futures contracts to have a different price sensitivity than the assets in the spot markets?

One reason for the difference in price sensitivity is that the futures contracts and the cash assets are traded in different markets. Because spot securities (e.g., government bonds) and futures contracts (e.g., on the same bonds) are traded in different markets, the shift in spot rates may differ from the shift in futures rates (i.e., they are not perfectly correlated). A second reason for the difference is that the balance sheet asset or liability being hedged is not the same as the underlying security on the futures contract. For instance, an FI may hedge interest rate changes on the FI’s entire balance sheet with T-bond futures contracts written on 20-year maturity bonds with a duration of 9.5 years. The interest rates on the various assets and liabilities on the FI’s balance sheet and the interest rates on 20-year T-bonds do not move in a perfectly correlated (or one-to-one) manner.

21.

Consider the following balance sheet (in millions) for an FI: Assets Duration = 10 years

$950

Liabilities Duration = 2 years Equity

a. What is the FI's duration gap?

The duration gap is 10 - (860/950)(2) = 8.19 years.

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$860 90

b. What is the FI's interest rate risk exposure?

The FI is exposed to interest rate increases. The market value of equity will decrease if interest rates increase. c. How can the FI use futures and forward contracts to put on a macrohedge?

The FI can hedge its interest rate risk by selling future or forward contracts. d. What is the impact on the FI's equity value if the relative change in interest rates is an increase of 1 percent? That is, R/(1+R) = 0.01. E = -8.19(950,000)(0.01) = -$77,800 e. Suppose that the FI macrohedges using Treasury bond futures that are currently priced at 96. What is the impact on the FI's futures position if the relative change in all interest rates is an increase of 1 percent? That is, R/(1+R) = 0.01. Assume that the deliverable Treasury bond has a duration of nine years. F = -9(96,000)(0.01) = -$8,640 per futures contract. Since the macrohedge is a short hedge, this will be a profit of $8,640 per contract. f. If the FI wants to macrohedge, how many Treasury bond futures contracts does it need?

To macrohedge, the Treasury bond futures position should yield a profit equal to the loss in equity value (for any given increase in interest rates). Thus, the number of futures contracts must be sufficient to offset the $77,800 loss in equity value. This will necessitate the sale of $77,800/8,640 = 9.005 contracts.

22.

Refer again to problem 21. How does consideration of basis risk change your answers to problem 21?

In problem 21, we assumed that basis risk did not exist. That allowed us to assert that the percentage change in interest rates (R/(1+R)) would be the same for both the futures and the underlying cash positions. If there is basis risk, then (R/(1+R)) is not necessarily equal to (Rf/(1+Rf)). If the FI wants to fully hedge its interest rate risk exposure in an environment with basis risk, the required number of futures contracts must reflect the disparity in volatilities between the futures and cash markets. a. Compute the number of futures contracts required to construct a macrohedge if [Rf/(1+Rf) / R/(1+R)] = br = 0.90 If br = 0.9, then: N = − ( DA - k DL ) A = − 8.19(950,000) = − 10 contracts 16 © 2022

f

DF  PF  br

9  96,000  0.90

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b. Explain what is meant by br = 0.90.

When br = 0.90, this means that the implied rate on the deliverable bond in the futures market moves by 0.9 percent for every 1 percent change in discounted spot rates (i.e., R/(1+R) = 0.9). c. If br = 0.90, what information does this provide on the number of futures contracts needed to construct a macrohedge?

If br = 0.9 then the percentage change in cash market rates exceeds the percentage change in futures market rates. Since futures prices are less sensitive to interest rate shocks than cash prices, the FI must use more futures contracts to generate sufficient cash flows to offset the cash flows on its balance sheet position.

23.

An FI is planning to hedge its $100 million bond instruments with a hedge using Eurodollar interest rate futures. How would the FI estimate br = [Rf/(1+Rf) / R/(1+R)] to determine the exact number of Eurodollar futures contracts to hedge?

One way of estimating br (or the ratio of changes in yields of futures to the yields on the underlying security) involves regressing the changes in bond yields against Eurodollar futures.

The estimated slope of the line is the estimate of basis risk that is used to provide the exact number of contracts needed to hedge. Note that historical estimation of the basis risk is not a guarantee that it will remain the same in the future.

24.

Village Bank has $240 million worth of assets with a duration of 14 years and liabilities worth $210 million with a duration of 4 years. In the interest of hedging interest rate risk, Village Bank is contemplating a macrohedge with interest rate T-bond futures contracts now selling for 102-21 (32nds). The T-bond underlying the futures contract has a duration of nine years. If the spot and futures interest rates move together, how many futures contracts must Village Bank sell to fully hedge the balance sheet?

NF =

25.

− (DA − kDL ) A − (14 −(0.875)4)$240m = = − 2728contracts 9 x $102,656 DF x PF

Assume an FI has assets of $250 million and liabilities of $200 million. The duration of the assets is six years and the duration of the liabilities is three years. The price of the futures contract is $115,000 and its duration is 5.5 years. a. What number of futures contracts is needed to construct a perfect hedge if br = 1.10?

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Nf =

− (DA - k DL)A −[6 −(0.8x3)]$250,000,000 − $900,000,000 = = = −1,293.57contracts (Df x Pf xbr) 5.5x$115,000x1.10 $695,750

b. If Rf/(1+Rf) = 0.0990, what is the expected R/(1+R)? br = (Rf/(1+Rf))/(R/(1 + R)) => R/(1 + R) = (Rf/(1+Rf))/br = 0.0990/1.10 = 0.09 26.

Suppose an FI purchases a $1 million 91-day (360-day year) Eurodollar futures contract trading at 98.50. a. If the contract is reversed two days later by selling the contract at 98.60, what is the net profit?

Profit = (0.9860 - 0.9850) x 91/360 x 1,000,000 = $252.78 b. What is the loss or gain if the price at reversal is 98.40?

Loss = (0.9840 - 0.9850) x 91/360 x 1,000,000 = -$252.78 27.

Dudley Hill Bank has the following balance sheet: Assets (in millions) A $425

$425 Further,

Liabilities and Equity (in millions) L $380 E 45 . $425

DA = 6 years DL = 2 years

The interest rate on both the assets and the liabilities is 8 percent. The bank manager receives information from an economic forecasting unit that interest rates are expected to rise from 8 to 9 percent over the next six months. a. Calculate the potential loss to Dudley Hill’s net worth (E) if the forecast of rising rates proves to be true. E = −[DA − kDL ]A R 1+R ,

so that E = −[6 − 380 (2)]425m 0.01 = -$16,574,074 425

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The bank could expect to lose $16,574,074 in shareholders’ net worth should the interest rate forecast be accurate. Since the FI started with a net worth of $45 million, the loss of $16,574,074 is almost 37 percent of its initial net worth position. b. Suppose the manager of Dudley Hill Bank wants to hedge this interest rate risk with Tbond futures contracts. The current futures price quote is $122.03125 per $100 of face value for the benchmark 20-year, and the minimum contract size is $100,000, so PF equals $122,031.25. The duration of the deliverable bond is 14.5 years. That is, D F = 14.5 years. How many futures contracts will be needed? Should the manager buy or sell these contracts? Assume no basis risk.

From the equation for NF, we can now solve for the correct number of futures positions to sell (NF).

NF =

[DA −kDL ]A DFPF

NF =

[6−(380/ 425)2]425m = 1,011.611992 14.5122,031.25

Since the bank is exposed to interest rate increases, it should sell these contracts. c. Verify that selling T-bond futures contracts will indeed hedge the FI against a sudden increase in interest rates from 8 to 9 percent, a 1 percent, interest rate shock.

On-Balance-Sheet: As shown above, when interest rates rise by 1 percent, the FI loses $16,574,074 in net worth (∆E) on the balance sheet: E = −[6 − 380 (2)]425m 0.01 = -$16,574,074 425

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Off-Balance-Sheet: Since there is no basis risk, [R/(1 + R)] = [RF/(1 + RF)], and the change in the value of the futures position is: ΔF = −14.5(−1,011.611992) 122,031.25  0.01 1.08) = $16,574,074 The value of the off-balance-sheet futures position (∆F) falls by $16,574,074 when the FI sells 1,011.61192 futures contracts in the T-bond futures market. Such a fall in value of the futures contracts means a positive cash flow to the futures seller as the buyer compensates the seller for a lower futures price through the marking-to-market process. d. If the bank had hedged with Eurodollar futures contracts that had a market value of $98 per $100 of face value, how many futures contracts would have been necessary to fully hedge the balance sheet?

If futures contracts are used, the duration of the underlying asset is 0.25 years, the face value of the contract is $1,000,000, and the number of contracts necessary to hedge the bank is: NF =

− (DA −kDL )A − (6 −(380 / 425)2)$425m − $1,790,000,000 = = =− 7,306.122449contracts 0.25x$980,000 $245,000 D F x PF 20 © 2022

e. How would your answer for part (b) change if the relationship of the price sensitivity of futures contracts to the price sensitivity of underlying bonds were br = 1.15?

The number of contracts to hedge the bank is: N = F

− (DA − kDL )A DF x PF x br

=

− (6 − (0.9)4)$150m

= − 879.6626015 contracts

14.5 x $122,031.25x1.15

The number of contracts necessary to hedge the bank would decrease to 879.6626015 contracts. f. Verify that selling T-bond futures contracts will indeed hedge the FI against a sudden increase in interest rates from 8 to 9 percent, a 1 percent, interest rate shock. Assume the yield on the T-bond underlying the futures contract is 8.45 percent as the bank enters the hedge and rates rise by 1.154792 percent.

On-Balance-Sheet: As shown above, when interest rates rise by 1 percent, the FI loses $16,574,074 in net worth (∆E) on the balance sheet: E = −[6 − 380 (2)]425m 0.01 = -$16,574,074 425

1.08

Off-Balance-Sheet: When interest rates rise by 1.154792 percent on the T-bond underlying the futures contract, the change in the value of the futures position is: ΔF = −14.5(−879.6626015) 122,031.25  0.01154792 1.0845 ) = $16,574,079 28.

An FI has an asset investment in euros. The FI expects the exchange rate of $/€ to increase by the maturity of the asset. a. Is the dollar appreciating or depreciating against the euro?

The dollar is depreciating as it will take more dollars per € in the future. b. To fully hedge the investment, should the FI buy or sell euro futures contracts?

The FI should buy € futures. c. If there is perfect correlation between changes in the spot and futures contracts, how should the FI determine the number of contracts necessary to hedge the investment fully?

A sufficient number of futures contracts should be purchased so that a profit (loss) on the futures position will just offset a loss (profit) on the asset portfolio. If there is perfect correlation between the spot and futures prices, the number of futures contracts can be determined by dividing the value of the foreign currency asset portfolio by the foreign currency size of each 21 © 2022

contract. If the spot and futures prices are not perfectly correlated, the value of the long asset

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position at maturity must be adjusted by the hedge ratio before dividing by the size of the futures contract.

29.

What is meant by tailing the hedge? What factors allow an FI manager to tail the hedge effectively?

Gains from futures contract positions typically are received throughout the life of the hedge from the process of marking to market the futures position. These gains can be reinvested to generate interest income cash flows that reduce the number of futures contracts needed to hedge an original cash position. Higher short-term interest rates and less uncertainty in the pattern of expected cash flows from marking to market the futures position will increase the effectiveness of this process.

30.

What does the hedge ratio measure? Under what conditions is this ratio valuable in determining the number of futures contracts necessary to fully hedge an investment in another currency?

The hedge ratio measures the relative sensitivity of futures prices to changes in the spot exchange rates. This ratio is particularly helpful when the changes in futures prices are not perfectly correlated with the changes in the spot exchange rates.

31.

What technique is commonly used to estimate the hedge ratio? What statistical measure is an indicator of the confidence that should be placed in the estimated hedge ratio? What is the interpretation if the estimated hedge ratio is greater than 1? Less than 1?

A common method to estimate the hedge ratio is to regress recent changes in spot prices on recent changes in futures prices. The estimated slope coefficient () from the regression equation is the estimated hedge ratio or measure of sensitivity between spot prices and futures prices. A value of  greater than one means that changes in spot prices are greater than changes in futures prices, and the number of futures contracts must be increased accordingly. A value of  less than one means that changes in spot prices are less than changes in futures prices, and the number of futures contracts can be decreased accordingly. The degree of confidence is measured by the value of R2 for the regression. If the R2 from the regression equation is equal to one, this implies perfect correlation between the two price variables.

32.

An FI has assets denominated in British pounds of $125 million and pound liabilities of $100 million. The exchange rate of dollars for pounds is currently $1.60/£. a. What is the FI's net exposure?

The net exposure is $125 million - $100 million = $25 million. b. Is the FI exposed to a dollar appreciation or depreciation?

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The FI is exposed to a dollar appreciation, or a decline in the pound relative to the dollar. c. How can the FI use futures or forward contracts to hedge its FX rate risk?

The FI can hedge its FX rate risk by selling forward or futures contracts in pounds, assuming the contracts are quoted as $/£, that is, in direct quote terms in the U.S. d. If a futures contract is currently trading at $1.55/£, what is the number of futures contracts that must be utilized to fully hedge the FI's currency risk exposure? Assume the contract size on the British pound futures contract is £62,500.

Assuming that the contract size for British pounds is £62,500, the FI must sell Nf = ($25 million/1.55)/£62,500 = 258 pound sterling futures contracts. e. If the British pound exchange rate falls from $1.60/£ to $1.50/£, what will be the impact on the FI's cash position?

The cash position will experience a loss if the pound depreciates in terms of the U.S. dollar. The loss would be equal to (($25 million/$1.60) x 1.50) - $25 million = $23,437,500 - $25 million = -$1,562,500. f. If the British pound futures exchange rate falls from $1.55/£ to $1.45/£, what will be the impact on the FI's futures position?

The gain on the short futures hedge is: NF x £62,500 x Ft = -258(£62,500)($1.45 - $1.55) = +$1,612,500 g. Using the information in parts (e) and (f), what can you conclude about basis risk?

In cases where basis risk occurs, a perfect hedge is not possible.

33.

An FI is planning to hedge its one-year, 100 million Swiss franc (SF)-denominated loan against exchange rate risk. The current spot rate is $0.60/SF. A 1-year SF futures contract is currently trading at $0.58/SF. SF futures are sold in standardized units of SF125,000. a. Should the FI be worried about the SF appreciating or depreciating?

The FI should be worried about the SF depreciation because it will provide fewer dollars per SF. b. Should the FI buy or sell futures to hedge against exchange rate risk exposure?

The FI should sell SF futures contracts to hedge this exposure.

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c. How many futures contracts should the FI buy or sell if a regression of past changes in the spot exchange rates on changes in future exchange rates generates an estimated slope of 1.4?

Nf = (Long asset position x h)/(Futures contract size) = SF100m x 1.4/SF125,000 = 1,120 contracts d. Show exactly how the FI is hedged if it repatriates its principal of SF100 million at year end, the spot exchange rate of SF at year-end is $0.55/SF, and the forward exchange rate is $0.5443/SF. The original loan in dollars = SF100 x $0.60 = $60 million, and the loan value in dollars at year end = SF100 x $0.55 = $55 million. The balance sheet has decreased in value by $5,000,000.

The gain from hedge = ($0.58 - $0.5443) x SF125,000 x 1,120 = $4,998,000. The net loss is reduced to just $2,000 by hedging the FX rate risk.

34.

A U.S. FI has a long position in £75,500,000 assets funded with U.S. dollar denominated liabilities. The FI manager is concerned about the £ appreciating relative to the dollar and is considering a hedge of this FX risk using £ futures contracts. The manager has regressed recent changes in spot £ exchange rate on changes in £ futures contracts. The resulting regression equation is: ΔSt = 0.09 + 1.5ΔFt. Further, the Cov(ΔSt, ΔFt) was found to be 0.06844, σΔSt = 0.3234, and σΔFt = 0.2279. Pound futures contracts are sold in standardized units of £62,500. Calculate the number of futures contracts needed to hedge the risk of the £75,500,000 asset. Calculate the hedging effectiveness of these futures contracts. To what extent can the manager have confidence that the correct hedge ratio is being used to hedge the FI’s FX risk position?

Nf =

£75,500,000 x 1.5

= 1,812 contracts

£62,500

R2 = [0.06844/(0.3234 x 0.2279)]2 = 86.23% The manager can have high confidence that the correct hedge ratio is being used to hedge the FI’s FX risk position.

35.

An FI has made a loan commitment of SF10 million that is likely to be taken down in six months. The current spot rate is $0.60/SF. a. Is the FI exposed to the dollar’s depreciating or appreciating relative to the SF? Why?

The FI is exposed to the dollar depreciating, because it would require more dollars to purchase the SF10 million if the loan is drawn down as expected. b. If the spot rate six months from today is $0.64/SF, what amount of dollars is needed if the loan is taken down and the FI is unhedged?

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The FI needs $0.64 x SF10 million = $6.4 million to make the SF-denominated loan. c. If the FI decides to hedge using SF futures, should it buy or sell SF futures?

The FI should buy SF futures if it decides to hedge against the depreciation of the dollar. d. A six-month SF futures contract is available for $0.61/SF. What net amount would be needed to fund the loan at the end of six months if the FI had hedged using the SF10 million futures contract? Assume that futures prices are equal to spot prices at the time of payment (i.e., at maturity).

If it has hedged using futures, the FI will gain ($0.64 - $0.61) x SF10 million = $300,000 on its futures position. Thus, the net payment will be $6.1 million.

36.

A U.S. FI has assets denominated in Swiss francs (SF) of 75 million and liabilities of 125 million. The spot rate is $0.6667/SF and one-year futures are available for $0.6579/SF. a. What is the FI’s net exposure?

The net exposure is –SF50 million (SF75 million – SF125 million). b. Is the FI exposed to dollar appreciation or depreciation relative to the SF? The FI is exposed to depreciation of the dollar. If the dollar weakens, the FI will need to pay more dollars to cover its SF liabilities than it will receive for its assets. c. If the SF spot rate changes from $0.6667/SF to $0.6897/SF, how will this impact the FI’s currency exposure? Assume no hedging.

The loss would be SF50,000,000($0.6667 - $0.6897) = -$1,150,000. d. What is the number of futures contracts necessary to fully hedge the currency risk exposure of the FI? The contract size is SF125,000 per contract.

The number of contracts = SF50,000,000/SF125,000 = 400 contracts. e. If the SF futures exchange rate falls from $0.6579/SF to $0.6349/SF, what will be the impact on the FI’s futures position?

The loss on the futures position would be 400 contracts x SF125,000 x ($0.6349 - $0.6579) = -$1,150,000.

37.

What is a credit forward? How is it structured?

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A credit forward is a forward agreement that hedges against an increase in default risk on a loan (a decline in the credit quality of a borrower) after the loan rate is determined and the loan is issued. The credit forward specifies a credit spread on a benchmark bond issued by a bank borrower. The credit spread measures a risk premium above the risk free rate to compensate for default risk.

38.

What is the gain on the purchase of a $20 million credit forward contract with a modified duration of seven years if the credit spread between a benchmark Treasury bond and a borrowing firm’s debt decreases by 50 basis points?

The gain would be (ΦT - ΦF) x MD x $20 million = 0.005 x 7 x $20 million = $700,000.

39.

How is selling a credit forward similar to buying a put option?

After the loan is made, the FI sells a credit forward. If the credit risk of the borrower decreases sufficiently that the spread over the benchmark bond increases, the forward seller (the FI) will realize a gain at the maturity of the forward contract that will offset the decrease in value of the loan. Thus, the FI benefits as the credit risk of the borrower decreases. This is the exact same situation as a put option buyer when the stock price goes down.

If the credit risk improves, the lender FI will pay the forward buyer because the benchmark spread will have decreased. However, since the spread can only decrease to zero, the FI has limited loss exposure. This is similar to paying a premium on a put option.

40.

A property-casualty (PC) insurance company purchased catastrophe futures contracts to hedge against losses during the hurricane season. At the time of purchase, the market expected a loss ratio of 0.75. After processing claims from a severe hurricane, the PC company actually incurred a loss ratio of 1.35. What amount of profit did the PC company make on each $25,000 futures contract?

The payoff = actual loss ratio x $25,000 = 1.35 x $25,000 = $33,750.

41.

What is the primary goal of regulators in regard to the use of futures by FIs? What guidelines have regulators given banks for trading in futures and forwards?

Regulators of banks have encouraged the use of futures for hedging and have discouraged the use of futures for speculation. Banks are required to (1) establish internal guidelines regarding hedging activity, (2) establish trading limits, and (3) disclose large contract positions that materially affect bank risk to shareholders and outside investors. Finally, FASB requires all firms to reflect the mark to market value of their derivative positions in their financial statements.

Because of their lack of regulation and because of the significant role that over-the-counter (OTC) derivative securities played in causing the financial crisis, in the summer of 2009 the Obama administration proposed a plan to regulate OTC derivatives. Part of the Wall Street 27 © 2022

Reform and Consumer Protection Act is the Volker Rule which prohibits U.S. depository institutions (DIs) from engaging in proprietary trading (i.e., trading as a principal for the trading account of the bank). This includes any transaction to purchase or sell derivatives. Thus, only the investment banking arm of the business is allowed to conduct such trading. The Volcker Rule was implemented in April 2014 and banks had until July 21, 2015 to be in compliance. The result has been a reduction in derivative securities held off-balance-sheet by these financial institutions. As noted in the introduction, the use of derivatives by commercial banks has dropped from $249.3 trillion in June 2011 to $202.6 trillion in 2015.

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Integrated Mini Case: HEDGING INTEREST RATE RISK WITH FUTURES CONTRACTS Use the following December 31, 2018 market value balance sheet for Bank One to answer the questions below.

Assets (in thousands of $s) T-bills T-bonds Loans

Value Duration $1,500 0.75 4,250 9.50 15,500 12.50

Liabilities/Equity (in thousands of $s) NOW accounts CDs Federal funds Equity

Value Duration $ 6,250 0.50 7,500 7.55 5,500 0.10 2,000

The bank’s manager thinks rates will increase by 0.50 percent in the next 3 months. To hedge this interest rate risk the manager will use June T-bond futures contracts. The T-bonds underlying the futures contracts have a maturity = 15 years, a duration = 14.25 years, and a price = 108-10 or $108,312.50. Assume that interest rate changes in the futures market relative to the cash market are such that br = 0.885.

1. Calculate the leverage adjusted duration gap (DGAP) for Bank One. DA = [(1,500/21,250)(0.75) + (4,250/21,250)(9.50) + (15,500/21,250)(12.50)] = 11.07058824 years DL = [(6,250/19,250)(0.50) + (7,500/19,250)(7.55) + (5,500/19,250)(0.10)] = 3.13246753 years DGAP = 11.07058824 – (19,250/21,250)(3.13246753) = 8.2329 years 2. Using the DGAP model, if interest rates on assets and liabilities increase such that RA/(1 + RA) = RL/(1 +RL) = 0.0075, calculate the change in the value of assets and liabilities and the new value of the assets and liabilities for Bank One. ∆A = -11.07058824 x 21,250,000 x 0.0075 = -$1,764,375 => New asset value = $21,250,000 -$1,764,375 = $19,485,625 ∆L = -3.13246753 x 19,250,000 x 0.0075 = -$452,250 => New liabilities value = $19,250,000 - $452,250 = $18,797,750 3. Calculate the change in the market value of equity for Bank One if rates increase such that R/(1 +R) = 0.0075. ∆E = -8.2329 x 21,250,000 x 0.0075 = -$1,312,125 => New equity value = $2,000,000 - $1,312,125 = $687,875 4. Calculate the correct number of futures contracts needed to hedge the bank’s interest rate risk (do not round to the nearest whole contract). Make sure you specify whether you should enter the hedge with a short or long futures position.

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[11.07058935−((19,250 / 21,250)x3.13246753)]$21,250,000 =128.0787946contracts 14.25x$108,312.50x0.885 Since DGAP > 0, if interest rates increase, then MVE decreases. So, short futures contracts.

Nf =

5. Calculate the change in the bank’s market value of equity and the change in the value of the T-bond futures position for the bank if interest rates increase by 0.55 percent from the current rate of 6 percent on the T-bonds and increase 0.65 percent from the current rate of 8 percent on the balance sheet assets and liabilities. ∆E = -8.2329 x 21,250,000 x (0.0065/1.08) = -$1,052,940 ∆F = -14.25 x -128.0785 x 108,312.50 x (0.0055/1.06) = $1,025,717

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Solutions to End-of-Chapter Questions and Problems: Chapter Twenty-Three 1.

How does using options differ from using forward or futures contracts?

Both options and futures contracts are useful in managing risk. Other than the pure mechanics, the primary difference between these contracts lies in the requirement of what must be done on or before maturity. Futures and forward contracts require that the buyer or seller of the contracts must execute some transaction. The buyer of an option has the choice to execute the option or to let it expire without execution. The writer of an option must perform a transaction only if the buyer chooses to execute the option.

2.

What is a call option?

A call option gives the purchaser the right (but not the obligation) to buy the underlying security at a prespecified exercise or strike price on or before a specified maturity date.

3.

What must happen to interest rates for the purchaser of a call option on a bond to make money? How does the writer of the call option make money?

A call option on a bond allows the owner to buy a bond at a specific price. For the owner of the option to make money, he/she should be able to immediately sell the bond at a higher price. Thus, for the bond price to increase, interest rates must decrease between the time the option is purchased and the time it is executed. The writer of the call option makes a premium from the sale of the option. If the option is not exercised, the writer maximizes profit in the amount of the premium. If the option is exercised, the writer stands to lose a portion or the entire premium and may lose additional money if the price on the underlying asset moves sufficiently far.

4.

What is a put option?

A put option is a contract that gives the owner the right (but not the obligation) to sell the underlying asset to the writer of the option at the agreed exercise price on or before a specified maturity date.

5.

What must happen to interest rates for the purchaser of a put option on a bond to make money? How does the writer of the put option make money?

The put option on a bond allows the owner to sell a bond at a specific price. For the owner of the option to make money, he/she should be able to buy the bond at a lower price immediately prior to exercising the option. Thus, for the bond price to decrease, interest rates must increase between the time the option is purchased and the time it is executed. The writer of the put option makes a premium from the sale of the option. If the option is not exercised, the writer maximizes profit in the amount of the premium. If the option is exercised, the writer stands to lose a portion or the entire premium, and may lose additional money if the price on the underlying asset moves sufficiently far.

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6.

Consider the following: a. What are the two ways to use call and put options on T-bonds to generate positive cash flows when interest rates decline? Verify your answer with a diagram.

The FI can either (a) buy a call option or (b) sell a put option on interest rate instruments, such as T-bonds, to generate positive cash flows in the event that interest rates decline. In the case of a call option, positive cash flows will increase as long as interest rates continue to decrease. See Figure 23-1 in the text as an example of positive cash flows minus the premium paid for the option. Although not labeled in this diagram, interest rates are decreasing as you move from left to right on the x-axis. Thus, bond prices are increasing.

The sale of a put option generates positive cash flows from the premium received. Figure 23-4 shows that the profit will decrease as the price of the bond falls. Of course, this can only happen if interest rates are increasing. Again, although not labeled in this diagram, interest rates are increasing as you move from right to left on the x-axis. b. Under what balance sheet conditions would an FI use options on T-bonds to hedge its assets and/or liabilities against interest rate declines?

An FI would use call options on T-bonds to hedge an underlying cash position that decreases in value as interest rates decline. This would be true if, in the case of a macrohedge, the FI's duration gap is negative and the repricing gap is positive. In the case of a microhedge, the FI can hedge a single fixed-rate liability against interest rate declines. c. Is it more appropriate for FIs to hedge against a decline in interest rates with long calls or short puts?

An FI is better off purchasing calls as opposed to writing puts for two reasons. First, regulatory restrictions limit an FI's ability to write naked short options. Second, since the potential positive cash inflow on the short put option is limited to the size of the put premium, there may be insufficient cash inflows in the event of interest rate declines to offset losses in the underlying cash position.

7.

In each of the following cases, identify what risk the manager of an FI faces and whether the risk should be hedged by buying a put or a call option. a. A commercial bank holds three-month CDs in its liability portfolio.

The bank faces the risk that interest rates will decrease. The bank should buy a call option. If rates fall, the CDs will rise in value resulting in a loss in equity value. But, the decrease in interest rates also raises the price of the security underlying the call option.

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Thus, the bank can gain from the option exercise, buying the underlying security at the exercise price and then selling the underlying security at a higher, market price. This gain will offset the loss in value from the increase in the value of the CDs the bank experiences in the spot market. b. An insurance company plans to buy bonds in two months.

The insurance company (IC) is concerned that interest rates will fall, and thus the price of the bonds will rise. The IC should buy call options on bonds. As rates fall, the underlying bond prices increase, but can be bought for less than the market price by exercising the call option. The bonds purchased with the options can be sold immediately for a gain that can be applied against the increase in the price of the bonds bought by the IC in the spot market and held on the balance sheet. Alternatively, the bonds bought through the exercise of the call option can be kept and placed in the IC’s portfolio if they are the desired type of asset. c. A savings bank plans to sell Treasury securities it holds in its investment portfolio next month.

The savings bank will incur a loss on the sale if rates rise and the value of the Treasury securities falls. The thrift should buy a put option on Treasury securities that allows the sale of the bonds at or near the current price. d. A U.S. bank lends to a French company with the loan payable in euros.

The U.S. bank will incur a loss on the loan if the dollar appreciates (euros depreciate).

Thus, the bank should buy a put to sell euros at or near the current exchange rate. e. A mutual fund plans to sell its holding of stock in a British company.

The mutual fund will incur a loss on the sale if the dollar appreciates (£s depreciate).

Thus, the fund should buy a put to sell £s at or near the current exchange rate. f. A finance company has assets with a duration of six years and liabilities with a duration of 13 years.

The FI is concerned that interest rates will fall, causing the value of the liabilities to rise more than the value of the assets which would cause the value of the equity to decrease.

Thus, the finance company should buy a call option on bonds.

8.

Consider an FI that wishes to use bond options to hedge the interest rate risk in its bond portfolio. a. How does writing call options hedge the risk when interest rates decrease?

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In the case where the FI is long in the bonds on the balance sheet, writing a call option will provide extra cash flow in the form of a premium. But, falling interest rates will cause the value of the bond to increase, and eventually the option will be exercised at a loss to the writer. However, the loss is offset by the increase in value of the long bond.

Thus, the initial goal of maintaining the interest rate return on the long bond can be realized. b. Will writing call options fully hedge the risk when interest rates increase?

Explain.

Writing call options provides a premium that can be used to offset losses in the bond portfolio, caused by rising rates, up to the amount of the premium. Any additional losses beyond the value of the option premium are not protected. c. How does buying put options reduce the losses on the bond portfolio when interest rates rise?

When interest rates increase, the value of the bond portfolio falls. But the put option allows for the sale of the bonds at or near the original price. Thus, the profit potential from the exercise of the put option increases as interest rates continue to increase, although it is tempered by the amount of premium that was paid for the put option. d. Diagram the purchase of a bond call option against the combination of a bond investment and the purchase of a bond put option.

The profit of a bond call option is given in Figure 23-1. If the price of the bond falls below the exercise price, the purchaser of the call loses the premium. As the price of the bond increases beyond the exercise price, the purchaser recovers the premium and then realizes a net profit. Figures 23-7 and 23-8 give the individual and net profit of holding a bond long and the purchase of a put option. The put option produces a profit if bond prices drop. This profit will offset the loss on the long bond caused by the decrease in the bond value. If bond prices increase, the option will not be exercised and the investor will realize a gain from the increase in the bonds value. Thus, the call option or the combination of long bond and put option give the same results.

9.

What are the regulatory reasons why FIs seldom write options?

Regulators view writing options, especially naked options that do not identifiably hedge an underlying asset or liability position, to be risky because of the large loss potential.

Indeed, bank regulators prohibit banks from writing puts or calls in certain areas of risk management.

10. What are the problems of using the Black-Scholes option pricing model to value bond options? What is meant by the term pull-to-par?

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First, the Black-Scholes model assumes unrealistically that short-term interest rates are constant, which they generally are not. Second, the model assumes that the variance of returns on the underlying asset is constant over time. In fact, the variance may increase in the initial life of a bond, but it must decrease during the final stages of the bond’s life because the bond must trade at par at maturity. The decrease in variance of returns over the final portion of a bond’s life is called the pull-to-par.

11. An FI has purchased a two-year, $1,000 par value zero-coupon bond for $867.43.

The FI will hold the bond to maturity unless it needs to sell the bond at the end of one year for liquidity purposes. The current one-year interest rate is 7 percent and the one-year rate in one year is forecast to be either 8.04 percent or 7.44 percent with equal likelihood. The FI wishes to buy a put option to protect itself against a capital loss if the bond needs to be sold in one year. a. What is the yield on the bond at the time of purchase?

PV0 = FVxPVIFn=2,i=? => $867.43 = $1,000 x PVIFn=2,i=? => i = 7.37 percent b. What is the market-determined, implied one-year rate one year before maturity?

E(r1) = (0.5 x 8.04 percent) + (0.5 x 7.44 percent) = 7.74 percent c. What is the expected sale price if the bond has to be sold at the end of one year?

E(P1) = $1,000/(1.0774) = $928.16 d. Diagram the bond prices over the two-year horizon.

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Binomial Model of Bond Prices Problem 25-11.d $1,000

$925.58

0.25 0.25

$867.43

$1,000

0.5 0.5 0.25

$930.75

0

0.25 $1,000

1

2

Time in Years

e. If the FI buys a put option with an exercise price equal to your answer in part (c), what will be its value at the end of one year?

Put Option Exercise $928.16 $928.16

Value of Put Option = $2.58 = $0.00

Bond Price - $925.58 - $930.75

Probability x 0.5 x 0.5 Total value

Weighted Value = $1.29 = $0.00 = $1.29

f. What should be the premium on the put option today?

PV = $1.29/1.07 = $1.2056 g. Diagram the value for the put option on the two-year, zero-coupon bond.

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Binomial Model of Bond Prices Problem 25-11.g $0=Max(0,0) Max[928.16-925.58,0]=$2.58 0.25 0.25 $1.2056

0.5

$0=Max(0,0)

0.5 0.25 0.25

Max[928.16-930.75,0]=0.0 $0=Max(0,0)

0

1

2

Time in Years

h. What would have been the premium on the option if the one-year interest rates at the end of one year were expected to be 8.14 percent and 7.34 percent?

The bond prices for the respective interest rates are $924.73 and $931.62. The expected one-year rate and the expected one-year bond price are the same. Further, the call price of the option is the same.

Put Option Exercise $928.16 $928.16

Value of Put Option = $3.43 = $0.00

Bond Price - $924.73 - $931.62

Probability x 0.5 x 0.5 Total value

Weighted Value = $1.716 = $0.000 = $1.716

PV = $1.716/1.07 = $1.60 12. A pension fund manager anticipates the purchase of a 20-year, 8 percent coupon Treasury bond at the end of two years. Interest rates are assumed to change only once every year at year-end, with an equal probability of a 1 percent increase or a 1 percent decrease. The Treasury bond, when purchased in two years, will pay interest semiannually. Currently, the Treasury bond is selling at par. a. What is the pension fund manager's interest rate risk exposure?

The pension fund manager is exposed to interest rate declines (price increases).

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b. How can the pension fund manager use options to hedge this interest rate risk exposure?

This interest rate risk exposure can be hedged by buying call options on either financial securities or financial futures. c. What prices are possible on the 20-year T-bonds at the end of year 1 and year 2?

Currently, the bond is priced at par, $1,000 per $1,000 face value. At the end of the first year, either of two interest rates will occur. (a) Interest rates will increase 1 percent to 9 percent (50 percent probability of either occurrence). The 20-year 8 percent coupon Treasury bond's price will fall to $907.9921 per $1,000 face value. (b) Interest rates will decrease 1 percent to 7 percent (50 percent probability of occurrence). The 20-year 8 percent coupon Treasury bond's price will increase to $1,106.7754 per $1,000 face value.

At the end of two years, one of three different interest rate scenarios will occur. (a) Interest rates will increase another 1 percent to 10 percent (25 percent probability of occurrence). The 20 year 8 percent coupon Treasury bond's price will fall to $828.4091 per $1,000 face value. (b) Interest rates will decrease 1 percent to 8 percent or increase 1 percent to 8 percent (50 percent probability of occurrence). The 20-year 8 percent coupon Treasury bond's price will return to $1,000 per $1,000 face value. (c) Interest rates will decrease another 1 percent to 6 percent (25 percent probability of occurrence). The 20-year 8% coupon Treasury bond's price will increase to $1,231.1477 per $1,000 face value. d. Diagram the prices over the two-year period.

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$828.41

$907.99

$1,000.00

0.25 0.25

0.5

$1,000.00

0.5 0.25 0.25 $1,106.78

0

$1,231.15

1

2

Time in Years

e.

If options on $100,000, 20-year, 8 percent coupon Treasury bonds (both puts and calls) have a strike price of 101, what are the possible (intrinsic) values of the option position at the end of year 1 and year 2?

The call option's intrinsic value at the end of one year will be either: (a) Zero if the price of a $100,000 20-year Treasury bond is $90,799.21 (in the scenario that interest rates rise to 9 percent); or (b) $110,677.54 - $101,000 (strike price) = $9,677.54 if the price of a $100,000 20-year Treasury bond is $110,677.54 (in the scenario that interest rates fall to 7 percent).

The call option's intrinsic value at the end of two years will be either: (a) Zero if the price of a $100,000 20-year Treasury bond is $82,840.91 (in the scenario that interest rates rise to 10 percent); or (b) Zero if the price of a $100,000 20-year Treasury bond is $100,000 (in the scenario that interest rates stay at 8 percent); or (c) $123,114.77 - $101,000 (strike price) = $22,114.77 if the price of a $100,000 20-year Treasury bond is $123,114.77 (in the scenario that interest rates fall to 6 percent). f.

Diagram the possible option values.

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$0=Max(82,840.91-101,000,0) Max[90,799.21-101,000,0]=$0 0.25 0.25 0.5 $0=Max(100,000-101,000,0) 0.5 0.25 0.25 Max[110,677.54-101,000,0]=9,677.54 $0=Max(123,114.77-101,000,0)=$22,114.77

0

1

2

Time in Years

g. What is the option premium? (Use an 8 percent discount factor.)

PV = ($9,677.54 x 0.5)/1.08 + ($22,114.17 x 0.5 x 0.25)/(1.08)2 = $6,850.32 13. Why are options on interest rate futures contracts preferred to options on cash instruments in hedging interest rate risk?

Options on futures can be more attractive to FIs than options on an underlying asset when it is cheaper or more convenient to deliver futures contracts on the asset rather than the actual asset. For example, trading options on T-bond futures contracts rather than options on T-bonds ensures that a highly liquid asset will be delivered and that problems associated with accrued interest and the determination of which long-term bond to deliver are avoided. Another advantage is that price information about futures contracts (the underlying asset on the option) is generally more readily available than price information on the T-bonds themselves (T-bond price information can be obtained only by surveying bond dealers). Finally, bond or interest rate futures options are generally preferred to options on the underlying bond because they combine the favorable liquidity, credit risk, homogeneity, and marking-to-market features of futures with the same asymmetric payoff functions as regular puts and calls.

14. Consider Figure 23-13. What are the prices paid for the following futures options: a. December T-bond calls at $155. => 3 63/64% x $100,000 = $3,984.375 per $100,000 contract. b. March 10-year T-note puts at $127.50. => 2 8/64% x $100,000 = $2,125.00 per $100,000 contract. c. March Eurodollar calls at 98.87 percent.

Because the underlying security on options on Eurodollar futures is a 90 day Eurodollar CD, each 1 basis point is equal to $25 ($1m x 0.0001 x 90/360) => 54.25 bpts x $25 11 © 2022

= $1,356.25 per $1,000,000 contract.

15. Consider Figure 23-13 again. What happens to the price of the following? a. A call when the exercise price increases.

=> The call value decreases.

b. A call when the time until expiration increases.

=> The call value increases.

c. A put when the exercise price increases.

=> The put value increases.

d. A put when the time to expiration increases.

=> The put value increases.

16. An FI manager writes a call option on a T-bond futures contract with an exercise price of 11400 at a quoted price of 0-55. a. What type of opportunities or obligations does the manager have?

The manager is obligated to sell the interest rate futures contract to the call option buyer at the price of $114,000 per $100,000 contract, if the buyer chooses to exercise the option. If the writer does not own the bond at the time of exercise, the bond must be purchased in the market. The call writer receives a premium of $859.375 from the sale of the option. b. In what direction must interest rates move to encourage the call buyer to exercise the option?

Interest rates must decrease so the market price of the underlying bond increases.

17. What is the delta of an option ()?

The delta of an option measures the change in the option value for a $1 change in the value of the underlying asset. The delta of a call option will always be between 0 and 1.0, and the delta of a put option will always be between –1.0 and 0.

18. An FI has a $100 million portfolio of six-year Eurodollar bonds that have an 8 percent coupon. The bonds are trading at par and have a duration of five years. The FI wishes to hedge the portfolio with T-bond options that have a delta of -0.625.

The underlying long-term Treasury bonds for the option have a duration of 10.1 years and trade at a market value of $96,157 per $100,000 of par value. Each put option has a premium of $3.25 per $100 of face value. a. How many bond put options are necessary to hedge the bond portfolio?

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Np =

DxP = 5x$100,000,000 =823.74824contracts  xDxB 0.625x10.1x$96,157 b. If interest rates increase 100 basis points, what is the expected gain or loss on the put option hedge?

A $100,000 20-year, eight percent bond selling at $96,157 implies a yield of 8.4 percent. P = Np x  x (-D) x B x R/(1 + R) = 824 x (-0.625) x (-10.1) x $96,157 x 0.01/1.084 = $4,614,028 gain c. What is the expected change in market value on the bond portfolio? B = -5 x $100,000,000 x 0.01/1.08 = -$4,629,630 d. What is the total cost of placing the hedge?

The price quote of $3.25 is per $100 of face value. Therefore, the cost of one put contract is $3,250, and the cost of the hedge = 824 contracts x $3,250 per contract = $2,678,000. e. Diagram the payoff possibilities.

The diagram of this portfolio position and the corresponding hedge is given in Figures 23-7 and 23-8. f. How far must interest rates move before the payoff on the hedge will exactly offset the cost of placing the hedge? P = 824 x 3,250 = 824 x (-0.625) x (-10.1) x $96,157 x R /1.084 Solving for the change in interest rates gives R = ($3,250 x 1.084)/(0.625 x 10.1 x $96,157) = 0.005804 or 0.58 percent. g. How far must interest rates move before the gain on the bond portfolio will exactly offset the cost of placing the hedge? B = 3,250 x 824 = -5 x $100,000,000 x R /1.08 Again solving for R = ($3,250 x 824 x 1.08)/(5 x $100,000,000) = -.0057845 or -0.58 percent. h. Summarize the gain, loss, and cost conditions of the hedge on the bond portfolio in terms of changes in interest rates.

If rates increase 0.58 percent, the portfolio will decrease in value by an amount that is approximately equal to the gain on the hedge. This position corresponds to the intersection of the profit function from the put and the X-axis in Figure 23-7. The FI is 13 © 2022

out the cost of the hedge, which also will be the case for any other increase in interest

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rates. In effect, the cost of the hedge is the insurance premium to assure the yield on the portfolio at the time the hedge is placed.

If rates decrease approximately 0.58 percent, the gain on the portfolio will offset the cost of the hedge, and the put option will not be exercised. This position is shown by the intersection of the X-axis and the net profit function in Figure 23-8. Any decrease in rates beyond 0.58 percent will generate positive profits for the portfolio in excess of the cost of the hedge.

19. Corporate Bank has $840 million of assets with a duration of 12 years and liabilities worth $720 million with a duration of seven years. Assets and liabilities are yielding 7.56 percent. The bank is concerned about preserving the value of its equity in the event of an increase in interest rates and is contemplating a macrohedge with interest rate options. The call and put options have a delta () of 0.4 and –0.4, respectively. The price of an underlying T-bond is 104.53125 (104 34/64), its duration is 8.17 years, and its yield to maturity is 7.56 percent. a. What type of option should Corporate Bank use for the macrohedge?

The duration gap for the bank is [12 – (720/840)7] = 6. Therefore, the bank is concerned that interest rates may increase and it should purchase put options. As rates rise, the value of the bonds underlying the put options will fall, but they will be puttable at the higher put option exercise price. b. How many options should be purchased?

The bonds underlying the put options have a market value of $104,531.25. Thus, Np =

DGAPxA  x Dx B

=

6x$840,000,000

=14,753.75or14,754contracts

0.4x8.17x$104,531.25

c. What is the effect on the economic value of the equity if interest rates rise 50 basis points?

The change in equity value is: ΔE = –DGAPxAx(R/(1+R)) = -6($840,000,000)(0.005/1.0756) = -$23,428,784. d. What will be the effect on the hedge if interest rates rise 50 basis points? P = Np(|| x D x B x R/(1+R)) = 14,754 x 0.4 x 8.17 x $104,531.25 x 0.005/1.0756 = $23,429,185 gain e. What will be the cost of the hedge if each option has a premium of $0.875 per $100 of face value?

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A price quote of $0.875 is per $100 face value of the put contract. Therefore, the cost per contract is $875, and the cost of the hedge is $875x14,754 = $12,909,750. f. Diagram the economic conditions of the hedge.

The diagram of this portfolio position and the corresponding hedge is given in Figures 23-7 and 23-8. In this particular case, the profit function for the net long position of the bank (DGAP = 6) should be considered as the profit function of the bond in Figure 23-7. g. How much must interest rates move against the hedge for the increased value of the bank to offset the cost of the hedge?

Let E = $12,909,750, and solve the equation in part (c) above for R. Then, R = $12,909,750 x 1.0756/($840,000,000 x (-6)) = -0.002755 or -0.2755 percent. h. How much must interest rates move in favor of the hedge, or against the balance sheet, before the payoff from the hedge will exactly cover the cost of the hedge?

Use the equation in part (d) above and solve for R. Then, R = ($12,909,750 x 1.0756)/[14,754 x 0.4 x 8.17 x $104,531.25] = 0.002755 or 0.2755 percent. i. Formulate a management decision rule regarding the implementation of the hedge.

If rates increase 0.2755 percent, the equity will decrease in value approximately equal to the gain on the hedge. This position corresponds to the intersection of the profit function from the put and the X-axis in Figure 23-7. The FI is out the cost of the hedge, which also will be the case for any other increase in interest rates. In effect, the cost of the hedge is the insurance premium to assure the value of the equity at the time the hedge is placed.

If rates decrease approximately 0.2755 percent, the gain on the equity value will offset the cost of the hedge, and the put option will not be exercised. This position is shown by the intersection of the X-axis and the net profit function in Figure 23-8. Any increase in rates beyond 0.2755 percent will generate positive increases in value for the equity in excess of the cost of the hedge.

20. An FI has a $200 million asset portfolio that has an average duration of 6.5 years.

The average duration of its $160 million in liabilities is 4.5 years. Assets and liabilities are yielding 10 percent. The FI uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta () of the put options has been estimated at -0.3 and the average duration of the T-bonds is seven years.

The current market value of the T-bonds is $96,000.

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a. What is the modified duration of the T-bonds if the current level of interest rates is 10 percent?

MD = D/(1+0.10) = 7/1.10 = 6.3636 years b. How many put option contracts should the FI purchase to hedge its exposure against rising interest rates? The face value of the T-bonds is $100,000.

Np =

[DA - k DL]x A  x Dx B

= [6.5 - 4.5(0.80)] x $200,000,000/[(0.3) x (7.0) x (96,000)] = 2,876.98 or 2,877 contracts

c. If interest rates increase 50 basis points, what will be the change in value of the equity of the FI? The change in equity value is: ΔE = –DGAP x A x (R/(1+R)) = -2.9($200,000,000)(0.005/1.10) = -$2,636,364 d. What will be the change in value of the T-bond option hedge position? P = Np(|| x D x B x R/(1=R)) = 2,877 x 0.3 x 7 x $96,000 x 0.005/(1.10) = $2,636,378 gain e. If put options on T-bonds are selling at a premium of $1.25 per face value of $100, what is the total cost of hedging using options on T-bonds?

Premium on the put options = 2,877 x $1.25 x 1,000 = $3,596,250. f. Diagram the spot market conditions of the equity and the option hedge.

The diagram of this portfolio position and the corresponding hedge is given in Figures 23-7 and 23-8. In this particular case, the profit function for the net long position of the bank (DGAP = 2.9) should be considered as the profit function of the bond in Figure 237. g. What must be the change in interest rates before the change in value of the balance sheet (equity) will offset the cost of placing the hedge?

Let E = $3,596,250, and solve the equation in part (c) above for R. Then, R = $3,596,250 x 1.10/($200,000,000 x -2.9) = -0.00682 or -0.68 percent. h. How much must interest rates change before the profit on the hedge will exactly cover the cost of placing the hedge?

Use the equation in part (d) above and solve for R. Then 17 © 2022

R = $3,596,250/[2,877 x 0.3 x 7 x $96,000/1.10] = 0.00682 or 0.68 percent. i. Given your answer in part (g), what will be the net gain or loss to the FI? If rates decrease by 0.68 percent, the increase in value of the equity will exactly offset the cost of placing the hedge. The options will be allowed to expire unused since the price of the bonds will be higher in the market place than the exercise price of the option.

21. A mutual fund plans to purchase $10 million of 20-year T-bonds in two months.

The bonds are yielding 7.68 percent. These bonds have a duration of 11 years. The mutual fund is concerned about interest rates changing over the next two months and is considering a hedge with two-month options on T-bond futures contracts.

Two-month calls with a strike price of 105 are priced at 1-25 and puts of the same maturity and exercise price are quoted at 2-09. The delta of the call is 0.5 and the delta of the put is -0.7. The current price of a deliverable T-bond is $103.2500 per $100 of face value, its duration is nine years, and its yield to maturity is 7.68 percent. a. What type of option should the mutual fund purchase?

The mutual fund is concerned about interest rates falling which would imply that bond prices would increase. Therefore, the FI should buy call options to guarantee a certain purchase price. b. How many options should it purchase?

N = C

D xA

=

11 x $10,000,000

= 236.75 or 237 call options

 x D x B 0.5 x 9 x $103,250 c. What is the cost of these options?

The quote for T-bond options is 1-25, or 1 25/64 = $1.390625 per $100 face value. This converts to $1,390.625 per $100,000 option contract. The total cost of the hedge is 237 x $1,390.625 = $329,578.125. d. If rates change +/-50 basis points, what will be the impact on the price of the desired T-bonds?

For a rate increase, the B = -11 x $10,000,000 x (0.005)/1.0768 = -$510,773. If rates decrease, the value of the bonds will increase by $510,773. e. What will be the effect on the value of the hedge if rates change +/- 50 basis points?

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If rates decrease, the value of the underlying bonds, and thus the option value, increases. C = Nc x ( x (-D) x B x R/(1+R)) = 237 x 0.5 x (-9) x $103,250x(-0.005/(1.0768)) = $511,312. This occurs because the FI can buy the bonds at the exercise price and sell them at the higher market price. If rates rise, the options will expire without value because the bonds will be priced lower in the market. f. Diagram the effects of the hedge and the spot market value of the desired Tbonds.

The profit profile of the call option hedge is given in Figure 23-1, and the profile of a long bond is shown in Figure 23-5. The profit profile of the call option is less than the bond by the amount of the premium, but the call option profile illustrates less opportunity for loss. g. What must be the change in interest rates to cause the change in value of the purchased T-bonds to exactly offset the cost of placing the hedge?

The premium on a $100,000 option is $1,390.625 and the mutual fund purchased 237 option contracts. The yield in the market on the deliverable bond is 7.68 percent.

Therefore, from the equation used in part (d), we can solve for R = [1,390.625 x 237 x 1.0768]/[11 x $10,000,000] = 0.003226 or 0.3226 percent. If rates increase 0.3226 percent, the present value of the existing $10,000,000 bond in the market place will decrease by $1,390.625 x 237, or $329,578.125. The savings on the bond purchase will offset the premium on the call option.

22. An FI must make a single payment of 500,000 Swiss francs in six months at the maturity of a CD. The FI’s in-house analyst expects the spot price of the franc to remain stable at the current $1.02/SF. But as a precaution, the analyst is concerned that it could rise as high as $1.07/SF or fall as low as $0.97/SF. Because of this uncertainty, the analyst recommends that the FI hedge the CD payment using either options or futures. Six-month call and put options on the Swiss franc with an exercise price of $1.02/SF are trading at 4 cents and 2 cents per SF, respectively. A six-month futures contract on the Swiss franc is trading at $1.02/SF. a. Should the analyst be worried about the dollar depreciating or appreciating?

The analyst should be worried about the dollar depreciating. b. If the FI decides to hedge using options, should the FI buy put or call options to hedge the CD payment? Why? The analyst should buy call options on Swiss francs, because if the dollar depreciates to $1.07/SF, the call options will be in-the-money.

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c. If futures are used to hedge, should the FI buy or sell Swiss franc futures to hedge the payment? Why? The FI should buy futures, because if the dollar depreciates to $1.07/SF, the cash flows will be positive on the futures position. d. What will be the net payment on the CD if the selected call or put options are used to hedge the payment? Assume the following three scenarios: the spot price in six months will be $0.97, $1.02 or $1.07/SF. Also assume that the options will be exercised.

Using call options, the net payments are: Future spot prices Premium on call options (0.04 x 500,000) Gain/loss on exercise Purchase of spot Net payment

$0.97 -$ 20,000 0 -$485,000 -$505,000

$1.02 -$ 20,000 0 -$510,000 -$530,000

$1.07 -$20,000 +$25,000 -$535,000 -$530,000

e. What will be the net payment if futures had been used to hedge the CD payment? Use the same three scenarios as in part (d).

Using futures, the net payments are: Future Spot prices $0.97 Gain/loss on futures -$ 25,000 Purchase of spot -$485,000 Net payment -$510,000

$1.02 0 -$510,000 -$510,000

$1.07 $ 25,000 -$535,000 -$510,000

f. Which method of hedging is preferable after the fact?

Ex-post it appears that hedging with futures will result in the lowest payments in dollars, at least until the spot reaches $0.98/SF, at which time both net payments will be similar.

If the dollar appreciates beyond $0.98/SF, i.e. to $0.96/SF or $0.95/SF, then the option hedge result in lower payments. Once again, this is an ex-post conclusion. Ex-ante, it depends on your projections of the expected future spot rates.

23. An American insurance company issued $10 million of one-year, zero-coupon GICs (guaranteed investment contracts) denominated in Swiss francs at a rate of 5 percent. The insurance company holds no SF-denominated assets and has neither bought nor sold francs in the foreign exchange market. a. What is the insurance company's net exposure in Swiss francs?

The net exposure is (0 - $10 million) + (0 - 0) = -$10 million (FX assets - FX liabilities plus FX bought minus FX sold).

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b. What is the insurance company's risk exposure to foreign exchange rate fluctuations?

The insurance company has SF liabilities (i.e., it is short in the Swiss franc) and is exposed to an appreciation of the Swiss franc. c. How can the insurance company use futures to hedge the risk exposure in part (b)? How can it use options to hedge?

The insurance company can hedge its risk exposure by entering a long hedge by: (a) buying Swiss franc futures and/or (b) buying Swiss franc call options. d. If the strike price on SF options is $1.0425/SF and the spot exchange rate is $1.0210/SF, what is the intrinsic value (on expiration) of a call option on Swiss francs? What is the intrinsic value (on expiration) of a Swiss franc put option?

(Note: Swiss franc futures options traded on the Chicago Mercantile Exchange are set at SF125,000 per contract.)

Since the strike price is US$1.0425/SF and the spot exchange rate is $1.0210/SF, the put option is in the money, but the call is not. The intrinsic value of the put option is $1.0425 - $1.0210 = $0.0215 per Swiss franc. Since each Swiss franc option is worth SF125,000, each put option's intrinsic value upon expiration is (125,000)($0.0215) = $2,687.50. e. If the June delivery call option premium is 0.32 cents per franc and the June delivery put option is 10.7 cents per franc, what is the dollar premium cost per contract? Assume that today's date is April 15.

The call option premium is ($0.0032)(125,000) = $400. The put option premium is ($0.107)(125,000) = $13,375. f. Why is the call option premium lower than the put option premium?

The put option premium is higher because it is in-the-money and the call option is not.

However, since there is time until expiration, both options' values exceed their intrinsic values.

24. An FI has made a loan commitment of SF10 million that is likely to be taken down in six months. The current spot exchange rate is $1.0210/SF. a. Is the FI exposed to the dollar depreciating or the dollar appreciating? Why? The FI is exposed to the dollar depreciating, because it would require more dollars to purchase the SF10 million if the loan is drawn down in six months as expected.

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b. If the FI decides to hedge using SF futures, should it buy or sell SF futures?

The FI should buy SF futures if it decides to hedge against a depreciation of the dollar. c. If the spot rate six months from today is $1.0610/SF, what dollar amount is needed in six months if the loan is drawn down?

If the FI had remained unhedged, it would require $1.0610 x SF10,000,000 = $10.61 million to make the SF-denominated loan. d. A six-month SF futures contract is available for $1.0310/SF. What is the net amount needed at the end of six months if the FI has hedged using the SF10 million of futures contract? Assume futures prices are equal to spot prices at the time of payment, that is, at maturity.

If the FI has hedged using futures, it will gain ($1.0610 - $1.0310) x SF10 million = $300,000 on its futures position. Its net payment will be $10.31 million. e. If the FI decides to use options to hedge, should it purchase call or put options?

It should purchase call options if it has to hedge against the likely draw down. f. Call and put options with an exercise price of $1.031/SF are selling for $0.02 and $0.03 per SF, respectively. What would be the net amount needed by the FI at the end of six months if it had used options instead of futures to hedge this exposure?

Premium on call options = $0.02 x SF10m = $200,000. Purchase at spot = $1.061 x SF10 million = $10.61 million. Gain on options = $0.03 x SF10 million = $300,000. Its net payment will be $10.31 million.

25. What is a credit spread call option?

A credit spread call option has a payoff that increases as the yield spread against some specified benchmark bond increases above the exercise spread. The increased payoff compensates the lender for decreases in value caused by an increase in the credit risk of the borrower.

26. What is a digital default option?

This option pays a stated amount in the event of a loan default. If the loan is repaid in its entirety, the option expires unexercised.

27. How do the cash flows to the lender for a credit spread call option hedge differ from the cash flows for a digital default option?

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In both cases, the maximum loss to the call option purchaser is the amount of the premium paid for the option. The digital default option has a one-time, lump-sum cash payment at the time the loan defaults. The payoff for the credit spread option increases as the default risk increases. See Figures 23-17 and 23-18 for a visual illustration of the payoff profiles.

28. What is a catastrophe call spread option? How do the cash flows of this option affect the buyer of the option?

A catastrophe call spread option is a call option on the loss ratio incurred in writing catastrophe insurance with a capped (or maximum) payout. For a premium the purchaser of this option receives a hedge against a range of loss ratios that may occur, where the loss ratio is the amount of losses divided by the insurance premiums. For loss ratios below the minimum in the option, the option expires out-of-the-money. For loss ratios between the minimum and the maximum stated ratios, the option holder receives an increasing payoff as the loss ratio increases. For loss ratios in excess of the maximum ratio in the option, the holder of the option receives a maximum payoff equal to the maximum ratio in the option coverage. Thus, there is a cap or ceiling to the amount of payoff or benefit that can be received from this option.

29. What are caps? Under what circumstances would the buyer of a cap receive a payoff?

A cap is a call option on interest rates. If market interest rates rise above some stated amount, the writer of the option pays to the holder the excess interest on some amount of money. For this insurance, the buyer of the option pays a premium. This option would be a valuable interest rate risk management vehicle for an FI that is borrowing money in the variable rate market.

30. What are floors? Under what circumstances would the buyer of a floor receive a payoff?

A floor is a put option on interest rates. The buyer receives a minimum interest rate should market rates fall below some minimum level. This option would be a valuable interest rate risk management vehicle for an FI that is lending money in the variable rate market.

31. What are collars? Under what circumstances would an FI use a collar?

A collar is a combination of a cap and a floor. A collar occurs when an FI takes a simultaneous position in a cap and a floor, such as buying a cap and selling a floor. The idea here is that the FI wants to hedge itself against rising rates but wants to finance the cost of the cap. One way to do this is to sell a floor and use the premiums on the floor to pay the premium on the purchase of the cap.

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32. How is buying a cap similar to buying a call option on interest rates?

If interest rates increase above the exercise rate, the buyer of the cap has the right to call or purchase money at the exercise interest rate rather than paying the higher rate in the market. If interest rates decrease, the buyer of the cap is not obligated to take a loss by calling the cap.

33. Under what balance sheet circumstances would it be desirable to sell a floor to help finance a cap? When would it be desirable to sell a cap to help finance a floor?

An FI that is funding fixed-rate assets with floating-rate liabilities may find it valuable to buy a cap for the purpose of protecting against increases in interest rates on the funding side of the balance sheet. This cap may be funded in part by selling a floor if the FI is confident that interest rates will not decrease below the floor exercise price. It would be desirable to sell a cap and to buy a floor if interest rates are volatile downward and the FI has a positive duration gap.

34. Use the following information to price a three-year collar by purchasing an in-themoney cap and writing an out-of-the-money floor. Assume a binomial options pricing model with an equal probability of interest rates increasing 2 percent or decreasing 2 percent per year. Current rates are 7 percent, the cap rate is 7 percent, and the floor rate is 4 percent. The notional value is $1 million. All interest payments are annual payments as a percent of notional value, and all payments are made at the end of year 2 and the end of year 3.

7% Cap Valuation t=1

t = 2 (beg.)

t = 2 (end)

9% (0.50)

$20,000

7% spot 5% (0.50)

t = 3 (beg.)

11% (0.25)

t = 3 (end) $40,000

7% (0.50)

$0

3% 0.25)

$0

$0

Cap price = 0.50 ($20,000)/(1.07)(1.09)+0.25($40,000)/(1.07)(1.09)(1.11) = $16,298.56 Note: If interest rates are 9%, the cap is in-the-money with an interest rate differential (over the cap rate) of 2%. Two percent of $1 million face value equals $20,000.

4% Floor Valuation t=1

t = 2 (beg.)

t = 2(end)

9% (0.50)

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t = 3(beg.)

11% (0.25)

t = 3(end) $0

7% spot 5% (0.50)

7% (0.50)

$0

3% (0.25)

$10,000

$0

Floor price = 0.25 ($10,000)/(1.07)(1.05)(1.03) = $2,160.37 The cost of the collar = cap price - floor price = $16,298.56 - $2,160.37 = $14,138.19 35. Use the following information to price a three-year collar by purchasing an out-ofthe-money cap and writing an in-the-money floor. Assume a binomial options pricing model with an equal probability of interest rates increasing 2 percent or decreasing 2 percent per year. Current rates are 4 percent, the cap rate is 7 percent, and the floor rate is 4 percent. The notional value is $1 million. All interest payments are annual payments as a percent of notional value, and all payments are made at the end of year 2 and the end of year 3.

7% Cap Valuation t=1

t = 2 (beg.)

t = 2 (end)

6% (0.50)

$0

2% (0.50)

$0

4% spot

t = 3 (beg.)

8% (0.25)

t = 3 (end) $10,000

4% (0.50)

$0

0% (0.25)

$0

Cap price = 0.25 ($10,000)/ (1.04)(1.06)(1.08)=$2,099.80 4% Floor Valuation t=1

t = 2 (beg.)

t = 2 (end)

6% (0.50)

$0

2% (0.50)

$20,000

4% spot

t = 3 (beg.)

8% (0.25)

t = 3 (end) $0

4% (0.50)

$0

0% (0.25)

$40,000

Floor price = 0.50 ($20,000)/(1.04)(1.02) +0.25($40,000)/(1.04)(1.02)(1.00) = $18,853.70 The cost of the collar = cap price - floor price = $2,099.80 - $18,853.70 = -$16,753.90 36. Contrast the total cash flows associated with the collar position in question 34 against the collar in question 35. Do the goals of FIs that utilize the collar in question 34 differ from those that put on the collar in question 35? If so, how?

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The collar in problem 34 is used as an interest rate hedge. The collar in problem 35 is a source of fee income for the bank. The collar in problem 34 purchases a lot of insurance against increasing interest rates. For that reason it is expensive. The collar in problem 35 purchases very little insurance against increasing interest rates. For that reason it is a less expensive hedge than the collar in problem 34.

37. An FI has purchased a $200 million cap of 9 percent at a premium of 0.65 percent of face value. A $200 million floor of 4 percent is also available at a premium of 0.69 percent of face value. a. If interest rates rise to 10 percent, what is the amount received by the FI? What are the net savings after deducting the premium?

Premium for purchasing the cap = 0.0065 x $200 million = $1,300,000. If interest rates rise to 10 percent, cap purchasers receive $200 million x 0.01 = $2,000,000. The net savings is $700,000. b. If the FI also purchases a floor, what are the net savings if interest rates rise to 11 percent? What are the net savings if interest rates fall to 3 percent?

If the FI also purchases the floor: Premium = 0.0069 x $200 million = $1,380,000, and the total premium = $1,380,000 + $1,300,000 = $2,680,000.

If interest rates rise to 11 percent, the cap purchaser receives 0.02 x $200m = $4,000,000, and the net savings = $4,000,000 - $2,680,000 = $1,320,000.

If interest rates fall to 3 percent, the floor purchaser receives 0.01 x $200 million = $2,000,000, and the net savings = $2,000,000 - $2,680,000 = -$680,000. c. If, instead, the FI sells (writes) the floor, what are the net savings if interest rates rise to 11 percent? What if they fall to 3 percent?

If the FI sells the floor, it receives net $1,380,000 minus the cost of the cap of $1,300,000 = +$80,000.

If interest rates rise to 11 percent, cap purchasers receive 0.02 x $200m = $4,000,000.

The net the net savings = $4,000,000 + $80,000 = $4,080,000.

If interest rates fall to 3 percent, floor purchasers receive 0.01 x $200 million = $2,000,000. The net savings to the FI = $-2,000,000 + 80,000 = -$1,920,000. d. What amount of floors should the FI sell in order to compensate for its purchases of caps, given the above premiums?

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The FI needs to sell: NVf x 0.0069 = $1,300,000, or NVf = $188,405,795 worth of 4 percent floors.

38. What credit risk exposure is involved with buying caps, floors, and collars for hedging purposes?

These hedging vehicles are over-the-counter contracts that have counterparty credit risk not present with exchange-traded futures and options contracts. Because contracts often are long-term in nature, a default at the end of any one year may mean that the FI (a) loses the benefits expected at that time, (b) must incur additional costs of arranging additional coverage for the remaining years of the original contract, and (c) may pay less favorable premiums because of changes in the market.

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Integrated Mini Case: Hedging Interest Rate Risk with Futures versus Options On January 4, 2018, an FI has the following balance sheet (rates = 10 percent) Assets A

200m

DA = 6 years

L E

Liabilities/Equity 170m DL = 4 years 30m

DGAP = [6 – (170/200)4] = 2.6 years > 0 The FI manager thinks rates will increase by 0.75 percent in the next three months. If this happens, the equity value will change by: E = −[6 − 170 (4)]200m 0.0075 = −$3,545 ,455 1.10

200

The FI manager will hedge this interest rate risk with either futures contracts or option contracts.

If the FI uses futures, it will select June T-bonds to hedge. The duration on the T-bonds underlying the contract is 14.5 years, and the T-bonds are selling at a price of $114.34375 per $100, or $114,343.75. T-bond futures rates, currently 9 percent, are expected to increase by 1.25 percent over the next three months.

If the FI uses options, it will buy puts on 15-year T-bonds with a June maturity, an exercise price of 113, and an option premium of 1 36 64 percent. The spot price on the Tbond underlying the option is $135.71875 per $100 of face value. The duration on the Tbonds underlying the options is 14.5 years, and the delta of the put options is -0.75.

Managers expect these T-bond rates to increase by 1.24 percent from 7.875 percent in the next three months.

If by April 4, 2018, balance sheet rates increase by 0.8 percent, futures rates by 1.4 percent, and T-bond rates underlying the option contract by 1.3 percent, would the FI have been better off using the futures contract or the option contract as its hedge instrument? Explain why For the hedge with futures contracts:

br = 0.0125 / 0.0075 = 1.681957 1.09

1.10

N =

[6−(170 / 200)4]200m

F

14.5114,343.751.681957

= 186.46959 contracts

On April 4, 2018, as the FI gets out of the futures hedge: Loss on balance sheet E = −[6 − 170 (4)]200m 0.008 = 200

Gain off balance sheet (futures)

F = −14.5(−186.46959) 114,343.75 0.014 = −

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$3,781,818

1.10

$3,970,909

1 .

0 9

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The net gain is $3,970,909 - $3,781,818 = $189,091 For a hedge with option contracts:

br = 0.0124 / 0.0075 = 1.6859019, 1.07875

1.1

N =

[6−(170 200 )4]200m

o

0.7514.5135,718.751.6859019

= 208.9786545 contracts

On April 4, 2018, as the FI gets out of the option hedge: Gain off balance sheet (options) 0 = 208.9786545(−0.75)(−14.5)135,718.75 0.0130 =

Loss on balance s h eet E =− [6− 170 (4)]200m0.0 0 8 = 200

1.1

1.07875

-$3,781,818

$3,717,009

The net gain is $3,621,701 - $3,717,009 = -$64,809 In this case, the FI would be better off hedging with futures contracts rather than option contracts.

If by April 4, 2018, balance sheet rates actually fall by 0.75 percent, futures rates fall by 1.05 percent, and T-bond rates underlying the option contract fall by 1.24 percent, would the FI have been better off using the futures contract or the option contract as its hedge instrument?

For the hedge with futures contracts:

br = 0.0125 / 0.0075 = 1.681957 1.09

N =

[6−(170 / 200)4]200m

F

14.5114,343.751.681957

1.10

= 186.46959 contracts

On April 4, 2018, as the FI gets out of the futures hedge: Loss on balance sheet

E = −[6 − 170 (4)]200m −0.0075 = 200

Gain off balance sheet (futures)

F = −14.5(−186.46959) 114,343.75 −0.0105 =

1.10

1.09

− $2,978,182

$3,545,454

The net gain is $3,545,454 - $2,978,182 = $567,272 For a hedge with option contracts:

br = 0.0124 / 0.0075 = 1.6859019, 1.07875

1.1

N =

[6−(170 200 )4]200m

o

0.7514.5135,718.751.6859019

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= 208.9786545 contracts

On April 4, 2018, as the FI gets out of the option hedge, the value of the T-bond underlying the put option has increased. The FI does not have to exercise these options if the loss on exercise is greater than the option premium. Thus:

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Loss on balance sheet

E =−[6− 170 (4)]200m −0.0075 200

Gain off balance sheet (options) Exercise: 0 = 208.9786545(−0.75)(−14.5)135,718.75−0.0124 =

1.1

1.07875

= $3,545,454

-$3,545,454 No exercise: O=208.9786545100,000(-1 36/64%) = -$326,529

The FI will not exercise the options, taking the loss. Rather, it will let the options expire unused. Thus, the net gain is $3,545,454 - $326,529 = $3,218,925 In this case, the FI would be much better off hedging with option contracts rather than futures contracts.

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Solutions for End-of-Chapter Questions and Problems: Chapter Twenty-Four 1.

Explain the similarity between a swap and a forward contract.

A forward contract requires delivery or taking delivery of some commodity or financial security at a specified time in the future at a price specified at the time of origination. In a swap, each party promises to deliver and/or receive a pre-specified series of payments at specific intervals over a specified time horizon. In this way, a swap can be considered to be the same as a series of forward contracts.

2.

Forward, futures, and option contracts had been used by FIs to hedge risk for many years before swaps were invented. If FIs already had these hedging instruments, why did they need swaps?

Although similar in many ways, the following distinguishing characteristics cause the instruments to be differentiated: (a)

A swap can be viewed as a portfolio of forward contracts with different maturity dates.

Since cash flows on forward contracts are symmetric, the same can be said of swaps. This is in contrast to options, whose cash flows are asymmetric (truncated either on the positive or negative side depending upon the position).

(b)

The introduction of a swap intermediary reduces the credit risk exposure and the information and monitoring costs that are associated with a portfolio of individual forward contracts.

(c)

Options are marked to market continuously, swaps are marked to market at coupon payment dates, and forward contracts are settled only upon delivery (at maturity).

Therefore, the credit risk exposure is greatest under a forward contract, where no third party guarantor exists as in options (the options clearing corporation for exchange-traded options) and swaps (the swap intermediary).

(d)

The transactions cost is highest for the option (the nonrefundable option premium), next for the swap (the swap intermediary's fee), and finally for the forward (which has no up-front payment).

(e)

Finally, swaps also have a longer maturity than any other instrument and provide an additional opportunity for FIs to hedge longer term positions at lower cost. Moreover, since the package of forward contracts mirrors debt instruments, the swap provided FIs with a hedge instrument that is attractive and less costly than separate forward contracts.

3.

Distinguish between a swap buyer and a swap seller. In which markets does each have the comparative advantage?

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The swap buyer makes the fixed-rate payments in an interest rate swap and the swap seller makes the variable-rate payments. This distinction occurs by convention. The notation in this text refers to the comparative advantage party as that which makes the specific swap payment.

Thus, the buyer has the comparative advantage in fixed-rate payments, while the seller has the comparative advantage in variable-rate payments.

4.

An insurance company owns $50 million of floating-rate bonds yielding LIBOR plus 1 percent. These loans are financed with $50 million of fixed-rate guaranteed investment contracts (GICs) costing 10 percent. A bank has $50 million of auto loans with a fixed rate of 14 percent. The loans are financed with $50 million of CDs at a variable rate of LIBOR plus 4 percent. a. What is the risk exposure of the insurance company?

The insurance company (IC) is exposed to falling interest rates on the asset side of the balance sheet. b. What is the risk exposure of the bank?

The bank is exposed to rising interest rates on the liability side of the balance sheet. c. What would be the cash flow goals of each company if they were to enter into a swap arrangement?

The IC wishes to convert the fixed-rate liabilities into variable-rate liabilities by swapping fixedrate payments for variable-rate payments. The bank wishes to convert variable-rate liabilities into fixed-rate liabilities by swapping variable-rate payments for fixed-rate payments. d. Which FI would be the buyer and which FI would be the seller in the swap?

The bank will make fixed-rate payments and therefore is the buyer in the swap. The IC will make variable-rate payments and therefore is the seller in the swap. e. Diagram the direction of the relevant cash flows for the swap arrangement.

Please see the diagram at the top of the next page. Note that the fixed-rate swap payments from the bank to the insurance company will offset the payments on the fixed-rate liabilities that the insurance company has incurred. The reverse situation occurs regarding the variable-rate swap payments from the insurance company to the bank. Depending on the rates negotiated and the maturities of the assets and liabilities, both FIs now have durations much closer to zero on this portion of their respective balance sheets.

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Bank Fixed-rate assets

Swap Cash Flows

Insurance Company

Fixed-rate swap payments

Variable-rate assets

Variable-rate swap payments

Variable-rate

Cash Financing

Fixed-rate

f. What are reasonable cash flow amounts, or relative interest rates, for each of the payment streams?

Determining a set of reasonable interest rates involves an analysis of the benefits to each FI. That is, does each FI pay lower interest rates with the swap than contractually obligated without the swap? Clearly, the direction of the cash flows will help reduce interest rate risk.

One feasible swap is for the IC to pay the bank LIBOR + 2.5 percent, and for the bank to pay the IC 12 percent. The net financing cost for each firm is given below.

Bank Cash market liability rate LIBOR + 4% Minus swap rate -(LIBOR + 2.5%) Plus swap rate + 12% Net financing cost (rate) 13.5%

Insurance Company 10.0% -12.0% +(LIBOR + 2.5%) LIBOR + 0.5%

Whether the two firms would negotiate these rates depends on the relative negotiating power of each firm, and the alternative rates for each firm in the alternate markets. That is, the fixed-rate liability market for the bank and the variable-rate liability market for the insurance company.

5.

In a swap arrangement, the variable-rate swap cash flow streams often do not fully hedge the variable-rate cash flow streams from the balance sheet due to basis risk. a. What are the possible sources of basis risk in an interest rate swap?

First, the variable-rate index on the liabilities in the cash market may not match perfectly the variable-rate index negotiated into the swap agreement. This source of basis risk is similar to the cross-hedge risk in the use of futures contracts. Second, the premium over the index in the cashmarket variable-rate liability may change over time as credit (default) risk conditions change. b. How could the failure to achieve a perfect hedge be realized by the swap buyer?

Swap pricing normally is based on a fixed notional amount over the life of the swap. If the dollar 3 © 2022

value of the fixed-rate asset portfolio of the buyer decreases over time, a fixed-notional amount

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swap agreement may not accurately reflect the desired interest-rate risk goals of the buyer over the life of the swap. This situation could occur as loans are amortized (repaid in the normal context) or as prepayment rates change on either loans or bonds as macroeconomic conditions change. c. How could the failure to achieve a perfect hedge be realized by the swap seller?

The swap seller is subject to basis risk as discussed in part (a) above.

6.

A commercial bank has $200 million of four-year maturity floating-rate loans yielding the T-bill rate plus 2 percent. These loans are financed with $200 million of four-year maturity fixed-rate deposits costing 9 percent. The commercial bank can issue four-year variablerate deposits at the T-bill rate plus 1.5 percent. A savings bank has $200 million of fouryear maturity mortgages with a fixed rate of 13 percent. They are financed with $200 million of four-year maturity CDs with a variable rate of the T-bill rate plus 3 percent. The savings bank can issue four-year long-term debt at 12.5 percent. a. Discuss the type of interest rate risk each FI faces.

The commercial bank is exposed to a decrease in rates that would lower interest income, while the savings bank is exposed to an increase in rates that would increase interest expense. In either case, profit performance would suffer. b. Propose a swap that would result in each FI having the same type of asset and liability cash flows.

One feasible swap would be for the commercial bank to send variable-rate payments of the T-bill rate + 1 percent (T-bill + 1%) to the savings bank and to receive fixed-rate payments of 9 percent from the savings bank. c. Show that this swap would be acceptable to both parties.

The swap flows are shown below.

Savings Bank Fixed-rate assets 13%

Swap Cash Flows Fixed-rate swap payments

Commercial Bank

9.0%

Variable-rate assets T-bill + 2%

T-bill + 1% Variable-rate swap payments

Variable-rate liabilities @ T-bill + 3%

Cash Financing Markets

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Fixed-rate liabilities @ 9%

Given these patterns of cash flows associated with the swap, the commercial bank and savings bank will realize the following financing costs.

Cash market liability rate Minus swap rate Plus swap rate Net financing cost rate Rate available on: Variable-rate debt Fixed-rate debt

Savings Bank T-bill + 3% -(T-bill + 1%) + 9% 11%

Commercial Bank 9% -9% +(T-bill + 1%) T-bill + 1%

12.5% T-bill + 1.5%

As a result of the swap, the bank has transformed its four-year, fixed-rate interest payments into variable-rate payments, matching the variability of returns on its assets. Further, through the interest rate swap, the bank effectively pays T-bill plus 1 percent for its financing. Had it gone to the debt market, the bank would pay T-bill plus 1.5 percent. Thus, the swap allows the bank to manage its interest rate risk at an overall savings of 0.5 percent better than market rates. The savings bank has transformed its variable-rate interest payments into fixed-rate payments, matching the fixed rate of return on its assets. Further, through the interest rate swap, the savings bank effectively pays 11 percent for its financing. Had it gone to the debt market, the bank would pay 12.5 percent. Thus, the swap allows the savings bank to manage its interest rate risk at an overall savings of 1.5 percent better than market rates. d. The realized T-bill rates over the four-year contract period are as follows: End of Year 1 2 3 4

T-bill Rate 1.75% 2.00 2.25 2.50

Calculate the realized cash flows on the swap and the net interest yield for the savings bank and the commercial bank over the contract period.

The realized cash flows on the swap agreement are as follows:

End of Year 1 2 3 4

T-bill rate 1.75% 2.00 2.25 2.50

Cash Payment by bank $5.5m 8.0m 8.5m 7.0m

T-bill rate + 1% 2.75% 4.00 4.25 3.50 6 © 2022

Cash Net payment payment by made by savings bank savings bank $22m $16.5m 22m 14.0m 22m 13.5m 22m 15.0m

The net interest yield on the assets minus the cost of liabilities plus the swap for the commercial bank is locked at 1 percent [(T-bill + 2%) – (T-bill + 1%)] for the four-year swap contract period.

The net interest yield on the assets minus the cost of liabilities plus the swap for the savings bank is locked at on is 2 percent (13% - 11%) for the four-year swap contract period.

An adjustment to make the net interest yield equal at 1.5 percent would be to have the savings bank pay a fixed rate of 9.5 percent or receive a variable rate of T-bill + 0.5 percent. Obviously, many rate combinations could be negotiated to achieve acceptable rate spreads and to achieve the desired interest rate risk management goals. e. What are some of the practical difficulties in arranging this swap?

The floating rate assets may not be tied to the same rate as the floating rate liabilities. This would result in basis risk. Also, if the mortgages are amortizing, the interest payments would not match those on the notional amount of the swap.

7.

Bank 1 can issue five-year CDs at an annual rate of 11 percent fixed or at a variable rate of LIBOR plus 2 percent. Bank 2 can issue five-year CDs at an annual rate of 13 percent fixed or at a variable rate of LIBOR plus 3 percent. a. Is a mutually beneficial swap possible between the two banks?

A mutually beneficial swap exists because comparative advantage exists. b. Where is the comparative advantage of the two banks?

Bank 1 has a comparative advantage in the fixed-rate market because the difference in fixed rates is 2 percent in favor of Bank 1. Bank 2 has the comparative advantage in the variable-rate market because the difference in variable rates is only –1 percent against Bank 1. One way to compare the rate alternatives is to utilize the following matrix.

Bank 1 Bank 2 Difference

Variable Rate LIBOR + 2% LIBOR + 3% -1%

Fixed Rate 11% 13% -2%

c. What is an example of a feasible swap?

Many rate combinations are possible to achieve a reduced interest charge. The following is a framework to achieve the outside boundaries of acceptable interest rates using the matrix of possible rates shown in part (b).

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Using the rates shown for Bank 1 as the negotiated swap rates will give the entire interest rate advantage to Bank 2. The diagram and payoff matrix below verifies this case.

Bank 2 Fixed-rate assets

Swap Cash Flows Fixed-rate swap payments

Bank 1 Variable-rate assets

11.0% LIBOR+2% Variable-rate swap payments Cash Financing Markets

Variable-rate liabilities @ LIBOR+3%

Fixed-rate liabilities @ 11%

The relative payoffs are given below: Cash market liability rate Minus swap rate Plus swap rate Net financing cost (rate)

Bank 2 LIBOR+3% -(LIBOR+2%) + 11% 12.0%

Bank 1 11% -11% +(LIBOR+2%) LIBOR+2%

Bank 1 is paying the rate it could achieve in the variable rate market. Thus, Bank 1 receives no benefit to these swap rates. Now consider the rates shown for Bank 2 in the matrix of rates in part (b).

Bank 2 Fixed-rate assets

Swap Cash Flows Fixed-rate swap payments

Bank 1 Variable-rate assets

11.0% LIBOR+1% Variable-rate swap payments

Variable-rate liabilities @ LIBOR+3%

Cash Financing Markets

Fixed-rate liabilities @ 11%

In this case, Bank 2 is receiving the exact rate it owes on the liabilities and it is paying the rate necessary if it was in the fixed-rate market. Bank 1 receives the entire 1 percent benefit as it is paying net 1 percent less than it would need to pay in the variable-rate market.

The relative payoffs are given below: Cash market liability rate Minus swap rate Plus swap rate Net financing cost rate

Bank 2 LIBOR+3% -(LIBOR+1%) + 11% 13%

8 © 2022

Bank 1 11% -11% +(LIBOR+1%) LIBOR+1%

Any swap rate combination between these two boundaries that yields a total saving in combined interest cost becomes a feasible set of negotiated swap rates. The exact set of rates will depend on negotiating position of each bank and the expected interest rates over the life of the swap. As an example, consider the average of the two fixed-rate payments and the average of the two variable-rate payments. The relative payoffs are given below: Cash market liability rate Minus swap rate Plus swap rate Net financing cost rate

Bank 2 LIBOR+3.0% -(LIBOR+2.5%) + 12.0% 12.5%

Bank 1 11.0% -12.0% +(LIBOR+2.5%) LIBOR+1.5%

In each case, the banks are paying 0.5 percent less than they would in the relative desired cash markets.

8.

First Bank can issue one-year, floating-rate CDs at prime plus 1 percent or fixed-rate CDs at 12.5 percent. Second Bank can issue one-year floating-rate CDs at prime plus 0.5 percent or fixed-rate at 11.0 percent. a. What is a feasible swap with all of the benefits going to First Bank?

The possible interest rate alternatives faced by each firm are given below:

First Bank Second Bank Difference

Variable Rate Prime+1.0% Prime+0.5% 0.5%

Fixed Rate 12.5% 11.0% 1.5%

The interest rate difference is 1.5 – 0.5 = 1.0 percent. Second Bank has the comparative advantage in the fixed-rate market and First Bank has the comparative advantage in the variablerate market. A set of swap rates within the feasible boundaries that will give all the benefits to First Bank is 11 percent fixed rate and Prime + 0.5 percent variable rate. b. What is a feasible swap with all of the benefits going to Second Bank?

A set of rates within the feasible boundaries that will give all the benefits to Second Bank is 12.5 percent fixed rate and Prime + 1.0 percent variable rate. c. Diagram each situation.

Diagram of all the benefits going to First Bank.

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First Bank Fixed-rate assets

Swap Cash Flows Fixed-rate swap payments

Second Bank Variable-rate assets

11.0% Prime+0.5% Variable-rate swap payments

Variable-rate liabilities @ Prime+1%

Cash Financing Markets

Fixed-rate liabilities @ 11%

The payoff matrix that demonstrates that all of the benefits go to First Bank follows.

Cash market liability rate Minus swap rate Plus swap rate Net financing cost rate

First Bank Prime+1% -(Prime+0.5%) + 11% 11.5%

Second Bank 11.0% -11.0% +(Prime+0.5%) Prime+0.5%

The net cost for First Bank is 11.5 percent, or 1 percent less than it would pay in the fixed-rate cash market. The net cost for Second Bank is exactly the same as it would pay in the variablerate cash market.

Diagram of all the benefits going to Second Bank.

First Bank Fixed-rate assets

Variable-rate liabilities @ Prime+1%

Swap Cash Flows Fixed-rate swap payments

Second Bank Variable-rate assets

12.5% Prime+1.0% Variable-rate swap payments Cash Financing Markets

Fixed-rate liabilities @ 11%

The net cost for First Bank is 12.5 percent, which is exactly what it would pay in the fixed-rate cash market. The net cost for Second Bank is Prime - 0.5 percent, or 1 percent less than it would pay in the variable-rate cash market. The payoff matrix that illustrates that all of the benefits go to Second Bank follows.

Cash market liability rate Minus swap rate Plus swap rate Net financing cost rate

First Bank Prime+1% -(Prime+1%) + 12.5% 12.5% 10 © 2022

Second Bank 11.0% -12.5% +(Prime+1%) Prime-0.5%

d. What factors will determine the final swap arrangement?

The primary factor that will determine the final distribution of the swap rates is the present value of the cash flows for the two parties. The most important no-arbitrage condition is that the present value of the expected cash flows made by the buyer should equal the present value of the expected cash flows made by the seller. Secondary factors include the negotiating strengths of either party to the transaction.

9.

Two multinational FIs enter their respective debt markets to issue $100 million of two-year notes. FI A can borrow at a fixed annual rate of 11 percent or a floating rate of LIBOR plus 50 basis points, repriced at the end of the year. FI B can borrow at a fixed annual rate of 10 percent or a floating rate of LIBOR, repriced at the end of the year. a. If FI A is a positive duration gap insurance company and FI B is a money market mutual fund, in what market(s) should each firm borrow to reduce its interest rate risk exposure?

FI A will prefer to borrow in the fixed-rate debt market in order to generate positive cash flows when interest rates increase. This will offset the impact of an increase in interest rates, which would cause the market value of the FI's equity to decline. FI B will prefer to borrow in the floating rate debt market so as to better match the duration of its short-term assets. b. In which debt market does FI A have a comparative advantage over FI B? The matrix of possible interest rates is given below.

FI A FI B Difference

Fixed rate 11.0% 10.0% 1.0%

Variable rate LIBOR+0.5% LIBOR % 0.5%

FI A has a comparative advantage in the floating-rate market and FI B has a comparative advantage in the fixed-rate market. This is because the default risk premium of FI A over FI B is 50 basis points in the floating-rate market and 100 basis points in the fixed-rate market. c. Although FI A is riskier than FI B and therefore must pay a higher rate in both the fixed-rate and floating-rate markets, there are possible gains to trade. Set up a swap to exploit FI A's comparative advantage over FI B. What are the total gains from the swap? Assume a swap intermediary fee of 10 basis points.

The total gains to the swap are 50 basis points (the price differential on FI A's default risk premium over FI B) less 10 basis points (the swap intermediary fee). Both FI A and B can exploit this price differential by issuing debt in the debt market in which they have comparative 11 © 2022

advantage and then swapping the interest payments. The 40 basis points can be allocated to either FI A and/or FI B according to the terms of the swap. A possible set of feasible swap rates that give all of the gains to FI A (see part (d) below) is illustrated here.

FI A Fixed-rate assets

Variable-rate liabilities @ LIBOR+0.5%

Swap Cash Flows Fixed-rate swap payments

FI B Variable-rate assets

10.0% LIBOR % Variable-rate swap payments Cash Financing Markets

Fixed-rate liabilities @ 10%

Evidence that FI A receives all of the benefits is given in the payoff matrix below.

FI A Cash market liability rate LIBOR+0.5% Minus swap rate -(LIBOR %) Plus swap rate + 10.0% Net financing cost rate 10.5% Less intermediary fee 0.1% Financing cost rate net of fee 10.6%

FI B 10.0% -10.0% +(LIBOR %) LIBOR %

FI A is paying the intermediary fee, since FI B is receiving no benefits from this swap transaction. The 40 basis point net differential could be shared in a number of other combinations where FI A received most (exploited) of the benefit. d. The gains from the swap can be apportioned between FI A and FI B through negotiation. What terms of swap would give all the gains to FI A? What terms of swap would give all the gains to FI B? All the gains go to FI A if FI B pays LIBOR for FI A's floating rate debt. Then FI A must pay 10 percent for FI B's fixed-rate debt plus 50 basis points on FI A's floating rate debt plus 10 basis points for the swap intermediary's fee. The total fixed annual interest cost to FI A is 10.6 percent, a savings of 40 basis points over the cash-market fixed rate of 11 percent. This swap rate apportionment is illustrated in part (c) above.

All the gains go to FI B if FI A pays 11 percent for FI B’s fixed-rate, 10 percent debt. Then FI B pays LIBOR plus 50 basis points on FI A's floating rate debt for a net savings of 50 basis points.

The savings occurs because FI B receives an excess 1 percent from FI A, but must pay 50 basis points more to FI A than it would pay in the cash floating-rate market. FI A must pay 11 percent against FI B's fixed-rate debt, but receives its exact liability payment from FI B. A diagram of this allocation is given below.

12 © 2022

FI A Fixed-rate assets

Swap Cash Flows Fixed-rate swap payments

FI B Variable-rate assets

11.0% LIBOR+0.5% Variable-rate swap payments Cash Financing Markets

Variable-rate liabilities @ LIBOR+0.5%

Fixed-rate liabilities @ 10%

In this example, FI B would pay the swap intermediary fee of 10 basis points, and thus would realize a net, after-fee savings of 40 basis points. The payoff matrix is given below.

FI A LIBOR+0.5% -(LIBOR+0.5 %) + 11.0% 11.0%

Cash market liability rate Minus swap rate Plus swap rate Net financing cost rate Less intermediary fee Financing cost rate net of fee

FI B 10.0% -11.0% +(LIBOR+0.5 %) LIBOR-0.5% 0.1% LIBOR-0.4%

e. Assume swap pricing that allocates all gains from the swap to FI A. If FI A buys the swap from FI B and pays the swap intermediary's fee, what are the realized net cash flows if LIBOR is 8.25 percent?

FI A (in millions of dollars) Pays out fixed rate ($10.00) Receives LIBOR from B $8.25 Pays floating-rate to creditors (LIBOR+0.5%) ($8.75) Pays intermediary fee ($0.10) Net cash inflow ($10.60)

FI B Pays out LIBOR Receives fixed rate from A Pays fixed-rate to creditors

($8.25) $10.00 ($10.00)

Net cash inflow

($8.25)

This solution is an extension of the diagram in part (c) and the explanation at the beginning of part (d) above where LIBOR is 8.25 percent. The summary shows the effective cost rate converted to dollars for the total cash flows of each FI. However, the cash flows in a swap arrangement include only the differential cash flows between the two parties. Thus, at the end of the year, FI A would pay $1.75m ($10.00m - $8.25m) to FI B and $0.10m to the intermediary for a total cash flow on the swap arrangement of $1.85m. FI B receives $1.75m from FI A. f. If FI A buys the swap in part (e) from FI B and pays the swap intermediary's fee, what are the realized net cash flows if LIBOR is 11 percent? Be sure to net swap payments against cash market payments for both FIs. FI A (in millions of dollars) Pays out fixed rate ($10.00)

FI B Pays out LIBOR 13 © 2022

($11.00)

Receives LIBOR from B $11.00 Pays floating-rate to creditors (LIBOR+0.5%)($11.50) Pays intermediary fee ($0.10) Net cash inflow ($10.60)

Receives fixed rate from A $10.00 Pays fixed-rate to creditors ($10.00)

Net cash inflow

($11.00)

Even though LIBOR has increased to 11 percent, FI A’s total effective cost rate has not changed.

The rate remains at 10.60 percent, or a total of $10.60 million. However, the cost rate for FI B has increased because LIBOR has increased. Thus, the actual cash flows in the swap transaction now are such that FI B pays $1.00m ($11m - $10m) to FI A, and that FI A receives $1.00m and pays out $0.10m to the intermediary. Each FI, of course, must pay the cash market liability rates. g. If all barriers to entry and pricing inefficiencies between FI A's debt markets and FI B's debt markets were eliminated, how would that affect the swap transaction?

If relative prices are the same in the markets of both FI A and FI B, then there are no potential gains to trade and therefore no swap transaction can take place. Each FI will issue debt in their respective debt markets.

10.

What are off-market swap arrangements? How are these arrangements negotiated?

An off-market swap is a customized swap arrangement where one party pays to the other party a fee to relax certain terms of the swap agreement. Terms that are relaxed often include interest rates, the use of special indexes, and changes in the notional values as the swap matures.

11.

Describe how an inverse floater swap works to the advantage of an investor who receives coupon payments of 10 percent minus LIBOR if LIBOR is currently at 4 percent. When is it a disadvantage to the investor? Does the issuing party bear any risk?

An inverse floater pays coupon interest of 10% - 4% to the investor at current rates. Thus, an investor who purchases this instrument at LIBOR will receive a return of 6%. If LIBOR decreases below 4 percent, the investor receives a higher return. However, the danger occurs if LIBOR rises above 10 percent, in which case the investor receives nothing and may be stuck with this investment. The losses will depend on the opportunity costs associated with these funds. The issuing party only pays the LIBOR rate less the 4 percent (unless it has been swapped) and is subject to the risk that the LIBOR rates will decline.

12.

An FI has $500 million of assets with a duration of nine years and $450 million of liabilities with a duration of three years. The FI wants to hedge its duration gap with a swap that has fixed-rate payments with a duration of six years and floating-rate payments with a duration of two years. What is the optimal amount of the swap to effectively macrohedge against the adverse effect of a change in interest rates on the value of the FI’s equity?

Using the formula, 14 © 2022

NS = [(DA - kDL)A]/(DFixed – DFloating) = [(9 – 0.9 x 3)$500 million]/(6 – 2) = $787.5 million.

13.

A U.S. thrift has most of its assets in the form of Swiss franc-denominated floating-rate loans. Its liabilities consist mostly of fixed-rate dollar-denominated CDs. What type of currency risk and interest rate risk does this FI face? How might it use a swap to eliminate some of these risks?

The thrift is exposed to a drop in interest rates and a devaluation of the Swiss franc. It might want to change its assets to fixed-rate dollar-denominated assets. Alternatively, if it could find a counterparty willing to receive floating-rate francs while paying fixed-rate dollars, the thrift could reduce its interest rate risk and its exchange rate risk.

14.

A Swiss bank issues a $100 million, three-year Eurodollar CD at a fixed annual rate of 7 percent. The proceeds of the CD are lent to a Swiss company for three years at a fixed rate of 9 percent. The spot exchange rate is SF1.50/$. a. Is this expected to be a profitable transaction?

This transaction is expected to be profitable since the spread is 2 percent. b. What are the cash flows if exchange rates are unchanged over the next three years?

The 2 percent spread on $100 million (SF150 million) is $2 million. Converting into Swiss francs at the spot exchange rate yields an annual expected cash flow of SF3 million. The cash flows are as follows: t 1 2 3

Eurodollar CD Cash Outflow (US$) 7m 7m 107m

Swiss loan cash inflow (SF) 13.5m 13.5m 163.5m

(SF) 10.5m 10.5m 160.5m

Spread (SF) 3m 3m 3m

c. What is the risk exposure of the bank's underlying cash position?

This spread will be reduced or eliminated if the SF depreciates relative to the U.S. dollar. That is, if it takes more SFs to purchase U.S. dollars, it will be more costly for the bank to repay the Eurodollar CD using SF loan proceeds. d. How can the Swiss bank reduce that risk exposure?

The Swiss bank can undertake a short currency hedge if it wants to protect itself against exchange rate risk exposure.

15 © 2022

e. If the US dollar is expected to appreciate against the SF to SF1.65/$, SF1.815/$, and SF2.00/$ over the next three years, respectively, what will be the cash flows on this transaction? t 1 2 3

Eurodollar CD Cash Outflow (US$) 7m 7m 107m

(SF) 11.550m 12.705m 214.000m

Swiss loan cash inflow (SF) 13.5m 13.5m 163.5m

Spread (SF) 1.950m 0.795m (50.500m)

f. If the Swiss bank swaps US dollar payments for SF payments at the current spot exchange rate, what are the cash flows on the swap? What are the cash flows on the entire hedged position? Assume that the U.S. dollar appreciates at the rates in part (e). t 1 2 3

Cash flow (SF) 11.55m 12.705m 214.00m

Swap payments(SF) 10.5m 10.5m 160.5m

Net swap cash flow (SF) 1.05m 2.205m 53.5m

Total cash flow 3m 3m 3m

The cash flows of the underlying cash position from part (e) are added to the net cash flows from the swap hedge (column four) to give the total cash flows in column five. That is, at the end of the first year, the spread on the loan CD is SF1.95m. The swap generates a net cash flow of SF1.05m for a total end of year 1 spread of SF3 million. At the end of year 2, the SF0.795m loan CD spread plus the SF2.205m net swap cash flow equals SF3m. At the end of year 3, the SF50.5m loss on the loan CD position is offset by the SF53.5m gain on the swap for a total cash flow of SF3m. Therefore, the hedged position locks in the annual 2 percent spread. g. What are the cash flows on the swap and the hedged position if actual spot exchange rates are as follows: End of year 1: SF1.55/US$ End of year 2: SF1.47/US$ End of year 3: SF1.48/US$ t 1 2 3

CD cash flow (SF) 10.85m 10.29m 158.36m

Swap payments(SF) 10.5m 10.5m 160.5m

Net swap cash flow (SF) 0.35m (0.21m) (2.14m)

Total cash flow 3m 3m 3m

Total end of year 1 cash flows are net swap cash flows of SF0.35m plus the loan - CD spread of SF2.65m (SF13.5m - SF10.85m). Total end of year 2 cash flows are -SF0.21m on the swap plus SF3.21m (SF13.5m - SF10.29m). End of year 3 cash flows are -SF2.14m on the swap plus SF5.14m on the loan - CD spread (SF163.5m - SF158.36m). The loan cash flows in SF are given in column four of part (e).

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h. What would be the bank's risk exposure if the fixed-rate Swiss loan was financed with a floating rate U.S. $100 million, three-year Eurodollar CD? The Swiss bank is now exposed to both exchange rate risk and interest rate risk. If the SF depreciates against the U.S. dollar and/or the Eurodollar CD floating rate increases, the spread on the unhedged position will be reduced. i. What type of hedge is appropriate if the Swiss bank in part (h) wants to reduce its risk exposure?

If the bank wants to hedge its risk exposure, it should enter a short currency hedge and a short interest rate hedge. j. If the annual Eurodollar CD rate is set at LIBOR and LIBOR at the end of years 1, 2, and 3 is expected to be 7 percent, 8 percent, and 9 percent, respectively, what will be the cash flows on the bank's unhedged cash position? Assume no change in exchange rates. t 1 2 3

Eurodollar CD cash outflow (US$) 7m 8m 109m

Swiss loan cash inflow (SF) 13.5m 13.5m 163.5m

(SF) 10.5m 12.0m 163.5m

Spread (SF) 3m 1.5m 0m

The spread on the underlying cash position is reduced when rates increase even if exchange rates are held constant. k. What are the cash flows on the bank's unhedged cash position if exchange rates are as follows: End of year 1: SF1.55/US$ End of year 2: SF1.47/US$ End of year 3: SF1.48/US$ t 1 2 3

Eurodollar CD cash outflow (US$) 7m 8m 109m

Swiss loan cash inflow (SF) 13.5m 13.5m 163.5m

(SF) 10.85m 11.76m 161.32m

Spread (SF) 2.65m 1.74m 2.18m

Without the swap, the cost to the bank of meeting the Eurodollar CD payments at the end of year 1 would be SF10.85m (US$7m x 1.55). At the end of year 2 the cost would be SF11.76m (US$8m x 1.47). At the end of year 3, the cost would be SF161.32m (US$109m x 1.48).

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l. What are both the swap and total hedged position cash flows if the bank swaps out its floating rate US$ CD payments in exchange for 7.75 percent fixed-rate SF payments at the current spot exchange rate of SF1.50/$?

Net swap t Cash flow (SF) Swap payments(SF) cash flow (SF) Total cash flow 1 10.85m $7.75mx1.5=11.625m (0.775m) 1.875m 2 11.76m $7.75mx1.5=11.625m 0.135m 1.875m 3 161.32m $107.75mx1.5=161.625m (0.305m) 1.875m The total cash flows are: End of year 1 = swap loss of SF0.775m plus spread of SF2.65m.

End of year 2 = swap gain of SF0.135m plus spread of SF1.74m.

End of year 3 = swap loss of SF0.305m plus spread of SF2.18m.

The swap hedge locks in both an interest spread of 1.25 percent (9% - 7.75%) and an exchange rate of SF1.5. Based on a face value of $100m (SF150m), this yields a profit of $1.25m or SF1.875 million each year. m. If forecasted interest rates are 7 percent, 10.14 percent, and 10.83 percent over the next three years, respectively, and exchange rates over the next years are those in part (k), calculate the cash flows on an 8.75 percent fixed-floating-rate swap of U.S. dollars to Swiss francs at SF1.50/$.

Net swap t Cash flow (SF) Swap payments(SF) cash flow (SF) Total cash flow 1 10.85m 13.125m (2.275m) 0.375m 2 14.906m 13.125m 1.781m 0.375m 3 164.028m 163.125m 0.903m 0.375m The second year annual interest on the floating rate CD would have been US$10.14m or SF10.85m (at the prevailing exchange rate of SF1.47/$). The third year annual interest on the floating rate CD would have been US$110.83m or SF164.028m (at the prevailing exchange rate of SF1.48/$). The fixed swap interest payment was SF13.125 ($8.75m x 1.50) in each year. The swap hedge locks in a spread of 0.25 percent at SF1.50 for an annual cash flow of SF0.375million. Year 1 cash flows = SF13.5m – SF10.85m – SF2.275m. Year 2 cash flows = SF13.5m – SF14.906m + SF1.781m. Year 3 cash flows = SF163.5m – SF164.028m + SF0.903m.

15.

Bank A has the following balance sheet information (in millions): Assets Rate-sensitive assets Fixed-rate assets

$50 150

Total assets

$200

Liabilities and Equity Rates-sensitive liabilities Fixed-rate liabilities Net worth Total liabilities and equity

$75 100 25 $200

Rate-sensitive assets are repriced quarterly at the 91-day Treasury bill rate plus 150 basis points. Fixed-rate assets have five years until maturity and are paying 9 percent annually.

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Rate-sensitive liabilities are repriced quarterly at the 91-day Treasury bill rate plus 100 basis points. Fixed-rate liabilities have two years until maturity and are paying 7 percent annually. Currently, the 91-day Treasury bill rate is 6.25 percent. a. What is the bank's current net interest income? If Treasury bill rates increase 150 basis points, what will be the change in the bank's net interest income?

Interest income = 50(0.0625 + 0.015) + 150(0.09) = $17.375 million, and interest expense = 75(0.0625 + 0.01) + 100(0.07) = $12.4375 million. Thus, net interest income = $4.9375 million.

After the interest rate increase, interest income = 50(0.0775 + 0.015) + 150(0.09) = $18.125 million, interest expense = 75(0.0775 + 0.01) + 100(0.07) = $13.5625 million, and net interest income = $4.5625 million for a decline of $375,000. b. What is the bank's repricing or funding gap? Use the repricing model to calculate the change in the bank's net interest income if interest rates increase 150 basis points.

Funding gap = Rate sensitive assets - Rate sensitive liabilities = 50 - 75 = - $25 million. The repricing model states that NII = GAP( R) = -25(0.015) = - $0.375 million. The bank is exposed to interest rate increases since interest expense increases more than interest income. c. How can swaps be used as an interest rate hedge in this example?

A short hedge can be used to hedge the bank's interest rate risk exposure. The short hedge can be implemented by selling futures or forward contracts, buying put options, or buying a swap of liabilities. Swapping liabilities allows the institution to make fixed-rate liability payments in exchange for a counter-party making the floating rate payments. Similarly, the FI could also swap assets. The short hedge can be accomplished by swapping out fixed-rate asset payments in exchange for floating-rate asset payments.

16.

Use the following information to construct a swap of asset cash flows for the bank in problem 15. The bank is a price taker in both the fixed-rate market at 9 percent and the rate-sensitive market at the T-bill rate plus 1.5 percent. A securities dealer has a large portfolio of rate sensitive assets funded with fixed-rate liabilities. The dealer is a price taker in a fixed-rate market paying 8.5 percent and a floating-rate market paying the 91-day T-bill rate plus 1.25 percent. All interest is paid annually. a. What is the interest rate risk exposure to the securities dealer?

The securities dealer is exposed to interest rate declines. b. How can the bank and the securities dealer use a swap to hedge their respective interest rate risk exposures?

The two counterparties can use a swap to hedge their respective interest rate risk exposures. The bank would swap out fixed-rate payments in exchange for floating-rate payments to yield 18

positive cash flows when interest rates increase. The securities dealer would swap out floatingrate payments in exchange for fixed-rate payments to yield positive cash flows when interest rates decrease. c. What are the total potential gains to the swap?

The total gains to the swap trade are 25 basis points. This is because the bank earns a 25 basis point premium in the floating-rate market and a 50 basis point premium in the fixed-rate market. d. Consider the following two-year swap of cash flows: An annual fixed-rate cash flow of 8.6 percent in exchange for a floating-rate cash flow of T-bill plus 125 basis points. The swap intermediary fee is 5 basis points. How are the swap gains apportioned between the bank and the securities dealer if they each hedge their interest rate risk exposures using this swap?

Bank

Swap Cash Flows Variable-rate Fixed-rate swap payments liabilities T-bill+1.25%

8.6%

Securities Dealer Fixed-rate liabilities

Variable-rate swap payments

Fixed-rate

Cash Financing Markets

Variable-rate

assets @ 9.0%

Cash market asset rate Minus swap rate Plus swap rate Net financing cost rate Minus swap intermediary fee Minus cash market rate Net gain from swap

assets @

Bank 9.00% -8.60% T-bill+1.25% T-bill+1.65% -0.05% T-bill+1.60% T-bill+1.50% 0.10%

T-bill+1.25%

Securities Dealer T-bill+1.25% -(T-bill+1.25%) 8.60% 8.60%

8.50% 0.10%

The securities dealer gains 10 basis points because it obtains fixed-rate cash inflows at 8.6 percent instead of the 8.5 percent available in its cash market. The bank gains 10 basis points because it obtains floating rate cash inflows at T-bill + 1.60 percent instead of the T-bill + 1.50 percent available in its cash market. The remaining 5 basis points goes to the swap intermediary. e. What are the realized cash flows if T-bill rates at the end of the first year are 7.75 percent and at the end of the second year are 5.5 percent? Assume that the notional value of the swap is $107.14 million.

At the end of the first year (in millions of dollars): 19

Bank Cash Flows

Securities Dealer Cash Flows

20

Swap cash inflows 107.14(0.0775 + 0.016) = $10.0176 Cash market cash flows 107.14(0.09) = $9.6426 Net swap gain (loss) $0.375

107.14(0.086) =

$9.214

107.14(0.0775 + 0.0125) = $9.6426 ($0.4286)

The dealer pays the bank $375,000 to offset the decline in net interest income when interest rates increase (see part a) and pays the swap intermediary $53,600 (5 basis points), for a total cost of $428,600 when interest rates increase 150 basis points.

At the end of the second year, interest rates decline to 5.5%.

Bank Cash Flows Dealer Cash Flows Swap cash inflows 107.14(0.0550 + 0.016) = $7.607 107.14(0.086) = Cash market cash flows 107.14(0.09) = $9.6426 107.14(0.055 + 0.0125) = Net swap gain (loss) ($2.036)

$9.214 $7.232 $1.982

The bank pays the dealer $1.982 million and pays the swap intermediary $53,600 (5 basis points), for a total cost of $2.036 million when interest rates decrease 75 basis points. f. What are the sources of the swap gains to trade?

The gains to the swap trade emanate from the pricing discrepancy in the two cash markets. That is, the bank earns a 50 basis point premium in the fixed-rate market, while only a 25 basis point premium in the floating rate market. The swap allows both the bank and the securities dealer to exploit their own comparative advantage in their respective cash market. g. What are the implications for the efficiency of cash markets?

There must be some barrier that prevents the two firms from directly transacting in the other's cash market (or equivalently raises the costs of these cross-market transactions). This barrier may consist of regulatory restrictions or tax considerations. If, however, the barrier results from information asymmetries, these potential gains to trade can be expected to disappear as the swap market develops.

17.

Consider the following currency swap of coupon interest on the following assets: 5 percent (annual coupon) fixed-rate U.S. $1 million bond 5 percent (annual coupon) fixed-rate bond denominated in Swiss francs (SF) Spot exchange rate: SF1.5/$ a. What is the face value of the SF bond if the investments are equivalent at spot rates?

U.S. $1 million is equivalent to SF1.5 million face value.

21

b. What are the realized cash flows, assuming no change in spot exchange rates? What are the net cash flows on the swap?

Interest payments on the U.S. bond are 0.05(U.S.$1 million) = $50,000. In Swiss francs, interest payments are 0.05(SF1.5 million) = SF75,000. At spot exchange rates, these two cash flows are identical. There are no net swap cash flows. c. What are the cash flows if the spot exchange rate falls to SF0.50/$? What are the net cash flows on the swap?

Coupon payments on the U.S. bond are $50,000, which is equivalent to SF25,000. Coupon payments on the Swiss franc bond are SF75,000, which is equivalent to $150,000. The net cash flows on the swap are $100,000, or SF50,000. The counterparty that swaps in Swiss franc bond payments receives the cash flows. The counterparty that swaps in the U.S. dollar payments makes the payments. d. What are the cash flows if the spot exchange rate rises to SF2.25/$? What are the net cash flows on the swap?

Coupon payments on the U.S. bond are $50,000, which is equivalent to SF112,500. Coupon payments on the Swiss franc bond are SF75,000, which is equivalent to $33,333. The net cash flows on the swap are $16,667, or SF37,500. The counterparty that swaps in U.S. dollar bond payments receives the cash flows. The counterparty that swaps in the Swiss franc payments makes the payments. e. Describe the underlying cash position that would prompt the FI to hedge by swapping dollars in exchange for Swiss francs.

The FI is swapping dollar cash flows in exchange for Swiss francs so as to balance a U.S. dollardenominated liability.

18.

Consider the following fixed-floating-rate currency swap of assets: 5 percent (annual coupon) fixed-rate U.S. $1 million bond and floating-rate SF1.5 million bond set at LIBOR annually. Currently LIBOR is 4 percent. The face value of the swap is SF1.5 million. The spot exchange rate is SF1.5/$. a. What are the realized cash flows on the swap at the spot exchange rate?

Coupon payments on the U.S. bond are $50,000, which is equivalent to SF75,000. Coupon payments on the Swiss franc bond are SF60,000 at the spot rate of LIBOR of 4%, which is equivalent to $40,000. The net cash flows on the swap are $10,000, or SF15,000. The counterparty that swaps in U.S. dollar bond payments receives the cash flows. The counterparty that swaps in the Swiss franc payments makes the payments. b. If the 1-year forward rate is SF1.538 per US$, what are the realized net cash flows on the swap? Assume LIBOR is unchanged.

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Coupon payments on the U.S. bond are $50,000, which at forward rates, is equivalent to SF76,900. Coupon payments on the Swiss franc bond are SF60,000, which is equivalent to $39,012. The net cash flows on the swap are $10,988, or SF16,900. The counterparty that swaps in U.S. dollar bond payments receives the cash flows. The counterparty that swaps in the Swiss franc payments makes the payments. c. If LIBOR increases to 6 percent, what are the realized cash flows on the swap?

Evaluate at the forward rate.

Coupon payments on the U.S. bond are $50,000, which at forward rates, is equivalent to SF76,900. Coupon payments on the Swiss franc bond are SF90,000 at the spot rate of LIBOR of 6 percent, which is equivalent to $58,518. The net cash flows on the swap are U.S. $8,518, or SF13,100. The counterparty that swaps in Swiss franc bond payments receives the cash flows.

The counterparty that swaps in the U.S. dollar payments makes the payments.

19.

Give two reasons why credit swaps have been the fastest-growing form of swaps in recent years?

First, FIs remain more likely to fail because of credit risk than either interest rate risk or FX risk.

Second, credit swaps allow for the maintenance of long-term relationships without the FI bearing the full exposure to the credit risk of the customer.

20.

What is a total return swap?

A total return swap involves swapping an obligation to pay interest at a specified fixed or floating rate for payments representing the total return on a loan or a bond of a specific amount.

The swap can be designed to cover any change in value of the principal as well as just the interest. This type of swap often is used when there is exposure to a change in the credit risk of the counterparty.

21.

How does a pure credit swap differ from a total return swap? How does it differ from a digital default option?

The total return swap includes an element of interest rate risk, while the pure credit swap has stripped this risk from the contract. In a pure credit swap, the lender makes a fixed fee or payment premium to the counterparty in exchange for the potential coverage of any loss due to a specific borrower defaulting on a loan. The swap is not tied to interest rate changes. The pure credit swap is similar in payoff to a digital default option with the exception that the premium is paid over the life of the swap rather than at the initiation of the risk coverage as with the option.

22.

Why is the credit risk on a swap lower that the credit risk on a loan?

The credit risk on a swap is lower than that of a loan for the following reasons:

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a) In most cases, payments are made through netting by novation, which nets all payments with one counterparty, further reducing the possibility of default. b) Swaps do not involve the exchange of principal payments. They only involve the swapping of interest payments, so the most a counterparty can lose is the difference in the interest payments. c) Swaps made by parties with poor credit ratings are usually backed by lines of credit, effectively making them collateralized loans, and further reducing their risks.

23.

What is netting by novation?

Netting by novation involves the process of combining all contracts between two parties to determine the differential amount that must be forwarded from one party to another. Thus, all fixed-rate and variable-rate contracts are combined for a net payment. This reduces the potential for loss when some contracts are in-the-money and some contracts are out-of-the-money.

24.

What role did the swap market play in the financial crisis of 2008-2009?

The financial crisis showed just how much risk the swap market can present to FIs and the global financial system. Specifically, as the subprime mortgage market began to fail in the summer of 2008, subprime mortgage pools that FIs bought were overrated and ended up falling precipitously in value as foreclosures rose on the underlying mortgage pools. Many of the credit default swaps were written on these subprime mortgage securities. Thus, as mortgage securities started to fail, buyers of the CDS contracts wanted to be paid for these losses. AIG was a major writer of these CDS securities. As of June 30, 2008, AIG had written $441 billion worth of swaps on corporate bonds and mortgage-backed securities. And, when mortgage-backed securities started going bad, AIG had to make good on billions of dollars of credit default swaps.

The problem was exacerbated by the fact that so many FIs were tied to one another through these deals. Lehman Brothers alone had made more than $700 billion worth of swaps, and many of them were backed by AIG. As the value of these insured-referenced entities fell, AIG had massive write-downs and additionally had to post more collateral. Soon it became clear that AIG was not going to be able to cover its losses. The result was massive write-downs at banks, investment banks, and insurance companies that had purchased the CDS contracts. Indeed, the reason the federal government stepped in and bailed out AIG was that the insurer was something of a last backstop in the CDS market. While banks and hedge funds were playing both sides of the CDS business—buying and trading them and thus offsetting whatever losses they took—AIG was simply providing the swaps and holding onto them. Had AIG been allowed to default, every FI that had bought a CDS contract from the company would have suffered huge losses in the value of the insurance contracts they had purchased, causing them their own credit problems.

Global funding market pressures were also evident in the virtual shut-down of the FX swap market during the financial crisis. This risk was driven by demand for dollar funding from global financial institutions, particularly European financial institutions. As many of these institutions increasingly struggled to obtain funding in the unsecured cash markets, they turned to the FX swap market as a primary channel for raising dollar funding. This extreme demand for dollar funding led a sizable shift in FX forward prices, with the implied dollar funding rate 24

observed in FX swaps on many major currencies rising sharply above that suggested by the other relative interest measures such as the dollar OIS (overnight index swap) rate and the dollar Libor.

Dealers reported that bid-ask spreads on FX swaps increased to as much as 10 times the levels that had prevailed before August 2007. During the quarter, the spread of the three month FX swap-implied dollar rate from euro and sterling—US dollar FX forward points—over the dollar Libor fixing rate widened to around 330 and 260 basis points, respectively, in early October after the Lehman failure.

The following problem refers to material in Appendix 24A. 25.

The following information is available on a three-year swap contract. One-year maturity zero-coupon discount yields are currently priced at par and pay a coupon rate of 5 percent.

Two-year maturity zero-coupon discount yields are currently 5.51 percent. Three-year maturity zero-coupon discount yields are currently 5.775 percent. The terms of a three-year swap of $100 million notional value are 5.45 percent annual fixed-rate payments in exchange for floating-rate payments tied to the annual discount yield. a. If an insurance company buys this swap, what can you conclude about the interest rate risk exposure of the company's underlying cash position?

Buying the swap is a short hedge position that is profitable when interest rates increase.

Therefore, the insurance company's underlying cash position is exposed to interest rate increases, e.g., as in a positive duration gap and/or a negative repricing gap. b. What are the realized cash flows expected over the three-year life of the swap?

If the year 1 discount yields are: d1 = 5 percent, d2 = 5.51 percent, and d3 = 5.775 percent, then the expected future spot rates can be calculated from the implied forward rates: (1.0551)2 = (1.05)[1 + E(1r1)] => E(1r1)= 6.02 percent (1.05775)3 = (1.0551)2[1 + E(2r1)] => E(2r1) = 6.31 percent End of year-1 expected cash flows: Cash outflow -$5.45 million + Cash inflow $5 million = -$0.45 million net cash outflow End of year-2 expected cash flows: Cash outflow -$5.45 million + Cash inflow $5.51 million = $0.06 million net cash inflow End of year-3 expected cash flows: Cash outflow -$5.45 million + Cash inflow $5.775 million = $0.325 million net cash inflow c. What are the realized cash flows that occur over the three-year life of the swap if d2 = 4.95 percent and d3 = 6.1 percent?

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If the year 1 discount yields are: d1 = 5 percent, d2 = 4.95 percent, and d3 = 6.1 percent, then the expected future spot rates can be calculated from the implied forward rates: (1.0495)2 = (1.05)[1 + E(1r1)] => E(1r1)= 4.90 percent (1.061)3 = (1.0495)2[1 + E(2r1)] => E(2r1) = 8.44 percent End of year-1 expected cash flows: Cash outflow -$5.45 million + Cash inflow $5 million = $045 million net cash outflow End of year-2 expected cash flows: Cash outflow -$5.45 million + Cash inflow $4.90 million = $0.55 million net cash outflow End of year-3 expected cash flows: Cash outflow -$5.45 million + Cash inflow $8.44 million = $2.99 million net cash inflow

Integrated Mini Case: Hedging Interest Rate Risk with Futures versus Options versus Swaps On January 4, 2018, an FI has the following balance sheet (rates = 8 percent) Assets A

450m

DA = 8 years

L E

Liabilities/Equity 396m DL = 4 years 54m

DGAP = [8 – (396/450)4] = 4.48 years > 0 The FI manager thinks rates will increase by 0.55 percent in the next three months. If this happens, the equity value will change by: E = −[8 − 396 (4)]450m 0.0055 = −$10 ,266 ,667 450

1.08

The FI manager will hedge this interest rate risk with either futures contracts, option contracts, or swap contracts.

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If the FI uses futures, it will select June T-bonds to hedge. The duration on the T-bonds underlying the contract is 14.5 years and the T-bond futures are selling at a price of $110.53125 per $100, or $110,531.25. T-bond futures rates, currently 5 percent, are expected to increase by 0.75 percent over the next three months.

If the FI uses options, it will buy puts on 15-year T-bonds futures with a June maturity, an exercise price of 109, and an option premium of 36 64 percent. The spot price on the T-bond underlying the option is $115.78125 per $100 of face value. The duration on the T-bonds underlying the options is 14.5 years and the delta of the put options is -0.85. Managers expect these T-bond rates to increase by 0.7 percent from 5.25 percent in the next three months.

If the FI uses swaps, a swap agent offers a swap involving DFixed = 8 years (based on the 15-year Treasury bond rate) and DFloating = 1 year (based on Treasury bills).

If by April 4, 2018, balance sheet rates increase by 0.5 percent, futures rates by 0.7 percent, and T-bond rates underlying the option contracts by 0.66 percent, calculate the on- and off-balancesheet cash flows to the FI when using futures contracts, option contracts, and swap contracts as its hedge instrument.

For the hedge with futures contracts:

br = 0.0075 / 0.0055 = 1.4025974 N = 1.05

F

1.08

[8−(396 / 450)4]450m

= 896.818 contracts

14.5110,531.251.4025974

On April 4, 2018, as the FI gets out of the futures hedge: Loss on balance sheet

Gain off balance sheet (futures)

E = −[8 − 396 (4)]450m 0.005 = 450

− $9,333,333

F = −14.5(−896.818) 110,531.25 0.007 =

1.08

1.05

$9,582,222

The net gain is $9,582,222 - $9,333,333 = $248,889 For a hedge with option contracts:

br = 0.007 / 0.0055 =1.3059814, N = 1.0525

o

1.08

= 1,081.7536 contracts

[8−( 396 450 )4]450m 0.8514.5115,781.251.3059814

On April 4, 2018, as the FI gets out of the option hedge: Loss on balance sheet E = −[8− 396(4)]450m 0.005 = 450

Gain off balance sheet (options) 0 =1,081.7536(−0.85)(−14.5)115,781.25 0.0066 =

1.08

1.0525

-$9,333,333

$9,680,000 27

The net gain is $9,333,333 - $9,680,000 = $346,667

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For a hedge with swap contracts: N = s

[8−(396450)4]450m

= $288,000,000 buy swap

8−1

On April 4, 2018 as the FI gets out of the swap hedge: Loss on balance sheet E = −[8− 396(4)]450m 0.005 = 450

Gain off balance sheet (swaps) ∆Swap value = (8 - 1) × $288,000,000 × 0.0005/1.08

1.08

-$9,333,333

$9,333,333

The net gain is $9,333,333 - $9,333,333 = $0 In this case, the FI would be better off hedging with option contracts rather than futures or swap contracts.

If by April 4, 2018, balance sheet rates actually fall by 0.25 percent, futures rates fall by 0.35 percent, and T-bond rates underlying the option contract fall by 0.34 percent, calculate the on and off-balance-sheet cash flows to the FI when using futures contracts, option contracts, and swap contracts as its hedge instrument.

On April 4, 2018, as the FI gets out of the futures hedge: Loss on balance sheet

E = −[8 − 396 (4)]450m −0.0025 = 450

Gain off balance sheet (futures)

F = −14.5(−896.818) 110,531.25 −0.0035 =

1.08

1.05

− $4,791,111

$4,666,667

The net gain is $4,666,667 - $4,791,111 = -$124,444 For a hedge with option contracts: On April 4, 2018, as the FI gets out of the option hedge, the value of the T-bond underlying the put option has increased. The FI does not have to exercise these options if the loss on exercise is greater than the option premium. Thus: Loss on balance sheet

E = −[8− 396(4)]450m −0.0025 450

Gain off balance sheet (options) Exercise: 0 =1,081.7536(−0.85)(−14.5)115,781.25−0.0034 =

1.08

1.0525

= $4,666,667

-$4,986,667 No exercise: O=1,081.7536100,000(-36/64%) 29

= -$608,486

30

The FI will not exercise the options, taking the loss. Rather, it will let the options expire unused.

Thus, the net gain is $4,666,667 - $608,486 = $4,058,181 For a hedge with swap contracts: On April 4, 2018, as the FI gets out of the swap hedge: Loss on balance sheet E = −[8− 396 (4)]450m −0.0025 = 450

Gain off balance sheet (swaps) ∆Swap value = (8 - 1) × $288,000,000 × -0.0025/(1.08))

1.08

$4,666,667

-$4,666,667

The net gain is $4,666,667 - $4,666,667 = $0 In this case, the FI would again be better off hedging with option contracts rather than futures or swap contracts.

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Solutions for End-of-Chapter Questions and Problems: Chapter Twenty-Five 1.

What is the difference between loans sold with recourse and loans sold without recourse from the perspective of both sellers and buyers?

Loans sold without recourse means that the credit risk is transferred entirely to the buyer. In the event the loan is defaulted, the buyer of the loan has no recourse to the seller for any claims.

Thus, the originator of the loan can take it off the balance sheet after selling the loan. In the case of a sale with recourse, credit risk is still present for the originator because the buyer could transfer ownership of the loan back to the originator. Thus, from the perspective of the buyer, loans with recourse bear the least amount of credit risk.

2.

A bank has made a three-year $10 million loan that pays annual interest of 8 percent. The principal is due at the end of the third year. a. The bank is willing to sell this loan with recourse at an interest rate of 8.5 percent.

What price should it receive for this loan?

If the bank sells with recourse, it should expect: ($0.80m) x PVAn=3, k=8.5 + ($10m) x PVn=3, k=8.5 = $9.8723 million b. The bank has the option to sell this loan without recourse at a discount rate of 8.75 percent. What price should it receive for this loan?

If the bank sells without recourse, it should expect: ($0.80m) x PVAn=3, k=8.75 + ($10m) x PVn=3, k=8.75 = $9.8093 million c. If the bank expects a 0.5 percent probability of default on this loan, is it better to sell this loan with or without recourse? It expects to receive no interest payments or principal if the loan is defaulted.

If sold with recourse and the expected probability of default is taken into account, it should expect to receive (0.995) x $9.8723 = $9.8229, which is still higher than selling it without recourse. So, it should sell it with recourse.

3.

What are some of the key features of short-term loan sales?

Short-term loan sales usually consist of maturities between one and three months and are secured by the assets of a firm. They usually are sold in units of $1 million or more and are made to firms that have investment grade credit ratings. Banks have originated and disposed of short-term loans as an effective substitute for commercial paper, which has similar characteristics to short-term loans. The accessibility of commercial paper by more and more corporations has reduced the volume of these short-term loans for loan sales purposes.

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4.

Why are yields higher on loan sales than on commercial paper issues with similar maturity and issue size?

Commercial paper issuers generally are blue chip corporations that have the best credit ratings.

Banks may sell the loans of less creditworthy borrowers, thereby raising required yields. Indeed, since commercial paper issuers tend to be well-known companies, information, monitoring, and credit assessment costs are lower for commercial paper issues than for loan sales. Moreover, since there is an active secondary market in commercial paper, but not for loan sales, the commercial paper buyer takes on less liquidity risk than does the buyer of a loan sale.

5.

What are highly leveraged transactions? What constitutes the federal regulatory definition of an HLT?

A highly leveraged transaction is a loan to finance an acquisition or merger. Often the purchase is a leverage buyout with a resulting high leverage ratio for the borrower. U.S. federal bank regulators have adopted a definition that identifies an HLT loan as one that (1) involves a buyout, acquisition, or recapitalization and (2) doubles the company’s liabilities and results in a leverage ratio higher than 50 percent, results in a leverage ratio higher than 75 percent, or is designated as an HLT by a syndication agent.

6.

How do the characteristics of an HLT loan differ from those of a short-term loan that is sold?

Some of the common characteristics of the two types of loans are listed below:

7.

Short-term loans Secured by the assets of borrowing firm.

HLT loans Secured by the assets of the borrowing firm.

Short-term maturity (90 days or less).

Long-term maturity (often 3 to 6 years).

Yields closely tied to the commercial paper rate.

Floating rates tied to LIBOR, the prime rate, or a CD rate (plus 200 or more basis points).

Sold in units of $1 million and up.

Strong covenant protection.

Loans to investment grade borrowers or better.

Classified as nondistressed or distressed.

What is a possible reason why the spreads on HLT loans perform differently than do the spreads on high-yield bonds?

Spreads on HLT loans behave more like the spreads on investment grade bonds than the spreads on high-yield bonds. A possible reason is that HLT loans are more senior in bankruptcy proceedings and that they have greater collateral backing than do high-yield bonds.

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8.

City Bank has made a 10-year, $2 million loan that pays annual interest of 10 percent. The principal is expected to be paid at maturity. a. What should City Bank expect to receive from the sale of this loan if the current market interest rate on loans of this risk is 12 percent?

Market value of loan: ($0.20m) x PVAn=10,k=12 + ($2m) x PVn=10,k=12 = $1.774 million b. The price of loans of this risk is currently being quoted in the secondary market at bidoffer prices of 88-89 cents (on each dollar). Translate these quotes into actual prices for the above loan.

The prices of these loans are being quoted at 88 cents and 89 cents to the dollar. In the case of the above loan, it will translate into $1.56 ($1.774 million x 0.88) and $1.58 million ($1.774 million x 0.89), i.e., a dealer is willing to buy such loans at $1.56 million and sell them at $1.58 million. c. Do these prices reflect a distressed or nondistressed loan? Explain.

This loan is categorized as distressed since it is selling at prices below $0.90 to the dollar. It usually indicates a higher than average leverage of the borrower and more default risk, making it a less tradable instrument.

9.

What is the difference between loan participations and loan assignments?

In a loan participation, the buyer does not obtain total control over the loan. In an assignment, all rights are transferred upon sale, thereby giving the buyer a direct claim on the borrower.

The unique features of participations in loans are: • The holder (buyer) is not a party to the underlying credit agreement so that the initial contract between loan seller and borrower remains in place after the sale.

• The loan buyer can exercise only partial control over changes in the loan contract’s terms. The holder can vote only on material changes to the loan contract, such as the interest rate or collateral backing.

The economic implication of these features is that the buyer of the loan participation has a double risk exposure: a risk exposure to the borrower and a risk exposure to the loan selling FI. Specifically, if the selling FI fails, the loan participation bought by an outside party may be characterized as an unsecured obligation of the FI rather than as a true sale if there are grounds for believing that some explicit or implicit recourse existed between the loan seller and the loan buyer. Alternatively, the borrower’s claims against a failed selling FI may be set off against its loans from that FI, reducing the amount of loans outstanding and adversely impacting the buyer of a participation in those loans. As a result of these exposures, the buyer bears a double monitoring cost as well.

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Because of the monitoring costs and risks involved in participations, loans are sold on an assignment basis in more than 90 percent of the cases on the U.S. domestic market. The key features of an assignment are: • All rights are transferred on sale, meaning the loan buyer now holds a direct claim on the borrower.

• Transfer of U.S. domestic loans is normally associated with a Uniform Commercial Code filing (as proof that a change of ownership has been perfected).

While ownership rights are generally much clearer in a loan sale by assignment, frequently contractual terms limit the seller’s scope regarding to whom the loan can be sold. In particular, the loan contract may require either the FI agent or the borrower to agree to the sale. The loan contract may also restrict the sale to a certain class of institutions, such as those that meet certain net worth/net asset size conditions.

Currently, the trend appears to be toward loan contracts being originated with very limited assignment restrictions. This is true in both the U.S. domestic and the foreign loan sales markets.

The most tradable loans are those that can be assigned without buyer restrictions. In addition, the nonstandardization of accrued interest payments in fixed-rate loan assignments (trade date, assignment date, coupon payment date) adds complexity and friction to this market. Moreover, while the FI agent may have a full record of the initial owners of the loans, it does not always have an up-to-date record of loan ownership changes and related transfers following trades. This means that great difficulties often occur for the borrower, FI agent, and loan buyer in ensuring that the current holder of the loan receives the interest and principal payments due. Finally, the buyer of the loan often needs to verify the original loan contract and establish the full implications of the purchase regarding the buyer’s rights to collateral if the borrower defaults.

10.

What are the difficulties in completing a loan assignment?

A significant number of contractual problems, trading frictions, and costs can occur with loan assignments. First, the initial loan contract may require the FI and/or borrower to agree to the sale, although the current trend is toward contracts with very limited assignment restrictions.

Second, complexities in the calculation of accrued interest often require assignment of floatingrate loans to occur only on the anniversary or repricing dates of the loan. The FI agent who distributes the interest payments may have difficulty in keeping up-to-date records regarding ownership changes of the loan. Finally, the buyer of the loan must verify the original loan contract regarding the buyer’s rights to collateral in the event the borrower defaults on the loan.

11.

Who are the buyers of U.S. loans and why do they participate in this activity?

The buyers of loans include (1) investment banks because they are often involved with the initial transaction that leads to the issuance of the debt; (2) vulture funds since they invest in portfolios of risky loans; (3) domestic banks in order to circumvent regional banking and branching restrictions so as to increase regional and customer diversification; (4) foreign banks in order to obtain a presence in the U.S. market without incurring the costs of a branch network; (5) 4 © 2022

insurance companies and pension funds in attempts to earn higher yields, when permissible; (6) closed- and open-end bank loan mutual funds to earn fee income on loan syndications; and (7) non-financial corporations to earn higher yields. a. What are vulture funds?

Vulture funds are specialized hedge funds that are established to invest in distressed loans. The funds may be active in the sense that the purchased loans provide leverage to restructure deals or alter the operation of the borrower. b. What are three reasons the interbank market has been shrinking?

First, the interbank market has relied heavily on correspondent banking where banks provide services to maintain relationships. The increase in competition and the increasingly consolidated banking market is causing correspondent relationships to weaken. Second, concerns about counterparty risk and moral hazard have increased. In particular, moral hazard is the risk that the selling bank will seek to offload its “bad” loans (via loan sales), keeping the “good” loans in its portfolio. Third, the barriers to nationwide banking have been largely eliminated by the passage of the Riegle-Neal Interstate Banking and Efficiency Act of 1994. c. What are reasons a small bank would be interested in participating in a loan syndication?

Many small banks have limited opportunities to diversify their loan portfolios. The loan sale market is one method that allow these banks to achieve some diversification in their loan portfolios, at least at the regional level.

12.

Who are the sellers of U.S. loans and why do they participate in this activity?

The primary sellers of loans include (1) major money center banks for the purpose of reducing capital requirements, diversifying the loan portfolio, reducing reserve requirements, and increasing liquidity; (2) foreign banks for the same reasons as the money center banks; (3) investment banks because of their role as market makers; and (4) U.S. government agencies including The Resolution Trust Corporation, before it was dissolved, to dispose of assets obtained upon closure of troubled institutions in the course of resolving the thrift crisis. a. What is the purpose of a bad bank?

Bad banks are created by commercial banks for the purpose of liquidating portfolios of nonperforming assets or loans. Bank management is given the incentive to maximize the value realized in the sale of the assets. b. What are the reasons why loan sales through a bad bank will be value enhancing?

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Some of the reasons for selling or liquidating bad loans through a special purpose vehicle such as a bad bank include: (1)

The use of workout specialists in managing the liquidation.

(2)

The improvement in the reputation of the good bank after removal of the bad assets from the balance sheet. This improved reputation allows the good bank to have better access to deposit and funding markets.

(3)

The ability to dispose of bad assets without concern about liquidity because of the lack of deposits.

(4)

The ability to customize incentive agreements for managers that generate enhanced values from loan sales.

(5)

The increased informational symmetry about the value of the good bank’s assets, since a (typically) large share of the bad assets have been removed from the balance sheet. c. What impact has the 1996 Federal Debt Improvement Act had on the loan sale market?

This act authorizes federal agencies to sell delinquent and defaulted loan assets. In cases such as the RTC liquidation of real estate loans in the early 1990s, market watchers estimated a moderate supply-side effect because of the large amount of real estate loans that had to be liquidated.

13.

In addition to managing credit risk, what are some other reasons for the sale of loans by FIs?

The reasons for an increase in loan sales, apart from hedging credit risk, include: (a)

Removing loans from the balance sheet by sale without recourse reduces the amount of deposits necessary to fund the FI, which in turn decreases the amount of regulatory reserve requirements that must be kept by the FI.

(b)

Originating and selling loans is an important source of fee income for the FIs.

(c)

One method to improve the capital ratio for an FI is to reduce assets. This approach often is less expensive than increasing the amount of capital.

(d)

The sale of FI loans to improve the liquidity of the FIs has expanded the loan sale market.

This has made FI loans even more liquid and reduced FI liquidity risk even farther. Thus, by creating the loan sales market, the process of selling the loans has improved the liquidity of the asset for which the market was initially developed.

(e)

Finally, loan sales have been considered a substitute for securities underwriting.

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14.

What are factors that may deter the growth of the loan sale market in the future? Discuss.

Several factors may deter the growth of the loans sales market. First, because of the ability for large banks to underwrite commercial paper through investment bank subsidiaries, the need to sell short-term bank loans as an imperfect substitute for commercial paper has decreased.

Second, if customers perceive the sale of its loan by an FI as an adverse statement about the customer’s value to the FI, the FI may choose to not sell the loan for fear of decreasing revenue from the customer relationships. Third, the distressed loan sale market has slowed because of legal implications from the sale of HLT loans. Other creditors have questioned whether the secured position of the FI is valid in the case of bankruptcy or other distressed-firm proceedings.

15.

In addition to hedging credit risk, what are five factors that are expected to encourage loan sales in the future? Discuss the impact of each factor.

The reasons for an increase in loan sales, apart from hedging credit risk, include: (a)

New capital requirements for credit risk, which suggests a further need for FIs to reduce their risky portfolios and replace them with lower risk assets. This suggests increased loan sales activity.

(b)

Market value accounting since FASB 115 makes it easier to trade different categories of loans.

(c)

Loan sales as trading instruments, which make it attractive for commercial banks and investment banks to specialize in specific loan categories and to market them effectively, since they require only brokerage functions as opposed to performing asset transformations.

(d)

The increased involvement of the federal government in the loan sales market (through its direct purchases of distressed loans held by financial institutions and its takeover of mortgage giants Fannie Mae and Freddie Mac) during the financial crisis is seen as a reason for growth in the loan sale market.

(e)

The ability to allocate loan credit ratings should cause more investors to enter the market.

(f)

The growth of distressed loans in international markets should provide opportunities for U.S. domestic investors to enter this market at substantially reduced prices.

16.

An FI is planning the purchase of a $5 million loan to raise the existing average duration of its assets from 3.5 years to 5 years. It currently has total assets worth $20 million, $5 million in cash (0 duration) and $15 million in loans. The FI’s liabilities have an average duration of 5 years. All the loans are fairly priced. a. Assuming it uses the cash to purchase the loan, should the FI purchase the loan if its duration is seven years?

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The duration of the existing loanw is: 0 + $15m/$20m(X) = 3.5 years => Existing loan duration = 4.667 years If it purchases $5 million of loans with an average duration of 7 years, the FI’s portfolio duration will increase to $5m/$20m(7) + $15m/$20m(4.667) = 5.25 years. In this case, the average duration will be above 5 years (of its liabilities). The FI may be better off seeking another loan with a slightly lower duration. b. What asset duration loans should the FI purchase in order to raise its average duration to five years?

The FI should seek to purchase a loan of the following duration: $5m/$20m(X) + $15m/$20m(4.667 years) = 5 years => X = duration = 6 years.

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Solutions for End-of-Chapter Questions and Answers: Chapter Twenty-Six 1.

What has been the effect of securitization on the asset portfolios of financial institutions?

In addition to serving as another mechanism to hedge interest rate exposure gaps, securitization has provided a method to make asset portfolios more liquid, has provided an important source of fee income, and has helped to reduce the effects of regulatory taxes.

2.

What are the primary functions of GNMA? What is timing insurance?

GNMA is a government-owned agency with two major functions. The first is sponsoring mortgage-backed securities programs by FIs such as banks, thrifts, and mortgage bankers. The second is acting as a guarantor to investors in mortgage-backed securities regarding the timely pass-through of principal and interest payments on their sponsored bonds. Timing insurance guarantees that the holder of pass-through securities will receive interest and principal payments at the calendar date promised. This service is provided in many mortgage-backed securities offerings by GNMA. 3.

How does FNMA differ from GNMA?

FNMA is a private corporation whose stock trades on major exchanges, while GNMA is directly owned by the government. However, on September 7, 2008, the Federal Housing Finance Agency (FHFA) placed Fannie Mae (and Freddie Mac) in conservatorship. As conservator, the FHFA was given full powers to control the assets and operations of the firms. Dividends to common and preferred shareholders were suspended, but the U.S. Treasury put in place a set of financing agreements to ensure that the GSEs continue to meet their obligations to bondholders.

This means that the U.S. taxpayer basically was the guarantor behind about $5 trillion of GSE debt. This step was taken because a default by either of the two firms, which were battered by the downturn in housing and credit markets, could have caused severe disruptions in global financial markets, made home mortgages more difficult and expensive to obtain, and had negative repercussions throughout the economy. Whereas GNMA sponsors mortgage-backed programs, FNMA actually creates pass-through securities by buying and holding mortgages on its balance sheet. These mortgage purchases often are financed by the issuance of bonds in the capital markets. The securities that are created are called mortgage-backed securities (MBS).

4.

How does FHLMC differ from FNMA? How are they the same?

The Federal Home Loan Mortgage Corporation performs duties similar to FNMA for the savings institution industry. Like FNMA, FHLMC is a private corporation whose stock trades on major exchanges. Also like FNMA, on September 7, 2008, the Federal Housing Finance Agency (FHFA) placed Freddie Mac in conservatorship. As conservator, the FHFA was given full powers to control the assets and operations of the firms. Dividends to common and preferred shareholders were suspended, but the U.S. Treasury put in place a set of financing agreements to ensure that the GSEs continue to meet their obligations to bondholders. FHLMC buys mortgage 1 © 2022

pools and swaps MBS for loans. FHLMC also sponsors conventional loan pools and FHA/VA mortgage pools, and provides timing insurance on the securities it issues.

5.

What three levels of regulatory taxes do FIs face when making loans? How does securitization reduce the levels of taxation?

The three levels of taxes faced by FIs when making loans are a) capital requirements on loans to protect against default; b) reserve requirements on demand deposits for funding the loans; and c) deposit insurance to protect the depositors. If the loans are securitized, FIs end up only servicing the loans since the loans no longer are on the balance sheet. As a result, no capital is required to protect against default risk. Further, reserve requirements and deposit insurance will be reduced if liabilities are also reduced. However, if the cash proceeds from the loan sales are used to invest in other assets, then the taxes will still remain in place.

6.

An FI is planning to issue $100 million in BB rated commercial loans. The FI will finance the loans by issuing demand deposits. a. What is the minimum capital required under Basle III?

The minimum capital required on commercial loans = $100m x 1.0 x 0.08 = $8 million. b. What is the minimum amount of demand deposits needed to fund this loan assuming there is a 10 percent average reserve requirement on demand deposits?

Since there is an interaction between the demand deposits and cash reserves held, the answer requires solving the following, assuming the $8 million is funded by equity and the reserve requirements are kept as cash: $100m + (0.10 x DD) = DD + 8m => DD = 92m/0.9 = $102.22 million c. Show a simple balance sheet with total assets, total liabilities, and equity if this is the only project funded by the bank.

Assets Cash Loan Total

$10.22m $100.00m $110.22m

Liabilities Demand deposits Equity

$102.22m 8.00m $110.22m

d. How does this balance sheet differ from Table 26-1? Why? Since the loans are Category 1 residential mortgages with a loan-to-value ratio between 60 and 80 percent, the example in Table 26-1 has a capital requirement of only 4 percent (8% x 0.5) of the face value of the loan. Because the loans in this problem are BB rated commercial loans, the bank must keep a full 8 percent of the loan to meet the risk-based capital ratio. Thus, the balance sheet is $0.45m less than the Table 26-1 example.

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7.

Consider the FI in problem (6). a. What additional risk exposure problems does the FI face?

First, the commercial loans financed with demand deposits present a serious duration gap problem. Second, the loans are not very liquid. Under worst-case liquidity scenarios, the FI faces the possibility of having to sell the loans at distressed prices. b. What are some possible solutions to the duration mismatch and the illiquidity problems?

The FI can lengthen the liability duration by issuing longer term CDs or capital notes, but this solution is difficult in that each time the FI issues a commercial or longer-term residential loan, it must rebalance the duration of the liabilities. A second solution is to use interest rate swaps or other derivative products to hedge the mismatch in cash flow streams. Neither of these techniques, however, resolves the problem of regulatory taxes. c. What advantages does securitization have in dealing with the FI’s risk exposure problems?

The process of securitization removes the loans from the balance sheet. Thus, the problems of duration, liquidity, and regulatory taxes disappear. Further, the FI recovers the initial investment and can repeat the loan origination process with potential to earn additional fees on the new originations.

8.

How are investors in pass-through securities protected against default risk emanating from the mortgagees and the FI/trustee?

Bondholders of residential mortgage pass-throughs are protected against mortgage default losses by the borrowers through FHA/VA housing insurance. In cases where the bank or the trustee defaults on the timely pass-through of the mortgage payments, GNMA will make the payments.

For this insurance guarantee, GNMA receives an insurance premium on each payment.

9.

What specific changes occur on the balance sheet at the completion of the securitization process? What adjustments occur to the risk profile of the FI?

At the conclusion of the securitization process, the FI will have (1) exchanged a loan balance for cash, (2) reduced significantly the duration of its assets, and likely the duration mismatch of the entire balance sheet, and (3) reduced the regulatory tax burden. The risk profile is potentially reduced in two ways. First, exchanging loans for cash removes any risk-based capital requirements for the FI. Second, if the cash is used to repay deposits, reserve requirements may be reduced.

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10.

Consider the mortgage pass-through example presented in Table 26-3. The total monthly payment by the borrowers reflecting a 12 percent mortgage rate is $1,028,610. The payment passed through to the ultimate investors reflecting an 11.5 percent return is $990,291. Who receives the difference between these two payments? How are the shares determined?

The difference in the two payments ($38,319) goes to the mortgage service provider and to GNMA for the insurance premium. If the total fee is 50 basis points, and GNMA receives 6 basis points for the insurance premium, GNMA would receive 12 percent (6/50) of the difference ($4,598) in the two payments, and the mortgage service provider would receive 88 percent (44/50) of the difference ($33,721) in the two payments.

11.

Consider a GNMA mortgage pool with principal of $20 million. The maturity is 30 years with a monthly mortgage payment of 10 percent per year. Assume no prepayments. a. What is the monthly mortgage payment (100 percent amortizing) on the pool of mortgages?

The monthly mortgage payment, PMT, is (the monthly interest rate is 0.10/ 12 = 0.00833): $20m = PVAn=360, k=0.8333 x (PMT) => PMT = $175,514.31 b. If the GNMA insurance fee is 6 basis points and the servicing fee is 44 basis points, what is the yield on the GNMA pass-through?

The GNMA's annual interest rate is 0.10 - 0.0044 - 0.0006 = 9.5 percent. The monthly interest rate is 0.095/12 = 0.0079167 or 0.79167 percent. c. What is the monthly payment on the GNMA in part (b)?

The monthly GNMA payment, PMT, is: $20m = PVAn=360, k=0.79167% x PMT => PMT = $168,170.84 d. Calculate the first monthly servicing fee paid to the originating FIs. The first monthly servicing fee, SF, is (the monthly fee rate is 0.44%/12 = 0.0367%): SF = (0.000367)$20m = $7,333. e. Calculate the first monthly insurance fee paid to GNMA. The first monthly insurance payment, IP, is (monthly insurance rate is 0.06%/12 = 0.005%): IP = (0.00005)$20m = $1,000 12.

Calculate the value of (a) the mortgage pool and (b) the GNMA pass-through in question 11 if market interest rates increase 50 basis points. Assume no prepayments. a. The mortgage pool's value, PV, is (the monthly discount rate is 10.5%/12 = 0.875%): 4 © 2022

PV = $175,514.31 x PVAn=360,k=0.875% = $19,187,359 b. The GNMA's value, PV, is (the monthly discount rate is 10%/12 = 0.8333%): PV = $168,170.84 x PVAn=360,k=0.8333% = $19,163,205.

13.

What would be the impact on GNMA pricing if a pass-through is not fully amortized?

What is the present value of a $10 million pool of 15-year mortgages with an 8.5 percent per year monthly mortgage coupon if market rates are 5 percent? The GNMA guarantee fee is 6 basis points and the FI servicing fee is 44 basis points. a. Assume that the GNMA is fully amortized.

There are 180 monthly payments (15 years x 12 months). The GNMA monthly coupon rate is 8.5% - 0.5% = 8 percent per year, and the monthly GNMA pass-through payment is: $10m= PVAn=180, k=0.6667% x PMT => PMT = $95,565.21.

The present value of the GNMA at a 5 percent market rate is: PV = $95,565.21 x PVAn=180, k=0.004167% = $12,084,721.63. b. Assume that the GNMA is only half amortized. There is a lump sum payment at the maturity of the GNMA that equals 50 percent of the mortgage pool's face value.

If there is a 50 percent amortization, the monthly GNMA pass-through payments are: $10m = PMT x PVAn=180, k=0.6667% + $5m x PVn=180, k=0.6667% => PMT = $81,115.94 The present value of the GNMA at a 5 percent market rate is: PV = $81,115.94 x PVA n=180, k=0.004167% + $5m x PVn=180, k=0.004167% = $12,623,051.35.

14.

What is prepayment risk? How does prepayment risk affect the cash flow stream on a fully amortized mortgage loan? What are the two primary factors that cause early payment?

Prepayment is the process of paying principal on a debt before the due date. In the case of an amortized loan that has fixed periodic payments, prepayment means that the lender will receive fewer of the fixed periodic payments, one or more payments of extra principal, and the final payment will be made before the final payment due date.

The two primary factors that cause prepayment are (1) the refinancing of the loan by the borrower because of better interest rates and (2) the economic reality of having the cash to repay before maturity. In the case of residential mortgages, this economic reality usually occurs with the sale of a house because of relocation. In the first case, investors must reinvest at lower rates and thus realize lower rates of return over their entire investment horizon. Housing turnover risk may or may not translate into losses for pass-through holders because interest rates could remain the same, allowing them to reinvest the early payments in other instruments paying similar rates.

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15.

Under what conditions do mortgage holders have a call option on their mortgages? When is the call option in the money?

As interest rates fall, mortgage holders can refinance at lower rates. When the present value of the savings from refinancing is greater than the cost of refinancing, the mortgage holders in effect have a call option that is in the money. Under these conditions the mortgage should be called and refinanced.

16.

What are the benefits of market yields that are less than the average rate in the GNMA mortgage pool? What are the disadvantages of this rate inversion? To whom do the good news and bad news accrue?

The two benefits of this economic effect are (1) that the value of the stream of mortgage cash flows is increased with the lower market discount rate and (2) that repayment risk decreases because the principal is recovered more quickly. The disadvantages are (1) that prepayments reduce the amount of interest payments in absolute terms and (2) that payments must be reinvested at lower interest rates. The good news primarily accrues to the lender in that a greater value is beneficial in case the lender is willing to sell the loan portfolio and because the reduced repayment risk is helpful for the overall risk of the FI. The bad news accrues primarily to the borrower in that the cost of raising funds has decreased.

17.

What is the weighted-average life (WAL) of a mortgage pool supporting pass-through securities? How does WAL differ from duration?

The weighted-average life is calculated as the product of the amount of principal payment times the timing of the payment divided by the total amount of principal outstanding. Duration differs from WAL by using the present value of cash flows relative to the current present value of the asset as the weights in calculating the average life.

18.

If 150 $200,000 mortgages in a $60 million 15-year mortgage pool are expected to be prepaid in three years and the remaining 150 $200,000 mortgages are to be prepaid in four years, what is the weighted-average life of the mortgage pool? Mortgages are fully amortized, with mortgage coupon rates set at 10 percent to be paid annually.

The annual mortgage payment is $60 million = PVAn=15, k=10% x PMT => PMT = $7,888,426.61.

Annual mortgage payments, with no prepayments, can be decomposed into principal and interest payments (in millions of $s): Year 1 2 3 4

Balance $60.000 58.112 56.034 53.749

Payment $7.888 7.888 7.888 7.888

Interest Payment $6.000 5.811 5.603 5.375 6 © 2022

Principal Payment $1.888 2.077 2.285 2.513

Remaining Principal $58.112 56.034 53.749 51.236

The first year's interest is $6 million (0.10 x $60 million). Deducting this from the first year's mortgage payment yields a principal payment of $1,888,426.61 at the end of the first year, and an outstanding principal $58,111,573.39.

The second year's interest payment is 0.10 x $58,111,573.39 = $5,8111,157.34. Deducting this from the annual mortgage payment yields a second annual principal payment of $2,077,269.27, for a principal outstanding of $56,034,304.12.

The third year's regular interest payment is $5.603 million. Deducting this from the annual mortgage payment yields a third annual principal payment of $2.285 million for a principal outstanding of $53,749,307.92.

The principal outstanding at the end of the fourth year, without prepayments, is $51,235,812.10.

However, at the end of the third year, half of the mortgages in the mortgage pool are completely prepaid. That is, at the end of the third year, an additional principal payment of 50% x $53,749,307.92 = $26,874,653.96 is received for a remaining outstanding principal balance of $26.875 million. The total third year principal payment is therefore $29.16 million = the regular principal payment of $2.285 million plus an extra payment of $26.875 million.

The fourth year annual interest payment is 10% x $26.875 million = $2.687 million, leaving a regular fourth year principal payment of $7.888 million - $2.687 million = $5,200,961.21. This end-of-fourth-year principal payment would have left an outstanding principal balance of $21,673,692.75, which is paid in full at the end of the year. Fourth year principal payments total $26.875 million = $5.201 million, plus $21.674 million.

Prepayments alter the annual cash flows for years 3 and 4 as follows (in millions of $s): Year 3 4

Balance 56.034 26.875

Payment 7.888 7.888

Interest 5.603 2.687

Principal 29.160 26.875

Calculating the weighted average life: Time Expected Principal Payments 1 1.888m 2 2.077m 3 29.160m 4 26.875m 60.000m WAL = 201.022/60 = 3.35 years 19.

Balance 26.875 0

Time x Principal 1.888 4.154 87.48 107.5 201.022

An FI originates a pool of 500 30-year mortgages, each averaging $150,000 with an annual mortgage coupon rate of 8 percent. Assume that the GNMA credit risk insurance fee is 6 basis points and that the FI's servicing fee is 19 basis points. a. What is the present value of the mortgage pool?

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PV = 500 x $150,000 = $75 million b. What is the monthly mortgage payment?

There are 360 monthly mortgage payments (30 years x 12 months). Monthly mortgage payments are $75,000,000 = PVAn=360, k=0.6667% x PMT => PMT = $550,323.43. c. For the first two payments, what portion is interest and what portion is principal repayment?

For the first monthly payment, the monthly interest is 0.08/12 x $75 million = $500,000.

Therefore, for the first monthly mortgage payment, $50,323.43 is repayment of principal.

For the second monthly payment, the principal outstanding is $75m - $50,323.43 = $74,949,676.57. The monthly interest payment is $499,664.51. The principal payment in the second month is $550,323.43 - $499,664.51 = $50,658.92. d. What are the expected monthly cash flows to GNMA bondholders?

The GNMA bond rate is 8% - (0.06% + 0.19%) = 7.75 percent. GNMA bondholders receive monthly payments of $75m = PVAn=360, k=0.0775/12 x PMT => PMT = $537,309.18. e. What is the present value of the GNMA pass-through bonds? Assume that the riskadjusted market annual rate of return is 8 percent compounded monthly.

The discount yield is 8 percent annually, compounded monthly. The present value of the GNMA pass-through bonds is PV = $537,309.18 x PVA n=360, k=0.6667% = $73,226,373.05. f. Would actual cash flows to GNMA bondholders deviate from expected cash flows as in part (d)? Why or why not?

Actual payments will equal expected payments if and only if no prepayments are made. If any mortgages are prepaid as a result of refinancing or homeowner mobility, then the monthly payments will change. In the month in which prepayments are made, monthly payments will increase to reflect the principal repayments. In all subsequent months, monthly payments will decline to reflect the lower face value of the pass-through bonds. g.

What are the expected monthly cash flows for the FI and GNMA?

GNMA and the originating FI share the difference between the monthly mortgage payments and the GNMA pass-through payments $550,323.43 - $537,309.18 = $13,014.25. The originating bank gets 19 out of the 25 basis points (or 76 percent) for a payment of $9,890.83 monthly.

GNMA receives the remaining 6 basis points (or 24 percent) for a payment of $3,123.42.

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h. If all of the mortgages in the pool are completely prepaid at the end of the second month, what is the pool's weighted-average life? Hint: Use your answer to part (c).

Time 1 mo.

2 mo.

Expected Principal Payments $50,323.43 $74,949,676.57 $75,000,000.00

Time x Principal $50,323.43 $149,899,353.10 $149,949,676.53

WAL = (149,949,676.53/75 million) = 1.9993 months The principal payment in the first month is $50,323.43. If the loan is paid off after month two, the principal payment in month two is $75 million - $50,323.43 = $74,949,676.57. i. What is the price of the GNMA pass-through security if its weighted-average life is equal to your solution for part (h)? Assume no change in market interest rates.

The GNMA with a weighted average life of 1.9993 months has only two cash flows. The first month's cash flow is $537,309.18. The second month's cash flow is $537,309.18 plus the extra principal repayment of $74,899,017.65 = $75,436,326.83. The present value of the GNMA is PV = [$537,309.18/(1.006667)] + [$75,436,326.83/(1.006667)2] = $74,974,229.44, where the monthly discount rate is 0.08/12. j. What is the price of the GNMA pass-through with a weighted-average life equal to your solution for part (h) if market yields decline by 50 basis points?

If market yields decline 50 basis points, to 7.5 percent compounded monthly, the present value of the GNMA is PV = [$537,309.18/(1.00625)] + [$75,436,326.83/(1.00625)2] = $75,036,111.70, where the monthly discount rate is 0.075/12.

20.

What is the difference between the yield spread to average life and the option-adjusted spread on mortgage-backed securities?

The yield spread to average life is the difference between the yield on mortgage-backed securities and the U.S. Treasury bond. The option-adjusted spread (OAS) subtracts the yield on a matched maturity Treasury bond from a yield to maturity of the mortgage-backed security after it has been adjusted for estimated prepayment behavior. The prepayment behavior is estimated and valued by the Bear Stearns’ division of J.P. Morgan Chase.

21.

Explain precisely the prepayment assumptions of the Public Securities Association prepayment model.

The Public Securities Association (PSA) model calculates an average rate of repayment based on past experience of prepayments on pools of mortgages. The model assumes a prepayment rate that increases 0.2 percent per month over the first 30 months, at which time the rate levels off at 6.0 percent per year.

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22.

What does an FI mean when it states that its mortgage pool prepayments are assumed to be 100 percent PSA equivalent?

Mortgage pool prepayments that are assumed to match exactly the PSA model are said to be 100 percent PSA equivalent.

23.

What factors may cause the actual prepayment pattern to differ from the assumed PSA pattern? How would an FI adjust for the presumed occurrence of some of these factors?

The factors that are assumed to cause the prepayment pattern to differ from the PSA rate include (1) the pool’s coupon rate relative to the current mortgage coupon rate; (2) the age of the mortgage pool; (3) whether the payments are fully amortized; (4) whether the mortgages in the pool can be assumed by new home buyers; (5) the size of the pool; (6) the geographic location of the mortgages; (7) whether the mortgages are conventional or nonconventional; and (8) the age and job status of the mortgagees in the pool.

If the FI assumes that any or all of these factors may cause prepayment to differ from 100 percent PSA behavior, the FI can make adjustments to better reflect what the FI thinks will be more accurate behavior patterns, such as 80 percent or 110 percent prepayment. Note that any estimate of prepayment behavior may not be realized exactly.

24.

What is the burnout factor? How is it used in modeling prepayment behavior? What other factors may be helpful in modeling the prepayment behavior of a given mortgage pool?

The burnout factor reflects the amount of the mortgage pool that has been prepaid prior to the month under consideration. The burnout factor is one of several factors that can be used to estimate a prepayment function. Other possible variables include age, collateral, geographic factors, and mortgage rate spread.

25.

What is the goal of prepayment models that use option pricing theory? How do these models differ from the PSA or empirical models? What criticisms often are directed toward these models?

Option models attempt to determine the yield spread of pass-through bonds over Treasuries using prepayment risk as a primary factor. Criticisms of OAS models are that they often do not include nonrefinancing incentives to prepay as well as the transaction and recontracting costs involved in refinancing.

26.

How does the price on a GNMA bond relate to the yield on a GNMA option from the perspective of the investor? What is the option-adjusted spread (OAS)?

The value of a GNMA bond is equal to the value of a standard Treasury bond of the same duration minus the value of the mortgage holder’s prepayment call option. The ability of the mortgage holder to prepay equals the bond investor writing a call option on the bond that is sold 10 © 2022

to the mortgagee. The option-adjusted spread between the GNMA bond and the T-bond should reflect the value of the option.

27.

Use the options prepayment model to calculate the yield on a $30 million, three-year, fully amortized mortgage pass-through where the mortgage coupon rate is 6 percent paid annually. Market yields are 6.4 percent paid annually. Assume that there is no servicing or GNMA guarantee fee. a. What is the annual payment on the GNMA pass-through?

The annual mortgage payment is $30m = PVAn=3, k=6% x PMT => PMT = $11,223,294. b. What is the present value of the GNMA pass-through?

The present value of the GNMA is PV = $11,223,294 x PVAn=3, k=6.4% = $29,779,354 c. Interest rate movements over time are assumed to change a maximum of 0.5 percent per year. Both an increase of 0.5 percent and a decrease of 0.5 percent in interest rates are equally probable. If interest rates fall 1.0 percent below the current mortgage coupon rates, all of the mortgages in the pool will be completely prepaid. Diagram the interest rate tree and indicate the probabilities of each node in the tree.

The probability tree is given below with the probability of each node followed by the corresponding interest rate. t=0

t=1

t=2

p = 0.25 p = 0.5

p = 0.50 p = 0.5

7.0%

6.5%

6%

p = 0.3750

6.5%

p = 0.3750

5.5%

p = 0.1250

4.5%

6.0%

5.5% p = 0.25

t=3 p = 0.1250 7.5%

5.0%

d. What are the expected annual cash flows for each possible situation over the three-year period?

The annual mortgage cash flows are: (Fixed)

Interest 11 © 2022

Principal

Remaining

Year Balance 1 $30,000,000 2 $20,576,706 3 $10,588,014

Payment $11,223,294 $11,223,294 $11,223,294

Payment $1,800,000 $1,234,602 $635,281

Payment $9,423,294 $9,988,692 $10,588,013

Principal $20,576,706 $10,588,014 $0

Year 1 Expected Cash Flows: There is a 50 percent chance of either a 5.5 percent or 6.5 percent market interest rate. Since neither rate triggers mortgage prepayments, a cash flow of $11,223,294 will be received with certainty.

Year 2 Expected Cash Flows: There is a 25 percent chance that interest rates will be 5.0 percent, a 50 percent chance that interest rates will be 6.0 percent, and a 25 percent chance that interest rates will be 7.0 percent. If interest rates are either 6 percent or 7 percent, no prepayments will be triggered, and the cash flow will be $11,223,294. If interest rates are 5.0 percent, all of the mortgages will be prepaid. Thus, the expected cash flows will be 0.75($11,223,294) + 0.25($11,223,294 + $10,588,014) = $8,417,470 + $5,452,827 = $13,870,297.

Year 3 Expected Cash Flows: Interest rates will be 4.5 percent with a 0.125 percent chance, 5.5 percent and 6.5 percent each with a 0.375 percent chance, or 7.5 percent with a 0.125 percent chance. Since there is a 25 percent chance that mortgages will be prepaid at the end of year 2, there is a 25 percent probability that investors will receive no cash flows at the end of year 3.

However, there is a 75 percent chance that mortgages will not be prepaid at the end of year two, so the expected cash flow will be 0.25($0) + 0.75($11,223,294) = $8,417,470. e.

The Treasury bond yield curve is flat at a discount yield of 6 percent. What is the optionadjusted spread on the GNMA pass-through?

The present value of the GNMA is $29,779,354 = [$11,223,294/(1+x)] + [$13,870,297/(1+x)2] + [$8,417,470/(1+x)3] => x = 6.4167 percent. Therefore, the option-adjusted spread is 6.4167 – 6.00 = 0.4167 percent.

28.

Use the options prepayment model to calculate the yield on a $12 million, five-year, fully amortized mortgage pass-through where the mortgage coupon rate is 7 percent paid annually. Market yields are 8 percent paid annually. Assume that there is no servicing or GNMA guarantee fee. a. What is the annual payment on the GNMA pass-through?

The annual mortgage payment is $12m = PVAn=5, k=7% x PMT => PMT = $2,926,688. b. What is the present value of the GNMA pass-through?

The present value of the GNMA is PV = $2,926,688 x PVAn=5, k=8% = $11,685,418. c. Interest rate movements over time are assumed to change a maximum of 1 percent per year. Both an increase of 1 percent and a decrease of 1 percent in interest rates are 12 © 2022

equally probable. If interest rates fall 3 percent below the current mortgage coupon rates, all mortgages in the pool will be completely prepaid. Diagram the interest rate tree and indicate the probabilities of each node in the tree. t=0

t=1

t=2

t=3

t=4

p = 0.0625 p = 0.125 p = 0.25 p = 0.5

9%

8%

p = 0.375 p = 0.50

p = 0.5

p = 0.2500

7%

p = 0.3750 p = 0.375

p = 0.25

p =0 .2500 p = 0.125

d.

p = 0.3125

9%

p = 0.3125

7%

p = 0.15625

5%

p = 0.03125

3%

6%

5% p =0 .0625

11%

8%

7%

6%

p = 0.15625

10%

9%

8%

t=5 13%

12%

11%

10%

p = 0.03125

4%

What are the expected annual cash flows for each possible situation over the five-year period?

The annual mortgage cash flows are: Year Balance 1 $12.000m 2 9.913m 3 7.680m 4 5.291m 5 2.734m

(Fixed) Payment $2.927m 2.927m 2.927m 2.927m 2.927m

Interest Payment $0.840m 0.694m 0.538m 0.370m 0.191m

Principal Payment $2.087m 2.233m 2.389m 2.557m 2.734m

Remaining Principal $9.913m 7.680m 5.291m 2.734m 0.0

Year 1 Expected Cash Flows: There is a 50 percent chance of either a 9 percent or 7 percent market interest rate. Since neither rate triggers mortgage prepayments, a cash flow of $2,926,688 will be received with certainty.

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Year 2 Expected Cash Flows: There is a 25 percent chance that interest rates will be 6 percent, a 50 percent chance that interest rates will be 8 percent, and a 25 percent chance that interest rates will be 10 percent. Since none of these rates triggers mortgage prepayments, a cash flow of $2,926,688 will be received with certainty.

Year 3 Expected Cash Flows: Interest rates will be 5 percent, 7 percent, 9 percent, or 11 percent.

Since none of these rates triggers mortgage prepayments, a cash flow of $2,926,688 will be received with certainty.

Year 4 Expected Cash Flows: Interest rates will be 4 percent, 6 percent, 8 percent, 10 percent, or 12 percent. The only rate that triggers prepayments is the 4 percent rate, which occurs with a probability of 6.25 percent. At the end of year 4, loan prepayments (in excess of the regular annual mortgage payment) are equal to $2.734 million which is the remaining principal after the regular payment in year 4. Expected end-of-year-4 cash flows are 0.0625($2.734 + $2.927) + 0.9375($2.927) = $3.097875 million.

Year 5 Expected Cash Flows: Interest rates will be either 3 percent, 5 percent, 7 percent, 9 percent, 11 percent, or 13 percent. There is a 6.25 percent probability that investors will receive no cash flows (the event that interest rates will be either 3 percent or 5 percent), since all mortgages were prepaid at the end of year 4. Therefore, end-of-year-5 expected cash flows are 0.0625($0) + 0.9375($2.927) = $2.744 million. e. The Treasury bond yield curve is flat at a discount yield of 6 percent. What is the option-adjusted spread on the GNMA pass-through?

The present value of the GNMA is $11,685,417 = [$2,926,688/(1+x)] + [$2,926,688/(1+x)2] + [$2,926,688/(1+x)3] + [$3,097,875/(1+x)4] + [$2,743,770/(1+x)5] => x = 8.0044 percent.

Therefore, the spread is 8.0044 – 6.00 = 2.0044 percent.

29.

What conditions would cause the yield on pass-through securities with prepayment risk to be less than the yield on pass-through securities without prepayment risk?

In situations where there is sufficient early prepayment, the yield on the pass-through securities with prepayment risk may be lower because the benefits of receiving the principal earlier offset the loss of interest income in a discounted cash flow analysis.

30.

What is a collateralized mortgage obligation (CMO)? How is it similar to a pass-through security? How does it differ? In what way does the creation of a CMO use market segmentation to redistribute prepayment risk?

A CMO is a series of pass-through securities that have been allocated into different groups or tranches. Each tranche typically has a different interest rate (coupon) and any prepayments on the entire CMO typically are allocated to the tranche with the shortest maturity. Thus, prepayment risk does not affect the tranches with longer lives until the earlier tranches have been 14 © 2022

retired. Many of the tranches in the CMO receive interest rates that are lower than the average pass-through requirement because of the limited prepayment risk protection.

31.

Consider $200 million of 30-year mortgages with a coupon of 10 percent per year paid quarterly. a. What is the quarterly mortgage payment?

There are 120 quarterly payments over 30 years. The quarterly mortgage payments are $200m = PVAn=120, k=2.5% x PMT => PMT = $5,272,358.60. b. What are the interest and principal repayments over the first year of life of the mortgages?

Quarter Balance 1 $200,000,000 2 199,727,641 3 199,448,473 4 199,162,326

(Fixed) Payment $5,272,359 5,272,359 5,272,359 5,272,359

Interest Payment $5,000,000 4,993,191 4,986,212 4,979,058

Principal Payment $272,359 279,168 286,147 293,301

Remaining Principal $199,727,641 199,448,473 199,162,326 198,869,025

c. Construct a 30-year CMO using this mortgage pool as collateral. The pool has three tranches, where tranche A offers the least protection against prepayment and tranche C offers the most protection against prepayment. Tranche A of $50 million receives quarterly payments at 9 percent per year, tranche B of $100 million receives quarterly payments at 10 percent per year, and tranche C of $50 million receives quarterly payments at 11 percent per year.

Tranche A $50 million 9 percent

Principal amount Interest rate Quarterly interest on initial balance $1,125,000 Quarterly amortization

Tranche B $100 million 10 percent

Tranche C $50 million 11 percent

Total Issue $200 million 10 percent

$2,500,000

$1,375,000

$5,000,000 $5,272,359

d. Assume nonamortization of principal and no prepayments. What are the total promised coupon payments to the three classes? What are the principal payments to each of the three classes for the first year?

Regular tranche A interest payments are $1.125 million quarterly. If there are no prepayments, then the regular GNMA quarterly payment of $5,272,359 is distributed among the three tranches.

Five million is the total coupon interest payment for all three tranches. Therefore, $272,359 of principal is repaid each quarter. Tranche A receives all principal payments. Tranche A cash flows are $1,125,000 + $272,359 = $1,397,359 quarterly. The cash flows to tranches B and C are the scheduled interest payments.

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Tranche A amortization schedule: Quarter Balance 1 $50,000,000 2 49,727,641 3 49,449,154 4 49,164,401

Payment $1,397,359 1,397,359 1,397,359 1,397,359

Interest Payment $1,125,000 1,118,872 1,112,606 1,106,199

Principal Payment $272,359 278,487 284,753 291,160

Remaining Principal $49,727,641 49,449,154 49,164,401 48,873,241

Payment $2.500m 2.500m 2.500m 2.500m

Interest Payment $2.500m 2.500m 2.500m 2.500m

Principal Payment $0.0m 0.0m 0.0m 0.0m

Remaining Principal $100.000m 100.000m 100.000m 100.000m

Payment $1.375m 1.375m 1.375m 1.375m

Interest Payment $1.375m 1.375m 1.375m 1.375m

Principal Payment $0.0m 0.0m 0.0m 0.0m

Remaining Principal $50.000m 50.000m 50.000m 50.000m

Tranche B amortization schedule: Quarter Balance 1 $100.000m 2 100.000m 3 100.000m 4 100.000m Tranche C amortization schedule: Quarter 1 2 3 4

Balance $50.000m 50.000m 50.000m 50.000m

e. If, over the first year, the trustee receives quarterly prepayments of $10 million on the mortgage pool, how are these funds distributed?

The quarterly prepayments of $10 million will be credited entirely to tranche A until tranche A is completely retired. Then prepayments will be paid entirely to tranche B. The amortization schedule for tranche A for the first year is shown below. This amortization schedule assumes that the trustee has a quarterly payment amount from the mortgage pool of $5,272,359.

Interest Principal Remaining Quarter Balance Payment Payment Payment Principal 1 $50,000,000 $11,397,359 $1,125,000 $10,272,359 $39,727,641 2 39,727,641 11,397,359 893,872 10,503,487 29,224,154 3 29,224,154 11,397,359 657,543 10,739,816 18,484,338 4 18,484,228 11,397,359 415,898 10,981,461 7,502,877 However, since some of the mortgages will be paid off early, the actual payment received by the trustee from the mortgage pool will decrease each quarter. Thus, the payment for the second quarter will decrease from $5,272,359 to $5,008,381 (n = 119 quarters, i = 10 percent, mortgage principal = $189,727,641). The CMO amortization schedule for tranche A given that the mortgage payments decrease with the prepayments is given below. The revised mortgage payment for each quarter is shown in the last column.

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Quarter Balance 1 $50,000,000 2 39,727,641 3 29,488,132 4 19,281,902

Payment $11,397,359 11,133,381 10,869,713 10,606,344

Interest Payment $1,125,000 893,872 663,483 433,843

Principal Payment $10,272,359 10,239,509 10,206,230 10,172,501

Remaining Principal $39,727,641 29,488,132 19,281,902 9,109,401

Mortgage Payment $5,272,359 5,008,381 4,744,713 4,481,344

f. How are the cash flows distributed if prepayments in the first half of the second year are $20 million quarterly?

The amortization schedules for tranches A and B are shown below. Again the mortgage payments from the mortgage holders are assumed to decrease as the prepayments occur.

Amortization schedule for tranche A: Tranche Quarter Balance Payment 5 $9,109,401 $20,342,263

Interest Payment $204,961

Amortization schedule for tranche B: Tranche Quarter Balance Payment 5 $100,000,000 $13,527,900 6 88,972,100 23,689,967

Interest Payment $2,500,000 2,224,302

Principal Remaining Payment Principal $20,137,301 -$11,027,900

Mortgage Payment $4,218,263

Principal Payment $11,027,900 21,465,665

Mortgage Payment $4,218,263 3,689,967

Remaining Principal $88,972,100 67,506,435

g. How can the CMO issuer earn a positive spread on the CMO? The way the terms of the CMO are structured, the average coupon rate on the three classes equals the mortgage coupon rate on the underlying mortgage pool. However, given the more desirable cash flow characteristics of the individual classes, the FI may be able to issue the CMO classes at lower coupon rates. By splitting bondholders into different classes and by restructuring cash flows into forms more valued by different investor clienteles, the CMO issuer stands to make a profit. The difference between the sum of all coupon payments promised on all CMO tranches and the mortgage coupon rate on the underlying mortgage pool is the FI's servicing fee.

32.

Consider $100 million of 30-year mortgages with a coupon of 5 percent per year paid quarterly. a. What is the quarterly mortgage payment?

There are 120 quarterly payments over 30 years. The quarterly mortgage payments are $100m = PVAn=120, k=1.25% x PMT => PMT = $1,613,350. b. What are the interest and principal repayments over the first year of life of the mortgages?

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Quarter Balance 1 $100,000,000 2 99,636,650 3 99,268,759 4 98,896,269

(Fixed) Payment $1,613,350 1,613,350 1,613,350 1,613,350

Interest Payment $1,250,000 1,245,458 1,240,859 1,236,203

Principal Payment $363,350 367,891 372,490 377,146

Remaining Principal $99,636,650 99,268,759 98,896,269 98,519,123

c. Construct a 30-year CMO using this mortgage pool as collateral. The pool has three tranches, where tranche A offers the least protection against prepayment and tranche C offers the most protection against prepayment. Tranche A of $25 million receives quarterly payments at 4 percent per year, tranche B of $50 million receives quarterly payments at 5 percent per year, and tranche C of $25 million receives quarterly payments at 6 percent per year.

Tranche A Principal amount $25 million Interest rate 9 percent Quarterly interest on initial balance $250,000 Quarterly amortization

Tranche B $50 million 10 percent

Tranche C $25 million 11 percent

Total Issue $100 million 10 percent

$625,000

$375,000

$1,250,000 $1,613,350

d. Assume nonamortization of principal and no prepayments. What are the total promised coupon payments to the three classes? What are the principal payments to each of the three classes for the first year?

Regular tranche A interest payments are $250,000 quarterly. If there are no prepayments, then the regular GNMA quarterly payment of $1,613,350 is distributed among the three tranches. Five million is the total coupon interest payment for all three tranches. Therefore, $363,350 of principal is repaid each quarter. Tranche A receives all principal payments. Tranche A cash flows are $250,000 + $363,500 = $613,500 quarterly. The cash flows to tranches B and C are the scheduled interest payments.

Tranche A amortization schedule: Quarter Balance 1 $25,000,000 2 24,636,500 3 24,269,365 4 23,898,559

Payment $613,500 613,500 613,500 613,500

Interest Payment $250,000 246,365 242,694 238,986

Principal Payment $363,500 367,135 370,806 374,514

Remaining Principal $24,636,500 24,269,365 23,898,559 23,524,044

Payment $625,000

Interest Payment $625,000

Principal Payment $0.0m

Remaining Principal $50.000m

Tranche B amortization schedule: Quarter 1

Balance $50.000m

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2 3 4

50.000m 50.000m 50.000m

625,000 625,000 625,000

625,000 625,000 625,000

0.0m 0.0m 0.0m

50.000m 50.000m 50.000m

Payment $375m 375m 375m 375m

Interest Payment $375m 375m 375m 375m

Principal Payment $0.0m 0.0m 0.0m 0.0m

Remaining Principal $25.000m 25.000m 25.000m 25.000m

Tranche C amortization schedule: Quarter 1 2 3 4

Balance $25.000m 25.000m 25.000m 25.000m

e. If, over the first year, the trustee receives quarterly prepayments of $5 million on the mortgage pool, how are these funds distributed?

The quarterly prepayments of $5 million will be credited entirely to tranche A until tranche A is completely retired. Then prepayments will be paid entirely to tranche B. The amortization schedule for tranche A for the first year is shown below. This amortization schedule assumes that the trustee has a quarterly payment amount from the mortgage pool of $1,613,350.

Quarter Balance 1 $25,000,000 2 19,636,500 3 14,219,365 4 8,748,059

Interest Payment $250,000 196,365 142,194 87,481

Payment $5,613,500 5,613,500 5,613,500 5,613,500

Principal Payment $5,363,500 5,417,135 5,471,306 5,526,019

Remaining Principal $19,636,500 14,219,365 8,748,059 3,222,039

However, since some of the mortgages will be paid off early, the actual payment received by the trustee from the mortgage pool will decrease each quarter. Thus, the payment for the second quarter will decrease from $1,613,350 to $1,532,385 (n = 119 quarters, i = 5 percent, mortgage principal = $94,636,500). The CMO amortization schedule for tranche A given that the mortgage payments decrease with the prepayments is given below. The revised mortgage payment for each quarter is shown in the last column.

Quarter Balance 1 $25,000,000 2 19,636,500 3 14,300,480 4 8,992,143

Payment $5,613,500 5,532,385 5,451,342 5,370,210

Interest Payment $250,000 196,365 143,005 89,921

Principal Payment $5,363,500 5,336,020 5,308,337 5,280,289

Remaining Principal $19,636,500 14,300,480 8,992,143 3,711,854

Mortgage Payment $1,613,350 1,532,385 1,451,342 1,370,210

f. How are the cash flows distributed if prepayments in the first half of the second year are $10 million quarterly?

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The amortization schedules for tranches A and B are shown below. Again the mortgage payments from the mortgage holders are assumed to decrease as the prepayments occur.

Amortization schedule for tranche A: Tranche Quarter Balance Payment 5 $3,711,854 $10,288,986

Interest Payment $37,119

Principal Payment $10,251,867

Remaining Principal -$6,540,013

Mortgage Payment $1,288,986

Amortization schedule for tranche B: Tranche Quarter Balance Payment 5 $50,000,000 $7,165,283 6 43,459,987 11,817,739

Interest Payment $625,000 543,250

Principal Payment $6,540,013 11,274,489

Remaining Principal $43,459,987 32,185,498

Mortgage Payment $1,288,986 1,817,739

33.

How does a class Z tranche of a CMO differ from a class R tranche? What causes a Z class to have characteristics of both a zero-coupon bond and a regular bond? What factors can cause an R class to have a negative duration?

The Z class tranche has a stated coupon rate, but the accruing interest is not paid until all other classes of bonds have been paid. Thus, the tranche is like a zero-coupon bond. The R class tranche receives no interest or distribution until all other classes have been retired. At the time that all other tranches are paid off, the R class investors receive the remaining funds in the tranche. The reinvestment income can be quite large, and further, the value of the reinvested income grows as interest rates increase. Therefore, the duration can be negative.

34.

Why would buyers of class C tranches of collateralized mortgage obligations (CMOs) be willing to accept a lower return than purchasers of class A tranches?

Buyers of CMOs incur prepayment risks depending upon the class of tranches they have purchased. Purchasers of Tranche A incur the most risk because all prepayments will be passed on to them. Prepayments usually occur when interest rates are low and thus, pose high reinvestment risks to this group of buyers. On the other hand, Tranche C purchasers are protected from prepayment until Tranche B is exhausted and as a result are less likely to incur early prepayments unless interest rates reach so low as to create above-average levels of refinancing.

35.

What are mortgage-backed bonds (MBBs)? How do MBBs differ from pass-through securities and CMOs?

MBBs, or covered bonds, are bonds issued by FIs that have a block of assets, usually mortgages, serving as collateral against, or covering the payment on, the bonds. Contrary to CMOs and passthrough securities, the issuance of MBBs does not remove the mortgage assets from the balance sheet. Rather, the MBB bondholders have a first claim on the specific mortgage assets. The MBB bondholders receive a stated rate of interest that is not tied to the cash flows of the mortgage assets.

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36.

From the perspective of risk-management, how does the use of MBBs by an FI assist the FI in managing credit and interest rate risk?

The MBBs usually are over collateralized and therefore, may have a higher credit rating than the FI as a whole. As a result, the MBB may have a lower interest rate than uninsured deposits.

Further, the normally positive duration of the FI will be reduced because of the long-term, fixedrate nature of the bonds.

37.

Consider a bank with $50 million in long-term mortgages as assets. It is financing these mortgages with $30 million in short-term uninsured deposits and $20 million in insured deposits. To reduce its interest rate risk exposure and to lower its funding costs, the bank can segregate $35 million of the mortgages on the asset side of its balance sheet and pledge them as collateral backing a $30 million long-term MBB issue. Because the $30 million in MBBs is backed by mortgages worth $35 million, the mortgage-backed bond issued by the bank costs less to issue, in terms of required yield, than uninsured deposits. Thus, the bank can then use the proceeds of the $30 million bond issue to replace the $30 million of uninsured deposits. Show the bank’s balance sheet before and after the issue of the MBB.

Bank’s balance sheet of before issue of MBB (in millions of dollars) Assets Liabilities Long-term mortgages $50 Insured deposits Uninsured deposits $50 Bank’s Balance sheet after issue of MBB (in millions of dollars) Assets Collateral = (market value of $35 segregated mortgages) Other mortgages 15 $50 38.

Liabilities MBB issue Insured deposits

$20 30 $50

$30 20 $50

What are the reasons why an FI may prefer the use of either pass-through securities or CMOs to the use of MBBs?

First, MBBs freeze mortgages on the FI’s balance sheet for an extended period of time. This increases the illiquidity of the asset portfolio. Second, the amount of mortgages that are put up as security for the MBBs exceeds the amount of MBBs because of the overcollateralization requirements to improve the credit rating of the MBBs. Third, the continued existence of the mortgages on the balance sheet requires capital adequacy and reserve requirement taxes for the FI. Because of these problems, MBBs are the least used of the three basic vehicles of securitization in the United States. However, after the mortgage-backed security crisis, some 21 © 2022

U.S. regulators have reconsidered their opposition to these types of bonds because of their greater security offered to investors.

39.

What is an interest only (IO) strip? How do the discount effect and the prepayment effect of an IO create a negative duration asset? What macroeconomic effect is required for this negative duration effect to be possible?

A mortgage pass-through that has a claim only to the interest payments of underlying mortgages is an interest only strip. These IO strips are sensitive to two factors: the level of interest rates (discount effect) and the prepayment of mortgages. If market interest rates are above coupon rates, then the present value of the stream of interest payments declines. However, when rates decline, especially below coupon rates, it is quite likely that the prepayment effect may dominate and therefore the value of the instruments may also decline. When the value of a fixed-rate asset decreases as interest rates are declining, the duration of the asset is negative. If IO strips are created out of nonmortgage instruments, such as Treasury bonds, then the likelihood of prepayment is low and the relationship will be in one direction. That is, as interest rates rise, the present value of the income streams will decrease.

40.

What is a principal only (PO) strip? What causes the price-yield profile of a PO strip to have a steeper slope than a normal bond?

The holder of a principal only strip is entitled to the portion of the mortgage payments that reflects the payment of principal. As interest rates decrease, the discount effect will cause the value of the PO strip to increase. Further, as interest rates decrease, the prepayment effect also has a positive impact on the value of the PO strip. Thus, the double effect causes the rate sensitivity of a PO strip to be higher than that of a normal bond that is not subject to the prepayment effect.

41.

An FI originates a pool of real estate loans worth $20 million with maturities of 10 years and paying interest rates of 9 percent per year. a. What is the average payment received by the FI, including both principal and interest, if no prepayment is expected over the life of the loan?

The average payment is $20,000,000 = PVAn=10, k=9% x PMT => PMT = $3,116,401.80 b. If the loans are converted into pass-through certificates and the FI charges a servicing of 50 basis points, including insurance, what is the payment amount expected by the holders of the pass-through securities if no prepayment is expected? $20,000,000 = PVAn=10,k=8.5% x PMT => PMT = $3,048,154.10 c. Assume that the payments are separated into interest only (IO) and principal only (PO) payments, that prepayments of 5 percent occur at the end of years 3 and 4, and that the 22 © 2022

payment of the remaining principal occurs at the end of year 5. What are the expected annual payments for each instrument? Assume discount rates of 9 percent.

Year Balance Payment 1 $20,000,000.00 $3,116,401.80 2 18,683,598.20 $3,116,401.80 3 17,248,720.24 $3,978,837.81 4 14,822,267.25 $3,857,515.16 5 12,298,756.14 $13,405,644.19

Interest Principal Payment Payment $1,800,000.00 $1,316,401.80 $1,681,523.84 $1,434,877.96 $1,552,384.82 $2,426,452.99 $1,334,004.05 $2,523,511.11 $1,106,888.05 $12,298,756.14

Remaining Principal $18,683,598.20 $17,248,720.24 $14,822,267.25 $12,298,756.14 $0.00

d. What is the market value of IOs and POs if the market interest rates for instruments of similar risk decline to 8 percent?

The market value of the IO is found by discounting the interest payment column in part (c) at 8 percent. The PV = $6,074,497.66.

The market value of the PO is found by discounting the principal payment column in part (c) at 8 percent. The PV = $14,600,446.52.

Note that the PV of the total payments is $20,674,944.18 which is the sum of the PV of the IO and the PV of the PO. 42.

What are the factors that, in general, allow assets to be securitized? What are the costs involved in the securitization process?

In general the easiest assets to securitize are those that are homogenous and that can be valued with relative precision. The homogeneity involves the characteristics of the contracts, such as maturity, payment schedule, etc., while the valuation process is easiest if the underlying assets are traded in the market. The costs of the securitization process include credit risk insurance, guarantees, overcollateralization, valuation and packaging costs.

43.

How does an FI use securitization to manage interest rate, credit and liquidity risks?

Summarize how each of the possible methods of securitization products affects the balance sheet and profitability of an FI in the management of these risks.

In the process of intermediation on behalf of its customers, the FI assumes risk exposure. The FI can reduce that risk exposure by altering its product base, thereby affecting the portfolio mix obtained in the course of intermediation. However, this is likely to be quite costly in terms of customer good will and loss of business. Securitization enables FIs to manage risk exposure by changing their portfolio mix without alienating customers or changing the customer base and mix. That is, customers are still serviced and the FI continues to intermediate. Balance sheet alterations are made subsequent to and independent of the intermediation activity. Thus, the FI can make portfolio changes and still fulfill the function of the intermediary.

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Interest rate risk exposure is reduced by matching the durations of assets and liabilities.

Securitization enables the FI to accomplish this since the FI can determine which loans to package and sell off. Credit risk exposure is minimized by selling loans without recourse.

Securitization allows the FI to sell off unmatched assets. Finally, securitization reduces liquidity risk, since the FI does not have to fund the asset.

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