Solution Manual For Foundations of Investments An Introduction, 1st Edition by Troy Adair, John R. N

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

Table of Contents Questions .......................................................................................................................................... 2 Case Study ......................................................................................................................................... 7

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

Questions 1. Real vs. Financial Assets. Compare and contrast real assets with financial assets.

(LO 1-1) Answer: Real assets are assets that either contribute to production or create income or wealth. Most real assets have a physical existence, with the most common examples being real estate and land, machinery, precious metals, and commodities. However, certain intangible assets, such as patents, trademarks, and intellectual property, can also create income, so they are considered real assets, too.

Financial assets are nonphysical assets whose values are derived from either a contractual claim on real assets or the cash flows produced by those real assets.

Examples of financial assets include stocks, bonds, cash, bank deposits, certificate of deposits (CDs), loans made, corporate receivables, derivative securities, and cryptocurrencies.

The difference between real and financial assets is that real assets are used to produce economic output, while financial assets serve to allocate how that output is divided up.

2. Capital Flow: Corporate vs. Investor View. Regarding the flow of capital between investors, corporations, and the government, how does the view of the corporation differ from the view of the investor? (LO 1-2) Answer: Investors provide money to companies as capital. The companies use that capital to invest in projects. When the projects return cash flows to the firm, any profits are usually subject to taxation by federal, state, and/or local governments. Some of the remaining after-tax profits are retained in the firm to fund future operations and the rest are paid out to investors.

The corporation view of this system focuses on decisions concerning (1) the form and amount of funding received from investors, (2) which projects to put the funds in, (3) how to manage taxes, and (4) how much of the revenues of existing projects to keep versus paying back the firm’s investors.

The investors view of this system focus on decisions such as (1) which firms and what types of financial instruments to invest in, (2) what terms and maturities of return cash flows to seek, and (3) how to best manage the timing and amounts of taxes paid.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

3. Capital Flow Factors. What are the complicating factors that make the flow of capital among corporations and investors uncertain? (LO 1-2) Answer: Some of the complicating factors that make the flow of capital among corporations and investors uncertain are the following: The returns from projects in which firms have invested are not always positive, and those investments are not always profitable. The demand for the goods and services produced by those projects are often subject to change over time in a competitive macroeconomic environment. That change could negatively affect a firm’s operations as well as its ability to sell those products and services at their hoped-for prices.

Firms’ earnings can fluctuate and are not always as expected. Therefore, a firm cannot guarantee the amount and timing of the returns they can give back to investors. Even if firms could perfectly forecast the before-tax returns from their operations, they have no control over government tax regulations that impact final cash flows.

Furthermore, the prices of financial assets change because of those uncertainties, and as more information arrives about a particular company, the valuation of those assets also changes, which causes the price that the investor pays for those assets to change as well. Finally, there is a very large number of financial assets in which investors can invest, which make investing choices more complicated.

4. Valuation. What factors are involved in assessing value? (LO 1-3) Answer: The valuation of assets is the process of determining what an asset is worth today. It is based on finding today’s value of all the expected future cash flows that the asset will provide over the life of the asset.

From this definition, we see that there are three factors involved in valuing the asset: (1) the life of the asset, (2) the expected cash flows the asset will provide over its life, and (3) the risk of those cash flows to determine the discount rate used to find the present value of the cash flows.

Those factors vary from one asset to the other and make the valuation process complicated. For example, the expected cash flows on bonds are easier to calculate, while the expected cash flows on stocks are much more difficult to predict. Some assets have finite lives, while others have infinite lives. Also, the riskiness of assets is not the same, which requires different discount rates.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

5. Risk Aversion. What are the ramifications of an investor being risk averse? (LO 1-3) Answer: It is assumed that most rational investors are generally risk averse. This means that they will only take a risk when they feel they will be compensated for it with a higher expected return. But that doesn’t mean they’re all equally risk averse. An investor with a long-time horizon and considerable additional savings can afford to take risks that someone with a shorter horizon and less savings would be uncomfortable with.

Because of the differences in risk aversion, people invest in different types of assets with different risk profiles. A more risk-averse investor would invest in less risky assets, such as government bonds, while a less risk averse investor would invest in riskier assets, such as stocks.

However, the downside of being risk-averse is in the missed opportunity that comes along with taking on higher-risk, higher-reward investments if it leads you to avoid them altogether.

6. Market Efficiency. Why might a market be efficient? (LO 1-4) Answer: Financial markets are competitive markets where investors participate freely in the purchase and sale of stocks and bonds. Virtually anyone, from a child to a grandparent, may own an investment, even if it is just a savings account.

Competitive financial markets also tend to be extremely efficient at making sure that new information is rapidly taken into account by valuations. If new information suggests that cash flows from different assets will be different than previously thought, the market rapidly adjusts the asset’s price. Thus, an efficient financial market implies that a security’s current price embodies all the known information concerning its potential return and risk.

A truly efficient market eliminates the possibility of beating the market, because any information available to any trader is already incorporated into the market price. As the quality and amount of information increases, the market becomes more efficient reducing opportunities for arbitrage and above market returns.

7. Asset-Specific Risk. What is an asset-specific risk and how does it relate to portfolio diversification? (LO 1-5) Answer: An asset-specific risk, which is also called unsystematic risk or diversifiable risk, is a type of risk that is only related to one particular asset and doesn’t affect the other assets in the market. For example, if the rating on Walmart’s bonds is downgraded,

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

the price of the bonds would decrease, and their yield would increase. However, this change in the rating will not affect any other bonds in the market.

Asset-specific risk can be diversified away when a well-diversified portfolio with several assets is created. In such a portfolio, individual asset-specific risks are eliminated and only systematic risk or non-diversified risk remains.

8. Oil Prices and Diversification. How would an increase in oil prices impact petroleum companies and airline firms? How does this relate to diversification?

(LO 1-5) Answer: The change in oil prices is considered a systematic risk that affects all the companies in different degrees and manners; therefore, the impact of oil price changes cannot be diversified away.

A higher oil price may be good for petroleum companies (they can sell their product at a higher prices) but bad for airline firms (airlines are users of oil products and will end up paying higher prices). So, oil is a type of economic factor that cannot be diversified away by creating a well-diversified portfolio.

9. Financial Crisis Recovery. How did the recoveries after the financial crises of 2008 and 2020 differ for investor opportunities? (LO 1-6) Answer: The two most recent stock bear markets (defined as a 20% or greater decline) occurred in 2008 and 2020. However, their causes and recoveries were very different.

Both of these financial crises share an underlying cause: a sudden and dramatic increase in risk and uncertainty brought upon by an unexpected event, which caused a shift in expectations and risk aversion for large portions of the investment community.

The causes of the financial crises of 2008 have been extensively analyzed and well documented; the main culprits have been identified as excessive risk taking by banks and the bursting of the U.S. housing bubble, both combining to cause the value of securities tied to U.S. real estate to fall precipitously. It took about four years for the stock market to fully recover.

The primary initial causes of the COVID-19 financial crisis are even more easily identifiable: widespread lockdowns around the globe resulted in massive business closures, many of which will be permanent. The investors’ reaction to the pandemic news brought selling pressure that dropped the overall stock markets worldwide by about a third in a shocking six weeks. After the initial decline in March 2020,

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

investors bought the stock of technology firms, which ended 2020 with realizing great returns. Then, in 2021, as the pandemic slowly subsided, investors started buying back the travel-oriented firms that they had previously dumped in anticipation of pent-up travel demand.

The recovery from the COVID-19 pandemic was quicker than the recovery from the 2008 financial crisis.

10. Investment Professional Roles. Discuss four kinds of investment professionals, including their primary roles in the industry. (LO 1-7) Answer: The various roles include stockbroker, securities analyst, portfolio manager, financial planner, and investment banker. A stockbroker works with individuals and institutions in advising and executing buy and sell orders of selling financial securities.

1. A securities analyst is an expert in specific industries and provides advice about the valuation and prospects of firms in those industries.

2. A portfolio manager makes decisions on what to buy and sell in the creation or management of the portfolio.

3. A financial planner helps individuals and families navigate the process of saving, investing, and ultimately providing retirement income.

4. An investment banker is the intermediary between the companies and governments seeking new capital and investors with capital to offer. Thus, they work with companies to issue securities and distribute them to investors.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

Case Study Financial Information To be successful in this course and in your investment life, you will need access to good information. Investment professionals often have access to expensive information sources and analytical tools, like a Bloomberg Terminal. However, there are also many free financial websites that are very useful: • • • • • • •

Bloomberg: bloomberg.com CNN/Money: cnn.com/business Google: google.com/finance MarketWatch: marketwatch.com Morningstar: morningstar.com MSN Money: msn.com/en-us/money Yahoo! Finance: finance.yahoo.com

The purpose of this case is to explore one information source that you will use during this course and in your personal financial life. Start by choosing a public company to explore and finding its ticker symbol on Yahoo! Finance. Once you have found the company, locate the following information. a. From the Summary tab, find the closing stock price, PE ratio, earnings per share, dividend, capitalization, beta, and volume of shares traded. b. From the Financials tab, obtain an annual income statement and a balance sheet.

Comment on the firm’s financial statements. c. From the Statistics tab, obtain the valuation measures, profitability, management effectiveness, and share statistics. d. Historical stock price data can be found in the Historical Data. This is useful for obtaining a history of daily, weekly, or monthly stock returns. Select five years of monthly prices. Next, click the Download link to receive a csv file for your spreadsheet. Note that the data is sorted as oldest month first. Next, compute a monthly return using the Adj Close column (this column adjusts the price for dividends and share splits) for each month, starting at the second month. [Example: For spreadsheet row 3, compute the return as =(F3-F2)/F2]. Compute the five-year monthly average return. Comment on the monthly returns and average return.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

Example:

Solution a. When you go to finance.yahoo.com, select a company of your choosing and enter its name into the search tab. Yahoo! will find the company and provide the ticker symbol. In this solution, Walmart has been chosen as the company.

The default screen that opens in Yahoo! Finance is the Summary tab, as shown in the screenshot above.

The Summary tab provides summary information about the company.

The closing price of Walmart on Tuesday, 15 March, 2022, is $145.75.

The PE ratio is 29.93 (the PE ratio is calculated using the trailing 12-month EPS, shown in the parentheses as “TTM”).

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

The (12-month trailing) EPS is $4.87.

The dividend amount is $2.24: this is the annual dividend amount that Walmart is going to pay over the year or the next four quarters. (The quarterly dividend payment amount will be $0.56.)

The market capitalization is 404.376 billion.

Beta is 0.53.

The volume of shares traded on this day is 7,418,478 shares. b. There are several tabs where you can go to get different types of information. The Financials tab will provide you with the following:

As you can see, in the Financials tab, you will have access to income statement information, the balance sheet, and the statement of cash flows.

Notice that while most of the important information is available for free on Yahoo! Finance, not all of it is. Here, downloading the financial statements requires an additional subscription.

The financial statements for Walmart provide a positive picture about the company, as is shown in the screenshot below. The net income has been positive and growing over the past two years. The statement of cash flows also shows positive free cash flows for the past two years.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

c. The Statistics tab includes valuation measures, profitability, management effectiveness, and share statistics. These measures are explained in the textbook over several chapters; however, as you can see, Yahoo! Finance allows you to obtain those measures easily and freely for the most recent few years.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

Looking at the data below, you can see that Walmart has been doing well. The net profit margin is 2.39%, the operating profit margin is 4.53%, the return on assets is 6.52%, and the return on equity is 15.53%. There are numerous other measures that you can see and analyze.

d. The Historical Data tab provides historical data that you can download.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 01: Introduction to Investments

This solution was created on March 15, 2022. When you download the monthly adjusted stock prices from Yahoo! for March, you will see that for the data doesn’t yet give the adjusted closing price for the whole month. Thus, it is best not to use this last row in the return calculations.

In order to have five years of returns, you need to calculate 60 different return values. Keep in mind that in order to calculate the monthly return up to the end of February 2022, we need 61 monthly adjusted stock prices, starting with the February 1, 2017, data. The February 1, 2017, monthly adjusted price is the price at the end of the month for the month of February 2017. The calculation of the monthly returns is provided in the Excel spreadsheet.

The monthly returns show some variations: for some months, the return was negative, while for others it was positive. The average monthly return over the past five years came to 1.40%.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

Table of Contents Questions .......................................................................................................................................... 2 Case Study ......................................................................................................................................... 7

© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

Questions 1. Instruments vs. Securities. What are the fundamental differences between financial instruments and securities? (LO 2-1) Answer: A financial instrument is a contract that generates a financial asset to one of the parties involved, and an equity claim or financial liability to the other party. Equitybased financial instruments represent ownership of an asset, while debt-based financial instruments represent a loan made by an investor to the borrower, which could be a company or government.

All financial instruments can technically be traded, but those that are created with the specific intention of being publicly traded are called securities. Most financial instruments fall into one or more of the following five categories: equity securities, debt securities, money market instruments, derivative instruments, and foreign exchange instruments.

The Securities and Exchange Commission (SEC) heavily regulates publicly traded securities, but other types of financial instruments are less heavily regulated.

2. Primary vs. Secondary Market Transactions. Why do we differentiate between primary and secondary market transactions? (LO 2-2) Answer: When a company publicly sells new stocks and bonds for the first time, it does so in the primary capital market. This market is also called the new issues market. In many cases, the new issue takes the form of an initial public offering (IPO).

The secondary market is where securities are traded after the company has sold its offering on the primary market. It is also referred to as the stock market. The New York Stock Exchange (NYSE), London Stock Exchange, and Nasdaq are secondary markets. Small investors have a much better chance of trading securities on the secondary market since they are excluded from IPOs. Anyone can purchase securities on the secondary market as long as they are willing to pay the asking price per share.

3. Division of Capital, Risk, Return, and Control. Explain why bondholders are willing to accept a lower rate of return than stockholders in the same firm. (LO 2-3) Answer: Bondholders have priority on income and priority on assets over the stockholders in a firm.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

When a firm is solvent, the contractually obligated ordering of payout precedence that controlling shareholders have granted to the other classes/types of capital providers dictates that every period, debtholders get paid their promised payments first, then preferred shareholders, then common shareholders. As a result, you will often hear common shareholders referred to as “residual claimants,” in that they get paid out of whatever is left over after all the other capital providers get their promised payments.

Even if the firm becomes insolvent and goes into bankruptcy, the same general ordering or precedence in payouts holds true from the sale of the assets of the firm.

Shareholders will get paid (assuming there is any money left for them) after all other claimants—including fees owed to bankruptcy lawyers, taxes due to federal and state governments, debtholders, etc.—are paid.

Because of this priority on income and assets that bondholders enjoy, the risk that bondholders bear is lower compared to the stockholders in the same firm.

Therefore, bondholders would accept a lower rate of return than stockholders in the same firm.

4. Division of Capital, Risk, Return, and Control. Explain why equity ownership (stocks) is often much more valuable than debt ownership (bonds) in public corporations. (LO 2-3) Answer: The only returns that bondholders receive are those that they were promised when the bond was first issued by the company, which are the stated coupon rate paid in periodic interest payments and the bond’s maturity value paid at the end of its life.

Therefore, the bondholders do not receive anything when a company’s profitability and earnings increases.

Equity ownership provides limited liability to the stockholders. In addition, stockholders receive all the benefits when a firm grows and prospers, and its earnings and profitability increases. As long as the firm prospers, it may be able to pay dividends and grow; this growth would lead to increases in the stock price, which would generate capital gains in case the stockholder sold the shares. Of course, the stockholders bear the risk of the firm having negative earnings and not growing also.

Overall, the reason why equity ownership is considered to be more valuable than debt ownership is because equity owners benefit from the profitability of the firm, while debt owners get only what their debt contract specifies.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

5. Primary Market Equity Issue. What effect does a primary market equity issue have on the firm? What is this used for? (LO 2-4) Answer: Primary market equity issue is the sale of new stocks by a firm to raise capital.

Issuing new stock provides capital to the firm, which will be used to make investments in assets that will in turn increase production and profitability of the firm. However, when firms issue new equity, there is a dilution of earnings because there will be more shares outstanding and the company’s earnings will be divided among larger number of shareholders. Of course, the firm expects that the investments made by the capital provided by the issuance of new equity will increase the earnings so that the impact of this dilution is minimal.

6. Bond Rates and Maturity. If you have two bonds of different maturities issued by the same firm, which would you expect to have a higher coupon rate? Why? (LO 2-5) Answer: When a fixed-income debt instrument such as a bond is issued, the rate of interest to be paid by the borrower is established. This rate is frequently referred to as the bond’s coupon rate. The coupon rate is usually fixed over the lifetime of the bond.

The issuer of the bond usually matches the going market rate for similar bonds with similar risk characteristics when establishing the coupon rate on the bond. In general, there is no particular relationship between the coupon rate and bonds with different maturities. If two bonds of different maturities were issued by the same firm, the only reason one would have a higher coupon rate than the other is that they were issued at different times. Because the prevailing interest rates in the market were different, the coupon rates chosen were different.

However, the yield to maturity—which is the yield that the investor will earn if the debt instrument is held from the moment of purchase until it is redeemed at par (face value) at the maturity date—is in general higher as the maturity of the bond increases. The general relationship between the yield to maturity and the bond maturity is the longer the term to maturity, the higher the yield.

7. Primary Market Debt Retirement. Under what condition would a firm decide to retire some of its outstanding debt early? (LO 2-6) Answer: A callable bond is a type of bond that can be retired early by the issuer, before its maturity date, if it is in the best interest of the issuer to do so. In general, when a company has a callable bond issue with a high coupon rate and the current market rates are much lower, they will be better off retiring those bonds and borrowing at

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

the lower rates that exist in the market. Since the call feature is not in the best interest of the bondholder, the issuer usually pays a call premium above the par value when retiring the bond early.

8. Money Market Instruments. Why are money market instruments called that?

(LO 2-7) Answer: Money market instruments are highly marketable short-term debt securities. Due to the shortness of their term as well as the relative strength of the firms that issue them, money market instruments are generally low-risk investments and generally seen as providing investors with an alternative to savings and time deposits offered by banks. Because of this, they tend to offer lower yields than either stocks or debt securities.

Many money market instruments trade in large denominations among institutional investors. However, some money market instruments are available to individual investors via money market funds. Money market instruments include Treasury bills (T-bills), repurchase agreements (commonly referred to as repos), certificates of deposit (CDs), commercial paper issued by corporations, bankers’ acceptances, and tax anticipation notes.

Because money market instruments are short term, highly liquid, and relatively very safe, they are considered to be equivalent to cash. Because they can become cash quickly, the have been given the name money market instruments.

9. Futures vs. Options. What are the differences between futures contracts and options? (LO 2-8) Answer: A futures contract is a formal agreement between a buyer or seller and a commodity exchange. In the case of a purchase contract, the buyer agrees to accept a specific commodity that meets a specified quality in a specified month. In the case of a sale, the seller agrees to deliver the specified commodity during the designated month. Although a futures contract appears to involve a buyer and a seller, the actual contract is made between the individual and the exchange. If an individual buys a contract, the exchange guarantees the delivery (the sale). If an individual sells a contract, the exchange guarantees to take delivery (the purchase). If one of the parties were to default (e.g., the buyer), the seller’s contract is upheld by the exchange. Note that in a futures contract, both parties have the obligation to perform the terms of the contract at maturity.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

An option contract is the right to perform something but not the obligation, and that is the major difference between the options contract and a futures contract. An option is the right to buy or sell stock at a specified price within a specified time period. The value of an option is derived from (i.e., depends on) the underlying security for which the option is a right to buy or sell. Options take various forms, including calls, puts, and warrants. The holder of the option contract will only exercise the option if it is profitable and will let the contract expire unexercised if it is not profitable.

10. Foreign Exchange Instruments. Explain how a foreign exchange instrument could be used by an investor to hedge currency risk. (LO 2-9) Answer: Currency risk can be hedged by foreign exchange futures contracts. These are the two scenarios where an investor can use currency futures to hedge for currency risk.

Suppose a U.S. investor has an obligation to pay a large sum of money in euros in six months and would like to hedge for the currency risk. This investor can buy a futures contract on euros, which allows them to buy the euros in six months at a price that is determined in the futures contract today. Therefore, the investor hedges the currency risk by entering the long position in the futures contract. The investor does not need to worry about what will happen to the exchange rate of the euro relative to the dollar, as they already locked in the price of the euro with the futures contract.

Similarly, suppose a U.S. investor expects to receive a large sum of money from Europe in six months and would like to hedge for the currency risk. This investor can sell a futures contract on euros, which allows them to sell the euros in six months at the price that has been determined in the futures contract today. Therefore, the investor hedges the currency risk by entering the short position in the futures contract. The investor does not need to worry about what will happen to the exchange rate of the euro relative to the dollar, as they already locked in the price of the euro with the futures contract.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

Case Study Identify a publicly traded corporation that has at least two different classes of equity and investigate the firm to answer the following questions: a. How do the different classes vary in terms of risk, return, and control? b. Which class of shares was the “original” type of shares? Why do you think the other classes were issued? c. Identify bond issues by the firm. What are the coupon rates, maturity dates, and credit ratings of those bonds? d. Are options traded on this stock? What are the characteristics of these options?

Alphabet Inc., which is the name of the company known more widely as Google, has two different classes of equity listed: class A shares and class C shares.

(In fact, they have three different classes of equity, as they also have class B shares.

However, these shares are not tradeable and are only held by the founders or insiders.) a. Alphabet Inc. shares are listed on NASDAQ under the ticker symbol GOOGL and GOOG. GOOGL is the class A shares, while GOOG is the class C shares. Class A shares have one voting right per share, while class C shares do not have any voting rights. Therefore, owners of class C shares cannot vote, and thus have no control over the firm. Only class A share owners have voting rights and have control over the firm.

As for the risk, both shares have the same risk, as both shares are affected by the profitability and earning potential of the same company. In fact, on March 15, 2022, class A shares (GOOGL) were trading for $2,583.96, while class C shares (GOOG) were trading for $2,593.21. b. The original class of shares was class A. In 2014, the company issued class C shares (with no voting rights). The main reason for this was that the founders of the company wanted to keep control of the company, including the strategic direction. c. The FINRA website (https://finramarkets.morningstar.com/BondCenter/Default.jsp) includes a search tool that will produce a list of a company’s outstanding bonds. Alphabet Inc.’s outstanding bonds are listed below. Coupon rates, maturity dates, and credit ratings of those different issues of bonds appear in the screenshot.

Note also that the last row in the table shows a bond issue that has already matured (on 5/19/2021). The data also give the price of each bond issue as well as the yield to maturity.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

As an example, you can click on the first bond issue to get more detailed information. This issue has a particular symbol, GOOG4358366, as well as a particular Committee on Uniform Securities Identification Procedures (CUSIP) ID, 02079KAB3. It has a maturity date of 02/25/2024, its coupon rate is 3.375%, and the frequency of the coupon payments is semi-annual. The bond is investment grade: it has a AA+ rating by S&P and an Aa2 rating by Moody’s. It is callable; its last traded price is $102.77 of par, with par value of $1,000. So, the last traded price in actual dollars is $1,027.70. d. To find options data, use any of the websites listed in the textbook (such as Yahoo!

Finance). The screenshot below shows the options chains for Alphabet Inc., class A shares GOOGL. There are options on the class C shares, too. Options are created by an exchange, not by the company. The exchange creates different options depending on the demand for those options. In the case of Alphabet, there are call options and put options, with weekly expirations and numerous strike prices. There are options expiring on Friday 18 March, Friday 1 April, etc. Option contracts, whether they are calls or puts, are created for 100 of the underlying security. So, in the case of calls and put contracts on Alphabet Inc., the call option gives the right to buy 100 of the underlying shares, while the put option gives the right to sell 100 of the underlying shares. The strike price of the option is the price at which you can either buy or sell the underlying shares. As you can see in the listings from Yahoo!, the Alphabet Inc. options have strike prices that vary by different increments, such as $50, $20, $10. or $5. Again, the exchange creates those option chains depending on the popularity of a particular stock and its demand.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 02: Types and Attributes of Financial Instruments

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 9 Case Study ....................................................................................................................................... 24

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Questions 1. Stock Exchanges. What is the difference between an agency auction market and an over-the-counter (OTC) negotiated market? Include in your answer an example of both types of markets. (LO 3-1) Answer: The agency auction market is a type of market where buy and sell orders meet directly on the trading floor or electronic market, and prices are determined by the interplay of supply and demand. An example of an agency auction market is the New York Stock Exchange (NYSE). Trading on the NYSE takes place in the form of bids and offers by exchange members, who are acting as agents for institutions or individual investors.

Over-the-counter markets do not have physical locations; instead, trading is conducted electronically. This is very different from an auction market system. In an OTC market, dealers act as market-makers by quoting prices at which they will buy and sell a security, currency, or other financial products.

The over-the-counter negotiated market is a type of market where security prices are negotiated between buyers and sellers. In the negotiated market, the buyers and sellers negotiate the price of the security; this is unlike the auction market described above, where prices are determined by supply and demand. An example of a negotiated market is the NASDAQ stock market in the United States, which is virtually an OTC market.

2. Foreign Securities. What is an American depository receipt (ADR)? Give examples.

(LO 3-2) Answer: An American depository receipt (ADR) is a certificate created and issued by a financial institution or investment bank that allows foreign stocks or bonds to be listed and traded on a U.S. exchange.

There are two types of ADRs. Sponsored ADRs are created when the firm wants the securities to trade in the United States. The firm employs a bank to perform the paperwork to create the ADRs and to act as transfer agent. In this case, the costs are absorbed by the firm. All ADRs listed on the NYSE are sponsored ADRs. Unsponsored ADRs are created when a brokerage firm believes there will be sufficient interest in a stock or bond to make a market in the security. The brokerage firm buys a block of securities and hires a commercial bank to create the ADRs and to act as a transfer agent. However, fees for this service and for converting dividend payments from the foreign currency into U.S. dollars will be paid by the stockholders, not the issuing firm.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

An example of a sponsored ADR is the Japanese car manufacturer Toyota Motor Corporation’s ADR listed on NYSE. An example of an unsponsored ADR is the German car manufacturer Volkswagen’s ADR, which is traded on the OTC market.

3. Stock Index Design. What are the differences between a price-weighted index and a value-weighted index? What are the implications of those differences? (LO 3-3) Answer: A price-weighted index is a stock index construction method where the numerator is the sum of each stock price that is included in the index. The denominator is a divisor that starts as the number of stocks in the index initially, but over time the divisor gets adjusted for changes in the number of shares outstanding for a firm and the firms in the index, such as stock-splits. The price-weighted index is impacted mostly by the price of the firm. The firms with the highest prices drive the index value.

A value-weighted index is a different stock index construction method that uses the market capitalization instead of the prices. The market capitalization is the price of a stock times the number of outstanding shares. A value-weighted index is constructed by dividing the sum of the market capitalization of each stock included in the index every day, by the initial value of the sum of the market capitalization of each stock on the day the index was constructed. This ratio is multiplied by an index base value. In a value-weighted index, the firms with the largest sizes drive the index value.

In a price-weighted index, stocks with larger values have more impact on the index value than stocks with smaller values. In a value-weighted index, the largest companies in terms of their capitalization have the largest impact on the index value. Also, the value-weighted index does not need to adjust for stock splits.

4. Major Stock Indexes. What are the major stock indexes, and what are they trying to measure? (LO 3-4) Answer: In finance, a stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current stock price levels with past prices to calculate market performance.

The major stock indexes are listed below, along with a brief summary of what they measure.

The Dow Jones Industrial Average (DJIA) is the first stock index and was invented in 1884. The DJIA is composed of the 30 largest companies in the United States. The

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

DJIA is a price-weighted index, with the divisor being 0.147 from the original 30 because of all the adjustments that happened over the years.

The Standard & Poor’s 500 Index is a very popular value-weighted market index composed of 500 different stocks. These stocks are from the most important companies in each of the 11 sectors of the economy. The S&P 500 Index covers about 80% of the total U.S. equity market capitalization.

The Nasdaq Composite Index includes over 2,500 companies that trade on the Nasdaq Stock Exchange. Many of these are foreign companies. The Nasdaq Composite is value-weighted index driven by the largest companies, which are mostly technology-oriented firms.

FT Wilshire Equity Indexes, Russell Indexes, and MSCI Global Indexes are also popular.

5. Brokerage Firms. What are the differences in services and costs between a fullservice stock brokerage firm and a discount online brokerage firm? (LO 3-5) Answer: A full-service brokerage firm provides clients with investment research, financial advice, retirement services, and other services and products in addition to buying/selling securities. The firm pays for these services through high commission costs on the buy and sell trades, which can amount to hundreds of dollars.

Examples of full-service broker-dealers include CitiFinancial, Merrill Lynch Wealth Management, and Morgan Stanley.

A discount brokerage firm charges a low commission per trade, but doesn’t provide their clients with advice. Examples of discount broker firms include E-Trade Financial Corp., Fidelity Investments, Charles Schwab Corp., Interactive Brokers, and TD Ameritrade.

An online broker has no human interaction and simply executes your trades. These companies charge deeply discounted commissions (less than $5 per trade). Popular examples include Robinhood, Webull, TradeStation, and Coinbase.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

6. Trading Orders. What is the difference between each pair of items? (LO 3-6) Answer: a) market order and limit order b) fill or kill order and good until canceled order c) stop order and stop loss order 1. A market order is a type of order where the trade (buy/sell) happens at the best price currently available. A market order guarantees the execution of the order but not the price. Sometimes, when the market is moving too fast, the executed price can be very different from the quoted price.

A limit order is a type of order to trade (buy/sell) at a specific price or better. The limit order guarantees the price but does not guarantee execution. Sometimes, when the market is moving too fast, the limit order may not be executed at all.

2. A fill or kill order is a type of buy or sell order that must be executed immediately (filled) once it reaches the market maker. If it cannot be executed in its entirety immediately, it will be canceled (killed).

Good until canceled order is a type of order that remains open until it is executed or canceled by the trader. It is in effect an indefinite order.

3. A stop order is a market order to buy or sell a stock when the price reaches a specific price designated by the trader, which is called the stop price. The stop order becomes a market order once the stop price is reached.

A stop loss order is the same as the stop order. The stop loss order is a stop order to sell at a specific price designated by the trader. The purpose of the stop loss order is to limit the amount of loss when the stock price starts declining.

7. Brokerage Firms. Why is it riskier to buy stock on margin? (LO 3-7) Answer: Buying stocks with borrowed money is called buying on margin. Buying stocks on margin is very risky for investors because it magnifies returns but also magnifies losses. Big gains become bigger gains, but big losses become bigger losses. Thus, the use of margin account debt can greatly amplify the typical risks of stock and bond investors. In addition, the process forces the investor to implicitly agree to sell in the event of a sharp downturn in the value of their portfolios. Temporary market downturns can cause a margin call and force the liquidation of margin account securities at ruinously low prices. The following points should be considered by the investor when buying on margin:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

1. The interest on the borrowed funds is a short-term rate that your broker sets, and the rate will increase with a general increase in interest rates.

2. While the Federal Reserve sets the minimum margin requirement, your broker can set a higher minimum rate and can raise that minimum rate without giving you advance written notice.

3. If you receive a margin call, the brokerage firm can determine which assets in your account will be sold to meet the margin call.

4. If you receive a margin call, you are not entitled to an extension of time.

5. It is possible to lose more funds than you deposit with the broker, and you are responsible for that additional loss.

8. Short Selling. The following questions concern short selling. (LO 3-8) Answer: a) When should an investor sell short?

When the investor identifies a company with poor and deteriorating fundamentals, then they could profit from the expected decline in the company's stock price using a short sell order to sell the stock short without owning it. Therefore, an investor should sell short only when the stock price is expected to decline in the future. b) How can investors sell stock they do not own?

Investors can sell stocks short that they do not own by borrowing them from their broker and then putting in the order to sell them short. Basically, a short sale is the sale of borrowed stocks. c) How is a short position closed?

The short position is closed when the investor who has the short position open puts the order to repurchase identical shares, hopefully at a lower price, to return to the lender to cover the short. This trade is called covering the short.

Basically, covering the short is done by buying stock in the market and returning it back to the broker. d) How does the investor profit from a short sale?

The investor profits from a short sale if the stock price declines as expected and the investor covers the short at a lower price than the price was sold for.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

e) What is the risk associated with a short position?

The risk associated with short selling is when the investor is wrong about the expectation they have about the stock. After the short sale is made, instead of the price declining, the price starts going up, with no sign of reversing course.

Short sellers lose enormous amounts of money when they are on the wrong side of an overpriced stock that continues to gallop skyward.

9. Federal Regulations. What are the main securities laws passed by Congress to regulate the investment industry? What part of the industry does each law regulate?

(LO 3-9) Answer: The Securities Act of 1933, the Securities Exchange Act of 1934, and the Sarbanes−Oxley Act of 2002 are the backbone of securities regulation.

The Securities Act of 1933 primarily concerns the issuing of new securities. It requires that new securities be “registered” with the Securities and Exchange Commission (SEC).

The Securities Exchange Act of 1934 (and subsequent amendments) extends the regulation to existing securities. This act forbids market manipulation, deception and misrepresentation of facts, and fraudulent practices. The SEC was also created by this act to enforce the laws pertaining to the securities industry. Under the Securities Exchange Act of 1934, publicly held companies are required to keep current the information on file with the SEC. This is achieved by having the firm file timely reports with the SEC. The Sarbanes−Oxley Act of 2002 was intended to restore public confidence in the securities markets. Sarbanes−Oxley called for the independence of auditors and the creation of the Public Company Accounting Oversight Board, whose purpose is to oversee the auditing of the financial statements of publicly held companies. The board has the power to establish audit reporting rules and standards and to enforce compliance by public accounting firms. Firms and individuals who conduct audits are prohibited from performing non-audit services for clients that they audit.

Corporate responsibility and financial disclosure require a publicly held firm’s CEO and chief financial officer (CFO) to certify that the financial statements do not contain untrue statements or material omissions. Thus, the analyst and investment bank divisions need to be independent of each other. Sarbanes−Oxley seeks to create or strengthen a firewall between securities analyst and investment banking divisions.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

10. SIPC. What is the purpose of the Securities Investor Protection Corporation (SIPC)?

(LO 3-10) Answer: The Securities Investor Protection Corporation (SIPC) is an agency created by the federal government to insure brokerage firms. The SIPC (www.sipc.org) is managed by a seven-member board of directors. Five members are appointed by the president of the United States, and their appointments must be confirmed by the Senate. Two of the five represent the public, and three represent the securities industry. The remaining two members are selected by the secretary of the treasury and the Federal Reserve board of governors.

The SIPC performs a role like that of the FDIC. Its objective is to preserve public confidence in the securities markets and industry. Although the SIPC does not protect investors from losses resulting from fluctuations in security prices, it does insure investors against losses arising from the failure of a brokerage firm. The insurance provided by the SIPC protects a customer’s cash and securities up to $500,000. (Only $100,000 of the $500,000 insurance applies to cash balances on an account.) If a brokerage firm fails, the SIPC reimburses the firm’s customers up to this specified limit. If a customer’s claims exceed the $500,000 limit, that customer becomes a general creditor for the remainder of the funds. The cost of this insurance is paid for by the brokerage firms that are members of the SIPC. All brokers and dealers that are registered with the SEC and all members of national securities exchanges must be members of the SIPC.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Problems 1. Price-Weighted Index. Suppose a given component of the DJIA is priced at $60 while another is priced at $110. If the divisor is 0.11, how much does the index change when the $60 stock loses 10% and when the $110 stock gains 10%? (LO 3-3) Stock A Stock B Divisor

Old Price $60.00 $110.00 0.11

New Price $54.00 $121.00

Answer: Index Change =

45.45

The price-weighted index is calculated using the following equation:

 P Price Index = n

t

i =1 it

divisor

The numerator is the sum of the prices of the constituents of the index at time t, and the divisor is the value of the denominator.

The initial value of the index is: (60 + 110) / 0.11 = 1,545.45 The first stock loses 10%, and its price becomes 60 × 0.9 = $54 The second stock gains 10%, and its price becomes 110 × 1.1 = $121 The change in the value of the index is: 1,590.91 − 1,545.45 = 45.46 2. Price-Weighted Index. Consider a price-weighted index like the DJIA with only three stocks. If the stock prices are $30, $50, and $70, and the divisor is 0.18, what is the index level? If the stocks change to $25, $53, and $76, what would the new index level be and what is the index return? If the $76 stock conducted a 2-for-1 stock split, what should the new divisor be? (LO 3-3) Stock A Stock B Stock C Divisor =

original price $30.00 $50.00 $70.00 0.18

new price $25.00 $53.00 $76.00

Answer: original index level = new index level = index return =

833.33 855.56 2.67%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

If Stock C has a 2 for 1 split, the price drops to $38 new divisor = 0.1356 The price-weighted index is calculated using the following equation:

 P Price Index = n

t

i =1 it

divisor

The numerator is the sum of the prices of the constituents of the index at time t, and the divisor is the value of the denominator.

The price-weighted index value is: (30 + 50 + 70) / 0.18 = 833.33 The new value of the price-weighted index is: (25 + 53 + 76) / 0.18 = 855.56 The index return is: (855.56 − 833.33) / 833.33 = 0.0267 or 2.67% If the stock priced $76 had split 2-for-1, then right after the split, its price would be 76 / 2 =$38.

The index value will not change due to the split and will remain at 855.56, so we can calculate the new divisor value by solving for the divisor: (25 + 53 + 38) / Dnew = 855.56 Dnew = (25 + 53 + 38) / 855.56 = 0.1356 3. Value-Weighted Index. Consider a market value-weighted index like the S&P 500 Index with only three stocks. The first stock price is $50 and has 300 shares outstanding. The second and third stocks sell for $65 and $90 with shares outstanding of 100 and 200, respectively. Each stock originally had 100 shares each that sold for $30, $75, and $50, respectively. If the base index value is 100, what is the value of the index? (LO 3-3)

Stock A Stock B Stock C Base value

Current Shares Price 300 $50.00 100 $65.00 200 $90.00

Original Shares Price 100 $30.00 100 $75.00 100 $50.00

100

Answer: Index Level = 254.8387 The value-weighted index is calculated using the equation below:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Value-weighted index =

total current market value of all firms in index × index base value original market value of firms in index

=

 PQ t t × index base value  P0Q0

Using the information provided for the three stocks, the value-weighted index is equal to: Value-weighted index = [(50 x 300 + 65 × 100 + 90 × 200) / (30 × 100 + 75 × 100 + 50 × 100)] × 100 = 254.84 4. Value-Weighted Index. Suppose that Apple Inc. represents a 5% weighting on a value-weighted index. If the index is at 8,000, and Apple’s stock price increases by 10%, how much will this cause the index to increase? (LO 3-3) Apple Inc Index level Price increase

5% 8000 10%

Answer: Index change =

40

Apple Inc. represents 5% of weighting on this index, therefore its impact on the index will be 5%. If the price of Apple Inc. increases by 10%, then the index value will increase as well.

To calculate the amount of increase of the index, we can simply multiply the price increase of the Apple stock multiplied with its weight on the index, times the index level, to see the resulting increase.

The amount that will increase is equal to: 0.05 × 0.1 × 8,000 = 40 5. Price vs. Value-Weighted Indexes. Two stock indexes, one price-weighted average and one value-weighted index, are to be created from the following three stocks: Lifestyle Retail (share price = $24.15, shares outstanding = 20.67 million), Frenzy Fast Food (share price = $32.75, shares outstanding = 1,272 million), and Mango Tech, Inc. (share price = $39.83, shares outstanding = 817.17 million). (LO 3-3) a. If the divisor for the price-weighted average is 0.9673, what is the index value? b. If the beginning value of the value-weighted index is $74,705.06 million and the Index base value is 100, what is the current value of this index? c. If the price of the three stocks change to Lifestyle = $30, Frenzy = $35, and Mango = $35, what is the value of the two indexes? Why are they different?

Lifestyle Retail

price $24.15

shares (millions) 20.67

new price $30.00

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Frenzy Fast Food Mango Tech, Inc

$32.75 $39.83

Price-weighted divisor = Initial value = Base value =

1272 817.17

$35.00 $35.00

0.9673 $74,705.60 100

Answer: a. Price index value b. Value weighted index c. New Price Index Value c. New Value Index Value

100.00 100.00 103.38 98.71

The 3 stocks' prices are relatively similar and 2 of the 3 stocks increased in price, thereby increasing the Price-Weighted Index Lifestyle Retail is tiny compared to the other 2 stocks and therefore makes little impact on a value-weighted index. Of the other 2, one stock declined in value more than the other one increased, thereby decreasing the Value-Weighted Index a. The price-weighted index value is: (24.15 + 32.75 + 39.83) / 0.9673 = 100 a. The value-weighted index is: [(24.15 × 20.67 + 32.75 × 1,272 + 39.83 × 817.17) / 74,705.06] × 100 = 100 b. The new value of the price-weighted index becomes: (30 + 35 + 35) / 0.9673 = 103.38 The new value of the value-weighted index becomes: [(30 × 20.67 + 35 × 1,272 + 35 × 817.17) / 74,705.06] × 100 = 98.71 We notice the price-weighted index increased while the value-weighted index decreased. The price-weighted index is driven by price, and we notice that Lifestyle’s price increased by $5.85, Frenzy’s price increased by 2.25, and Mango’s price decreased by $4.83, so the overall increase in price of the three stocks was 5.85 + 2.25 − 4.83 = $3.27 and that caused the index to increase.

The value-weighted index is driven by market capitalization, and we see that Lifestyle has the lowest market capitalization, while Frenzy and Mango have much higher market capitalization. The weighting of Lifestyle is just 0.67% of the index, while Frenzy’s weighting is 55.76% and Mango’s weighting is 43.57; therefore, the larger decrease in the price of Mango impacted the index more than the lower increase of Frenzy, thus the value-weighted index decreased.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

6. Bid−Ask Spreads. Giant firm American International Group, Inc. (AIG) has a bid of 35.34 and an ask of 35.39, whereas small company Ambac Financial Group, Inc. (ABK) has a bid of 3.07 and an ask of 3.11. Calculate the bid−ask spread as a percentage of the ask price for each firm. What do these calculations tell you about the cost of trading small-cap versus large-cap stocks? (LO 3-6) Bid $35.34 $3.07

American International Group Ambac Financial Group

Ask $35.39 $3.11

Answer: American International Group Ambac Financial Group

Bid-Ask Spread 0.14% 1.29%

There is a high trading cost for small cap stocks because they have a larger bid-ask spread.

The bid−ask spread is the difference between the bid price and the ask price. It is calculated as the ask price minus the bid price. The spread represents the profit margin for the market maker.

The bid−ask spread as percentage of ask is calculated as follows: (Ask − Bid) / Ask. For AIG: (35.39 − 35.34) / 35.39 = 0.1413% For ABK: (3.11 − 3.07) / 3.11 = 1.286% The bid−ask spread is higher for the ABK. Small caps usually do not have deep trading done as large caps, that’s why the bid−ask spread on small caps tend to be higher than on large caps. In general, when the security has a deep market and trades a lot, the spread gets smaller.

7. Market Depth. Verizon Communications (VZ) has a bid of 36.05 and a bid size of 1,000. The ask is 36.07, and the ask size is 800. How much money is represented for you to sell shares? (LO 3-6) Verizon Communications

Bid $36.05

Bid Size 1000

Ask $36.07

Ask Size 700

Answer: Sell Market Value =

$ 36,050.00

The investor sells at the bid price: the bid price is the price the dealer is going to give to buy the shares from the investor. The amount of money from this transaction given in the information is 36.05 × 1,000 = $36,050.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

8. Market Depth. MBIA, Inc. (MBI) has a bid of 6.99, a bid size of 1,500, an ask of 7.00, and an ask size of 800. How much money is represented for you to buy shares? (LO 3-6) MBIA

Bid $6.99

Bid Size 1500

Ask $7.00

Ask Size 800

Answer: Buy Market Value =

$5,600.00

The investor buys at the ask price. The ask price is the price the dealer is going to offer to sell the shares to the investor. The amount of money from this transaction given in the information is 800 × 7 = $5,600.

9. Market and Limit Orders. One order is a market order for the purchase of 200 shares. A second order is a fill or kill limit order set at $49.50 for the purchase of 200 shares. When the two orders arrive at the stock exchange, the bid quote is $49.48 and the ask quote is $49.52. What is the value of each trade? (LO 3-6) Market Order Limit order

Buy (shares) 200 200 Limit Price Bid $49.48

$49.50

Ask $49.52

Answer: Market order trade Limit order trade

$9,904.00 $ -

The market order to buy 200 shares will be executed at the best available price at the market at the time the order arrives. In the example, the ask price is $49.52, so the order will be executed at the quoted ask price. The value of the trade will be: 49.52 × 200 = $9,904 The fill or kill limit order to buy 200 shares at $49.50 will not be executed and will be killed since the limit price is lower than the best available ask price, and the order if not executed immediately gets canceled.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

10. Margin for Long Position. A stock sells for $10 per share. You purchase 100 shares using 50% margin. A year later, the price has risen to $15.50. What is the initial equity you must have to initiate the trade? What is your percent equity position at the end of the year? (LO 3-7) Price $10.00

Shares 100

Margin 50%

New Price $15.50 Answer: Initial equity = New % equity =

$500.00 67.7%

The total value of the purchase is 10 × 100 = $1,000. Using 50% margin means you can borrow 50% of the purchase value. The amount borrowed is 0.5 × 1,000 = $500.

Therefore, the initial equity that you need to have to make this trade is only $500.

The percent equity position is calculated using the following formula:

Percent equity =

equity stock value − debt = stock value stock value

Percent equity = (15.50 × 100 − 500) / 15.5 × 100 = 0.6774 or 67.74% 11. Margin for Short Position. A stock sells for $50 per share. You sell short 100 shares using 50% margin. A year later, the price has fallen to $43.50. What is the initial equity you must have to initiate the trade? What is your percent equity position at the end of the year? (LO 3-7) Price $50.00

Shares 100

Margin 50%

New Price $43.50 Answer: Initial equity = New % equity =

$ 2,500.00 72.4%

You sell 100 shares using 50% margin. The value of the stock sold is equal to 50 × 100 = $5,000. With 50% margin requirement, you have to deposit 0.5 × 5,000 = $2,500 with the broker for the margin requirement.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Therefore, the initial equity that you need to have in the account to initiate the trade is $2,500.

A year later, the price is $43.50.

To find the equity position at the end of the year, we use the following formula: Percentage equity =

equity stock value when sold + cash − current stock value = current stock value current stock value

Percentage equity after one year = (5,000 + 2,500 − 43.50 × 100) / 43.50 × 100 = 0.7241 or 72.41%.

12. Margin Call. Assume an investor went long on Citigroup, Inc.(C) at a price of $25.55 using 50% margin. At what price would the investor face a 30% maintenance margin call? (LO 3-7) Price $25.55

initial margin 50%

maintenance margin 30%

Answer: Margin Call Price

$18.25

The investor went long using 50% margin, which means for every share purchased, 50% was borrowed. The borrowed amount is 0.5 × 25.55 = $12.775 per share.

To find the price level where the investor will face 30% maintenance margin call, we solve the following:

0.30 =

stock price − $12.775 stock price

0.3 stock price = stock price − 12.775 0.7 stock price = 12.775 Stock price = $18.25 Once the stock price goes lower than $18.25, the investor will get a 30% maintenance margin call.

13. Margin Call. Assume an investor shorted GE at a price of $46.43 using 50% margin.

At what price would the investor face a 30% maintenance margin call? (LO 3-7) GE

Price $46.43

initial margin 50%

maintenance margin 30%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Answer: Margin Call Price

$53.57

The investor shorted GE at $46.43 using 50% margin. This means that the investor has to deposit 0.5 × 46.43 = $23.22 per share as the margin requirement.

The initial deposit will be $23.22 per share to initiate this trade.

To find the price at which level the investor will face 30% maintenance margin call, we solve the following equation, finding the stock price when the percentage equity equals 30%.

Percentage equity =

equity stock value when sold + cash − current stock value = current stock value current stock value

0.3 = (46.43 + 23.22 − P) / P 0.3P = 69.65 − P 1.3P = 69.65 P = 69.65 /1.3 = $53.58 The investor will get 30% margin call once the stock price crosses $53.58.

14. Returns Using Margin. You purchase 100 shares of stock at $100. The margin requirement is 40%. What are the dollar and percentage returns if: (LO 3-7) a. you sell the stock for $112 and bought the stock for cash? c. you sell the stock for $90 and bought the stock on margin? d. you sell the stock for $60 and bought the stock on margin?

Price $100.00

Shares 100

Margin 40%

Price-A $112.00

Price-B $90.00

Price-C $60.00

Answer: a) b) c)

Dollar Percentage Dollar Percentage Dollar Percentage

$1,200.00 12.0% $(1,000.00) −25.0% $(4,000.00) −100.0%

You purchase 100 shares of a stock at $100. The total value of the stocks is 100 × 100 = $10,000.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

a. If you bought the stock for cash, then you did not use margin and had to use your own $10,000 for the initial investment.

You sold the stock for $112, for a total value of 112 × 100 = $11,200.

The dollar return is 11,200 − 10,000 = $1,200.

The percentage return is 1,200 / 10,000 = 0.12 or 12%. b. You sell the stock for $90 using 40% margin.

In this case, for the 40% margin requirement, you need to deposit 0.4 × 10,000 = $4,000 from your money and borrow the rest, $6,000. You need only $4,000 as the initial investment to initiate the trade.

You sell the stock for $90, for a total value of 90 × 100 = $9,000. $6,000 will be returned to the broker to pay off the borrowed margin amount, so you are left with $3,000.

The dollar return of is $3,000 − $4,000 = −$1,000; a loss of $1,000.

The percentage return is −1,000 / 4,000 = −0.25 or −25% loss. c. You sell the stock for $60 using 40% margin.

In this case, for the 40% margin requirement, you need to deposit 0.4 × 10,000 = $4,000 from your money and borrow the rest, $6,000. You need only $4,000 as the initial investment to initiate the trade.

You sell the stock for $60, for a total value of 60 × 100 = $6,000; $6,000 will be returned to the broker to pay off the borrowed margin amount. You are left with 0 (nothing).

The dollar return of is 0 − $4,000 = −$4,000; a loss of $4,000.

The percentage return is −4,000 / 4,000 = −1 or −100% loss.

15. Short Position Margin. Assume an investor shorted 1,000 shares of Pfizer, Inc. (PFE) at $21.55 using 50% margin. Following a sharp rise in the stock to $26, the investor has received a maintenance margin call. At this point, the investor is required to wire sufficient funds to bring account equity back to 50%. How much in additional funds must be added to the account? (LO 3-7) Pfizer

Price $21.55

Shares 1000

initial margin 50%

New Price $26.00

Answer: Original equity Additional Funds

$10,775.00 $6,675.00

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

The investor shorted 1,000 shares of PFE at $21.55. The total value of the trade is 21.55 × 1,000 = $21,550.

Using 50% margin, the investor has to deposit 0.5 × 21,550 = $10,775 with the broker to initiate this trade.

The investor received a maintenance call when the stock price reached $26.

The total value of the stock when the stock price is $26 is $26,000 (26 × 1,000).

When the stock price is $26, the investor’s equity value is equal to 21,550 + 10,775 − 26,000 = $6,325.

In order to bring the account equity back to 50% margin, the following should be satisfied: (6,325 + additional funds) / 26,000 = 0.5 The amount of the additional funds then can be solved: 6,323 + additional funds = 0.5 × 26,000 Additional funds = 13,000 − 6,325 = $6,675 16. Cash vs. Margin Investing. Investor A makes a cash purchase of 100 shares of AB&C common stock for $55 a share. Investor B also buys 100 shares of AB&C but uses margin. Each holds the stock for one year, during which dividends of $5 a share are distributed. The margin requirement is 60%, and the interest rate is 10% annually on borrowed funds. What is the dollar amount and percentage earned by each investor if they sell the stock after one year? (LO 3-7) (a) (b) (c) (d)

$40 $55 $60 $70

Investor A Investor B

Price $55.00 $55.00

Shares 100 100

Equity $5,500.00 $3,300.00

Debt $$2,200.00

Margin 60%

Dividend $5.00 $5.00

Interest rate 10%

Answer: Investor A Investor B

Price Ending $40 Investor A

Dollar ($1,000.00)

Dividends $500.00 $500.00

Interest Cost $$220.00

Percentage −18.18%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Investor B

($1,220.00)

−36.97%

$55

Investor A Investor B

$500.00 $280.00

9.09% 8.48%

$60

Investor A Investor B

$1,000.00 $780.00

18.18% 23.64%

$70

Investor A Investor B

$2,000.00 $1,780.00

36.36% 53.94%

Investor A purchases the stock AB&C using cash only. The total value of the stock is 55 × 100 = $5,500.

Investor B purchases the stock AB&C using the margin account. The margin is 60%, which means investor B will invest 0.6 × 5,500 = $3,300 and borrow the rest, $2,200.

Both investors will hold the stock for one year.

Both investors A and B will receive the dividend paid by the stock; each will receive 5 × 100 = $500 in dividends.

Investor B will pay interest on the amount borrowed. Over one year, the interest expense for investor B will be 0.1 × 2,200 = $220 The dollar amount and the percentage earned by each investor is calculated for parts a, b, c, and d. a. Investor A: Dollar amount = (40 × 100 − 5,500) + 500 = −$1,000 Percentage return = −1,000 / 5,500 = −18.18% Investor B: Dollar amount = (40 × 100 − 5,500) + 500 − 220 = −$1,220 Percentage return = −1,220 / 3,300 = −36.97% b. Investor A: Dollar amount = (55 × 100 − 5,500) + 500 = $500 Percentage return = 500 / 5,500 = 9.09% Investor B: Dollar amount = (55 × 100 − 5,500) + 500 − 220 = $280 Percentage return = 280 / 3,300 = 8.48% c. Investor A: Dollar amount = (60 × 100 − 5,500) + 500 = $1,000 Percentage return = 1,000 / 5,500 = 18.18%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Investor B: Dollar amount = (60 × 100 − 5,500) + 500 − 220 = $780 Percentage return = 780 / 3,300 = 23.64% d. Investor A: Dollar amount = (70 × 100 − 5,500) + 500 = $2,000 Percentage return = 2,000 / 5,500 = 36.36% Investor B: Dollar amount = (70 × 100 − 5,500) + 500 − 220 = $1,780 Percentage return = 1,780 / 3,300 = 53.94% 17. Short Selling and Return. An investor sells a stock short for $36 a share. A year later, the investor covers the position at $30 a share. If the margin requirement is 60%, what is the percentage return earned on the investment? (LO 3-7) Sell short at Cover at Margin Required

$36.00 $30.00 60%

Answer: Return % =

27.78%

The investor is using 60% margin, therefore the amount that the investor needs to deposit to sell short is 36 × 0.6 = $21.6 per share.

The investor covers the short at $30 per share, therefore the investor is making a profit of $6 per share.

The percentage return is equal to 6 / 21.6 = 27.78%.

18. Short Selling and Return. A speculator sells a stock short for $50 a share using a 50% margin. The company pays a $2 annual cash dividend. A year later, the seller covers the short position at $42. What is the percentage return on the position (excluding the impact of any interest expense and commissions)? (LO 3-7) Price $50.00

Dividend $2.00

Margin 50%

New Price $42.00

Answer: Return %

24.0%

The speculator is using 50% margin, therefore the amount that the speculator needs to deposit to sell short is 50 × 0.5 = $25 per share.

The speculator covers the short at $42 per share; therefore, the investor is making a profit of $8 per share. In addition, there will be a $2 dividend that the investor will have to pay while having the short position open. Since the stock paid a dividend of

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

$2 per share, then the short position is liable for this dividend payment. The net dollar amount that the investor will make is 8 − 2 = $6.

The percentage return is 6 / 25 = 24%.

19. Cash vs. Margin. Investor A buys 100 shares of SLM Inc. at $35 a share and holds the stock for a year. Investor B buys 100 shares on margin. The margin requirement is 60%, and the interest rate on borrowed funds is 8%. (LO 3-7) a. What is the interest cost for investor A? b. What is the interest cost for investor B? c. If they both sell the stock for $40 after a year, what percentage return does each investor earn? In both cases, the value of the stock has risen the same. Why are the percentage returns different?

Investor A Investor B

Price $35.00 $35.00

Shares 100 100

Margin

Interest Rate

60%

8%

New Price $40.00 $40.00

Answer: Interest cost Investor A Interest cost Investor B Return A Return B

$ $112.00 14.29% 18.48%

Using margin leverages up a return because less of the investor's capital is deployed. However, paying interest costs dimishes some of the return. a. There is no interest cost for investor A since margin was not used. b. The margin is 60%. Investor B buys 100 shares for a total value of 100 × 35 = $3,500. Using the 60% margin, investor B has to deposit 0.6 × 3,500 = $2,100 from their own money, while borrowing the rest, $1,400.

The interest cost on the borrowed amount over one year is equal to 0.08 × 1,400 = $112. c. Both investors sell the stock for $40 after one year.

The dollar return for investor A is 40 × 100 − 3,500 = $500.

The percentage return for investor A is 500/3,500 = 14.29%.

The dollar return for investor B is 40 × 100 − 3,500 − 112 = $388.

The percentage return for investor B is 388/2,100 = 18.48%.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

The percentage returns are different because investor B had to use only $2,100 of their own money because they used margin, while investor A did not use margin and had to use $3,500 of their own money. Using margin, though, will require additional interest payment on the borrowed amount.

20. Short Position Maintenance Margin. Assume a speculator sold 3,000 shares of mortgage lender Fannie Mae (FNM) short at $30 with an initial margin of 50% and subsequently received a 30% maintenance margin call. Calculate the dollar amount that must be deposited to bring the account equity back up to 50%. (LO 3-7) Price $30.00

Shares 3000

Initial margin 50%

Maintainence 30%

Answer: Original equity = Additional Fund =

$45,000.00 $20,769.23

The speculator sold 3,000 shares at $30 each, so the total value of the short position is 30 × 3,000 = $90,000. Using 50% margin, the speculator has to deposit 0.5 × 90,000 = 45,000 in order to initiate the trade.

The speculator received 30% margin call. Using the equation below, we can calculate the price of the stock when the speculator received the margin call.

Percentage equity =

equity stock value when sold + cash − current stock value = current stock value current stock value

0.3 = (90,000 + 45,000 − current stock value) / current stock value 0.3 current stock value = 135,000 − current stock value 1.3 current stock value = 135,000 Current stock value = $103,846.15 The stock price per share when the speculator received the margin call is equal to $103,846.15 / 3,000 = $34.62 (you don’t need to calculate the stock price).

The dollar amount that the speculator needs to deposit to bring the margin account to 50% is found using the same equation as above.

0.5 = (135,000 − 103,846.15 + Amount) / 103,846.15 0.5 × 103,846.15 = 31,153.85 + Amount 51,923.075 = 31,153.85 + Amount Amount = 51,923.075 − 31,153.85 = $20,769.23

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Case Study Investing an Inheritance The Kelleher brothers, Victor and Darin, could not be more different. Victor is assertive and enjoys taking risks, while Darin is reserved and exceedingly risk averse. Both have jobs that pay well and provide fringe benefits, including medical insurance and pension plans. You are the executor for their grandfather’s estate and know that each brother will soon inherit $85,000. Neither has an immediate need for the cash, which could be invested to meet some long-term financial goal.

Once the funds have been received, you expect Victor to acquire some exceedingly risky investment (if he does not immediately squander the money). You would be surprised, however, if Darin chose to do anything other than place the funds in a low-yielding savings account. Neither alternative makes financial sense to you, so before the distribution of the funds, you decide to offer financial suggestions that would reduce Victor’s risk exposure and increase Darin’s potential return.

Given the brothers’ ages and financial condition, you believe that equity investments are appropriate. Such investments may satisfy Victor’s propensity to take risks and increase Darin’s potential return without excessively increasing his risk exposure (willingness to assume risk). Currently, the stock of Choice Juicy Fruit is selling for $70 and pays an annual dividend of $1.80 a share. The company’s line of low-to-no-sugar juice offers considerable potential. The margin requirement set by the Federal Reserve is 50%, and brokerage firms are charging 5% on funds used to purchase stock on margin. While commissions vary among brokers, you decide that $70 for a 100-share purchase or sale is a reasonable amount to use for illustrative purposes. Currently, commercial banks are paying only 3% percent on savings accounts.

To give the presentation focus, you decide to answer the following questions: 1. What is the percentage return earned by Darin if he acquires 100 shares, holds the stock for a year, and sells the stock for $80?

2. What is the percentage return earned by Victor if he acquires 100 shares on margin, holds the stock for a year, and sells the stock for $80? What advantage does buying stock on margin offer Victor?

3. What would the percentage returns be if the sale prices had been $50 or $100?

4. What would the impact be on the brothers’ returns if the rate of interest charged by the broker increased to 10%?

5. If the maintenance margin requirement were 30% and the price of the stock declined to $50, what impact would that have on each brother’s position? At what price of the stock would they receive a margin call?

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

Answer: 1. If Darin buys 100 shares for $70, then the total amount needed for this trade is 70 × 100 = $7,000.

Also, Darin has to pay $70 commission to make the purchase, therefore the total initial investment needed to initiate this trade is $7,070.

During the year, the stock will pay $1.80 dividend per share, so the total dividend Darin will receive is 100 × 1.8 = $180.

If Darin sells the shares after one year for $80 per share, then the total proceeds from the sale will be 80 × 100 = $8,000. In addition, Darin will pay $70 commission to sell the shares.

The dollar amount resulting from those trades will be as follows: Dollar amount = 8,000 − 7,000 + 180 − 70 − 70 = $1,040 The percentage return earned by Darin will be: Return = 1,040 / 7,070 = 14.71% 2. Victor uses 50% margin for the same trade. By using margin, Victor needs to deposit 0.5 × 7,000 = $3,500 plus the commission of $70 to initiate the trade. The initial investment made by Victor will be $3,570.

Victor will borrow $3,500 at 5% interest. So, over the year period, the interest expense will be 0.05 × 3,500 = $175.

Victor will also receive the $1.80 dividend per share, for a total of $180.

After one year, Victor will sell the shares for $80 per share, and pay $70 commission to sell.

The dollar amount resulting from those trades will be as follows: Dollar amount = 8,000 − 7,000 + 180 − 175 − 70 − 70 = $865 The percentage return earned by Victor will be: Return = 865 / 3,570 = 24.23% Buying the stock on margin provided Victor with a higher return on the investment, but there was also the additional interest charge that was paid for borrowing on margin.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 03: Measuring Return and Risk

3. We calculate the percentage return for Victor and Darin for the sale price of $50 or $100.

For Darin, who does not use margin, the initial investment will remain $7,070.

If the sale price is $50: Dollar amount = 5,000 − 7,000 + 180 − 70 − 70 = −$1,960 Percentage return = −1,960 / 7,070 = −27.72% If the sale price is $100: Dollar amount = 10,000 − 7,000 + 180 − 70 − 70 = $3,040 Percentage return = 3,040 / 7,070 = 43% For Victor, who uses margin, the initial investment will remain $3,570.

Also, the interest expense will remain $175 over one year.

If the sale price is $50: Dollar amount = 5,000 − 7,000 + 180 − 175 − 70 − 70 = −$2,135 Percentage return = −2,135 / 3,570 = −59.80% If the sale price is $100: Dollar amount = 10,000 − 7,000 + 180 − 175 − 70 − 70 = $2,865 Percentage return = 2,865 / 3,570 = 80.25% 4. Darin’s return will not be affected if the rate of interest charged by the broker increases to 10% because Darin is not using margin. So the return will remain as it was.

Victor’s return will decrease because he is using margin, and the increase in the rate will increase the amount of interest he has to pay the broker. The annual interest charge will become 0.1 × 3,500 = $350. Therefore, Victor’s return will be reduced.

5. Darin will not get a margin call, because Darin is not using margin.

Victor is using margin. When the stock price declines to $50, we can calculate the percentage equity Victor will have: Percentage equity = 5,000 − 3,500 / 5,000 = 0.3 This means that if the stock price declines below $50 by $0.01, then Victor will receive margin call.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 8 Case Study ....................................................................................................................................... 26

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Questions 1. Mutual Fund Advantages and Disadvantages. What are the advantages and disadvantages of owning mutual funds? (LO 4-1) Answer: The advantages of owning mutual funds include the following: 1. Professional management of money 2. The benefit of ownership in a diversified portfolio 3. The potential savings in commissions, as the investment company buys and sells in large blocks 4. Custodial services (e.g., the collecting and disbursing of funds) The disadvantages of owning mutual funds include the following: 1.

2.

3.

4.

The transacting costs of mutual funds, such as load fees The holding costs of mutual funds, such as management fees and 12b-1 fees The mutual fund incurs expenses when buying and selling assets, such as stocks Tax liabilities that will result from distributions of the mutual funds

2. Mutual Fund Costs. Describe the different costs of buying, owning, and selling mutual funds. (LO 4-2) Answer: There are several types of costs related to mutual funds. Transacting costs are the commissions that some mutual funds charge to investors. Those commissions are called load fees. They can take several forms, such as front-end loads, back-end loads, and no-load funds. Investors also pay a variety of other expenses. The costs associated with researching specific assets, brokerage fees charged when the fund buys and sells securities, and compensation to management are all mutual fund costs that are charged quarterly to the fund investors. These expenses are the cost of owning the shares and are wrapped together as the management fee.

Some funds also charge investors an additional amount to cover marketing and distribution costs. These marketing charges are formally referred to as 12b-1 fees, after the 1980 U.S. SEC rule that permits this practice.

A mutual fund is required to report all of the annual costs to the investors together as the expense ratio. The expense ratio adds both the management fee and the 12b-1 fees into one percentage. It is computed at the fund level, not the investor level, as the total annual fund expenses divided by the total assets of the portfolio.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

3. Mutual Fund Objectives. What are the various investment objectives and Morningstar categories for mutual funds? (LO 4-3) Answer: Morningstar categorizes funds within one of nine broad asset classes: U.S. Stock, Sector Stock, Balanced, International Stock, Alternative, Commodities, Taxable Bond, Municipal Bond, and Money Market. Most mutual funds fall into one of four main categories − money market funds, bond funds, stock funds, and target date funds.

Each type has different features, risks, and rewards. When a stock mutual fund defines its investment objective, it is identifying a specific type of stock—though not individual stocks—that will be the core of its portfolio. Sometimes the objective is quite broad.

The Morningstar style box (see Figure 4-3) summarizes the portfolio strategy of a particular fund. The style box is a diagram that illustrates the location of a fund’s portfolio based on the portfolio’s average market capitalization and value/growth orientation.

4. Mutual Fund Performance. How can you assess a mutual fund’s performance over time? (LO 4-4) Answer: Mutual fund performance is best measured by the fund's total return, consisting of dividend and interest income and both realized and unrealized appreciation. A fund's total return is reflected by the change in the value of an investment in the fund over time. Mutual funds produce current income for shareholders from investments in interest-bearing securities, such as short-term and long-term bonds, and from dividends paid on common stocks owned by the fund. After expenses, all mutual fund income is paid out to fund shareholders in the form of income distributions. Depending on the type of fund, income distributions may be paid monthly for money market funds and short-term bond funds or on a quarterly, semiannual, or annual basis for stock and long-term bond funds. Fund shareholders can choose to receive income distributions in cash or to have their dividends reinvested in additional shares of the fund. You designate the method of dividend payment when you open an account and can change your selection at any time.

When securities in the fund portfolio have risen in value, the fund generates unrealized capital gains. Unrealized capital gains raise the net asset value (NAV) of a fund. If a fund sells securities at a profit, a taxable capital gain is realized. Realized capital gains are typically allocated to mutual fund shareholders in December in the form of a capital gains distribution. When a fund pays out realized capital gains, the fund's NAV is reduced by the amount of the distribution. As in the case of income

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

dividends, capital gains distributions may be received by a shareholder in cash or reinvested for further appreciation. Of course, stocks and bonds can also fall in value, and funds periodically incur capital losses that reduce the NAV. Likewise, you can suffer losses on your mutual fund investments by selling shares at a lower price lower than they paid.

Mutual fund performance over time can be compared to its own past results and to results of its peers, called benchmarks. Morningstar and other financial data providers compile and provide mutual fund performance information. In addition, Morningstar provides a rating for each fund, often called the star rating. It is a purely backward-looking quantitative measure of a fund’s past performance. Funds are ranked within their category (large blend, small value, etc.) and issued from one to five stars, with five being the best. Morningstar also provides the Morningstar Analyst Rating, which provides a forward-looking assessment of a fund’s ability to outperform its peer group over a full market cycle. Funds are assigned a rating of Gold, Silver, Bronze, Neutral, or Negative, which reflects analysts’ conviction in a fund’s prospects. Analysts evaluate funds based on five key pillars—People, Parent, Process, Performance, and Price. Each analyst evaluation comes from face-to-face interviews with the fund management team, along with analysis of proprietary Morningstar data and fund documents.

5. ETF Advantages. What advantages do ETFs have over mutual funds? (LO 4-5) Answer: Exchange-traded funds (ETFs) are pools of assets similar to mutual funds, but traded as stocks. ETFs provide portfolio diversification benefits, just like mutual funds. The investor can choose a wide variety of ETFs depending on their needs; there are ETFs that track stock market indexes and sector ETFs that track particular sectors. There are a large variety of ETFs that track international markets, the bond market, value and growth styles, and other strategies. ETFs are more flexible than mutual funds.

They offer the following advantages: (1) portfolio diversification; (2) a passive portfolio with minimal turnover, resulting in lower operating expenses; (3) lower taxes, as the index fund has few realized capital gains; and (4) intraday buying and selling. Another advantage for sophisticated investors is the opportunity to sell short an index through an ETF, which cannot be done with a mutual fund.

6. ETF Investment Objectives. What are the various investment objectives of ETFs? (LO 4-6) Answer: ETFs became popular by tracking broad stock indexes. Later on, ETFs were created to track other securities, like bonds; other ETFs became increasingly specialized and

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

covered increasingly smaller and more narrowly defined segments of the financial market.

There are a large number of ETFs that track U.S. equity using broad stock measures.

There are ETFs that track bond indexes and others that track international equity indexes. There are also ETFs with a commodity or hybrid investment objective.

There are also ETFs that track particular sectors of the economy, such as the retail or technology sector. One type of ETF that has gained in popularity is the leveraged ETF, which seeks to duplicate a multiple of the daily change in an index.

7. ETF vs. Closed-End Funds. Compare and contrast closed-end funds with ETFs. (LO 4-7) Answer: Closed-end funds (CEF) are similar to ETFs in the sense that they are bought and sold through the securities markets, like ETFs. The shares are originally sold to the public through an initial public offering (IPO) and subsequently trade on an exchange. However, unlike ETFs, no new shares are created after the listing. The number of shares and the dollar amount of debt that the company may issue are prespecified. The only way to purchase CEFs is from another investor who is selling it.

Since the number of shares can’t expand and contract to meet changes in demand, CEF shares prices may often deviate from the fund’s net asset value (NAV). Thus, while ETF prices are very close to their NAV, a CEF can experience large discounts or premiums to NAV. 8. Premiums and Discounts. What are fund premiums and discounts and how do they complicate fund performance? (LO 4-8) Answer: A fund’s premium or discount is the difference in the price that the fund is trading from its NAV value. The formula to calculate the discount or premium is given below.

Discount or Premium =

Price − NAV NAV

Investors in closed-end funds earn returns in a variety of ways. First, if the CEF collects dividends and interest on its portfolio, this income is distributed to the stockholders. Second, if the value of the firm’s assets increases, the company may sell the assets and realize the gains. These profits are then distributed as capital gains. Such distributions usually occur in a single payment near the end of the calendar year and, for most individuals, the tax year. Third, the NAV of the portfolio

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

may increase, which will cause the market price of the company’s stock to rise. In this case, the investor may sell the shares in the secondary market and realize a capital gain. Fourth, the market price of the shares may rise relative to the NAV (i.e., the premium may increase, or the discount may decrease).

Some investors view the status of a discount or premium as an indicator to buy and sell CEFs. If the shares are selling for a sufficient discount, they are considered for purchase. If the shares are selling for a small discount or at a premium, they are sold. However, this strategy often frustrates investors because discounts sometimes get larger.

9. Hedge Fund Objectives. Describe a hedge fund structure. What are the primary differences between hedge funds and mutual funds, from the investor’s perspective? (LO 4-9) Answer: Hedge funds are pools of money that are used to acquire a variety of assets with the intent to earn high returns or produce return streams different from traditional stock and bond portfolios and to increase an investor’s ability to diversify. The strategies employed often require taking substantial risks and may not be allowed within a mutual fund. A simple example is that a hedge fund portfolio could consist entirely of one company stock, like Tesla. Mutual funds have diversification rules that would prevent this strategy.

In order to use investment strategies that are not available to mutual funds, hedge funds must raise capital in nonpublic offerings. Hedge funds are generally organized as limited partnerships, with the fund’s managers serving as general partners while the investors are limited partners. Hedge funds require higher investment amounts than mutual funds, which may not be accessible by any investor. The required investment is substantial, with minimums of $1,000,000 being common. Because hedge funds are private, they are not subject to many of the disclosure requirements and other regulations associated with mutual funds.

The hedge fund fee structure for many decades was typically referred to as a 2 and 20. This represents a management fee that is 2% of the value of the assets under management and an incentive fee of 20% of the fund’s performance. This is a very large cost to investors. Hedge funds would have to really perform well to overcome such high costs to investors.

Since a hedge fund is private, no secondary market exists for its shares. Once the individual invests in a hedge fund, that person cannot sell the shares. The fund generally has a withdrawal policy to define when and how an investor may liquidate a position. There are, however, significant limitations on the withdrawals. For

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

example, the hedge fund may refuse to repurchase shares until a period of time has elapsed. A one-year lockup is not unusual and longer periods are common. One reason a hedge fund uses a lengthy lockup is because their strategy may involve long-term investments.

Finally, traditional mutual funds are precluded from using risky strategies such as selling short or buying stocks and bonds of firms in bankruptcy, but hedge funds may follow such strategies.

10. REIT Objectives. What are real estate investment trusts? Describe the various REIT investment objectives. (LO 4-10) Answer: Real estate investment trusts (REITs) are a special form of closed-end fund that focus on real estate investments rather than stock or bond portfolios. For REITs, the investment portfolio comprises a pool of real estate assets that may include real estate property or loans on real estate property. To qualify as a REIT, the trust must distribute at least 90% of its taxable income to shareholders annually in the form of dividends. Thus, REITs are popular for investors seeking income.

A big advantage that REITs have over direct real estate ownership is liquidity. They can be easily and quickly bought and sold with minimal transaction costs, just like stocks.

REITs are commonly categorized by the type of real estate assets owned and by their focus on equity or debt instruments.

•

•

•

Equity REITs own real properties, and their value is determined by the value of their real estate holdings and the cash flow generated. Over 90% of publicly traded REITs are equity REITs. Mortgage REITs lend money to owners and developers of real estate and purchase existing mortgages or mortgage-backed securities. The price of mortgage REITs is determined by the net interest generated and the credit quality of their loan portfolios.

Hybrid REITs combine the investment strategies of equity REITs and mortgage REITs by investing in both properties and mortgages.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Problems 1. NAV Calculation. Suppose a mutual fund owned $322.2 million in stocks, owned $417.8 million in bonds, had $50.2 million in cash, had $1.3 million in liabilities, and had 25.6681 million shares outstanding. (LO 4-2) a. What is the fund’s NAV? b. The next day, the stock portion of the portfolio increases by 0.7% and the bond portion declines by 0.2%. The cash, liabilities, and shares outstanding remain unchanged. What is the new NAV? c. What is the return for investors that day? stocks bonds cash liabilities shares outstanding

in millions $ 322.2 $ 417.8 $ 50.2 $ (1.3) 25.6681

Change 0.70% −0.20%

Answer: A. B.

C.

Porfolio Value = NAV = New stock value = New bond value = Porfolio Value = NAV = Return =

$ 788.9 $ 30.735 $ 324.46 $ 416.96 $ 790.32 $ 30.790 0.18%

a. The NAV is the value of all the securities in the portfolio less any liabilities divided by the total number of shares issued to investors. Thus, the NAV is calculated as follows: NAV =

Total Value of Securities − Number of Shares

NAV = (322.2 + 417.8 + 50.2 − 1.3) / 25.6681 = $30.735. b. The next day, the value of the stock will be 322.2 × (1 + 0.007) = 324.4554 million The value of the bond will be 417.8 × (1 − 0.002) = 416.9644 million NAV = (324.4554 + 416.9644 + 50.2 − 1.3) / 25.6681 = $30.79 c. The return to the investor will be: (30.79 − 30.735) / 30.735 = 0.18% in one day

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

2. Open-End Fund. An open-end fund closes the day with an NAV of $56.684, total assets of $344,883,045, and shares outstanding of 6,084,310.299. You buy $8,000 worth of shares. How many shares do you buy? What is the new NAV, total assets of the fund, and shares outstanding? (LO 4-2) NAV total assets Shares outstanding Invest

$56.684 $344883045 6084310.299 $8,000.00

Answer: Shares total assets Shares outstanding NAV

141.133 $344891045.00 6084451.432 56.684

The NAV value is $56.684 and you buy $8,000 worth of shares. Therefore, the number of shares you buy is calculated as follows: Number of shares purchased = 8,000 / 56.684 = 141.133 shares The $8,000 is going to be added on to the value of the assets that the open-end fund has, so the new value of the total assets becomes: $344,883,045 + $8,000 = $344,891,045 Furthermore, because the mutual fund had 6,084,310.299 shares outstanding, and you purchased 141.133 shares, the new total number of shares will become: 6,084,310.299 + 141.133 = 6,084,451.432 shares We can calculate the value of the NAV as follows: New NAV = 344,891,045 / 6,084,451.432 = $56.684 3. Mutual Fund Returns. You own shares of three mutual funds, as shown below.

What is the value of the three positions and your total portfolio yesterday and today? What was your dollar value change? (LO 4-2) Shares NAV Yesterday Growth Stock Fund 214.658 $57.441 International Stock Fund 130.554 $36.119 High Grade Bond Fund 75.7664 $44.512

NAV Today $56.982 $38.052 $45.488

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Answer:

Portfolio =

Value Yesterday $12,330.17 $ 4,715.48 $ 3,372.51 $20,418.16

Value Today $12,231.64 $ 4,967.84 $ 3,446.46 $20,645.94

Change $(98.53) $252.36 $ 73.95 $227.78

To calculate the value of each position, we multiply the number of shares of each fund with the NAV value.

Yesterday: Growth Stock Fund value = 214.658 × 57.441 = $12,330.17 International Stock Fund value = 130.554 × 36.119 = $4,715.48 High Grade Bond Fund value = 75.7664 × 44.512 = $3,372.51 The total portfolio value is the sum of the values of the three funds: Portfolio value = $12,330.17 + $4,715.48 + $3,372.51 = $20,418.16 Today: Growth Stock Fund value = 214.658 × 56.982 = $12,231.64 International Stock Fund value = 130.554 × 38.052 = $4,967.84 High Grade Bond Fund value = 75.7664 × 45.488 = $3,446.46 The total portfolio value is the sum of the values of the three funds: Portfolio value = $12,231.64 + $4,967.84 + $3,446.46 = $20,645.94 The dollar value change between yesterday and today is: $20,645.94 − $20,418.16 = $227.78 4. Offer Price with Load. Consider the three mutual funds below with different frontend loads. You wish to purchase $5,000 of one fund. In each case, (LO 4-2) a. what would be the offer price? b. how many shares could you purchase? c. what would be the load fee?

High-Load Fund Low-Load Fund No-Load Fund

Load 5% 2% 0%

NAV $25.00 $25.00 $25.00

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Answer: A. Offer Price $26.3158 $25.5102 $25.0000

B. Shares 190.00 196.00 200.00

C. Load Fee $4,342.11 $4,362.24 $4,375.00

a. The offer price is calculated using the following equation: Offer Price =

NAV (1− Load Fee)

The offer price of each of the three funds is calculated below: High-Load Fund Offer Price = 25 / (1 − 0.05) = $26.3158 Low-Load Fund Offer Price = 25 / (1 − 0.02) = $25.5102 No-Load Fund Offer Price = 25 / (1 − 0) = $25 b. The number of shares you can purchase will be based on the offer price and not the NAV. To calculate the number of shares, we divide the amount that will be invested by the offer price. Since the amount that will be invested is $5,000, we calculate the number of shares by dividing it by the offer price calculated in part A. Number of shares of High-Load Fund = 5,000 / 26.3158 = 190 shares Number of shares of Low-Load Fund = 5,000 / 25.5102 = 196 shares Number of shares of No-Load Fund = 5,000 / 25 = 200 shares c. The load fee is calculated by subtracting from the $5,000 investment made in the fund, the actual amount purchased which is the number of shares times the NAV. Load Fee for High-Load Fund = 5,000 − (25 × 190) = $250 Load Fee for Low-Load Fund = 5,000 − (25 × 196) = $100 Load Fee for No-Load Fund = 5,000 − (25 × 200) = 0 5. Mutual Fund Costs. Mutual funds charge their management fees and 12b-1 fees quarterly. Specifically, they charge one-quarter of the advertised annual fees four times per year. Consider the three mutual funds below with different expense ratios. The NAV at the end of each quarter is shown. For each fund, what are the fees paid at each quarter and the sum for the year? The data are in the file, ch4_pr05.xlsx. (LO 4-2) Expense Ratio Shares NAV Qtr 1 NAV Qtr 2 NAV Qtr 3 NAV Qtr 4 High Expense 2.0% 200 $25.6250 $26.1375 $26.6603 $27.1935 Medium Expense 1.1% 200 $25.6250 $26.1952 $26.7780 $27.3738 Low Expense 0.3% 200 $25.6250 $26.2464 $26.8829 $27.5348

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Answer: High Expense Medium Expense Low Expense

Expense $25.63 $14.09 $ 3.84

$26.14 $14.41 $ 3.94

$26.66 $14.73 $ 4.03

$27.19 $15.06 $ 4.13

Total $105.62 $ 58.28 $ 15.94

The expense ratios provided in the example are given in annual terms; therefore, to calculate per-quarter fees, we have to take the expense ratio and divide it by 4.

To find the fees paid for each fund per quarter, we multiply the expense ratio divided by 4, with the product of the number of shares times the NAV value per quarter. Then take the sum of the four fees to find the total fee paid for the year.

The table below shows the amount of fees paid per quarter for each fund, and the total annual fee for the year in the last column.

Quarter 1 High Expense $25.6250 Medium Expense $14.0938 Low Expense $ 3.8438

Quarter 2 $26.1375 $14.4074 $ 3.9370

Quarter 3 $26.6603 $14.7279 $ 4.0324

Quarter 4 $27.1935 $15.0556 $ 4.1302

Year $105.6163 $ 58.2846 $ 15.9434

For example, for the High-Expense Fund, the fees for quarter 1 are calculated as follows: 0.02/4 × 25.6250 × 200 = 25.6250 6. Front-End vs. Back-End Loads. Calculate the future value of $10,000 invested for five years in a fund earning 12% per year and featuring a front-end load of 5%.

Perform the same calculation assuming a deferred back-end load of 5% instead. In terms of investment impact, what’s the difference between front-end and back-end loads? (LO 4-4) Investment $10,000 Return 12% Front load 5% Back load 5% Years 5 Answer: Front load Back load Starting investment $ 9,500 $ 10,000 After 5 years $16,742.25 $17,623.42 After back-end load $16,742.25 $16,742.25

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

The front end load of 5% will be charged when the investment is made. Therefore, we need to calculate the net amount that will be invested after the front-end load is deducted.

Actual investment amount is 10,000 × (1 − 0.05) = $9,500.

The $9,500 will earn 12% per year for five years, so we can calculate the amount that we will have at the end of 5 years, using TVM formulas.

Amount in five years = 9,500 × (1 + 0.12)5 = $16,742.25 The deferred back-end load is charged at the time the money is taken out of the fund, so with the case of the back-end load, the whole $10,000 will be invested in the fund, and after five years, the 5% load will be deducted.

First, we find how much the $10,000 will become in five years.

In five years, before back-end load = 10,000 × (1 + 0.12)5 = $17,623.42 The back-end load will be: $17,623.42 × 0.05 = $881.17 The after-fee amount left after five years is: $17,623.42 − $881.17 = $16,742.25 In this example, the two funds will have the same amount after five years, no matter how the load was applied.

7. Impacts of Costs on Return. A mutual fund has a 1.6% expense ratio and begins with a $124.655 NAV. It experiences the annual returns shown below. What are the end-of-year NAVs after fees for each year? What are the after-fee returns each year?

(LO 4-4) Money to Invest NAV Expense ratio Year 1 return Year 2 return Year 3 return Year 4 return Year 5 return

$10,000.00 $ 124.655 1.6% 5% −12% 18% 4% 23%

Answer: EOY NAV $128.794 $111.525 $129.494 $132.519 $160.390

Return 3.32% −13.41% 16.11% 2.34% 21.03%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

The end-of-year NAV value can be found by multiplying the return generated by the fund each year, with the beginning value of the NAV; and deducting the fees from this value by multiplying it with (1 − expense ratio).

End of Year 1 NAV = 124.655 × (1 + 0.05) × (1 − 0.016) = $128.794 End of Year 2 NAV = 128.794 × (1 − 0.12) × (1 − 0.016) = $111.525 End of Year 3 NAV = 111.525 × (1 + 0.18) × (1 − 0.016) = $129.494 End of Year 4 NAV = 129.494 × (1 + 0.04) × (1 − 0.016) = $132.519 End of Year 5 NAV = 132.519 × (1 + 0.23) × (1 − 0.016) = $160.390 The return for each year is given as follows: Year 1 Return = (128.794 − 124.655) / 124.655 = 3.32% Year 2 Return = (111.525 − 128.794) / 128.794 = − 13.41% Year 3 Return = (129.494 − 111.525) / 111.525 = 16.11% Year 4 Return = (132.519 − 129.494) / 129.494 = 2.34% Year 5 Return = (160.390 − 132.519) / 132.519 = 21.03% 8. Share Classes. A fund you are reviewing sells Class A shares with a front-end load of 5% and Class B shares with 12b-1 fees of 0.5% annually. Assume the portfolio rate of return net of operating expenses is 10% annually. Both have a NAV of $50, and you plan to invest $10,000. If you plan to sell the fund after four years, are Class A or Class B shares the better choice for you? (LO 4-4) front-end 12b-1 fees Return NAV Invest Years

Class A 5% 0 10% $ 50 $10,000 4

Class B 0 0.50% 10% $ 50 $10,000 4

$13,909

$14,377

Answer: Ending Value

Class B is better because it ends with more value.

To find which of the two classes of shares is the best, we calculate the after-fee return of each fund to see which one will provide the better return.

Class A shares: The 5% front-end load will be deducted from the $10,000 investment initially, then the return will be 10% annually. The return after four years will be as follows: Class A shares Return 4 years = 10,000 × (1 − 0.05) × (1 + 0.1)4 = $13,908.95

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Class B shares do not have front-end load; the 12b-1 fees will be deducted annually.

The return for class B shares after four years will be as follows: Class B shares Return 4 years = 10,000 × (1 + 0.1 − 0.005)4 = $14,376.61 Class B shares provide better return than class A shares.

9. Fund Distributions. A mutual fund in which you own 165.2595 shares begins the last quarter of the year with an NAV of $152.756 per share. At the end of the quarter, the fund declares an income distribution of $1.532 per share and a capital gains distribution of $2.095 per share. Before the distribution, the NAV of the fund is $168.908. If you want your distributions reinvested in more shares, how many shares will you have after the distribution? (LO 4-4) Shares owned NAV start Income distribution Capital gains distribution NAV before distribution

165.2595 $ 152.756 $ 1.532 $ 2.095 $ 168.908

Answer: Combined distribution Value of distribution NAV after distribution New shares Total shares

$ 3.627 $599.396 $165.281 3.6265 168.8860

The total amount of the distribution paid by the fund is the sum of the income and capital gains.

The total amount of distribution = 1.532 + 2.095 = $3.627 per share The total amount received will be the total amount of the distribution times the shares owned.

The total amount received = 3.627 × 165.2595 = $599.3962 The NAV value of the fund after the distribution will be equal to the NAV value before the distribution minus the total amount of the distribution per share.

NAV value after distribution = 168.908 − 3.627 = $165.281 To reinvest the total amount of the distribution into new shares, you will buy at the NAV value after the distribution, which is $165.281. The number of new shares that you will be able to purchase is equal to:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Number of new shares = 599.3962 / 165.281 = 3.6265 new shares The total number of shares that you will have will be: 165.2595 + 3.6265 = 168.886 shares 10. Tax Implications of Distributions. Assess the tax consequences of three mutual fund distributions. Fund A manages the portfolio in such a manner that no end-ofyear capital gains distribution is needed. Fund B has a large income distribution and moderate capital gains distribution. Fund C has a moderate income distribution and large capital gains distribution. The NAV of each is $55 before the distribution.

Conduct the analysis as if you owned $5,000 of each fund. Given the information below, what are the distributions and taxes owed for each fund if the tax rates are 24% for interest income and 15% capital gains? The data are in the file, ch4_pr10.xlsx. (LO 4-4) Pre-Distribution NAV Value Owned Income Gains Distribution Capital Gains Distribution

Fund A $55.00 $5,000

Fund B $55.00 $5,000

Fund C $55.00 $5,000

$1.00

$2.50

$1.00

$0.00

$1.00

$2.50

90.9091 $90.91 $0.00 $21.82

90.9091 $227.27 $90.91 $68.18

90.9091 $90.91 $227.27 $55.91

Answer: Shares owned Income Distribution Capital Gains Distribution Taxes owed

The amount owned is $5,000 in each of funds A, B and C. The pre-distribution NAV value of the three funds is also the same, $55. So the number of shares owned in each fund is equal to 5000 / 55 = 90.9091 shares.

We can calculate the total amount of each distribution and their taxes for each fund.

Fund A Income distribution = 90.91 × 1 = $90.91 Capital gains distribution = 0 Taxes = 0.24 × 90.91 = $21.82 Fund B Income distribution = 90.9091 × 2.5 = $227.27 Capital gains distribution = 90.90 × 1 = $90.91 Taxes = (0.24 × 227.28) + (0.15 × 90.91) = $68.18

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Fund C Income distribution = 90.91 × 1 = $90.91 Capital gains distribution = 90.9091 × 2.5 = $227.27 Taxes = (0.24 × 90.91) + (0.15 × 227.28) = $55.91 11. Buying ETFs. An ETF trades for $34.56 in the stock market. It costs you $10 commission to place a trade. How much does it cost to purchase 100 shares of the ETF? (LO 4-5) Answer: Price Shares Commission

$

Cost =

$3,466.00

$

34.56 100 10.00

To purchase 100 shares of the ETF, you will need the total amount to purchase those shares plus commission.

The total cost = (34.56 × 100) + 10 = $3,466 12. Tracking Error. Monthly returns for an ETF’s NAV and for the index it tracks are in the data file, ch4_pr12.xlsx. What is the ETF’s tracking error? (LO 4-5) Answer: The tracking error is calculated using the following formula: Tracking Error =



 NAV Return − Benchmark Return 2      t =1 n −1     n

The tracking error is the standard deviation of the difference between the portfolio returns and the benchmark returns. In order to calculate the standard deviation of this difference, first we find the difference of the returns between the portfolio and its benchmark.

Month 1 2 3 4 5 6 7

ETF's NAV 0.52% −2.24% 1.84% 3.15% −0.44% 2.18% 1.19%

Index 0.54% −2.26% 1.86% 3.15% −0.46% 2.18% 1.22%

Difference −0.02% 0.02% −0.02% 0.00% 0.02% 0.00% −0.03%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

8 9 10 11 12

0.14% 1.36% 3.23% 1.59% 0.21%

0.14% 1.39% 3.25% 1.60% 0.21%

0.00% −0.03% −0.02% −0.01% 0.00%

Average

−0.01%

Also, the average return of those difference is calculated as −0.01%. Then the standard deviation of a sample formula is used to calculate the Tracking Error.

Tracking Error = {[(−0.02 + 0.01)2 + (0.02 + 0.01)2 + (−0.02 + 0.01)2 + (0 + 0.01)2 + (0.02 + 0.01)2 + (0 + 0.01)2 + (−0.03 + 0.01)2 + (0 + 0.01)2 + (−0.03 + 0.01)2 + (−0.02 + 0.01)2 + (−0.01 + 0.01)2 + (0 + 0.01)2]/11}1/2 = 0.01732% 13. Leveraged ETF Performance. The SPDR Dow Jones Industrial Average ETF (ticker: DIA) aims to mimic the Dow Jones Industrial Average (DJIA) return. However, the ProShares Ultra Dow30 (ticker: DDM) and the ProShares UltraPro (ticker: UDOW) aim to double and triple the DJIA return, respectively. Consider that the NAVs of DIA, DDM, and UDOW all start at $350 and the DJIA earns 15% in the first year and −15% in the second year. If the three ETFs are successful in their objectives, what is the NAV of each ETF at the end of the second year? (LO 4-6) Year 1 Year 2

15% −15%

NAV NAV 1 NAV 2

DIA $ 350.00 $ 402.50 $ 342.13

DDM $ 350.00 $ 455.00 $ 318.50

UDOW $ 350.00 $ 507.50 $ 279.13

Answer: The NAV values of each of the three ETFs are calculated for the next two years.

DIA Year 1 NAV = 350 × (1 + 0.15) = $402.50 Year 2 NAV = 402.50 × (1 − 0.15) = $342.125 DDM (doubles the returns) Year 1 NAV = 350 × (1 + 0.3) = $455.00 Year 1 NAV = 455 × (1 − 0.3) = $318.50 UDOW (triples the returns) Year 1 NAV = 350 × (1+ 0.45) = $507.50 Year 2 NAV = 507.50 × (1 − 0.45) = $279.125

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

14. Short ETF Performance. The SPDR Dow Jones Industrial Average ETF (ticker: DIA) aims to mimic the Dow Jones Industrial Average (DJIA) return. However, the ProShares Short Dow30 (ticker: DOG) aims to short the DJIA and earn −1x the DJIA return. The ProShares UltraShort Dow30 (ticker: DXD) and ProShares UltraPro Short Dow30 (ticker: SDOW) aim to earn −2x and −3x the DJIA return, respectively.

Consider that the NAVs of DIA, DOG, DXD, and SDOW all start at $400 and the DJIA earns 12% in the first year and −12% in the second year. If the three ETFs are successful in their objectives, what is the NAV of each ETF at the end of the second year? (LO 4-6) Answer: Year 1 Year 2

12% −12%

NAV NAV 1 NAV 2

DIA $400.00 $448.00 $394.24

DOG $400.00 $352.00 $394.24

DXD $400.00 $304.00 $376.96

SDOW $400.00 $256.00 $348.16

DIA Year 1 NAV = 400 × (1 + 0.12) = $448.00 Year 2 NAV = 448 × (1 − 0.12) = $394.24 DOG (−1 times the return) Year 1 NAV = 400 × (1 − 0.12) = $352.00 Year 2 NAV = 352 × (1 + 0.12) = $394.24 DXD (−2 times the return) Year 1 NAV = 400 × (1 − 0.24) = $304.00 Year 2 NAV = 304 × (1 + 0.24) = $376.96 SDOW (−3 times the return) Year 1 NAV = 400 × (1 − 0.36) = $256.00 Year 2 NAV = 256 × (1 + 0.36) = $348.16

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

15. Closed-End Fund Returns. A closed-end investment company is currently selling for $10, and its NAV is $10.63. You decide to purchase 100 shares. During the year, the company distributes $0.75 in dividends. At end of the year, you sell the shares for $12.03. At the time of the sale, NAV is $13.52. What percentage return do you earn on the investment? What role does the NAV play in determining the percentage return? (LO 4-8) Answer: Price NAV Purchase Dividends

$10 $10.63 100 $0.75

Sell at Price Final NAV

$12.03 $13.52

Return =

27.80%

For a closed-end investment company, the selling price is what matters, because an investor will buy or sell it at the selling price and not the NAV price. Therefore, for the return calculations, the NAV does not play any role, only the selling price matters.

The investor purchases the fund for $10 per share and sells it for $12.03 per share.

Also, during the year, the investor receives $0.75 dividend per share.

Return = [(12.03 − 10) + 0.75] /10 = 27.80% 16. Premium Dynamics. Consider a closed-end fund that has a NAV of $10.50 and a price of $12.30. What is the closed-end fund’s premium in dollars and percentage? If the NAV were to increase 10% to $11.55 and the price rose to $13.16, what would be the return to the investor and the new premium? (LO 4-8) Answer: NAV $10.50 Premium $ Premium %

Price $12.30

New NAV $11.55

$1.80 17.14% Return

New Price $13.16

$1.61 13.94% 7.0%

A closed-end funds premium or discount can be calculated using the following formula:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Discount or Premium =

Price − NAV NAV

The fund’s premium is: Price − NAV = 12.30 − 10.50 = $1.80 The fund’s premium in percentage is: 1.8 / 10.50 = 17.14% With the increase in NAV and the price as given, the return to the investor is calculated based on the price only, because the investor will buy or sell at the fund’s price not NAV. Return to investor is: (13.16 − 12.30) / 12.30 = 6.99% The new premium is 13.16 − 11.55 = $1.61 The new premium in percentage is: 1.61 / 11.55 = 13.94% 17. Discount Dynamics. Consider a closed-end fund that has a NAV of $27.60 and a price of $23.20. What is the closed-end fund’s discount in dollars and percentage? If the NAV were to increase 10% to $30.36 and the price rose to $26.68, what would be the return to the investor and the new premium? (LO 4-8) Answer: NAV $27.60 Premium $ Premium %

Price $23.20

New NAV $30.36

$(4.40) −15.94% Return

New Price $26.68

$(3.68) −12.12% 15.0%

This is a similar problem to problem #16.

The fund’s discount is in dollars: 23.20 − 27.60 = − $4.40 The fund’s discount in percentage is: −4.40 / 27.6 = −15.94% After the increase of 10% in price and NAV, the return is calculated using the price only.

The return to investor = (26.68 − 23.20) / 23.20 = 15.00% The fund’s discount in dollars is: 26.68 − 30.36 = −$3.68 The fund’s discount in percentage is: −3.68 / 30.36 = −12.12%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

18. Hedge Fund Fees. Consider two investments. At the end of the year, before fees, you have a $1 million investment in a hedge fund that charges 1.5% in management fee and 15% in incentive fees over a threshold of 8%. Also at the end of the year is the second investment of $1 million in a mutual fund that has an expense ratio of 1.5%. Compute the fees for each investment if the hedge fund had earned 15% and the mutual fund had earned 12%. (LO 4-9) Answer:

Management fee Incentive fee Threshold Return

hedge fund $1,000,000 1.50% 15% 8% 15%

Intial Value Threshold Value net mgt fees Profit for Incentive Incentive Fee

$869,565.22 $939,130.43 $985,000.00 $ 45,869.57 $ 6,880.43

mutual fund $1,000,000 1.50% 0 12%

Total

hedge fund

mutual fund

$15,000 $ 6,880

$15,000

$21,880.43

$15,000

For both funds, the end of year value is $1 million before fees.

For the hedge fund: The hedge fund earned 15%. Knowing that the end-of-year value of the hedge fund is $1 million, we can calculate the beginning-of-year value.

Beginning of the year value = 1,000,000 / 1.15 = $869,565.22 The hedge fund will charge the management fees of 1.5% on the ending value of the hedge fund, which is $1 million.

The amount of the management fees = 1,000,000 × 0.015 = $15,000 The incentive fees of 15% will be charged over a threshold of 8%, net of management fees.

The value of the account net of management fees = 1,000,000 − 15,000 = $985,000 The threshold value above which the incentive fees will kick in is: 869,565.22 × 1.08 = $939,130.43 So, for the hedge fund to be able to charge incentive fees, the fund needs to be above the value of $939,130.43 after management fees. The fund is worth $985,000 after management fees so the hedge fund will be able to charge the incentive fees on the difference.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

The difference over which incentive fees will be charged = $985,000 − $939,130.43 = $45,869.57 Incentive fees = 0.15 × 45,869.57 = $6,880.43 The total fees that the hedge fund will charge equals to: Total fees = $15,000 + $6,880.43 = $21,880.43 The after-fee amount that will be left at the end of the year = 1,000,000 − 21,880.43 = $978,119.57 For the mutual fund: The expense ratio is 1.5%, which will be charged on the $1 million investment, so the amount of fees to be deducted for the mutual fund is: Fees = 0.015 × 1,000,000 = $15,000 The after-fee amount that will be left at the end of the year = 1,000,000 − 15,000 = $985,000 19. Hedge Fund Returns. Consider two investments. At the end of the year, before fees, you have a $1 million investment in a hedge fund that charges 1.5% in management fee and 15% in incentive fees over a threshold of 8%. Also at the end of the year is the second investment of $1 million in a mutual fund that has an expense ratio of 1.5%. Compute the after-fee return for each investment if the hedge fund had earned 15% and the mutual fund had earned 12%. (LO 4-9) Answer:

Management fee Incentive fee Threshold Return

hedge fund mutual fund $1,000,000 $1,000,000 1.50% 1.50% 15% 0 8% 15% 12%

hedge fund

Intial Value Threshold Value net mgt fees Profit for Incentive Incentive Fee

$869,565.22 $892,857.14 $939,130.43 Actual Return $985,000.00 $ 45,869.57 $ 6,880.43

Ending value net of fees

$978,119.57

Total =

mutual fund

$15,000 $ 6,880

$15,000

$21,880.43

$15,000

12.48%

10.32%

$985,000

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23

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

This problem is based on the same information as problem #18. So, we will use part of that solution.

To calculate the after-fee return for each fund, we need the beginning value for each fund.

For the mutual fund, the beginning value is: Beginning value of mutual fund = 1,000,000 / 1.12 = $892,857.14 We already found the after-fee value of the mutual fund in problem #18 to be $985,000.

Therefore, the after-fee return of the mutual fund is = (985,000 − 892,857.14) / 892,857.14 = 10.32% For the hedge fund, we already calculated the beginning value and the after-fee ending value of the hedge fund in problem #18.

The after-fee return of the hedge fund is = (978,119.57 − 869,565.22) / 869,565.22 = 12.48% Although the hedge fund fees were higher for the hedge fund, the after-fee return was higher than the mutual fund’s return.

20. Buying REITs. You wish to buy an equity REIT and a mortgage REIT in equal proportions. You have a total of $10,000 to invest in REITs. If the equity REIT is trading at $163.22 per share and the mortgage REIT is trading at $45.90 per share, how many shares of each REIT should you buy? (LO 4-10) Total Investment =

Price

$10,000 Equity $163.22

Mortgage $45.90

30.633501 30

108.9325 109

Answer: Share estimate Shares

Total value =

$9,899.70

You will invest $5,000 in each of the equity REIT and mortgage REIT to have equal proportions.

The number of shares of each REIT that you will buy is equal to the amount to be invested in each REIT, $5,000, divided by the price of each REIT.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Number of shares of equity REIT = 5,000 / 163.22 = 30.63 shares Number of shares of mortgage REIT = 5,000 / 45.90 = 108.93 shares REIT shares are listed on major stock exchanges, just like company shares, and in general, you must buy them in whole amounts. Therefore, you can buy 30 shares of equity REIT and 109 shares of mortgage REIT. Sometimes you can invest in REITS similar to mutual funds. In that case, you can purchase fractional number of shares.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

Case Study Is Berkshire Hathaway a Fund?

Warren Buffett started an investment partnership with $100 in 1956 and has gone on to accumulate a personal net worth of more than $100 billion. Today, Buffett, nicknamed the Oracle of Omaha, runs Berkshire Hathaway (BRK) like a combination of a private equity firm and a closed-end mutual fund. He combines a stable of wonderful operating businesses, such as Geico Insurance, with a handful of core investment holdings, such as stock in the Coca-Cola Company.

Buffett looks for companies that enjoy strong franchises, pricing flexibility, high return on equity (ROE), high cash flow, owner-oriented management, and predictable earnings growth. He also looks for companies that are not natural targets of regulation. Berkshire operates businesses in insurance (like GEICO), railroads (like BNSF Railway), energy, manufacturing (like Fruit of the Loom), service, and retailing. In addition, it takes large positions in other public firms. His largest investment positions are in Apple, Bank of America, The Coca-Cola Company, and American Express Company.

Each year, the investors and the media anticipate the Berkshire’s annual meeting. In preparation, Buffett writes his annual letter to shareholders. Over the years, his letters have provided many nuggets of investment advice, such as: • • • • • • • •

We simply attempt to be fearful when others are greedy and to be greedy only when others are fearful.

It's far better to buy a wonderful company at a fair price than a fair company at a wonderful price.

Price is what you pay. Value is what you get.

Whether we're talking about socks or stocks, I like buying quality merchandise when it is marked down.

Risk comes from not knowing what you're doing.

Beware of geeks bearing formulas.

Success in investing doesn't correlate with IQ . . . what you need is the temperament to control the urges that get other people into trouble in investing.

Our favorite holding period is forever.

If you think of Berkshire Hathaway as a fund, then its performance would be compared to the S&P 500 Index. Below is the annual returns of Berkshire Hathaway since 1965. Also shown is the annual return of the S&P 500 Index with dividends.

Given the data in the file, ch4_case_study.xlsx, compute and interpret the following:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 04: Mutual Funds and Other Investment Companies

1. What is the average annual return for BRK and for the S&P 500 Index: a. over the entire period? b. by decade?

Answer: a. The average return for BRK for the entire period was 24.35%, while the S&P 500 Index return was 11.59%. Berkshire Hathaway had more than double the return of the S&P 500 from 1965 until 2020. b. The table below provides the average return by decade for Berkshire Hathaway and the S&P 500. The performance of Berkshire Hathaway by decade was better than the S&P 500 up to 2010. For the period of 2010–2019, the performance was about the same, with a slightly higher return for the S&P 500. For the current decade starting in 2020, the only data we have in the case is the return for 2020, where the S&P 500 had a much better return than Berkshire Hathaway. It would be interesting to see how Berkshire Hathaway will do in the next few years.

Decade 1965–1969 1970–1979 1980–1989 1990–1999 2000–2009 2010–2019 2020

BRK Average Return 31.32% 32.84% 42.57% 23.70% 7.39% 13.98% 2.40%

S&P 500 with Dividends Average Return 6.36% 7.42% 18.08% 19.00% 1.22% 14.16% 18.40%

2. Which one experiences more volatility over time?

Answer: The standard deviation of Berkshire Hathaway over the entire period was 33.65%, while the S&P 500 had a standard deviation of 16.84%. Berkshire Hathaway was clearly more volatile over the period, with more than double the standard deviation of the S&P 500.

3. Compute the tracking error as if BRK was indexing to the S&P 500 Index.

Answer: The tracking error between BRK and the S&P 500 is quite large, at 29.55%. This large tracking error indicates that BRK return will not track the return of the S&P 500 closely, which is what we have noticed in the data and the results in parts 1 and 2.

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27

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 29

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Questions 1. Return Components. What are the primary components of return? (LO 5-1) Answer: There are two components of return: income and capital appreciation. Income is the cash flow that the asset provides over the holding period of the investment.

Examples of income are dividends from stocks, coupon payments from bonds, or rent from a real property; Sometimes income can be negative, such as when the repairs cost are higher than the rent received from a real property.

The capital appreciation is the change in the value of the asset over the holding period. This change can be positive if the asset value increased over the holding period, or it can be negative if the asset value decreased.

2. Holding Period Returns. What factors go into calculating a holding period return?

(LO 5-2) Answer: Holding period return is calculated on the basis of total returns from the asset or portfolio (income plus changes in value). It is particularly useful for comparing returns between investments held for different periods of time.

The formula for the holding period return is:

HPR =

Income + (PriceReceived − PricePaid ) PricePaid

3. Different Returns. What are the differences between the expected return, the required return, and the realized return? (LO 5-3) Answer: Expected return of an asset is the possible return that the asset may produce over a time period. This possible return can be estimated using a probability-based approach to make an educated guess of the different possibilities of income and selling prices of the asset to come up with the most probable return estimate that an asset may produce.

The realized return of an asset is the actual return that the asset produced over a time period over which the asset’s return is calculated, using the actual prices and the actual cash flows that were produced by this asset. You can only calculate the realized return after actually selling the asset and knowing the exact selling price, along with the exact amount of income generated by the asset.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

The required return is the minimum return the investor would want to earn to compensate for the risk of holding the asset. The difference between the expected return and the required return can be illustrated by an example. Suppose an investor wants a minimum return of 10% to buy an asset given the level of risk this asset has. However, the investor expects the asset to generate 15% return the following year based on the probabilistic forecasting method the investor used to predict the expected return of the asset.

4. Arithmetic and Geometric Averages. What is the basic difference between arithmetic and geometric average returns? Which will always be higher? (LO 5-4) Answer: The arithmetic average is the sum of a selected range of historical returns divided by the number of returns in the selected range.

The formula for the arithmetic average return is the following: n

r

Arithmetic Average = t =1 n

t

The geometric average return is the compound average annual return over a selected period of time; i.e, this annual geometric average will be earned annually over the selected period of time incorporating the compounding effect every year.

The geometric average return includes the compounding effect, while the arithmetic average return does not.

The formula for the geometric average return is the following:  n  Geometric Average =  n Π (1+ rt )  − 1  t =1   

The geometric average return is preferred over the arithmetic average return for investment performance calculations. Also, the arithmetic average return will always be higher than the geometric average return because it is a simple average while the geometric average incorporates the compounding effect.

When considering investment returns it is the geometric average, not arithmetic average, that matters. Understanding the difference between arithmetic and geometric average returns will cause you to invest differently and improve your investment profits by taking volatility into account.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

5. Adjusted Close Prices. How many adjusted close prices would you need to calculate the last 40 quarterly returns? Why? (LO 5-5) Answer: You will need quarterly adjusted close price data to calculate quarterly returns. The quarterly adjusted close price data is the price at the end of the quarter. To calculate the last 40 consecutive quarterly returns, you will need 41 quarterly adjusted close prices. Forty quarters are equivalent to 10 years of quarterly data. Each return calculation requires beginning value and ending value. For the first quarterly return calculation, we will need the beginning value of the quarter, which is the same as the ending value of the previous quarter, so that additional quarterly data is also needed. For example, if we need to calculate the quarterly returns over 1 year only, we will need 5 quarters of price data; if we need to calculate the quarterly returns over 2 years, we will need 9 quarters of price data, etc.

6. Data Staleness. How do the law of large numbers and data “staleness” fit together?

(LO 5-6) Answer: The law of large numbers (LLN) states that if you perform the same experiment a large number of times, then the result obtained will be close to the expected value of the experiment. The more you perform the experiment, the closer you will be to getting to the expected value.

In investments, when calculating expected returns, the LLN can be applied to get an estimate of the expected returns using a large number of historical returns.

According to LLN, the more historical returns are used, the better the estimate should be. However, by using a larger number and having to include older historical returns along with recent ones, we run into the issue of data staleness. Older historical returns were realized during different technological, competitive, and regulatory environments and are not necessarily representative of future such environments. That is the idea of data being stale, when the older data used to comply with LLN is not representative of the current or future environment.

7. Nominal Interest Rates. How would you go about constructing a nominal quarterly interest based on daily interest prices? (LO 5-7) Answer: The question is asking for the effective quarterly interest based on daily interest rates. Assuming the daily rate is the same, then we use the following formula to calculate the quarterly effective rate: Rquarterly = (1 + Rdaily) 365/4 – 1

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Assume there are 365 days with the daily rate.

In most situations, the daily rate may not be constant. In that case you can calculate the effective quarterly rate by multiplying each daily rate plus 1 together and subtracting 1 from the product, using the following formula: Rquarterly = (1 + R1) x (1 + R2) x (1 + R3) x…. (1 + Rt) – 1 Where t is the number of days in the quarter.

8. Standard Deviation. Why do we use the population standard deviation for probabilistic situations but the sample standard deviation when calculating standard deviation on historic data? (LO 5-8) Answer: When using the forward-looking, probabilistic approach to calculate expected returns, we are guessing about the future; therefore, the best approach is to make those guesses about the entire future population of possible returns. That is, we should include every expected return that could possibly happen, which is why the probabilities under that approach have summed up to 1.0. Thus, because of this approach, we use the population standard deviation for probabilistic situations.

When we are using the distribution of historic returns as a proxy for future expected returns, the past historic record is not the population of all eventual realized returns. It is only a sample that happened over that past period, and the future did not even happen yet. Therefore, we use the sample standard deviation when calculating standard deviation on historic data.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability. Thus the standard deviation of the sample is greater than that of the population.

9. Distribution Normality. What are the advantages of a stock’s returns being normally distributed? (LO 5-9) Answer: There are two major advantages of a stock returns being normally distributed: 1. The parameters of the normal distribution are well-known, which will allow us to easily “map” possible deviations of the realized returns from the expected return into probabilities using only the mean and standard deviation. Therefore, for the normal distribution, we only need the mean and standard deviation to map deviations from the mean into probabilities, which helps to greatly simplify the statistical analysis of the stock returns.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

2. The variables that are normally distributed can benefit from the fact that normal distributions are additive, in that the sum of two normally distributed variables will itself also be normally distributed.

10. Historical Relationship of Risk and Return. Historically, does higher risk always offer higher return? Why or why not? (LO 5-10) Answer: In most situations, assets with higher risk also provide higher returns. However this relationship is not always true. Some of the reasons for not having perfect relation: 1. Sometimes the data is studied over smaller samples and does not include the entire historic record. Further, even if the entire past record of historic data is used, that still does not include the entire population because there is still the future data that did not happen and is not included.

2. The future expectations of investors related to the risk and return relationships cannot be perfectly forecasted from historic data. It is possible that even though strict pricing of risk hasn’t held in the past, investors might still expect it to hold more strictly in the future.

3. The risk measured by the standard deviation represents the total risk of an asset. Some of that risk is diversifiable. In a well-diversified portfolio, a portion of the total risk can be reduced. Therefore, the standard deviation as a measure of risk may not be the best variable to represent risk, and another variable is needed that represents the portion of the standard deviation that we can’t get rid of in a well-diversified portfolio.

4. Instead of looking at assets in standalone basis, we look at classes of assets. An example is stocks, where we can combine certain stocks with common characteristics into classes, such as retail company stocks in a class for retailers.

The risk-return relationship is thus more consistent.

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Problems 1. Return Components. If you buy a share of stock for $12, earn total dividends $0.75 while owning it, and then sell it for $10, what is your dollar return? Your total rate of return? (LO 5-1) Answer: P0 = Div = P1 =

$12.00 $ 0.75 $10.00 Dollar Return = Total Rate of Return =

$ (1.25) −10.42%

Return has two components: income and capital appreciation. Income is the cash flow generated by the asset, while capital appreciation is the change in the value of the asset between the time you buy it and the time you sell it (i.e., the difference between the price received vs. the price paid).

The dollar value of the return is calculated using the following:

Total Return = Income + (PriceReceived − PricePaid ) The rate of return is calculated using the following:

r=

Income + (PriceReceived − PricePaid ) PricePaid

The dollar return is: 0.75 + (10 − 12) = −$1.25 The rate of return is: −1.25/12 = −0.1042 or −10.42% 2. Return Components. If you buy a bond for $1,059.05, earn interest payments totaling $34.00 during the year, and then sell it for $1,096.26, what is your income yield? Your capital gains yield? (LO 5-1) Answer: B0 = Interest = B1 =

$1,059.05 $ 34.00 $1,096.26 Income Yield = 3.21% Capital Gain Yield = 3.51%

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7

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Return has two components: income and capital appreciation. Income is the cash flow generated by the asset, while capital appreciation is the change in the value of the asset between the time you buy it and the time you sell it (i.e., the difference between the price received from the price paid).

Income yield is the income component of the return as a percentage of the price paid. For stocks the income yield is called dividend yield, while for bonds the income yield is called current yield.

The capital gain yield is the capital appreciation component of the return as a percentage of the price paid.

The income yield or the current yield in this example is equal to: 34 / 1,059.05 = 0.0321 or 3.21%.

The capital gain yield is equal to: (1,096.26 – 1,059.05) / 1,059.05 = 0.0351 or 3.51% 3. Holding Period Returns. The year-end closing prices of stock XYZ are shown below for the past five years. Ending in Year 5, what were the one-, two-, three-, four-, and fiveyear HPRs? (LO 5-2) XYZ Stock

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Price at End of Year

$23

$28

$34

$32

$34

$33

Dividends During Year

$ 3

$ 3

$ 3

$ 3

$ 3

$ 3

Answer: 1-Year HPR = 5.88% 2-Year HPR = 21.88% 3-Year HPR = 23.53% 4-Year HPR = 60.71% 5-Year HPR = 108.70% Return has two components: income and capital appreciation. Income is the cash flow generated by the asset, while capital appreciation is the change in the value of the asset between the time you buy it and the time you sell it (i.e., the difference between the price at the end of a period and the price at the beginning of a period).

The rate of return or the holding period return over a period of time is calculated as follows:

r=

Income + (PriceReceived − PricePaid ) PricePaid

In this example, income will be the dividends received over the period of calculation.

Pricereceived is the price at the end of the period.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Pricepaid is the price at the beginning of the period.

The question is asking to find several HPRs ending in Year 5, so the ending price will always be Year 5 price in this question.

1-year HPR = [3 + (33 − 34)] / 34 = 0.0588 or 5.88% (Buy at end of Year 4 and sell at Year 5) 2-year HPR = [3 + 3 + (33 − 32)] / 32 = 0.2188 or 21.88% (Buy at end of Year 3 and sell at Year 5) 3-year HPR = [3 + 3 + 3 + (33-34)] / 34 = 0.2353 or 23.53% (Buy at end of Year 2 and sell at year 5) 4-year HPR = [3 + 3+ 3 + 3 + (33 − 28)] / 28 = 0.6071 or 60.71% (Buy at end of Year 1 and sell at Year 5) 5-year HPR = [3 + 3 + 3 + 3 + 3 + (33 − 23)] / 23 = 1.087 or 108.7% (Buy at Year 0 and sell at Year 5) 4. Holding Period Returns. The year-end prices for one ounce of gold is shown below.

What is the five-year HPR for the periods 2011 to 2015 and 2016 to 2020? What is the 10-year HPR over that span? The data are in the file, ch5_pr04.xlsx. (LO 5-2) 2010

2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

$1405.50

$1531.00

$1657.50

$1,205.50

$1206.00

$1060.00

$1145.90

$1291.00

$1279.00

$1514.75

$1887.60

Answer: 2011 to 2015 HPR = −24.58% 2016 to 2020 HPR = 78.08% 2011 to 2020 HPR = 34.30% To calculate the holding period returns over a certain period with adjusted prices, the following formula can be used:

HPR =

Adjusted Priceend − Adjusted PriceBeg Adjusted PriceBeg

Where: Adjusted PriceEnd is the price at the end of the period.

Adjusted PriceBeg is the price at the beginning of the period.

The prices given in the table represent prices at the end of that year; therefore, the price at the beginning of the year is the ending price of the previous year.

5-year HPR for the period 2011 to 2015:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Adjusted PriceBeg = 1405.5 (This is the price at the beginning of 2011) Adjusted PriceEnd = 1060 HPR = (1060-1405.5) / 1405.5 = −0.2458 or −24.58% 5-year HPR for the period 2016 to 2020: Adjusted PriceBeg = 1060 (This is the price at the beginning of 2016) Adjusted PriceEnd = 1887.60 HPR = (1887.60 − 1060) / 1060 = 0.7808 or 78.08% 10-year HPR for the period 2011 to 2020: Adjusted PriceBeg = 1405.5 (This is the price at the beginning of 2011) Adjusted PriceEnd = 1887.60 HPR = (1887.60 − 1405.5) / 1405.5 = 0.3430 or 34.30% 5. Different Returns. An investment that cost $10 was expected to have a price of $12 at the end of the year but actually had a year-end price of $13. What were the expected and realized returns for the year? (LO 5-3) Answer: P0 = $10.00 E(P1) = $12.00 P1 = $13.00 Expected Return = 20.00% Realized Return = 30.00% To calculate the expected return and the realized return over one-year period, the HPR formula can be use: Adjusted Priceend − Adjusted PriceBeg HPR = Adjusted PriceBeg Adjusted PriceBeg is the cost of the investment, $10.

The expected return is calculated using the Adjusted PriceEnd as the expected price of $12.

The realized return is calculated using the Adjusted PriceEnd as the actual price of $13.

Expected Return = (12 − 10) / 10 = 0.20 or 20% Realized Return = (13 − 10) / 10 = 0.30 or 30%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

6. Different Returns. An investment that cost $20 was expected to have a price of $24 at the end of the year but actually had a year-end price of $18. What were the expected and realized returns for the year? (LO 5-3) Answer: $ 20.00 P0 = E(P1) = $ 24.00 P1 = $ 18.00 Expected Return = 20.00% Realized Return = −10.00% Similar problem as Problem 5.

Expected Return = (24 − 20) / 20 = 0.20 or 20% Realized Return = (18 − 20) / 20 = −0.10 or −10% 7. Arithmetic and Geometric Averages. Calculate the arithmetic and geometric average rates of return for the five-year period shown below. (LO 5-4)

Return

Year 1

Year 2

Year 3

Year 4

Year 5

6%

12%

4%

15%

8%

Answer: Arithmetic Average = 9.00% Geometric Average = 8.09% The arithmetic average is calculated as the sum of a selection of the historic returns divided by the number of returns. The formula is the following: n

r

Arithmetic Average = t =1 n

t

Arithmetic Average = (6 + 12 + 4 + 15 + 8) /5 = 9% The geometric average is the n-th root of the product of a selection of one plus historic returns subtracted by one at the end. The formula is the following:  n  Geometric Average =  n (1+ rt )  − 1  t =1   



Geometric Average = [(1 + 0.06) × (1 + 0.12) × (1 + 0.04) × (1 + 0.15) × (1 + 0.08)]1/5 −1 = 0.0893 or 8.93%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

8. Arithmetic and Geometric Averages. Calculate the arithmetic and geometric average rates of return for the 10-year period shown below. The data are in the file, ch5_pr08.xlsx. (LO 5-4)

Return

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

6%

12%

4%

15%

8%

3%

21%

6%

Year 9 Year 10 5%

18%

Answer: Arithmetic Average = 9.80% Geometric Average = 8.07% Similar problem as Problem 7.

Arithmetic Average = (6 + 12 + 4 + 15 + 8 + 3 + 21 + 6 + 5 + 18) / 10 = 0.098 or 9.8% Geometric Average = [(1 + 0.06) × (1 + 0.12) × (1 + 0.04) × (1 + 0.15) × (1 + 0.08) × (1 + 0.03) × (1 + 0.21) × (1 + 0.06) × (1 + 0.05) × (1 + 0.18)]1/10−1 = 0.0964 or 9.64% 9. Adjusted Close Prices. Historical data for Kohl's Corporate (KSS) are provided in the data file, ch5_pr09.xlsx. What were the monthly returns for the past 12 full months?

(Data from Yahoo! Finance) (LO 5-5) Answer: Not a full month!

18.76% 51.24% 14.89% −13.25% 12.18% −8.33% 8.06% 4.12% 31.21% −62.73% −8.42% −14.92% 8.38% When we download data from Yahoo! as monthly adjusted close price, this Adjusted Close column is the price as of the end of the month, on the date shown under the date column. So the last row’s adjusted close price of 44.70738 is the adjusted price at the end of November 2019 which coincides to beginning of December 2019. The

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12

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

adjusted close price in the row above, 48.45439, is the adjusted price at the end of December 2019, which coincides to beginning of January 2020.

Also, note that in this example, the first row shows the date of 12/11/2020, which means that this data was downloaded on that day most likely, and therefore the row below with the date 12/1/2020 does not provide the adjusted closing price at the end of the month of December 2020. So we have to be careful not to use this December 2020 data because it does not represent a full month.

In order to have 12 full months of monthly returns, we have to start with December 2019 return and end with November 2020 return to have a full 12 months of returns.

To calculate the holding period returns over a certain period with adjusted prices, the following formula can be used: HPR =

Adjusted PriceReceived − Adjusted PricePaid Adjusted PricePaid

December 2019 Return = (48.45439 − 44.70738) / 44.70738 = 0.0838 or 8.38% January 2020 Return = (41.22306 − 48.45439) / 48.45439 = −0.1492 or −14.92% February 2020 Return = (37.75164 − 41.22306) / 41.22306 = −0.0842 or −8.42% March 2020 Return = (14.06888 − 37.75164) / 37.75164 = −0.6273 or −62.73% April 2020 Return = (18.46 − 14.06888) / 14.06888 = 0.3121 or 31.21% May 2020 Return = (19.22 − 18.46) / 18.46 = 0.0412 or 4.12% June 2020 Return = (20.77 − 19.22) / 19.22 = 0.0806 or 8.06% July 2020 Return = (19.04 − 20.77) / 20.77 = −0.0833 or −8.33% August 2020 Return = (21.36 − 19.04) / 19.04 = 0.1218 or 12.18% September 2020 Return = (18.53 − 21.36) / 21.36 = −0.1325 or −13.25% October 2020 Return = (21.29 − 18.53) / 18.53 = 0.1489 or 14.89% November 2020 Return = (32.2 − 21.29) / 21.29 = 0.5124 or 51.24%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

10. Adjusted Close Prices. Historical data for NIKE, Inc. (NKE) are provided in the data file, ch5_pr10.xlsx. What was the total annual return for 2020? (Data from Yahoo!

Finance) (LO 5-5) Answer: 40.69% When we download data from Yahoo! as monthly adjusted close price, this Adjusted Close column is the price as of the end of the month, beginning on the date shown under the date column.

To calculate the holding period returns over a certain period with adjusted prices, the following formula can be used: HPR =

Adjusted Priceend − Adjusted PriceBeg Adjusted PriceBeg

The question is asking to calculate the total annual return for NIKE from the table above for the year 2020.

In order to calculate the return over 2020, the beginning price should be the adjusted closing price of 12/1/2019 because that price is the adjusted close price at the end of December 2019, which coincides with the beginning of January 2020. The ending price should be the adjusted closing price of 12/1/2020, because that is the adjusted close price at the end of December 2020.

The total annual return for 2020 = (140.6157 − 99.94835) / 99.94835 = 0.4069 or 40.69% 11. Data Staleness. Download all available monthly returns for Pfizer, Inc. (PFE) from Yahoo! Finance and calculate the average and standard deviation of monthly returns using the latest one-year, three-year, five-year, and seven-year periods, all ending at the end of 2020. If you were asked to use one of these sets of statistics as a proxy for your future expectations for PFE returns, which would you choose?

Why? (LO 5-6) Answer: 1-Year Average = 3-Year Average = 5-Year Average = 7-Year Average =

0.86% 0.73% 0.77% 0.70%

The date this solution was written is mid October 2021. Thus, the adjusted close price that will be attributed to October 2021 is not for the full month, and it is best not to use it.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

The returns for 1-year, 3-year, 5-year, and 7-year periods all ending at the end of 2020 are shown in the Excel file.

For 1-year returns, we include the adjusted close price of December 2019, so that we calculate the monthly return for January 2020.

For 3-year returns, we include the adjusted close price of December 2017, so that we calculate the monthly return for January 2018.

For 5-year returns, we include the adjusted close price of December 2015, so that we calculate the monthly return for January 2016.

For 7-year returns, we include the adjusted close price of December 2013, so that we calculate the monthly return for January 2014.

The results are provided in the Excel file and below.

1-Year Returns 3-Year Returns 5-Year Returns 7-Year Returns

Average 0.70% 0.73% 0.79% 0.74%

Standard Deviation 10.15% 6.98% 6.02% 5.60%

Pfizer is a successful pharmaceutical company that may be known for developing the drug Viagra but also more recently for developing a vaccine for Covid-19.

The average returns are rather close to each other, but there is some variation in the standard deviations. The statistics based on the 1-year returns would put too much emphasis on the most recent developments, notably the impact the Covid-19 vaccine has on the profitability of the company.

The statistics based on five years of returns seems to be the best choice, since it will not be too stale and include the impact of the recent developments.

The statistics based on the seven years would be considered too stale, as a lot has changed from seven years ago to now.

The statistics based on the three years may be considered too recent and skewed more towards the recent development.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

12. Data Staleness. Download all available monthly returns for Tesla, Inc. (TSLA) from Yahoo! Finance and calculate the average and standard deviation of monthly returns using the latest one-year, three-year, five-year, and seven-year periods all ending at the end of 2020. If you were asked to use one of these sets of statistics as a proxy for your future expectations for TSLA returns, which would you choose?

Why? (LO 5-6) Answer: 1-Years Average = 3-Years Average = 5-Years Average = 7-Years Average =

23.27% 8.99% 6.12% 5.32%

Similar problem as Problem 11.

The date this solution was written is mid October 2021. Thus, the adjusted close price that will be attributed to October 2021 is not for the full month, and it is best not to use it.

The returns for 1-year, 3-year, 5-year, and 7-year periods all ending at the end of 2020 are shown in the Excel file.

For 1-year returns, we include the adjusted close price of December 2019, so that we calculate the monthly return for January 2020.

For 3-year returns, we include the adjusted close price of December 2017, so that we calculate the monthly return for January 2018.

For 5-year returns, we include the adjusted close price of December 2015, so that we calculate the monthly return for January 2016.

For 7-year returns, we include the adjusted close price of December 2013, so that we calculate the monthly return for January 2014.

The results are provided in the Excel file and below.

1-Year Returns 3-Year Returns 5-Year Returns 7-Year Returns

Average 22.98% 9.22% 6.16% 5.17%

Standard Deviation 30.33% 23.28% 19.34% 17.71%

The statistics based on five years of returns seems to be the best choice, since it will not be too stale and will include the impact of the recent developments.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

13. Effective Interest Rates. You are offered a credit card with an APR of 21.4%, based on monthly compounding. What is the annual effective rate? If you took a cash advance of $100 against that card and made no payments for an entire year, how much would you owe at the end of that year? (LO 5-7) Answer: APR Compound per year Loan

21.4% 12 $100.00 Effective rate = Amount owed =

23.63% $123.63

To calculate the effective annual rate, we use the following formula that converts annual nominal rate or APR into effective rate.

REffective = (1+

Rnominal n ) −1 n

Where, Rnominal is the annual nominal rate Reffective is the annual effective rate n is the number of compounding periods per year Reffective = (1 + 0.214/12)12 − 1 = 0.2363 or 23.63%

In order to calculate the value of $100 cash advance at the end of the year, we have to use the effective annual rate to find the effective interest that is charged by the card over the year: Interest = $100 × 0.2363 = $23.63 The amount owed at the end of the year = $100 + 23.63 = $123.63 You can also use the Excel solution, which is based on Excel functions.

14. Nominal Interest Rates. A load has an annual effective rate of 9.38%. For monthly compounding, what is the annual percentage rate? What is the monthly rate charged? (LO 5-7) Answer: Effective Rate = 9.38% Compound per year = 12

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17

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

APR = 9.00% Monthly Rate = 0.75% To calculate the nominal annual rate or APR, we use the following formula that converts annual effective rate into nominal rate or APR. Rnominal = n × [(REffective + 1)1/ n − 1]

This formula is derived from the formula given below.

REffective = (1+

Rnominal n ) −1 n

Where, Rnominal is the annual nominal rate.

Reffective is the annual effective rate. n is the number of compounding periods per year.

To solve for the problem: Rnominal = 12 × [(0.0938+1)1/12 − 1] = 0.09 or 9%

The monthly rate is the annual rate divided by 12: Rnominal/12 = 9/12 = 0.75%.

You can also use the Excel solution, which is based on Excel functions.

15. Standard Deviation. You expect the economy to go through a boom, bust, or remain steady with probabilities of 0.3, 0.3, and 0.4. You are considering investing in a stock that you think will yield an HPR of 20% in a boom, −33% in a bust, and 6% in a steady state. What are your expected return and standard deviation in returns for that stock? (LO 5-8) Answer: State Boom Bust Steady

Probability 0.30 0.30 0.40

E(r) = Std Dev =

−1.50% 21.42%

HPR 20% −33% 6%

Squared Deviations 0.046225 0.099225 0.005625

The expected return is calculated using the following formula:

Probabilistic Expected Return = E (r ) =

n

( p × r ) t =1

t

t

Where,

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18

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

pt is the probability for each outcome. rt is the return for each outcome.

The standard deviation is calculated using the following formula:

σ =

n

 p × r − E (r )  t =1

2

t

t

The expected return is: E(r) = (0.3 × 20) + (0.3 × −33) + (0.4 × 6) = −1.5%

The expected standard deviation is: 2

2

= .3 × 20% + 1.5% + .3 × − 33% + 1.5% + .4 × 6% + 1.5%

2

= 21.42% Note in the expected standard deviation formula, the sign change to plus (+) is because the expected return value is negative. That is why the difference is changed to addition in this particular problem.

16. Probabilistic Expected Return. You know the past five annual returns of a stock to be 18%, −5%, 11%, −23%, and 8%. However, you believe that the −23% return is less likely to occur in the future than the rest. Thus, you place a probability of 0.08 on that return and 0.23 on each of the other four returns. What is the probabilistic expected return? (LO 5-4) Answer: Probability 0.23 0.23 0.23 0.08 0.23

HPR 18% −5% 11% −23% 8%

Probabilistic Expected Return = 5.52% Similar to Problem 15.

Expected Return = (0.23 × 18) + (0.23 × −5) + (0.23 × 11) + (0.08 × −23) + (0.23 × 8) = 5.52%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

17. Distribution Normality. Download all available monthly returns for NVIDIA Corporation (NVDA) from the Yahoo! Finance site. Create histograms for NVDA’s monthly returns for the past five years and for all available monthly returns ending in 2020. Which histogram seems to show NVDA as being closer to a normal distribution? (LO 5-9) 5-Year Analysis Min Return = −25.16% Max Return = 38.40% Mean = Std Dev =

5.50% 12.80%

Bin Start −40% −30% −20% −10% Bin Start 0% 10% 20% 30% 40%

Bin Frequency −40% 0 −30% 0 −20% 3 −10% 2 Bin Frequency 0% 13 10% 22 20% 12 30% 6 40% 2 More 0

Histogram of NVDA (5 years of monthly returns) 25

Frequency

20 15 10 5 0 -40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Bin

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Max Data Analysis Min Return = −48.66% Max Return = 82.62% Mean = Std Dev = Bin Start −90% −80% −70% −60% −50% −40% −30% −20% −10% Bin Start 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

3.71% 18.04% Bin Frequency −90% 0 −80% 0 −70% 0 −60% 0 −50% 0 −40% 1 −30% 6 −20% 15 −10% 28 Bin Frequency 0% 56 10% 77 20% 42 30% 19 40% 9 50% 3 60% 4 70% 0 80% 1 90% 1 More 0

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Histogram of NVDA (maximum monthly returns) 90 80 70

Frequency

60 50 40 30 20 10 0

Bin

Answer: The maximum data appears much closer to a normal distribution than the five years of data.

When we download data from Yahoo! as monthly adjusted close price, this Adjusted Close column is the price as of the end of the month, beginning on the date shown under the date column.

The date this solution was written is mid October 2021. Thus, the adjusted close price that will be attributed to October 2021 is not for the full month, and it is best not to use it. When you download data from Yahoo! in the future, you will have more data that will be downloaded.

To download all available monthly data for NVDA from Yahoo! finance, select “Max” for the time period and “Monthly” for frequency.

Calculate the monthly returns using adjusted close prices. Note that the data will be downloaded in ascending order, i.e., the oldest data will appear in the first row (2/1/1999).

Calculate the returns using adjusted close prices. As mentioned, the first row with date 2/1/1999 is the adjusted close price at the end of February, which coincides to beginning of March. Therefore, the first return we can calculate will be for March 1999. Also note that the last row in the Excel sheet shows the date of 10/1/2021.

This problem was solved in mid-October, and the data was downloaded in midOctober as well. Therefore, this row does not provide the adjusted close price for the full month of October 2021, so it is best not to use this last row.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Calculate the maximum return and the minimum return in order to get an idea about the range for the bins. Also, you can calculate the average and the standard deviation. The range can be selected from –90% to 90% because there are some positive returns with values close to 90% and to have symmetry in the values for the bins. (Bins can be selected in a variety of ways.)

Use the Histogram function in the data analysis toolpak under the data tab to create the histogram.

Select the input range and insert all the return values calculated in that box.

Select the bin range and insert the bin range values in that box.

In order to have the frequency distribution and the chart show in the same Excel sheet, select the output range and select where you want the bin frequency to show up (for example, under column O).

Finally, click the checkmark for chart output.

The second question, the analysis of the last 5 years of data can be done in the same Excel sheet or copy the data to another sheet. Select the monthly data for the past five years ending 2020, so you have to include the years 2016 to 2020. In order to calculate the return for the month of January 2016, the adjusted closing price of 12/1/2015 should also be included. This is the adjusted close price of end of December 2015, which is the beginning of January 2016. We will have 61 data points to calculate 60 monthly returns over a 5-year period.

The rest of the steps is similar to the previous part.

The bin range is selected from –40% to 40% because there are some returns close to 40% and to have the symmetry in the bin range.

We notice the histogram of the maximum data is much closer to the normal distribution than the 5-year monthly data.

18. Distribution Normality. Download all available monthly returns for Citigroup Inc. (C) from the Yahoo! Finance site. Create histograms for C’s monthly returns for the past five years and for the past 10 years ending in 2020. Which histogram seems to show C as being closer to a normal distribution? (LO 5-9) 5-Year Analysis Min Return = −33.63% Max Return = 32.96% Mean = Std Dev =

0.84% 10.40%

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23

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Bin Start −40% −30% −20% −10% 0% 10% 20% 30% 40%

Bin −40% −30% −20% −10% 0% 10% 20% 30% 40% More

Frequency 0 1 0 6 19 25 7 1 1 0

Histogram of Citigroup (5 years of monthly returns) 30

Frequency

25 20 15 10 5 0 -40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Bin

10-Year Analysis Min Return = −33.63% Max Return = 32.96% Mean = Std Dev = Bin Start −40% −30% −20% −10% 0% 10%

0.68% 9.53% Bin Frequency −40% 0 −30% 1 −20% 0 −10% 12 0% 38 10% 53

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24

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

20% 30% 40%

20% 30% 40% More

13 2 1 0

Histogram of Citigroup (10 years of monthly returns) 60

Frequency

50 40 30 20 10 0 -40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Bin

Answer: For Citigroup, using five years of data looks similar to using ten years of data.

This problem is a similar to Problem 17.

The date this solution was written is mid October 2021. Thus, the adjusted close price that will be attributed to October 2021 is not for the full month, and it is best not to use it.

The earlier adjusted close price will be for 1/1/1985.

The problem is asking to create the histograms for 5 years of returns ending in 2020 and 10 years of returns ending in 2020. The solution is provided in separate Excel sheets.

For the five year of monthly returns, note that we include the adjusted close price of 12/1/2015, the adjusted price at the end of December 2015 to calculate the monthly return for January 2016; we will have 61 data to calculate 60 monthly returns over a five year period.

The bins range is selected from –40% to 40%.

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25

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

For the 10 years of monthly returns, we include the adjusted close price of 12/1/2010, the adjusted price at the end of December 2010 to calculate the monthly return for January 2011; we will have 121 data to calculate 120 monthly returns over a 10-year period.

The bins range is selected from –40% to 40%.

The 10-year monthly return’s histogram looks very similar to the 5-year monthly return’s histogram. They are both close to the normal distribution.

19. Relationship Between Risk and Return. Download data from the Yahoo! Finance site to compute five years of monthly returns ending at the end of 2020 for the following four stocks: Citigroup (C), NVIDIA (NVDA), Tesla (TSLA), and Pfizer (PFE).

Compute the average and standard deviation of returns for each stock, graphing that average and standard deviation for each of the four stocks on a scatter plot.

Does there seem to be a positive relationship between risk and return over those five years? Why or why not? (LO 5-10)

Risk Versus Return 7% Tesla

6%

Average Return

NVIDIA 5% 4% 3% 2% 1% 0% 0.00%

Pfizer 5.00%

Citigroup 10.00%

15.00%

20.00%

25.00%

St Dev

Answer: Average Return Citigroup 1.04% NVIDIA 5.53% Tesla 6.16% Pfizer 0.79%

Std Dev. 10.50% 12.80% 19.34% 6.02%

The slope is upward sloping as expected. However, Citigroup appears to have earned less than it should have, given its risk.

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26

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

The Excel file contains the data downloaded from Yahoo! Finance for the four stocks.

For 5-year returns, we include the adjusted close price of December 2015, so that we calculate the monthly return for January 2016.

Risk vs. Return 7.00%

TSLA NVDA

6.00%

Std. Dev.

5.00% 4.00% 3.00% 2.00%

C

PFE

1.00% 0.00% 0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

Average

The scatter diagram shows the upward trend between risk and return. The higher the risk, the higher the return. Only for Citigroup stock C, the return seems to be slightly low compared to the risk.

20. Risk and Return Relationship. Graph risk versus return for the following 10 stocks on the same scatter plot. Do they show a positive relationship between risk and return? Which stocks stick out? Why? ch05_pr20.xlsx (LO 5-10) Stock 1 Stock 2 Stock 3 Stock 4 Stock 5 Stock 6 Stock 7 Stock 8 Stock 9 Stock 10 Return

6%

12%

4%

16%

8%

3%

21%

6%

5%

17%

Std Dev.

12%

17%

7%

21%

8%

4%

32%

10%

8%

29%

Answer: The slope is generally positively sloped between risk and return. Stock 5 appears to have earned more return than its risk merits and dominated Stock 9 because it has a higher return with the same risk.

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27

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Risk vs Return 25%

Stock 7 Average Return

20%

Stock 4 15%

Stock 10

Stock 2 10%

Stock 5 Stock 8

5%

Stock 6

0% 0%

Stock 1 Stock 9 Stock 3

5%

10%

15%

20%

25%

30%

35%

Std Dev

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28

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Case Study 1. Download all available historical monthly adjusted prices for Pfizer Inc. (PFE) and use it to answer the following questions: a. Over what one year calendar (January to December) holding period was the HPR the highest? The lowest? Research these time periods and provide an intuitive explanation or why. b. Graph the average and standard deviation in monthly returns for all the one year holding periods you used above, then graph all these combination of average and standard deviation in returns on a scatter plot. Over time, has PFE always consistently had higher average returns when the standard deviation was highest? Give examples to support your answer. c. Is the distribution of PFE monthly returns normally distributed? Provide a histogram to assess the distribution.

Answer: When we download all available historical monthly adjusted prices for Pfizer Inc. (PFE) from Yahoo! Finance, the data starts at 1/1/1985, which is the adjusted monthly price at the end of January 1985. We do not have the prior month’s (December 1984) adjusted close price data; therefore, we cannot calculate the returns for the year 1985 for the full year with 12 returns. Therefore, to have full 12 monthly returns per year, we start with the year 1986.

The table below presents the summary results for each year, the annual holding period return, the monthly average return, and the monthly standard deviation.

1) We notice the highest 1-year holding period return was for the year 1991 with an HPR of 112.77% and the lowest 1-year holding period return was for the year 2004 with an HPR of −22.30%.

Pfizer is a large pharmaceutical company that has been around for many years and has introduced numerous different drugs to consumers over the years. In 1991, Pfizer introduced the antidepressant drug “Zoloft” to the market. This is the most likely reason why the return 1991 was so high. Zoloft was a highly successful drug for Pfizer.

In 2003, Pfizer merged with another pharmaceutical company, Pharmacia.

Finance research has provided mixed evidence on the mergers, but mostly the research tends to show the underperformance of acquirers in the short term.

Furthermore, in 2004, Pfizer’s patent for the drug Lyrica was challenged in courts. In addition, Pfizer had legal issues and problems and in 2004 had to pay substantial fines to settle those legal issues. Those events are the most likely reasons why the holding period return in 2004 was the lowest.

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29

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Annual HPR 23.99% −21.37% 29.29% 24.17% 20.32% 112.77% −11.96% −2.28% 15.31% 66.70% 33.99% 81.92% 68.92% −21.50% 43.06% −12.47% −22.16% 17.75% −22.30% −10.63% 15.26% −8.14% −16.96% 8.20% 0.32% 28.78% 20.43% 26.21% 5.28% 7.09% 4.42% 15.90% 24.82% −6.91% 3.07%

Average Monthly Return 2.14% −1.48% 2.30% 1.99% 1.94% 6.88% −0.90% 0.10% 1.40% 4.42% 2.60% 5.44% 4.85% −1.63% 3.36% −0.97% −1.90% 1.50% −2.03% −0.71% 1.35% −0.61% −1.39% 1.10% 0.20% 2.26% 1.62% 2.04% 0.47% 0.72% 0.48% 1.29% 1.96% −0.46% 0.70%

Monthly Standard Deviation 8.57% 10.07% 5.65% 6.24% 9.36% 9.55% 5.70% 7.95% 6.68% 3.90% 5.32% 8.62% 9.12% 8.81% 8.54% 5.38% 5.94% 5.34% 3.42% 6.87% 5.91% 4.47% 5.60% 9.62% 6.19% 5.32% 3.68% 4.34% 3.11% 5.70% 5.14% 3.51% 4.59% 5.28% 10.15%

2) The scatter plot for Pfizer is shown below. There is a general positive trend line between the return and risk; however, this trend is not consistent for all the years. Actually, we notice on the graph too many inconsistencies regarding this positive relationship between the return and risk.

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30

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

a) For the different years where Pfizer's returns were negative, the different returns below the x-axis, the return did not match the level of risk; i.e., there was negative return for the positive risk taken, so the positive relationship between risk and return did not hold. b) Even for years when the return was positive, not every year saw the return compensated for the level of risk. For instance, for years 1996, 2011, and 2003, the risk was about the same for those three years, yet the returns varied. So for the same level of risk, there were different returns. c) Also, if we look at the rightmost side of the graph, we notice during the periods when the standard deviation was the highest, the returns varied considerably. There was very wide variation in the returns for high standard deviations. For example, in year 2020, the return was very low compared to the amount of risk (very high).

Pfizer Returns and Std. Deviation 8.00% 1991 7.00% 1997 1998

Average Monthly Return

6.00% 5.00%

1995

4.00%

2000 1996 1988 2011 2013 1989 2018 2012 2003 1994 2006 2017 2015 2016 2014 2010

3.00% 2.00% 1.00% 0.00% 0.00% -1.00%

2.00%

2007 2019 2005 1992 2001 4.00% 6.00% 2008 2002 2004

1986 1990 2009 2020 1993 8.00% 1999

10.00% 1987

12.00%

-2.00% -3.00%

Monthly Standard Deviation

d) The histogram provided below shows that the data is very close to the normal distribution.

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31

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 05: Measuring Return and Risk

Histogram

160 140 Frequency

120 100 80 60

Frequency

40 20 More

30%

25%

20%

15%

10%

5%

0%

-5%

-10%

-15%

-20%

-25%

-30%

0

Bin

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32

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 34

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Questions 1. Relationship Between Risky Assets. Why can two risky assets be combined into a portfolio that has less risk? (LO 6–1) Answer: Two risky assets from different sectors can be combined to lower the overall risk of a portfolio, without significantly affecting the expected returns. This principle is commonly referred to as diversification. The overall risk can be minimized only if the correlation of the expected returns between the two risky assets is negative. Since the assets chosen belong to different or diverse sectors, it is referred to as diversification.

When we combine two risky assets to form a portfolio of two assets, the stock price movements of those two assets determine the risk of the portfolio. Sometimes the two stock price movements will be in the same direction, while at other times they will be in the opposite direction. The direction between two stock price movements is the reason there may be a portfolio with less risk why when we combine those two stocks.

2. Comovement of Risky Assets. Describe the relationship between correlation of asset returns and diversification potential. (LO 6–2) Answer: Correlation coefficient or correlation is a statistical variable, often presented using the Greek letter ρ. The correlation is a relative measure of comovement between two variables. It describes the strength of the linear relationship between two variables. The correlation coefficient values can be only between –1 and +1. A correlation value of +1 means that returns from two different assets are perfectly in sync and that they will move perfectly together in tandem. Assets with a correlation of +1 do not provide any diversification benefit. A correlation value of –1 means that returns from two assets are perfectly inversely correlated and that they will move opposite to each other. A correlation value of 0 means that returns from two assets do not have any linear relationship between each other. The best opportunity for diversification and risk reduction occurs with assets that have negative correlation.

If you cannot find assets with negative correlation, assets with low positive correlation value provide some diversification benefits. Assets with high positive correlation value provide few diversification benefits.

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2

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

3. Asset Classes and Diversification. Which asset class has the best potential for combining into a portfolio for greater diversification? Why? (LO 6–3) Answer: The asset class with the best potential for combining into a portfolio for greater diversification among the asset classes discussed is bonds. Table 6-2 presents the correlation between different asset classes. The one asset class with negative correlation with all other asset classes is the Long-Term Treasury Bond asset class, which is proxied by the Vanguard Long-Term Treasury Fund Investor Shares (VUSTX) in this table. The table also shows that the largest negative correlation is the one between the S&P 500 Index and the Long-Term Treasury Bonds. Therefore, the text concludes that your portfolio should consist of both stocks and bonds to reduce risk no matter whether you are primarily a stock investor or bond investor.

4. Portfolio Risk. Portfolio return is the weighted average of the asset returns in the portfolio. Explain why portfolio standard deviation of returns is not the weighted average of the asset risks. (LO 6–4) Answer: The portfolio standard deviation includes the correlation term between the assets in the portfolio; because of that the portfolio standard deviation is not the weighted average of the asset risks. The formula for the standard deviation is:

σ Port =

 w ×σ +   2 × w × w × ρ ×σ ×σ N 2 i =1 i

2 i

N

i =1

N j =1 j ≠i

i

j

i, j

i

j

As we can see, the formula includes the correlation term in the second summation part. Because of the presence of the correlation variable, the portfolio standard deviation of returns is not the weighted average of the asset risks.

Only in a very special case, when the correlation coefficient among every asset in the portfolio is 0 (meaning ρi,j = 0 for all securities i and j included in the portfolio), does the portfolio standard deviation become equal to the weighted average of the assets risks because the double summation part will become equal to 0. However, this special case is extremely rare.

5. Dominating Portfolios. How do some portfolios dominate others? What does that mean? (LO 6–5) Answer: A portfolio can dominate others if for the same level of risk, it provides a higher return. For example, suppose Portfolio A has an expected return of 10% and risk given by the standard deviation of 8%, while Portfolio B has an expected return of 12% and standard deviation of 8%. Portfolio B would dominate Portfolio A because

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3

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

it provides a higher return for the same level of risk. Therefore, an investor who would be willing to take a risk of 8% should take Portfolio B, not A. Also, a portfolio can dominate others if the return it provides is higher while the risk it has is lower than other portfolios. Suppose Portfolio X has a return of 12% and a risk of 7%, while Portfolio Y has a return of 11% and a risk of 9%. In this example, Portfolio X dominates Portfolio Y because it has higher return and less risk.

Therefore, Portfolio 1 dominates Portfolio 2 if: • •

Portfolio 1 has higher return than Portfolio 2 and Portfolio 1’s risk is less or equal to Portfolio 2.

Portfolio 1 has higher or equal return to Portfolio 2 and Portfolio 1 has less risk than Portfolio 2.

Use of dominance principle asserts that those assets which show higher expected returns for the given level of risk will be selected. Dominant assets are called efficient portfolios whether they contain two or more assets. An aggressive investment strategy typically refers to a style of portfolio management that attempts to maximize returns by taking a relatively higher degree of risk. ... Such a strategy would therefore have an asset allocation with a substantial weighting in stocks and possibly little or no allocation to bonds or cash.

6. Diversifiable and Undiversifiable Risk. What kinds of risk can be diversified away through portfolio construction? What kinds of risks are not diversified away? (LO 6– 6) Answer: When we create a portfolio of risky assets, the unsystematic, company-specific, or diversifiable risk can be diversified, whereas the systematic, market, or undiversifiable risk cannot be diversified.

Systematic risk is the risk inherent to the market that investors are compensated for and that cannot be diversified no matter how well the portfolio is constructed.

Examples of systematic risk include inflation, macroeconomic factors, and environmental factors like climate change, natural disasters, and pandemics such as Covid-19, etc.

Unsystematic risk is diversifiable risk. Examples include managerial talent, employee strike, a new competitor entering a market, etc.

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4

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

7. Minimum Variance Portfolio. What is the minimum variance portfolio and why is it important? (LO 6–7) Answer: The minimum variance portfolio is a well-diversified portfolio containing all risky assets located on the efficient frontier with the lowest possible variance or risk. This portfolio will be dominant for that level of risk (lowest risk) and thus will provide the best return for the minimum risk that is has. It is important for an investor to know what the minimum variance portfolio is because that is the portfolio on the efficient frontier, which means it will provide the best risk-return combination possible and is a dominant portfolio. Therefore, if an investor wants an efficient portfolio with the lowest possible risk, the minimum variance portfolio is the best choice.

8. Efficient Portfolios. What makes a portfolio efficient? (LO 6–8) Answer: An efficient portfolio is either a portfolio that offers the highest expected return for a given level of risk, or one with the lowest level of risk for a given expected return. It is efficient because all risk taken results in expected return. The line that connects all these efficient portfolios is the efficient frontier.

9. Utility Theory. What does utility measure in the context of selecting a portfolio? (LO 6–9) Answer: Utility is a measure of a person’s welfare or satisfaction. In the context of risky portfolios, utility can be represented as a score to assess how much a person is better or worse off between portfolio choices with different risk and expected return characteristics. A popular utility equation is:

U = E (r ) −

1 Aσ 2 2

The variable A is a measure of a person’s level of risk aversion. The higher the value, the more a person doesn’t want to take risk. Risk is measured by the variance of returns, σ2. The equation shows that the utility is higher with higher expected return but lower with a higher risk. More risk-averse investors (as denoted with larger A) demand a higher expected return in order to invest in higher-risk portfolios. Also, for the same level of expected return and risk, a more risk-averse investor will have a lower utility score than a less-risk averse investor.

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5

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

10. Optimal Portfolio. What is the optimal portfolio for an investor? Do other investors desire that portfolio. Why? (LO 6–10) Answer: The optimal portfolio for a particular investor is the one on the efficient frontier that maximizes their utility. The optimal portfolio will be located at the intersection of the indifference curve and the efficient frontier. The indifference curve represents the utility function of each investor; in other words, the indifference curve represents the investor’s preferences for risk and return. Any point on the same indifference curve will have the same utility to the investor.

Different investors will have different optimal portfolios because each investor has different levels of risk aversion, and therefore a different indifference curve. So the indifference curve of one investor generally is different from that of another investor.

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Problems 1. Covariance. Compute the covariance between each of the three pairs of stocks A, B, and C with returns shown as: The data are in the file ch6_pr01.xlsx. (LO 6–2) Return A 12.0% −5.0% 3.0% 17.0% 8.5% −5.7% 8.6% 10.4%

Return B 5.2% −7.5% 8.4% 10.6% 9.4% 2.1% 3.7% 12.5%

Return C −1.5% 6.0% 11.3% 3.0% 18.6% 5.6% −6.8% 8.9%

Answer: COVa,b = COVa,c = COVb,c =

0.38% −0.11% 0.14%

The covariance can be calculated using the following formula:

 {(r − average return ) × (r − average return )} Covariance = N

ij

t =1

it

i

jt

j

N −1

We have to calculate first the average returns of each of the stocks A, B, and C. Average Return A = (12.0 − 5.0 + 3.0 + 17.0 + 8.5 − 5.7 + 8.6 + 10.4) / 8 = 6.1% Average Return B = (5.2 − 7.5 + 8.4 + 10.6 + 9.4 + 2.1 + 3.7 + 12.5) / 8 = 5.55% Average Return C = (−1.5 + 6.0 + 11.3 + 3.0 + 18.6 + 5.6 − 6.8 + 8.9) / 8 = 5.64% Covariance A,B = [(0.12 − 0.061) × (0.052 − 0.0555) + (−0.05 − 0.061) × (−0.075 − 0.0555) + (0.03 − 0.061) × (0.084 − 0.0555) + (0.17 − 0.061) × (0.106 − 0.0555) + (0.085 − 0.061) × (0.094 − 0.0555) + (−0.057 − 0.061) × (0.021 − 0.0555) + (0.086 − 0.061) × (0.037 − 0.0555) + (0.104 − 0.061) × (0.125 − 0.0555)] / 7 = 0.0038 or 0.38% Covariance A,C = [(0.12 − 0.061) × (−0.015 − 0.0564) + (−0.05 − 0.061) × (0.06 − 0.0564) + (0.03 − 0.061) × (0.113 − 0.0564) + (0.17 − 0.061) × (0.03 − 0.0564) + (0.085 − 0.061) × (0.186 − 0.0564) + (−0.057 − 0.061) × (0.056 − 0.0564) + (0.086−0.061) × (−0.068 − 0.0564) + (0.104 − 0.061) × (0.089 − 0.0564)] / 7 = −0.0011 or −0.11% Covariance B,C = [(0.052 − 0.0555) × (−0.015 − 0.0564) + (−0.075 − 0.0555) × (0.06 − 0.0564) + (0.084 − 0.0555) × (0.113 − 0.0564) + (0.106 − 0.0555) × (0.03 − 0.0564) + (0.094 − 0.0555) × (0.186 − 0.0564) + (0.021 − 0.0555) × (0.056 − 0.0564) + (0.037 − 0.0555) × (−0.068 − 0.0564) + (0.125 − 0.0555) × (0.089 − 0.0564)] / 7 = 0.0014 or 0.14%

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7

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

2. Correlation. Compute the correlation between each of the three pairs of stocks A, B, and C with returns shown as: The data are in the file ch6_pr02.xlsx. (LO 6–2) Return A 12.0% −5.0% 3.0% 17.0% 8.5% −5.7% 8.6% 10.4%

Return B 5.2% −7.5% 8.4% 10.6% 9.4% 2.1% 3.7% 12.5%

Return C −1.5% 6.0% 11.3% 3.0% 18.6% 5.6% −6.8% 8.9%

Answer: CORRa,b = 0.74 CORRa,c = −0.18 CORRb,c = 0.28 The correlation coefficient can be calculated with the following formula: Correlationij = ρij =

covarianceij σi × σ j

We already calculated the covariance in problem #1. In order to calculate the correlation coefficients, we need the standard deviation of each return.

Covariance A, B = 0.0038 Covariance A, C = − 0.0011 Covariance B, C = 0.0014 Standard Deviation Return A = {[(0.12 − 0.061)2 + (−0.05 − 0.061)2 + (0.03 − 0.061)2 + (0.17 − 0.061)2 + (0.085 − 0.061)2 + (−0.057 − 0.061)2 + (0.086 − 0.061)2 + (0.104 − 0.061)2 ] / 7 }1/2 = 0.08 or 8% Note the expression in the curly bracket, {}, should be taken to the square root; here we take it to the power 0.5 for that purpose.

Standard Deviation Return B = {[(0.052 − 0.0555)2 + (−0.075 − 0.0555)2 + (0.084 − 0.0555)2 + (0.106 − 0.0555)2 + (0.094 − 0.0555)2 + (0.021 − 0.0555)2 + (0.037 − 0.0555)2 + (0.125 − 0.0555)2] / 7}1/2 = 0.06 or 6% Standard Deviation Return C = {[(−0.015 − 0.0564)2 + (0.06 − 0.0564)2 + (0.113 − 0.0564)2 + (0.03 − 0.0564)2 + (0.186 − 0.0564)2 + (0.056 − 0.0564)2 + (−0.068 − 0.0564)2 + (0.089 − 0.0564)2]/7}1/2 = 0.08 or 8% Correlation A, B = 0.0038 / (0.08 × 0.06) = 0.79 Correlation A, C = −0.0011 / (0.08 × 0.08) = −0.17 Correlation B, C = 0.0014 / (0.06 × 0.08) = 0.29

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Note that there is a slight difference in the values given here vs. the values in the Excel sheet, and that is due to the rounding that was done in the calculations using formulas.

3. Correlation of Asset Classes. Compute the correlation between each of the three pairs of asset class returns shown. Which pairs of asset classes are the best to combine to reduce risk? The data are in the file ch6_pr03.xlsx. (LO 6–3) Answer: CORR(Russell,Bonds) CORR(Russell,French) CORR(Bonds,French)

−0.52 0.39 −0.70

1st best to combine = Bonds and French stocks 2nd best to combine = Russell 2000 and Bonds 3rd best to combine = Russell 2000 and French stocks In order to calculate the correlations between the three pairs of asset class returns, using formulas, we have to follow the procedures explained in problems 1 and 2.

Using formulas, calculate the average return for each of the three returns in the table. Since there are 12 data points in each return series, the average return is the sum of those returns divided by 12.

Average Return of Russell 2000 = 0.254% Average Return of Long-term Treasuries = 0.977% Average Return of French Stocks = 2.795% Then calculate the covariance between each pair of returns; the covariance is calculated using similar to the approach used in problem 1. The covariance is calculated between two pairs of returns, where the difference between the return and its average for each pair is multiplied and all those products together summed, and finally that sum is divide d by 11 (the divisor is the number of data points minus 1).

Covariance (Russell 2000, Treasuries) = − 0.00077 Covariance (Russell 2000, French Stocks) = 0.002531 Covariance (Treasuries, French Stocks) = −0.00109 Also, the standard deviations of each of the asset class returns must be calculated.

The standard deviation is calculated by taking the square root of the sum squared of the difference between each return value from its average return and then dividing those squared sums by 11.

Standard deviation Russell 2000 = 7.902% Standard deviation Long-term Treasuries = 1.858% Standard deviation French stocks = 8.289%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Finally to calculate the values of correlations, we divide the covariance by the standard deviation of each pair: Correlation (Russell 2000, Treasuries) = −0.00077 / (0.07902 × 0.01858) = −0.525 Correlation (Russell 2000, French Stocks) = 0.002531 / (0.07902 × 0.08289) = 0.3864 Correlation (Treasuries, French Stocks) = −0.00109 / (0.01858 × 0.08289) = −0.7077 Notice that it is much easier to use the CORREL function in Excel to calculate the correlations between different return series, especially when the returns consist of several data values.

To reduce risk, we choose the asset classes with the lowest correlations. The lowest correlation is between Treasuries and French stocks. The next lowest correlation is between Russell 2000 and Treasuries, and finally the highest correlation is between Russell 2000 and French stocks.

4. Portfolio Return. Stock X had a return of 8.5% last year. Stocks Y and Z earned −2.3% and 11.8%, respectively. What is the portfolio return under the following scenarios? (LO 6–4) a. The portfolio is equally weighted with the stocks. b. The portfolio holds stocks X, Y, and Z with weights 0.5, 0.3, and 0.2, respectively. c. The portfolio holds stocks X, Y, and Z with weights 0.25, 0.4, and 0.35, respectively.

Answer:

X Y Z

Return 8.50% −2.30% 11.80% Portfolio Return =

Portfolios Weights A Weights B Weights C 0.25 0.333 0.5 0.4 0.333 0.3 0.35 0.333 0.2 6.00%

5.92%

5.34%

The portfolio return is calculated using the following formula: E (rP ) =

 w × E (r ) N

i =1

i

i

Where wi is the portfolio weight, or percentage, devoted to a given security i, and E(ri) is the expected rate of return on security i.

Portfolio Return = (0.333 × 8.5%) + (0.333 × −2.3%) + (0.333 × 11.8) = 6% (Equally weighted means 1/3 = 0.333 of the allocation is done for each stock).

Portfolio Return = (0.5 × 8.5%) + (0.3 × −2.3%) + (0.2 × 11.8%) = 5.92% Portfolio Return = (0.25 × 8.5%) + (0.4 × −2.3%) + (0.35 × 11.8%) = 5.34%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

5. Portfolio Return. Given the returns below, what is the average portfolio return of a portfolio with weights of 0.4 in the Russell 2000, 0.4 in Treasuries, and 0.2 in French stocks? The data are in the file ch6_pr05.xlsx. (LO 6–4) Answer: Weight (Russell) Weight (Bonds) Weight (French)

Portfolio 0.40 4.25% 0.40 4.32% 0.20 0.38% −0.62% 1.82% −3.62% −7.82% 1.35% 2.95% 4.25% 2.89% 2.46% Average = 1.05%

There are two methods to solve this problem. The first method is to calculate the portfolio return for each row in the table using the weights given in the problem for the portfolio and then find the average portfolio return by calculating the average value as it is done in the Excel file.

The second method is to find the average return for each of the three assets and then find the return of the portfolio. Both methods will give the same answer.

First, calculate the average return of each asset: Average Return Russell 2000 = (7.390 + 4.082 + 0.460 − 5.440 + 0.169 − 8.229 − 19.488 + 7.587 + 4.007 + 5.180 + 6.087 + 1.247) / 12 = 0.2543% Average Return Long-term Treasuries = (−0.706 + 0.086 + 0.428 + 1.835 + 2.385 − 0.522 + 4.858 + 3.328 − 1.705 + 0.906 − 0.163 + 0.990) / 12 = 0.977% Average Return French Stocks = (7.875 + 13.25 + 0.145 + 4.129 + 4.016 − 0.622 − 9.865 − 15.066 + 10.162 + 9.096 + 2.583 + 7.841) / 12 = 2.795% The portfolio return will be: (0.4 × 0.2543) + (0.4 × 0.977) + (0.2 × 2.795) = 1.05%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

6. Portfolio Risk. Stock X has a standard deviation of 3.5% last year. Stocks Y and Z have risk levels of 6.3% and 4.8%, respectively. The correlation between the stocks is ρ(X,Y) = 0.2, ρ(X,Z) = 0.7, ρ(Y,Z) = −0.2. What is the portfolio standard deviation under the following scenarios? (LO 6–4) a. The portfolio is equally weighted with the stocks. b. The portfolio holds stocks X, Y, and Z with weights 0.5, 0.3, and 0.2, respectively. c. The portfolio holds stocks X, Y, and Z with weights 0.25, 0.4, and 0.35, respectively.

Answer: St. Dev. X 3.50% Y 6.30% Z 4.80%

Portfolios Weights A 0.333 0.333 0.333

Weights B 0.5 0.3 0.2

Correlations X,Y 0.2 X,Z 0.7 Y,Z −0.2

Squares Var 0.001225 0.003969 0.002304

Portfolio St. Dev. =

3.25% 3.24%

Weights C 0.25 0.4 0.35

Weights A 0.111111 0.111111 0.111111

Weights B 0.25 0.09 0.04

Weights C 0.0625 0.16 0.1225

3.34%

The portfolio standard deviation is calculated using the following formula: σPort =

 w ×σ +   2×w ×w ×ρ ×σ ×σ N

i =1

2 i

2 i

N

i =1

N j =1 j ≠i

i

j

i,j

i

j

Where wi and wj are the portfolio weights in securities i and j, respectively; σi2 is the variance of returns for individual securities; σi is the standard deviation of returns; and ρi,j is the correlation of returns for securities i and j.

Equally Weighted Portfolio means we have the weights in each stock equal to 1/3 = 0.3333.

St. Dev. Portfolio = [0.3332 × 3.52 + 0.3332 × 6.32 + 0.3332 × 4.82 + 2 × 0.333 × 0.333 × 3.5 × 6.3 × 0.2 + 2 × 0.333 × 0.333 × 3.5 × 4.8 × 0.7 + 2 × 0.333 × 0.333 × 6.3 × 4.8 × −0.2]1/2 = 3.25% Note that if we keep the standard deviation as a percentage in the formula, the answer will also be in percentage terms. Also, the expression in the brackets should be taken to the square root; here we take it to the power 0.5 for that purpose.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

St. Dev. Portfolio = [0.52 × 3.52 + 0.32 × 6.32 + 0.22 × 4.82 + 2 × 0.5 × 0.3 × 3.5 × 6.3 × 0.2 + 2 × 0.5 × 0.2 × 3.5 × 4.8 × 0.7 + 2 × 0.3 × 0.2 × 6.3 × 4.8 × −0.2]1/2= 3.24% St. Dev. Portfolio = [0.252 × 3.52 + 0.42 × 6.32 + 0.352 × 4.82 + 2 × 0.25 × 0.4 × 3.5 × 6.3 × 0.2 + 2 × 0.25 × 0.35 × 3.5 × 4.8 × 0.7 + 2 × 0.4 × 0.35 × 6.3 × 4.8 × −0.2]1/2= 3.34% 7. Portfolio Risk. Given the returns below, what is the standard deviation of return of a portfolio with weights of 0.4 in the Russell 2000, 0.4 in Treasuries, and 0.2 in French stocks? The data are in the file ch6_pr07.xlsx. (LO 6–4) Answer: Weight (Russell) Weight (Bonds) Weight (French)

0.40 0.40 0.20

St. Dev. =

Portfolio 4.25% 4.32% 0.38% −0.62% 1.82% −3.62% −7.82% 1.35% 2.95% 4.25% 2.89% 2.46% 3.63%

We already calculated the standard deviations and correlations for those three asset class returns in problem 3.

Standard deviation Russell 2000 = 7.902% Standard deviation Long-term Treasuries = 1.858% Standard deviation French stocks = 8.289% Correlation (Russell 2000, Treasuries) = −0.00077 / (0.07902 × 0.01858) = −0.525 Correlation (Russell 2000, French Stocks) = 0.002531 / (0.07902 × 0.08289) = 0.3864 Correlation (Treasuries, French Stocks) = −0.00109 / (0.01858 × 0.08289) = −0.7077 The portfolio with weights of 0.4 in the Russell 2000, 0.4 in Treasuries, and 0.2 in French stocks will have the following standard deviation: Standard deviation = [0.42 × 7.9022 + 0.42 × 1.8582 + 0.22 × 8.2892 + 2 × 0.4 × 0.4 × 7.902 × 1.858 × −0.525 + 2 × 0.4 × 0.2 × 7.902 × 8.289 × 0.3864 + 2 × 0.4 × 0.2 × 1.858 × 8.289 × −0.7077]1/2 = 3.6236% Notice again that it is much easier and less time consuming to use Excel.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

8. Portfolio Return and Risk. You own a portfolio with an expected return of 9.5% and standard deviation of 14.8%. You are considering reallocating 20% of the portfolio to a different asset class that has an expected return of 11% and standard deviation of 17%. The correlation between your portfolio and the other asset class is 0.7. What would be your new return and risk and how much did they change?

(LO 6–4) Answer:

Return St. Dev.

Current New Portfolio Asset 9.50% 11% 14.80% 17%

Correlation

0.7

Allocation

80%

Return St. Dev.

New Portfolio Difference 9.80% 0.30% 14.43% −0.37%

20%

The formulas used here are the same as used in the above problems.

After the reallocation, you will have 80% invested in the old portfolio and 20% in the new asset class.

Expected Return of New Portfolio = (0.8 × 9.5) + (0.2 × 11) = 9.8% Standard Deviation of New Portfolio = [0.82 × 14.82 + 0.22 × 172 + 2 × 0.8 × 0.2 × 14.8 × 17 × 0.7]1/2 = 14.43% The change in the expected return was an increase by 0.3%, from 9.5% to 9.8%.

The change in the standard deviation was a decrease by 0.37% from 14.8% to 14.43%.

9. Dominating Portfolios. Consider Stock Blue and Stock Red. Given the scenarios below, does one stock dominate the other? (LO 6–5) a. Stock Blue has a return and risk of 6% and 8%, while Stock Red has a return and risk of 5% and 7%. b. Stock Blue has a return and risk of 6% and 8%, while Stock Red has a return and risk of 6% and 7%. c. Stock Blue has a return and risk of 6% and 8%, while Stock Red has a return and risk of 5% and 9%.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Answer: Part A Blue Red

Avg. 6.0% 5.0%

Part B Avg. 6.0% 6.0%

St. Dev. 8.0% 7.0%

Part C Avg. 6.0% 5.0%

St. Dev. 8.0% 9.0%

St. Dev. 8.0% 7.0%

Ret Diff 1.0%

Ret Diff 0.0%

Ret Diff 1.0%

Risk Diff 1.0%

Risk Diff 1.0%

Risk Diff −1.0%

Stock Blue has a return of 6%, while Stock Red has a return of 5%; Stock Blue has risk of 8%, while Stock Red has a risk of 7%. In this scenario, there is no dominating stock. Stock Blue has a higher risk and thus a higher return.

Stock Blue has a return of 6%, while Stock Red has a return of 6%. Both stocks have the same return. Stock Blue has a risk of 8%, while Stock Red has a risk of 7%. Stock Red has lower risk. In this scenario, Stock Red is the dominating stock because it provides the same return as Stock Blue but at lower risk; therefore, Stock Red dominates Stock Blue.

Stock Blue has a return of 6%, while Stock Red has a return of 5%; Stock Blue has a risk of 8%, while Stock Red has a risk of 9%. Stock Blue has a higher return than Stock Red and has lower risk than Stock Red. In this scenario, Stock Blue is the dominating stock because it provides a higher return than Stock Red and has lower risk; therefore, Stock Blue dominates Stock Red. 10. Minimum Variance Portfolio. Find the minimum variance portfolio. What is the standard deviation? What is the allocation to the three asset classes? The data are in the file ch6_pr10.xlsx. (LO 6–7) Answer: Portfolio 11.78% 19.37% 18.91% −14.40%

U.S. Large Cap Emerging Markets Gold Sum =

Weights 46.1% 0.0% 53.9% 100.0%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Portfolio 25.16% 22.66% 6.07% 10.85% −0.46% 5.04% −5.18% 9.78% 16.89% −3.13% 24.06%

Weights Avg. return = St. Dev. =

9.83% 11.81% Used Solver: minimize J11 by changing J5:J7 with contraints of J5:J7 <= 1 and J8 =1

This problem is solved using Excel, following the procedure described in the textbook.

The first step is to select any arbitrary weights for the three stocks (there is no requirement that you have to select any particular weight for each stock). The text uses 33.33% for each stock. The weights are in Excel cells J5-J7. Also, in cell J8 calculate the sum of those weights, which should tally to 1. It is important to use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the three stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H5-H19. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as is done in cells J10 and J11.

To find the minimum variance portfolio, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver select the cell where you calculated the standard deviation, which is J11.

In the following line, click on Min, to minimize the value of the standard deviation and thus find the minimum variance portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J5 to J7.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1, and the sum of the weights is equal to 1. Using the locations of the weights and the sum in the Excel file, the 4 constraints will be as follows:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Cell J5 <= 1 Cell J6 <= 1 Cell J7 <= 1 Cell J8 = 1 Those are the steps to follow, finally making sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The standard deviation of the minimum variance portfolio is 11.81%. (The return is 9.83%.)

The allocation is 46.1% in U.S. Large Cap, 0% in Emerging Markets, and 53.9% in Gold.

Note: The Excel file shows the values of the standard deviations for each stock return in cells C21, D21, and E21. Those values are not necessary to solve the problem above; it just gives you an idea that the minimum variance portfolio has its standard deviation smaller than the three individual stocks’ standard deviation.

11. Minimum Variance Portfolio. Find the minimum variance portfolio. What is the standard deviation? What is the allocation to the three asset classes? The data are in the file ch6_pr11.xlsx. (LO 6–7) Answer: Portfolio 11.51% 30.76% −3.81% −40.09% 32.15% 21.13% 0.86% 18.15% 14.54% 16.69% 0.36% 6.23% 13.65% −9.18% 27.81%

U.S. Mid Cap European REIT Sum =

Weights 17.9% 28.5% 53.6% 100.0%

Avg. return = St. Dev. =

9.38% 18.44% Used Solver: minimize J11 by changing J5:J7 with contraints of J5:J7 <= 1 and J8 =1

This problem is solved using Excel, following the procedure described in the textbook. (Exact same approach as problem 10.)

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

The first step is to select any arbitrary weights for the three stocks; there is no requirement that you have to select any particular weight for each stock. The text uses 33.33% for each stock. The weights are in Excel cells J5-J7. Also, in cell J8 calculate the sum of those weights, which should tally to 1. It is important to use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the three stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H5-H19. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as done in cells J10 and J11.

To find the minimum variance portfolio, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver select the cell where you calculated the standard deviation, which is J11.

In the following line, click on Min, to minimize the value of the standard deviation and thus find the minimum variance portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J5 to J7.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1.

Using the locations of the weights and the sum in the Excel file, the four constraints will be as follows: Cell J5 <= 1 Cell J6 <= 1 Cell J7 <= 1 Cell J8 = 1 Those are the steps to follow, finally making sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The standard deviation of the minimum variance portfolio is 18.44%. (The return is 9.38%.)

The allocation is 17.9% in U.S. Mid Cap, 28.5% in European Stocks, and 53.6% in REIT. Note: The Excel file shows the values of the standard deviations for each stock return in cells C21, D21, and E21. Those values are not necessary to solve the

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

problem above, but it gives you an idea that the minimum variance portfolio has its standard deviation smaller than the three individual stocks’ standard deviation.

12. Efficient Portfolio. Given the three assets and returns below, find the highest return portfolio that has a standard deviation of 17%. What is the average return?

What is the allocation to the three asset classes? The data are in the file ch6_pr12.xlsx. (LO 6–8) Answer: Portfolio 11.52% 19.08% 14.66% −35.59% 35.92% 17.23% −1.28% 15.38% 18.32% 9.25% −3.31% 11.35% 22.57% −6.25% 27.68%

U.S. Large Cap Emerging Markets Gold Sum =

Weights 69.6% 19.6% 10.8% 100.0%

Avg. return = St. Dev. =

10.44% 17.00% Used Solver: maximize J10 by changing J5:J7 with contraints of J5:J7 <= 1 and J8 =1 and J11=0.17

This problem is solved using Excel, following the procedure described in the textbook.

The first step is to select any arbitrary weights for the three stocks; there is no requirement that you have to select any particular weight for each stock. The text uses 33.33% for each stock. The weights are in Excel cells J5-J7. Also, in cell J8 calculate the sum of those weights, which should tally to 1. It is important that you use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the three stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H5-H19. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as done in cells J10 and J11.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

To find the highest return portfolio with a standard deviation equal to 17%, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver select the cell where you calculated the return, which is J10.

In the following line, click on Max, to maximize the value of the return and thus find the highest return portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J5 to J7.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1.

Also, the value of the standard deviation should equal 17% or 0.17. Using the locations of the weights, the sum in the Excel file and the standard deviation cell, the five constraints will be as follows: Cell J5 <= 1 Cell J6 <= 1 Cell J7 <= 1 Cell J8 = 1 Cell J11 = 0.17 Those are the steps to follow, finally making sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The maximum return is 10.44%. That is the highest return portfolio for the set standard deviation of 17%.

The standard deviation of this portfolio should be calculated as 17%, since that’s what we set as constraint.

The allocation is 69.6% in U.S. Large Cap, 19.6% in Emerging Markets, and 10.8% in Gold.

Note: The Excel file shows the values of the standard deviations for each stock return in cells C21, D21, and E21. Those values are not necessary to solve the problem above. In this problem it can give you an idea as to whether setting a portfolio with a standard deviation of 17% is feasible.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

13. Efficient Portfolio. Given the three assets and returns below, find the highest return portfolio that has a standard deviation of 20.5%. What is the average return?

What is the allocation to the three asset classes? The data are in the file ch6_pr13.xlsx. (LO 6–8) Answer: Portfolio 10.51% 28.11% 11.73% −43.95% 34.13% 10.41% −9.06% 19.46% 27.46% −1.24% −1.85% 2.38% 24.76% −13.38% 25.88%

U.S. Mid Cap European REIT Sum =

Weights 26.8% 73.2% 0.0% 100.0%

Avg. return = St. Dev. =

8.36% 20.50% Used Solver: maximize J10 by changing J5:J7 with contraints of J5:J7 <= 1 and J8 =1 and J11=0.205

This problem is solved using Excel, following the procedure described in the textbook. (Similar problem to problem 12.)

The first step is to select any arbitrary weights for the three stocks; there is no requirement that you have to select any particular weight for each stock. The text uses 33.33% for each stock. The weights are in Excel cells J5-J7. Also, in cell J8 calculate the sum of those weights, which should tally to 1. It is important that you use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the three stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H5-H19. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as done in cells J10 and J11.

To find the highest return portfolio with a standard deviation equal to 20.5%, we have to use the Solver tool in Excel. The Solver can be found under the Data tab.

Once you open the solver, you have to do the following:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

In the “Set Objective” cell in Solver select the cell where you calculated the return, which is J10.

In the following line, click on Max, to maximize the value of the return and thus find the highest return portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J5 to J7.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1. Also, the value of the standard deviation should equal 20.5% or 0.205. Using the locations of the weights, the sum in the Excel file and the standard deviation cell, the five constraints will be as follows: Cell J5 <= 1 Cell J6 <= 1 Cell J7 <= 1 Cell J8 = 1 Cell J11 = 0.205 Those are the steps to follow, finally making sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The maximum return is 8.36%. That is the highest return portfolio for the set standard deviation of 20.5%.

The standard deviation of this portfolio should be calculated 20.5%, since that’s what we set as constraint.

The allocation is 26.8% in U.S. Mid Cap, 73.2% in European Stocks, and 0% in REIT. Note: The Excel file shows the values of the standard deviations for each stock return in cells C21, D21, and E21. Those values are not necessary to solve the problem above. In this problem it can give you an idea as to whether setting a portfolio with a standard deviation of 20.5% is feasible.

14. Efficient Portfolio. Given the three assets and returns below, find the lowest risk portfolio that has a return of 10.2%. What is the standard deviation of return? What is the allocation to the three asset classes? The data are in the file ch6_pr14.xlsx.

(LO 6–8) Answer: Portfolio 9.77%

U.S. Large Cap

Weights 69.7%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

18.24% 13.62% −28.62% 29.62% 18.49% 2.16% 13.92% 15.57% 8.95% −2.72% 10.93% 20.35% −4.70% 27.42%

Emerging Markets Gold Sum =

7.5% 22.8% 100.0%

Avg. return = St. Dev. =

10.20% 14.46% Used Solver: minimize J11 by changing J5:J7 with contraints of J5:J7 <= 1 and J8 =1 and J10=0.102

This problem is solved using Excel, following the procedure described in the textbook.

The first step is to select any arbitrary weights for the three stocks; there is no requirement that you have to select any particular weight for each stock. The text uses 33.33% for each stock. The weights are in Excel cells J5-J7. Also, in cell J8 calculate the sum of those weights, which should tally to 1. It is important that you use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the three stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H5-H19. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as done in cells J10 and J11.

To find the lowest risk portfolio with a return set to 10.2%, which means finding the standard deviation of the portfolio with a return equal to 10.2%, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver, select the cell where you calculated the standard deviation, which is J11.

In the following line, click on Min, to minimize the value of the standard deviation and thus find the lowest risk portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J5 to J7.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1.

Also, the value of the return should equal 10.2% or 0.102. Using the locations of the weights, the sum in the Excel file and the return cell, the five constraints will be as follows: Cell J5 <= 1 Cell J6 <= 1 Cell J7 <= 1 Cell J8 = 1 Cell J10 = 0.102 Those are the steps that you will need to follow, finally making sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The minimum standard deviation 14.46%. That is the lowest risk for this portfolio for the set return of 10.2%.

The return of this portfolio should be calculated 10.2%, since that’s what we set as constraint.

The allocation is 69.7% in U.S. Large Cap, 7.5% in Emerging Markets, and 22.8% in Gold.

Note: The Excel file shows the values of the standard deviations for each stock return in cells C21, D21, and E21 and the values of the average returns for each stock in cells C22, D22, and E22. Those values are not necessary to solve the problem above. In this problem, it can give you an idea at to whether setting the return of this portfolio to 10.2% will provide a feasible solution.

15. Efficient Portfolio. Given the three assets and returns below, find the lowest risk portfolio that has a return of 9.3%. What is the standard deviation of return? What is the allocation to the three asset classes? The data are in the file ch6_pr15.xlsx.

(LO 6–8) Answer: Portfolio 11.41% 31.22% −3.76% −40.13% 31.95% 20.75% 0.72%

U.S. Mid Cap European REIT Sum =

Weights 15.6% 30.4% 54.0% 100.0%

Avg. return = St. Dev. =

9.30% 18.45%

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24

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

18.25% 14.21% 16.37% 0.37% 5.99% 13.74% −9.27% 27.67%

Used Solver: minimize J11 by changing J5:J7 with contraints of J5:J7 <= 1 and J8 =1 and J10=0.093

This problem is solved using Excel, following the procedure described in the textbook. (Similar problem to problem 14 above.)

The first step is to select any arbitrary weights for the three stocks; there is no requirement that you have to select any particular weight for each stock. The text uses 33.33% for each stock. The weights are in Excel cells J5-J7. Also, in cell J8 calculate the sum of those weights, which should tally to 1. It is important that you use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the three stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H5-H19. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as done in cells J10 and J11.

To find the lowest risk portfolio with a return set to 9.3%, which means finding the standard deviation of the portfolio with a return equal to 9.3%, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver select the cell where you calculated the standard deviation, which is J11.

In the following line, click on Min, to minimize the value of the standard deviation and thus find the lowest risk portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J5 to J7.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1.

Also, the value of the return should equal 9.3% or 0.093. Using the locations of the weights, the sum in the Excel file and the return cell, the 5 constraints will be as follows: Cell J5 <= 1 Cell J6 <= 1

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25

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Cell J7 <= 1 Cell J8 = 1 Cell J10 = 0.093 Those are the steps that you will need to follow, finally make sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The minimum standard deviation 18.45%. That is the lowest risk for this portfolio for the set return of 9.3%.

The return of this portfolio should be calculated 9.3% since that’s what we set as constraint.

The allocation is 15.6% in US Mid Cap, 30.4% in European Stocks and 54% in REIT. Note: The Excel file shows the values of the standard deviations for each stock return in cells C21, D21 and E21; and the values of the average returns for each stock in cells C22, D22 and E22. Those values are not necessary to solve the problem above. In this problem, it can give you an idea whether setting the return of this portfolio to 9.3% will provide a feasible solution.

16. Efficient Portfolios. Given the four asset classes and returns below, find the portfolio indicated. What is the standard deviation of return and the allocation to the four asset classes? The data are in the file ch6_pr16.xlsx. (LO 6–8) a. Minimum variance portfolio. b. Portfolio with the lowest risk and a return of 9%. c. Portfolio with the lowest risk and a return of 10%.

Answer: Portfolio 22.28% 24.71% 33.12% −13.34% 40.46% 25.98% 0.60% 10.41% −21.01% −1.36% −12.19% 9.13%

European Pacific Emerging Gold Sum =

Weights 0.0% 0.0% 31.6% 68.4% 100.0%

Avg. return = St. Dev. =

10.00% 18.33%

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26

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Portfolio 18.61% −5.98% 18.58%

Weights

This problem is solved using Excel, following the procedure described in the textbook.

The first step is to select any arbitrary weights for the four stocks; there is no requirement that you have to select any particular weight for each stock. We can use 25% for each stock. The weights are in Excel cells J8-J11. Also, in cell J12 calculate the sum of those weights, which should tally to 1. It is important that you use the sum function and calculate the sum to be equal to 1.

The second step is to calculate the return of the portfolio composed of the four stocks, for each row of data, using the weights selected in step 1. The calculation of the portfolio return is provided in cells H8-H22. Once we have those returns, we can calculate the average return of the portfolio and the standard deviation of the portfolio as done in cells J14 and J15.

Part A To find the minimum variance portfolio, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver select the cell where you calculated the standard deviation, which is J15.

In the following line, click on Min, to minimize the value of the standard deviation thus to find the minimum variance portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J8 to J11.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1.

Using the locations of the weights and the sum in the Excel file, the four constraints will be as follows: Cell J8 <= 1 Cell J9 <= 1 Cell J10 <= 1 Cell J11<= 1 Cell J12 = 1

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27

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Those are the steps that you will need to follow, finally make sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

The standard deviation of the minimum variance portfolio is 12.92%. (The return is 8.02%.)

The allocation is 0% in European Stocks, 45.2% in Pacific Rim Stocks, 0% in Emerging Markets, and 54.8% in Gold.

Note: The Excel file shows the values of the standard deviations for each stock return in cells C24, D24, E24, and F24. Those values are not necessary to solve the problem above, but it gives you an idea that the minimum variance portfolio has its standard deviation smaller than the four individual stocks’ standard deviation.

Part B To find the lowest risk portfolio with a return set to 9%, which means finding the standard deviation of the portfolio with a return equal to 9%, we have to use the Solver tool in Excel. The Solver can be found under the Data tab. Once you open the solver, you have to do the following: In the “Set Objective” cell in Solver select the cell where you calculated the standard deviation, which is J15.

In the following line, click on Min, to minimize the value of the standard deviation thus to find the lowest risk portfolio.

In the “By Changing Variable Cells” cell in Solver select the cells that have the values of the weights, which will be cells J8 to J11.

To add the constraints, click on “Add” button and add the constraints such that the weight of each stock is less than or equal to 1 and the sum of the weights is equal to 1.

Also, the value of the return should equal 9% or 0.09. Using the locations of the weights, the sum in the Excel file and the return cell, the five constraints will be as follows: Cell J8 <= 1 Cell J9 <= 1 Cell J10 <= 1 Cell J11 <= 1 Cell J12 = 1 Cell J14 = 0.09 Those are the steps that you will need to follow, finally making sure that the box entitled “Make Unconstrained Variables Non-Negative” is checked. Finally, click on the Solve button to get the solution.

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28

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

The minimum standard deviation 14.39%. That is the lowest risk for this portfolio for the set return of 9%.

The return of this portfolio should be calculated 9%, since that’s what we set as constraint.

The allocation is 14.5% in European Stocks, 2.5% in Pacific Rim Stocks, 0% in Emerging Markets, and 83% in GOLD. Note: The Excel file shows the values of the standard deviations for each stock return in cells C24, D24, E24, and F24 and the values of the average returns for each stock in cells C25, D25, E25 and F22. Those values are not necessary to solve the problem above. In this problem, it can give you an idea as to whether setting the return of this portfolio to 9% will provide a feasible solution.

Part C Part C is solved in exact same fashion as part B, except the value of the return is set to 10%. All you have to do is to change the value of cell J14 to 0.10 in the constraints of the Solver and solve the problem.

The minimum standard deviation 18.33%. That is the lowest risk for this portfolio for the set return of 10%.

The return of this portfolio should be calculated 10%, since that’s what we set as constraint.

The allocation is 0% in European Stocks, 0% in Pacific Rim Stocks, 31.6% in Emerging Markets, and 68.4% in GOLD. 17. Utility. An investor with risk aversion of A = 3 reviews the four investments shown below. What utility does the investor get with each investment? Which should the investor choose? (LO 6–9) Investment A B C D

Expected Return 15% 10% 20% 8%

Standard Deviation 19% 17% 25% 12%

Answer: A B C D

Utility 0.0959 0.0567 0.1063 0.0584

A B C D

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29

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Choose

0.1063

C

The utility is calculated using the following equation: U = E (r ) −

1 2 Aσ 2

The variable A is a measure of a person’s level of risk aversion. The variance of returns is σ2. The expected return is E(r).

We calculate the utility for each of the investments A, B, C, and D. Utility of Investment A = 0.15 − (0.5 × 3 × 0.192) = 0.0959 Utility of Investment B = 0.10 − (0.5 × 3 × 0.172) = 0.0567 Utility of Investment C = 0.20 − (0.5 × 3 × 0.252) = 0.1063 Utility of Investment D = 0.08 − (0.5 × 3 × 0.122) = 0.0584 The Investment with the highest utility value is investment C; therefore, the investor should choose investment C. 18. Utility. Consider an investor with risk aversion of A = 4. The investor owns a portfolio with expected return of 10% and standard deviation of 15%. (LO 6–9) a. If an alternative portfolio had an expected return of 12%, what standard deviation would it need for the investor to be indifferent? b. Should the investor switch to a portfolio with expected return of 8% and standard deviation of 11%? Why or why not?

Answer: current utility =

0.055

a.

St. Dev. =

18.03%

b.

utility = Switch?

0.0558 yes

The utility is calculated using the following equation: U = E (r ) −

1 2 Aσ 2

The variable A is a measure of a person’s level of risk aversion. The variance of returns is σ2. The expected return is E(r).

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30

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

A) In order for the investor to be indifferent regarding the alternative portfolio, the utility of the two portfolios should be equal. That is, the investor’s owned portfolio’s utility should equal the utility of the alternative portfolio.

The utility of the owned portfolio is U = 0.1 − (0.5 × 4 × 0.152) = 0.055 Therefore, the utility of the alternative portfolio should also equal 0.055. We solve for the value of the standard deviation by using the same formula above. We use the letter S for the standard deviation: 0.055 = 0.12 − (0.5 × 4 × S2) 2S2 = 0.12 − 0.055 = 0.065 S2 = 0.0325 (This is the variance) S = 0.1803 or 18.03% (Taking the square root of the 0.0325) B) We first calculated the utility of the new portfolio in part B, and if the utility of this new portfolio is higher than the original portfolio owned by the investor, then that investor should switch.

Utility = 0.08 − (0.5 × 4 × 0.112) = 0.0558.

The utility of the original portfolio owned by the investor was 0.055; since the utility of this new portfolio is higher, then the investor should switch to this new portfolio.

19. Indifference Curves. Consider an investor with risk aversion of A = 3 and utility of 0.08. (LO 6–9) a. Compute the expected returns for which this investor would be indifferent for standard deviations of 7%, 10%, 13%, 16%, 20%, and 25%. b. Graph this indifference curve.

Answer: U= A= σ 7% 10% 13% 16% 20% 25%

0.08 3 Expected Return 8.74% 9.50% 10.54% 11.84% 14.00% 17.38%

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31

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

The expected return is calculated using the following equation: E (r ) = U +

1 2 Aσ 2

The variable A is a measure of a person’s level of risk aversion. The variance of returns is σ2. The utility is given by U. In this example, the utility value is 0.08, and we have to calculate the expected return for each of the values of the standard deviation given.

Standard deviation 7%; E(r) = 0.08 + (0.5 × 3 × 0.072) = 0.0874 or 8.74% Standard deviation 10%; E(r) = 0.08 + (0.5 × 3 × 0.102) = 0.0950 or 9.50% Standard deviation 13%; E(r) = 0.08 + (0.5 × 3 × 0.132) = 0.1054 or 10.54% Standard deviation 16%; E(r) = 0.08 + (0.5 × 3 × 0.162) = 0.1184 or 11.84% Standard deviation 20%; E(r) = 0.08 + (0.5 × 3 × 0.202) = 0.14 or 14% Standard deviation 25%; E(r) = 0.08 + (0.5 × 3 × 0.252) = 0.1738 or 17.38%

Indifference Curve 19%

17%

Expected Return

15%

13%

11%

9%

7%

5% 5%

10%

15%

20%

25%

Risk (Standard Deviation)

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32

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

20. Optimal Portfolio. Consider an investor with risk aversion of A = 3 is examining the portfolios along the efficient frontier. (LO 6–10) a. Compute the investor’s utility for each portfolio. b. Which of these would be the optimal portfolio?

Return St. Dev.

8.0% 9.0%

9.0% 9.2%

9.9% 9.8%

10.5% 10.4%

11.5% 11.9%

12.5% 14.0%

13.4% 17.0%

14.4% 21.0%

0.0846

0.0888

0.0938

0.0956

0.0907

0.0779

Answer: utility =

0.0679 0.0773

Optimal Portfolio at Maximum Utility 0.0956 The utility is calculated using the following equation: U = E (r ) −

1 2 Aσ 2

The variable A is a measure of a person’s level of risk aversion. The variance of returns is σ2. The expected return is E(r).

There are eight different return and risk measures in the table above; therefore, we will calculate the utility of each of those eight return and risk combinations.

Utility 1 = 0.08 − (0.5 × 3 × 0.092) = 0.0679 Utility 2 = 0.09 − (0.5 × 3 × 0.0922) = 0.0773 Utility 3 = 0.099 − (0.5 × 3 × 0.0982) = 0.0846 Utility 4 = 0.105 − (0.5 × 3 × 0.1042) = 0.0888 Utility 5 = 0.115 − (0.5 × 3 × 0.1192) = 0.0938 Utility 6 = 0.125 − (0.5 × 3 × 0.142) = 0.0956 Utility 7 = 0.134 − (0.5 × 3 × 0.172) = 0.0907 Utility 8 = 0.144 − (0.5 × 3 × 0.212) = 0.0779 Utility 6 is the highest with a value of 0.0956; therefore, the investor’s optimal portfolio is the one with expected return of 12.5% and risk of 14% given in standard deviation value.

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33

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Case Study Portfolios with Standard & Poor’s Sectors The famous S&P 500 Index represents Standard & Poor’s eleven sectors of the economy.

You can invest in the market as a whole through several available S&P 500 Index exchange traded funds (ETFs). You can also focus a portfolio on one or more sectors through Standard & Poor’s SPDR ETFs. All eleven sectors have an associated SPDR ETF. However, only nine of them have been available for at least ten years. The file, ch6_case_data.xlsx, shows 10 years of monthly returns for the nine sector ETFs with available data (prices obtained from Yahoo! Finance).

The sectors are Consumer Discretionary, Consumer Staples, Energy, Financials, Health Care, Industrials, Materials, Technology, and Utilities. The two missing sectors are Communications Services and Real Estate.

This case explores the risk/return relationships between the sectors and the various portfolios that can be formed with them. a. Compute the average monthly returns and standard deviation of returns for each of the nine sectors. What do you notice about the risk and return of these sectors? b. Compute the correlation between each of the nine sectors. What sector(s) appears to be less correlated with the others? c. Compute the minimum variance portfolio. What is the standard deviation and sector allocation for this portfolio? What do you observe about the portfolio allocation? d. Compute eight points on the efficient frontier and show the efficient frontier on a graph.

Answer: a. The average monthly return and the monthly standard deviation for each of the nine sectors based on the data above is given in the table below.

S&P Sector Consumer Discretionary Consumer Staples Energy Financials Health Care Industrials Materials Technology

Average Return 1.51% 0.96% 0.42% 1.36% 1.33% 1.21% 1.01% 1.71%

Standard Deviation 4.48% 3.40% 7.82% 5.19% 3.80% 4.73% 4.91% 4.50%

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34

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

Utilities

0.89%

4.08%

We notice some variations in the average return and the risk between different sectors. Interestingly, the Energy sector had the lowest average return of 0.42%, with the highest risk of 7.82%. The Technology sector had the highest return of 1.71% and a risk of 4.50%. The next sector with the second highest return was Consumer Discretionary with a return of 1.51% and a risk of 4.48%.

The graph of the Risk – Return relationship is given below. We notice that some sectors dominate others. The Energy sector does not provide the return for the level of risk it has. The Technology sector dominates Consumer Discretionary and, provides a higher return for almost the same amount of risk. (The difference between the Technology sector risk and the Consumer Discretionary sector is 0.02%.) Also we notice both Consumer Staples and Health Care sectors dominate Utilities. Health Care dominates Utilities, Materials, and Industrials sectors.

Risk - Return Technology Consumer Discretionary

1.80% 1.60%

Financials Health Care Industrials

1.40%

Return

1.20% Consumer Staples Utilities

1.00%

Materials

0.80% 0.60%

Energy

0.40% 0.20% 0.00% 0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

Standard Deviation

b. The correlations between the nine sectors is given in the table below.

Consumer Discretionary

Consumer Health Energy Financials Industrials Materials Technology Utilities Staples Care

Consumer Discretionary Consumer Staples

0.6635

Energy

0.6595

0.4010

Financials

0.7551

0.5343

0.7230

© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

35

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification Consumer Discretionary

Consumer Health Energy Financials Industrials Materials Technology Utilities Staples Care

Health Care

0.7519

0.6608

0.4752 0.6447

Industrials

0.8242

0.6475

0.7114 0.8666

0.7014

Materials

0.7983

0.5435

0.6936 0.7766

0.7000 0.8715

Technology

0.8416

0.6007

0.5476 0.6659

0.6497 0.7478

0.7242

Utilities

0.2807

0.6202

0.1350 0.1962

0.3533 0.2855

0.2150

0.2428

The correlation table shows that the Utilities sector has the lowest correlation with the other eight sectors. The lowest correlation is between Utilities and Energy with a correlation value of 0.1350, while the other sectors have higher correlation with each other. The highest correlation is between the Financials sector and the Industrials sector with a correlation of 0.8666. c. The minimum variance portfolio has a standard deviation of 3.097% with a return of 1.127%.

The allocation of the minimum variance portfolio is provided in the table below.

Consumer Discretionary Consumer Staples Energy Financials Health Care Industrials Materials Technology Utilities

Minimum Variance Portfolio 0.00% 31.38% 0.00% 0.73% 27.87% 0.00% 0.00% 10.86% 29.16%

The allocation among different sectors in the minimum variance portfolio is 31.38% in Consumer Staples, 0.73% in Financials, 27.87% in Health Care, 10.86% in Technology, and 29.16% in Utilities.

To find the minimum variance portfolio, we follow the procedure explained in the text, by using the Solver tool in Excel. The objective is to Minimize the standard deviation, by changing the weights with constraints that each weight is less than or equal to 1 and the sum of the weights equals to 1. d. The efficient frontier graph is provided below.

To calculate the different points on the efficient frontier, we follow the procedure explained in the text, by using the Solver tool in Excel. The objective is to Maximize the return, by changing the weights, with the constraints that each weight is less than or equal to 1 and the sum of the weights equals to 1. In doing so, we have to

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36

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 06: Portfolios and Diversification

use a particular value for the standard deviation as constraint. For example, if you select a standard deviation of 3.5%, you have to include that as a constraint, and Solver will find the maximum return for this standard deviation chose. You will repeat this procedure for several values chosen for the standard deviation.

1.80% 1.70% 1.60%

Return

1.50% 1.40% 1.30% 1.20% 1.10% 1.00% 2.50%

3.00%

3.50%

4.00%

4.50%

5.00%

Standard Deviation

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37

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 8 Case Study ....................................................................................................................................... 24

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Questions 1. Capital Allocation Line. How does adding a risk-free asset allow investors to obtain better opportunities than the efficient frontier? (LO 7-1) Answer: The risk-free asset by definition has no risk therefore it is located on the y-axis.

When combining the risk-free asset with the efficient frontier, the opportunity set expands, and the new opportunity set available to the investors is a straight line originating from the risk-free asset, which is tangent to the efficient frontier. The tangent line intersects with the efficient frontier in only one place. The intersection is depicted as portfolio P in the chapter. This line is called the Capital Allocation Line (CAL). You can see that the CAL dominates the efficient frontier in the graph shown below, because the portfolios on the CAL provide a higher return for the same level of risk than the portfolios on the efficient frontier. Only portfolio P, which is the common portfolio among the two, has the same return for its level of risk.

2. Optimal Portfolio. What are the dynamics involved in assessing your optimal portfolio on the capital allocation line? (LO 7-2) Answer: The optimal portfolio for an investor is the one that will provide the highest utility and will be located on the CAL. The optimal portfolio is the one with the highest indifference curve that is tangent to the capital allocation line. This particular optimal portfolio will be a combination of the risk-free asset and the portfolio P. An investor can achieve the optimal portfolio on the CAL through owning Portfolio P and either borrowing or lending at the risk-free rate.

An optimal portfolio located on the left of Portfolio P is achieved by owning Portfolio P and owning T-Bills, which is lending at the risk-free rate. An optimal portfolio to

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2

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

the right of P must use margin and borrow at the risk-free rate and invest all money in Portfolio P. 3. Market Portfolio. What is the market portfolio? What role does it play in the CAPM? (LO 7-3) Answer: A market portfolio is a theoretical bundle of investments that includes every type of asset available in the investment universe, with each asset weighted in proportion to its total presence in the market. The expected return of a market portfolio is identical to the expected return of the market as a whole.

The market portfolio is a portfolio that consists of all risky assets in the market. By including all the risky assets, it is completely diversified portfolio and it has only systematic risk; the nonsystematic risk is eliminated by diversification.

The theoretical assumption behind the market portfolio is that all investors have the same opportunity set of risky assets and the risk-free asset. Therefore, the intersection of the line coming from the risk-free asset that is tangent to the efficient frontier is the market portfolio. All investors would invest on the CML and own the market portfolio and some combination of lending or borrowing at the risk-free rate.

The market portfolio is completely diversified, therefore all unsystematic risk is eliminated. The only risk that remains is the systematic risk, and that is the only type of risk that should be priced. CAPM is based on this assumption that only the systematic risk of a security should be rewarded with a risk premium.

4. Expected Return. What data do you need to obtain to estimate beta of a stock and its expected return? (LO 7-4) Answer: To calculate the beta of a security, the covariance between the return of the security and the return of the market must be known, as well as the variance of the market returns. Covariance measures how two stocks move together.

To compute return covariances and variances, stock returns and market returns are needed. Five years of monthly returns are most commonly used.

In order to estimate the beta of a stock, you need to obtain the covariance of the stock and the market portfolio, and the variance of the market portfolio. Beta is calculated as the ratio of the covariance of the stock and the market to the variance of the market.

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3

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

In order to calculate the expected return of the stock, using the CAPM equation, you need to already have estimated beta or obtain the value of the beta. Also, you need an estimate of the expected return on the market portfolio and the expected return on the risk-free asset. Using those three variables, you can estimate the expected return of a stock using the CAPM equation.

5. Security Market Line. What are the differences between the security market line (SML) and the capital market line? What does the SML tell you? (LO 7-5) Answer: Capital market refers to a broad spectrum of tradable assets that includes the stock market as well as other venues for trading different financial products.

The stock market allows investors and banking institutions to trade specifically in stocks, either publicly or privately. Stocks are financial instruments that represent partial ownership of a company. Stock issuance is used extensively by companies as a means of raising capital. Within the stock market itself are primary and secondary markets that trade among banks underwriting stock and public investors trading stock, respectively.

Now a standard graph shows beta values across its x-axis and expected return across its y-axis. The risk-free rate, or beta of zero, is located at the y-intercept. The purpose of the graph is to identify the action, or slope, of the market risk premium.

In financial terms, this line is a visual representation of the risk-return tradeoff.

The security market line (SML) represents the relationship between risk and return of an individual security (micro level relationship). This relationship is also represented by the CAPM. Therefore, the SML is the graph of the CAPM. The Y-axis represents the return, while the X-axis represents the risk measured by the individual security’s beta. The systematic risk is the measure of risk used in SML. The capital market line (CML) plots the return against the total risk of a portfolio.

The CML is the relationship between the risk and return of portfolios (macro level relationship). In CML graph, the Y-axis represents the return and the X-axis represents the total risk measured by the standard deviation of the portfolio.

Therefore, the differences between the SML and CML are: The CML is a macro level representation of the relationship between risk and return, while the SML is the micro level representation. CML uses the total risk measure as measure of risk, while the SML uses the systematic risk only as the risk measure.

The SML being the graph of the CAPM explains that the return on an individual asset is a function of the risk-free rate and the company’s risk premium, which is the market risk premium times the beta of the company.

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4

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

6. CAPM Assumptions. What are the basic assumptions in the CAPM theory? Which ones seem unrealistic to you? (LO 7-6) Answer: The assumption of the CAPM theory are the following: • • • • • • • • •

Securities are efficiently priced.

Investors hold efficient portfolios.

It is possible to borrow and lend as much as desired at the risk-free rate.

Investors have the same expectations about investment risk and returns.

The model has a one-period time horizon.

Investments are infinitely divisible.

There are no market frictions, like no taxes or transaction costs.

Investors fully anticipate inflation.

Capital markets are in equilibrium.

None of those assumptions are very realistic in the real world. In particular, the assumption that investors can borrow or lend as much as desired at the risk-free rate is not realistic because the vast majority of individual investors don’t have this ability. Also, investors do not always hold well-diversified efficient portfolios, and research has shown security prices are not always efficiently priced in the market.

Most investors pay taxes; although there are non-taxable accounts, but we cannot assume that there are no taxes completely. All assets being infinitely divisible is also not very realistic.

7. Finding Company Betas. Betas can be found at various financial websites. Why are the betas found for a company often different? (LO 7-7) Answer: Most likely is that the services are using different benchmarks to represent the market against which the company is compared, e.g., one might use the S&P 500, another the New York Stock Exchange Composite Index, another the MSCI EAFE. The differences among the beta numbers reported on different financial websites is likely due to how those betas are calculated and how often the website data is estimated and updated.

There is no standard approach to estimate beta. Financial analysts often use five years of monthly returns and the S&P 500 Index as the proxy for the market portfolio. However, there are cases where three years of monthly returns are also used. Therefore, the length of time selected three years of monthly returns or five years of monthly returns or something else is a factor in the discrepancy of beta among different sites. Also, the use of the proxy for the market portfolio is another

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5

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

factor of the discrepancy. Finally, the last issue is the frequency of the updates that a website does is another factor.

8. Estimating Beta. What data would you use to estimate a company’s beta? How do you assess whether the proxy for the market portfolio is a good fit? (LO 7-8) Answer: In order to estimate a company’s beta, you need to have the returns of the company over a specific period, for example monthly returns over 5-year period. Also, you need to identify the market proxy that will be used in the estimation, and collect the monthly returns of this market proxy over the same period of time. Finally, you need to have the monthly returns of the risk-free asset, for example the monthly returns of the 3-month T-bills. To do the estimations, you have to calculate the excess monthly returns of the security, which is the difference between the security’s return and the risk-free asset’s return, and the excess monthly return of the market, which is the difference between the market’s return and the risk-free asset’s return.

To assess whether the proxy for the market portfolio is a good fit, use the R-square statistics. A higher value of the R-square provides a better goodness of fit; therefore, you can know if the chosen proxy for the market portfolio is a good fit or not.

9. Issues with Estimating Beta. What are the empirical criticisms of estimating beta?

(LO 7-9) Answer: The empirical criticisms of estimating beta are related to the model specification problems that provide different estimates for the beta if different input variables are used in the model.

The choice of the market proxy impacts the estimation process and the estimated beta value. This is called Market index bias, which results in a wide range of beta estimates caused by the fact that market indexes are only imperfect proxies for the market portfolio.

The choice of the time period over which the estimation is conducted also impacts the estimation process the value of the beta. The beta estimate will differ depending on the choice of the estimation time period; this issue is called the time interval bias.

Another criticism is related to the fact that the beta estimate will vary over time. This is the nonstationary beta problem. The beta you estimate today likely differs from the one you will estimate next year.

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

10. Portfolio Beta. Given individual securities in a portfolio, explain why estimating portfolio risk is much easier through portfolio beta than through portfolio standard deviation of returns. (LO 7-10) Answer: Estimating the portfolio risk with beta as the measure of risk involves knowing the betas of the individual securities in the portfolio and the proportion of each security in the portfolio. Having those values is relatively easy. The portfolio beta is calculated as the weighted sum of the individual securities’ betas in the portfolio with the weights being the proportions invested in each security.

The formula to calculate the portfolio beta is the following: β P =

n

 w ×β . i =1 i

i

Estimating the portfolio risk using the standard deviations of returns of each security in the portfolio is a more complicated calculation. To calculate the standard deviation of the portfolio, we need to have the standard deviation of each security and the correlations between each pair of securities in the portfolio in addition to the weights of each security in the portfolio.

The formula for the standard deviation of the portfolio is the following: σ Port =



N

w i2 × σ i2 +

i =1

N

  i =1

N j =12 × w i × w j × ρ i , j × σ i × σ j j ≠i

As you can see, this formula for the standard deviation of the portfolio is much more complicated than the formula for the beta of the portfolio.

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7

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Problems 1. Portfolios on CAL. Consider a CAL in which the risk-free rate is 2%, the risky portfolio P return is 10%, and the portfolio P risk is a standard deviation of 16%.

What are the expected returns and risk levels of these 3 portfolios? (LO 7-2) a. 25% risk-fee asset and 75% portfolio P b. 50% risk-free asset and 50% portfolio P c. Borrow 20% at risk-free rate, 120% portfolio P A 25% 75%

Risk-free rate = 2% Risk-free asset = Port P return = 10% Portfolio P = Port P std Dev = 16%

B 50% 50%

C −20% 120%

Answer: A Expected Return = 8.00% Std. Dev. = 12.00%

B C 6.00% 11.60% 8.00% 19.20%

Note: for Std. Dev. Solution, solve for equation 7−1.

The two equations to solve this problem are the following: E (R ) = R free +

RP − R free

σP

(

σ

E (R ) = R free + wP * RP − R free

)

The first equation will be used to solve for the standard deviation, while the second equation will be used to solve for the expected return. Note that we need to solve for the expected return first in order to be able to solve for the standard deviation. a. In Part A, the proportion invested in portfolio P is 75%, wp = 0.75. First, we solve for the expected return, and then we use the expected return to solve for the standard deviation.

Using the second equation: E(R) = 2 + 0.75 × (10 − 2) = 8% Using the first equation: 8 = 2 + [(10 − 2)/16] × σ 8 = 2 + 0.5 × σ σ = (8 − 2) / 0.5 = 12% b. Wp = 0.5. Using the second equation: E(R) = 2 + 0.5 × (10 − 2) = 6% Using the first equation: 6 = 2 + [(10 − 2)/16] × σ 6 = 2 + 0.5 × σ σ = (6-2) / 0.5 = 8%

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8

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

c. Wp = 1.2. Using the second equation: E(R) = 2 + 1.2 × (10 − 2) = 11.6% Using the first equation: 11.6 = 2 + [(10 − 2)/16] × σ 11.6 = 2 + 0.5 × σ σ = (11.6 − 2) / 0.5 = 19.2% 2. Portfolios on CAL. Consider a CAL in which the risk-free rate is 3%, the risky portfolio P return is 11%, and the portfolio P risk is a standard deviation of 17%.

What are the allocations to the risk-free asset and portfolio P needed to obtain the following expected returns? (LO 7-2) a. 5% expected return b. 10% expected return c. 13% expected return Risk-free rate = Port P return = Port P std Dev =

Expected Return =

3% 11% 17% A 5%

B 10%

C 13%

Answer: Portfolio P weight = Risk-free Asset weight =

A 25.00% 75.00%

B 87.50% 12.50%

C 125.00% −25.00%

To solve this problem, we use the following equation:

(

E (R ) = R free + wP * RP − R free

)

Using this equation, we solve for the Wp, the weight invested in portfolio P and then find the weight in the risk-free asset. a. 5 = 3 + Wp × (11 − 3) 5 − 3 = 8 Wp Wp = 2 / 8 = 0.25 or 25% The weight in the Risk-free is equal to: Wfree = 1 − Wp = 1 − 0.25 = 0.75 or 75%. b. 10 = 3 + Wp × (11 − 3) 10 − 3 = 8 Wp Wp = 7/8 = 0.875 or 87.5% The weight in the Risk-free is equal to: Wfree = 1 − Wp = 1 − 0.875 = 0.125 or 12.5%.

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9

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

c. 13 = 3 + Wp × (11 − 3) 13 − 3 = 8Wp Wp = 10/8 = 1.25 or 125% The weight in the Risk-free is equal to: Wfree = 1 − Wp = 1 − 1.25 = − 0.25 or −25%.

3. Portfolios on CML. The market portfolio has earned an average of 12% per year with a standard deviation of 18%. T-bills currently yield 1.5%. What are the expected return and asset allocation characteristics of portfolios with the following risk? (LO 7-3) a. 5% standard deviation b. 18% standard deviation c. 21% standard deviation Risk-free rate = Market Port return = Market std Dev =

1.5% 12% 18%

Standard Deviation =

A 5%

B 18%

C 21%

Answer: A Expected Return = 4.42% Allocation to Market = 27.78% Allocation to Risk-free Asset = 72.22%

B 12.00% 100.00% 0.00%

C 13.75% 116.67% −16.67%

The two equations to solve this problem are the following: E (R ) = R free +

RM − R free

σM

(

σ

E (R ) = R free + wM * RM − R free

)

Those two equations are the same ones used for the above two problems, except that Portfolio P is replaced with the Market Portfolio M. We solve for the expected return using the first equation, then use that expected return to solve for the WM using the second equation. a. Expected Return = 1.5 + (12 − 1.5) × 5/18 = 4.42% 4.42 = 1.5 + WM × (12 − 1.5) WM = 2.92/10.5 = 0.2781 or 27.80% in the Market Wfree = 1 − WM = 1 − 0.2781 = 0.722 or 72.2%

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10

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

b. Expected Return = 1.5 +(12 − 1.5) × 18/18 = 12% 12 = 1.5 + WM × (12 − 1.5) WM = 10.5/10.5 = 1 or 100% in the Market Wfree = 1 − WM = 1 − 1 = 0 % c. Expected Return = 1.5 +(12 − 1.5) × 21/18 = 13.75% 13.75 = 1.5 + WM × (12 − 1.5) WM = 12.25/10.5 = 1.1667 or 116.67% in the Market Wfree = 1 − WM = 1 − 1.1667 = −0.1667 or −16.67% 4. Portfolios on CML. The market portfolio has earned an average of 10.5% per year with a standard deviation of 15.5%. T-bills currently yield 1.8%. What are the standard deviation and asset allocation characteristics of portfolios with the following expected return? (LO 7-3) a. 3% expected return b. 10.5% expected return c. 11.5% expected return Risk-free rate = Market Port return = Market std Dev =

1.8% 10.5% 15.5%

Expected Return =

A 3.0%

B 10.5%

C 11.5%

A 2.14% 13.79% 86.21%

B 15.50% 100.00% 0.00%

Answer: Standard Deviation = Allocation to Market = Allocation to Risk-free Asset =

C 17.28% 111.49% −11.49%

We use the following two equations to solve for the problem: E (R ) = R free +

RM − R free

σM

(

σ

E (R ) = R free + wM * RM − R free

)

The problem is similar to problem 3. We find the standard deviation using the first equation and then solve for the WM using the second equation. a. Using the first equation: 3 = 1.8 + [(10.5 − 1.8)/15.5] × σ 3 − 1.8 = 0.5613 × σ σ = 2.14 %

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11

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Using the second equation: 3 = 1.8 + WM × (10.5 − 1.8) WM = 1.2/8.7 = 0.1379 or 13.79% Wfree = 1 − WM = 1 − 0.1379 = 0.8621 or 86.21% b. Using the first equation: 10.5 = 1.8 + [(10.5 − 1.8)/15.5] × σ 10.5 − 1.8 = 0.5613 × σ σ = 15.5 % Using the second equation: 10.5 = 1.8 + WM × (10.5 − 1.8) WM = 8.7/8.7 = 1 or 100% Wfree = 1 − WM = 1 − 1 = 0% c. Using the first equation: 11.5 = 1.8 + [(10.5 − 1.8)/15.5] × σ 11.5 − 1.8 = 0.5613 × σ σ = 17.28 % Using the second equation: 11.5 = 1.8 + WM × (10.5 − 1.8) WM = 9.7/8.7 = 1.1149 or 111.49% Wfree = 1 − WM = 1 − 1.1149 = −0.1149 or −11.49% 5. Beta. The market portfolio has a variance of excess returns of 0.0324. Given the covariances with the market excess returns of the following stock’s excess returns, what are those stock’s betas? (LO 7-4) a. 0.0162 covariance b. 0.0389 covariance Market Variance =

0.0324

Covariance =

A 0.0162

B 0.0389

Answer: Beta =

A 0.50

B 1.20

The beta of any stock can be calculated using the formula given below: β stock =

Cov (Rstock − R free , RM − R f ree )

σ M2

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12

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Where the numerator is the covariance of the of the stock’s excess return with the market excess return, and the denominator is the variance of the market excess returns. a. Beta = 0.0162 / 0.0324 = 0.5 b. Beta = 0.0389 / 0.0324 = 1.2 6. Expected Return from CAPM. The market portfolio has an expected return of 11.4% and the T-bill yield is 2.1%. Given the following betas, what are their expected returns? (LO 7-4) a. Beta = 0.6 b. Beta = 1.0 c. Beta = 1.5 Market Return = T-Bill Yield =

11.4% 2.1%

A 0.6

B 1.0

C 1.5

A 7.68%

B 11.40%

Beta = Answer:

Expected Return =

C 16.05%

The CAPM equation will be used to calculate the expected returns. The CAPM equation is the following:

(

E (R ) = R free + β × E (RM ) − R free

)

a. Expected Return = 2.1 + 0.6 × (11.4 − 2.1) = 7.68% b. Expected Return = 2.1 + 1 × (11.4 − 2.1) = 11.4% c. Expected Return = 2.1 + 1.5 × (11.4 − 2.1) = 16.05% 7. Returns and Premiums. A company’s expected return is 13.5% and it has a beta of 1.1. The market portfolio return is 12% and the risk-free rate is 2.3%. What is the company’s excess return and company risk premium? (LO 7-4) Company Return = 13.50% beta = 1.10 Market Return = 12.0% T-Bill Yield = 2.3%

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13

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Answer: Excess Return = 11.20% Risk Premium = 10.67% The Excess return is the difference between the company’s expected return and the risk-free rate.

The excess return = 13.5 − 2.3 = 11.2% The company’s risk premium is the beta times the market risk premium The company’s risk premium = 1.1 × (12 − 2.3) = 10.67% 8. Returns and Premiums. At the beginning of the year, you bought three stocks with betas shown below. The risk-free rate is 2.6%. Unfortunately, the market portfolio had a negative return of ‒8.7% during the year. What is the likely return for each company during the year? (LO 7-4) a. Beta = 0.6 b. Beta = 1.0 c. Beta = 1.5 Market Return = T-Bill Yield =

−8.7% 2.6%

A 0.6

B 1.0

Beta =

C 1.5

Answer: Expected Return =

A −4.18%

B −8.7%

C −14.35%

The CAPM equation will be used to calculate the returns. The CAPM equation is the following:

(

E (R ) = R free + β × E (RM ) − R free

)

a. Return = 2.6 + 0.6 × (−8.7 − 2.6) = −4.18% b. Return = 2.6 + 1.0 × (−8.7 − 2.6) = −8.7% c. Return = 2.6 + 1.5 × (−8.7 − 2.6) = −14.35%

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14

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

9. Under- or Over-Valued. A security market line can be characterized by a risk-free rate of 2.3% and a market portfolio return of 11.2%. Determine whether each of the following stocks are over- or under-valued. (LO 7-5) a. Expected Return of 12.4% with beta = 1.0 b. Expected Return of 14% with beta = 1.2 c. Expected Return of 7.5% with beta = 0.8 Market Return = T-Bill Yield =

11.2% 2.3%

Beta = Expected Return =

A 1.0 12.4%

B 1.2 14.0%

C 0.8 7.5%

Answer: A 11.20% 1.20%

B 12.98% 1.02%

C 9.42% −1.92%

A Under-valued

B Under-valued

C Over-valued

CAPM Expected Return = Return Diff =

To determine whether each of those stocks is correctly valued, over-valued, or under-valued, we have to find their expected returns using the CAPM equation, then compare the expected returns provided in the problem to their CAPM expected returns. In this problem, we have to assume that the provided return is the correct return that each stock should have and we will determine whether the CAPM is over- or under-valuing the returns. a. CAPM Expected Return = 2.3 + 1 × (11.2 − 2.3) = 11.2%; under-valued because the CAPM return is less than the expected return provided 12.4%. b. CAPM Expected Return = 2.3 + 1.2 × (11.2 − 2.3) = 12.98%; under-valued because the CAPM return is less than the expected return provided 14%. c. CAPM Expected Return = 2.3 + 0.8 × (11.2 − 2.3) = 9.42%; over-valued because the CAPM return is more than the expected return provided 7.5%.

10. Under- or Over-Valued. A security market line can be characterized by a risk-free rate of 3.1% and a market portfolio return of 13.1%. Analysts report the expected return they believe for each of the following three stocks. If these stocks are properly valued, what should their beta be? (LO 7-5) a. Expected Return of 12.0% b. Expected Return of 14.8% c. Expected Return of 8.5%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Market Return = T-Bill Yield =

Expected Return =

13.1% 3.1% A 12.0%

B 14.8%

C 8.5%

Answer: beta =

A 0.89

B 1.17

C 0.54

The returns provided by the analysts are also the expected returns according to the CAPM because the problem specifies the stocks are properly valued. Therefore, we use the CAPM equation to solve for the betas, using the provided returns as the expected returns of the CAPM. By rearranging the CAPM equation to solve for the beta, we get the expression of the beta as the excess return of the stock returns divided by the excess return of the market returns. a. Beta = (12 − 3.1) / (13.1 − 3.1) = 0.89 b. Beta = (14.8 − 3.1) / (13.1 − 3.1) = 1.17 c. Beta = (8.5 − 3.1) / (13.1 − 3.1) = 0.54 11. Alpha. During the year, the market portfolio earned a 9.4% return while the riskfree rate was 1.3%. The actual returns of three stocks and their betas are shown below. What is these stock’s alpha for the year? (LO 7-8) a. Actual Return of 10.4% with beta = 1.0 b. Actual Return of 10.5% with beta = 1.2 c. Actual Return of 8.5% with beta = 0.8 Market Return = T-Bill Yield =

Actual Return = beta =

9.4% 1.3% A 10.4% 1.00

B 10.5% 1.20

C 8.5% 0.80

Answer: alpha =

A 1.00%

B −0.52%

C 0.72%

To calculate the alpha for each stock, we subtract the CAPM return from the actual return provided.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

a. CAPM Return = 1.3 + 1.0 × (9.4 − 1.3) = 9.4% Alpha = 10.4 − 9.4 = 1% b. CAPM Return = 1.3 + 1.2 × (9.4 − 1.3) = 11.02% Alpha = 10.5 − 11.02 = −0.52% c. CAPM Return = 1.3 + 0.8 × (9.4 − 1.3) = 7.78% Alpha = 8.5 − 7.78 = 0.72% 12. Estimating Beta. In the data file, ch7_pr12.xlsx, two years of monthly excess returns for the S&P 500 Index and Stock W, use regression analysis or spreadsheet functions to estimate CAPM parameters of equation 7-9. What is Stock W’s alpha, beta, and the R2 fit of the estimation? What does the alpha estimate mean? (LO 7-8) Answer: alpha beta

0.21% 0.48

R2

0.118

Using the Spreadsheet functions, you can use the INTERCEPT, SLOPE, and RSQ functions to calculate the alpha, the beta, and the slope, respectively. When using those functions, you have to input the stock W excess return first into the y field, and then input the market excess return into the X field.

Alpha = 0.21% Beta = 0.48 R2 = 0.118 The alpha estimate is positive 0.21% means that this stock may have provided investors with higher returns than what should be expected given the firm’s level of market risk (beta).

The second approach to solve for this problem is to use the regression analysis in Excel. To do so, we use the “Data Analysis” under the Data tab. In the Regression data input window we input the company excess return range as the Y Range and the market excess return range for X. Also, we choose a cell for the output data and click OK. Notice you will get the same values as provided above: The Alpha is the value of the Intercept Coefficient The Beta is the value of the X Variable 1 Coefficient The R2 is the value of R squared statistics The one advantage of using regression analysis is the ability to verify the statistical significance of the estimates. For the case of Alpha, the p-value statistic is high,

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

which indicates that the alpha coefficient is not significant and therefore shouldn’t be given a lot of value in any analysis.

13. Estimating Beta. In the data file, ch7_pr13.xlsx, two years of monthly excess returns for the S&P 500 Index and Stock X, use regression analysis or spreadsheet functions to estimate CAPM parameters of equation 7-9. What is Stock X’s alpha, beta, and the R2 fit of the estimation? What does the alpha estimate mean? (LO 7-8) Answer: alpha beta R2

−1.54% 1.22

0.344

The CAPM parameters are the alpha and beta. Since this is a similar problem to problem 12, you can use the same two methods explained above.

Alpha = −1.54% Beta = 1.22 R2 = 0.344 The alpha estimate is negative 1.54%, which means that this stock may have provided investors with lower returns than what should be expected given the firm’s level of market risk (beta).

14. Estimating Beta. In the data file, ch7_pr14.xlsx, two years of monthly returns for the S&P 500 Index and Stock Y, and the annual yield for T-bills shown below. Use regression analysis or spreadsheet functions to estimate CAPM parameters of equation 7-9. What is Stock Y’s alpha, beta, and the R2 fit of the estimation? What does the alpha estimate mean? (LO 7-8) Answer: Alpha Beta R2

−1.84% 0.52

0.107

Note: T-Bill Yields are annual, so divide by 12 This is a similar problem to problems 12 and 13. However the Stock Y excess return and the market excess returns are not given directly. Instead, the annual return of Tbills is given. We have to convert the annual T-bill yields to monthly yields by dividing them by 12. Then we have to calculate the stock Y excess returns by subtracting the monthly T-bill returns from the monthly stock Y returns; also we have to calculate the Market excess returns by subtracting the monthly T-bill returns from the monthly market returns. Once we have created those two excess return

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

series, the rest of the problem is same as problem 13.

Alpha = 1.84% Beta = 0.52 R2 = 0.107 The alpha estimate is positive 1.84%, which means that this stock may have provided investors with higher returns than what should be expected given the firm’s level of market risk (beta).

15. Different Beta Estimates. You searched three different financial information websites looking for the beta of a company. The betas found are 1.08, 1.23, and 1.12. Given the return on the market portfolio of 12% and risk-free rate of 2.5%, what is the range (min and max) of company risk premiums suggested by these betas? (LO 7-9) beta = 1.08 beta = 1.23 beta = 1.12

Market return Risk-free rate

12% 2.50%

Answer: company risk premium min = 10.26% max = 11.69% The three different estimates of the beta show the minimum value of beta 1.08 and the maximum value of beta 1.23. We use those two values to calculate the range for the company’s risk premiums.

Minimum company risk premium = 1.08 × (12 − 2.5) = 10.26% Maximum company risk premium = 1.23 × (12 − 2.5) = 11.69% 16. Different Beta Estimates. You searched three different financial information websites looking for the beta of a company. The betas found are 0.95, 0.84, and 1.02. Given the return on the market portfolio of 11.5% and risk-free rate of 1.5%, what is the range (min and max) of the company’s expected return suggested by these betas? (LO 7-9) beta = 0.95 beta = 0.84 beta = 1.02

Market return Risk-free rate

11.5% 1.50%

Answer: company expected return min = 9.90% max = 11.70%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

The three different estimates of the beta show the minimum value of beta 0.84 and the maximum value of beta 1.02. We use those two values to calculate the range for the company’s expected returns using the CAPM equation.

Minimum Expected Return = 1.5 + 0.84 × (11.5 − 1.5) = 9.9% Maximum Expected Return = 1.5 + 1.02 × (11.5 − 1.5) = 11.70% 17. Portfolio Beta. Your portfolio is composed of 1,000 shares of LED stock (beta = 1.3) at a price of $32.45 per share, 500 shares of EPC (beta = 1.2) at $55.88 per share, 2,000 shares of FRED (beta = 0.7) at $22.57 per share, and 700 shares of GILL (beta = 0.9) at $48.90 per share. Calculate the beta of this four-stock portfolio. (LO 7-10) LED EPC FRED GILL

beta 1.3 1.2 0.7 0.9

shares 1000 500 2000 700

price $32.45 $55.88 $22.57 $48.90

Answer:

total =

Value $ 32,450.00 $ 27,940.00 $ 45,140.00 $ 34,230.00

Portion 0.23218 0.19991 0.32298 0.24492

$ 139,760.00

1.00 Portfolio Beta =

0.988

The beta of the portfolio is calculated using the following formula: βP =

n

 w ×β i =1

i

i

Where wi represents the weights or the proportions invested in each stock, and βi is the beta of each stock.

Stock LED EPC FRED GILL

Number of Shares 1000 500 2000 700

Price 32.45 55.88 22.57 48.90

Total value 32,450 27,940 45,140 34,230

weight 0.232 0.20 0.323 0.245

Total = 139,760 Portfolio beta = (0.232 × 1.3) + (0.2 × 1.2) + (0.323 × 0.7) + (0.245 × 0.9) = 0.988

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

18. Portfolio Beta. Your existing portfolio has a beta of 1.1 and a value of $100,000.

Examining each of the following cases separately, what would be the final portfolio beta? (LO 7-10) a. Sell $10,000 of the existing portfolio to buy a stock with a beta of 1.4 b. Convert 20% of the existing portfolio to a low-risk portfolio that has a beta of 0.5 c. You have an additional $15,000 in cash and buy a stock with a beta of 0.9 to add to the existing portfolio.

Existing Portfolio Value

beta 1.10 $ 100,000

beta= Addition =

A 1.4 $ 10,000

B 0.5 20%

C 0.9 $ 15,000

Answer: New Port beta =

A 1.13

B 0.98

C 1.07

The initial portfolio has a value of $100,000 and beta of 1.1. a. Sell $10,000 of the existing portfolio and buy a stock with beta 1.4. Selling $10,000 of existing portfolio amounts to 10,000/100,000 = 0.1, which is 10% of the portfolio. Therefore, 90% of the money will remain invested in the original portfolio with beta of 1.1.

The resulting new portfolio will have the following beta = (0.9 × 1.1) + (0.1 × 1.4) = 1.13 b. Convert 20% of the existing portfolio to another portfolio with beta 0.5 is essentially selling 20% of the original portfolio and investing it in the portfolio with beta 0.5; therefore, 80% of the money will remain in the original portfolio.

The resulting new portfolio will have the following beta = (0.8 × 1.1) + (0.2 × 0.5) = 0.98 c. Additional $15,000 is invested in a stock with beta 0.9. This will result in a new portfolio having a value of $115,000 of which $100,000 is invested in the original portfolio with beta 1.1 and $15,000 in the stock with beta 0.9.

The resulting new portfolio beta = (100,000/115,000 × 1.1) + (15,000/115,000 × 0.9) = 1.07

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

19. Portfolio Beta. Your existing portfolio has a beta of 0.9. There is a risker portfolio available that you could add to your existing portfolio. The riskier portfolio has a beta of 1.4. What portion of the existing portfolio and what portion of the riskier portfolio do you need to have a new portfolio with a beta of 1.1? (LO 7-10) beta 0.90 1.40

Existing Portfolio Riskier Portfolio

New Portfolio Beta = 1.1

Answer: Existing Portion = Riskier Portion =

60.00% 40.00%

The problem is asking how much in percentage you should sell from your existing portfolio and simultaneously buy the new riskier portfolio so that the resulting new portfolio will have a beta of 1.1.

Suppose we will sell z percent of the existing portfolio with beta 0.9.

And we will invest those z percent in the riskier portfolio with beta 1.4.

The resulting portfolio will have a beta of 1.1.

We can solve the value of z by setting up the portfolio beta formula with z as the unknown variable. (We used z as variable because we are using × for the product symbol).

After selling z percent, the original portfolio will have (1 − z) percent invested in it.

0.9 × (1-z) + 1.4 × z = 1.1 0.9 − 0.9z + 1.4z = 1.1 −0.9z + 1.4z = 1.1 − 0.9 0.5z = 0.2 z = 0.2/0.5 = 0.4 or 40% Therefore, if you sell 40% of the original portfolio, keeping 60% of your money in it, and with the 40% buying the new portfolio, the resulting portfolio will have a beta of 1.1.

20. Portfolio Beta. You are creating a portfolio with the following stocks. Note each of their beta and their portfolio weight are given. What is the portfolio beta? (LO 7-10) Stock L Stock M Stock N Stock O Stock P

Beta 1.5 1.1 0.6 0.8 1.2

Weight 0.20 0.15 0.22 0.20 0.23

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Answer: Portfolio Beta = 1.033 The portfolio beta will be calculated using the formula: βP =

n

 w ×β i =1

i

i

Portfolio beta = (0.2 × 1.5) + (0.15 × 1.1) + (0.22 × 0.6) + (0.2 × 0.8) + (0.23 × 1.2) = 1.033

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Case Study Estimating Disney’s Beta The Walt Disney Company, a worldwide entertainment company, was founded in 1923 and is based in Burbank, California. The company's Media Networks include Disney, ESPN, Freeform, FX, and National Geographic, and television broadcast network ABC. Its theme parks and resorts include Walt Disney World Resort in Florida, Disneyland Resort in California, Disneyland Paris, Hong Kong Disneyland Resort, and Shanghai Disney Resort.

There is also the Disney Cruise Line, Disney Vacation Club, National Geographic Expeditions, and Adventures by Disney and Aulani, a Disney resort and spa in Hawaii. The company's Studio Entertainment segment produces and distributes motion pictures under the Walt Disney Pictures, Twentieth Century Studios, Marvel, Lucasfilm, Pixar, Searchlight Pictures, and Blue Sky Studios banners. Its direct-to-consumer videos streaming services consist of Disney+/Disney+Hotstar, ESPN+, and Hulu.

This case involves downloading data and estimating the beta for The Walt Disney Company for several different indexes as the market proxy and for several different time periods. In data are in the file, ch7_case_study.xlsx. There are other broad-based stock indexes that can be used to proxy for the market portfolio other than the S&P500 Index. Whereas the S&P500 Index has about 500 of the largest stocks, the Russell 1000 Index contains the largest 1,000 companies and the Russell 3000 Index has the largest 3,000 firms. The Wilshire 5000 Index is an attempt to include all companies trading on the U.S. exchanges.

Estimate the alpha, beta, and R2 fit of Disney for using these market proxies and five years of monthly returns. Are you expecting a beta that is smaller or larger than one?

Step 1: Using the Yahoo! Finance website, or similar data source, download the monthly prices for the maximum time period possible for the following indexes: Russell 1000 (ticker ^RUI) Russell 3000 (ticker ^RUA) Wilshire 5000 (ticker ^W5000) Also, download the prices for Disney and the yields on the 13-Week T-bills: The Walt Disney Company (ticker DIS) 13-Week T-bills (ticker ^IRX) Step 2: Using the index and stock prices, compute the monthly returns for the five-year period ending June 2021. Note that you need 61 prices to compute 60 returns. Also, compute the monthly T-bill yield in percent from the annualized T-bill yield obtained.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

Step 3: Compute the excess monthly returns for the three indexes and for Disney.

Step 4: Compute Disney’s alpha, beta, and the R2 fit for the following scenarios: A. Market Proxy is Wilshire 5000, period is five years.

B. Market Proxy is Russell 3000, period is five years.

C. Market Proxy is Russell 1000, period is five years.

D. Market Proxy is Wilshire 5000, period most recent three years.

E. Market Proxy is Russell 3000, period most recent three years.

F. Market Proxy is Russell 1000, period most recent three years.

What do you observe about the estimates?

Solution The adjusted prices are downloaded in the Excel file from 6/1/2016 to 6/1/2021.

In order to compute the monthly returns for the five-year period ending June 2021. We need 61 prices starting with the end of the month of June 2016 (6/1/2016) to the end of the month of June 2021 (6/1/2021), which will give us 60 monthly returns.

For the 13-Week T-bill returns, the downloaded data already is a return, but given in annual terms; therefore, we have to divide it by 12 to calculate the monthly returns.

The excess returns are calculated by subtracting the monthly T-bill rate from the monthly returns of each index and Disney’s return.

The table below provides the results for Disney’s alpha, beta, and r square for six different specifications: Market Proxy is Wilshire 5000, period is five years Market Proxy is Russell 3000, period is five years Market Proxy is Russell 1000, period is five years Market Proxy is Wilshire 5000, period most recent three years Market Proxy is Russell 3000, period most recent three years Market Proxy is Russell 1000, period most recent three years

Alpha −0.15% −0.18% −0.18% 0.26% 0.22% 0.19%

Beta 1.16 1.17 1.18 1.18 1.20 1.21

R square 0.46 0.47 0.45 0.49 0.51 0.49

We notice consistency in the values when using the five years of data. The estimate of the beta was about the same using the three different proxies for the market. The choice of the proxy for the market portfolio did not alter dramatically the results. Also, alpha is negative using the three specifications for the market portfolio, with the Wilshire 5000 as proxy, it came to −0.15%, while with Russell 3000 and Russell 1000, it came to −0.18%. Finally, the r

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 07: Risk-Free and Risky Asset Allocation and the CAPM

square values also are very close to each other using the three different proxies for the market.

With the shorter estimation period, the three years of data, the estimates of the beta went up slightly, so there is a slight increase in the risk of Disney, given by its beta estimate. This can be attributed to the fact that this three year period includes the highly volatile Covid-19 period when the markets witnessed some large fluctuations due to the pandemic. We also notice the R square value increased with all three proxies for the market portfolio. Finally, the alpha values turned positive for this three year estimation period and had the highest value with Wilshire 5000 as the proxy for the market and the lowest value with Russell 1000 as the proxy for the market.

Overall, there is some consistency in the estimate values. The three year of data and the five year of data produce consistent estimates using three different proxies for the market.

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26

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Table of Contents Questions .......................................................................................................................................... 2 Problems ......................................................................................................................................... 10 Case Study ....................................................................................................................................... 34

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Questions 1. Arbitrage Pricing Theory. What are the problems with implementing the APT as an asset pricing model? (LO 8–1) Answer: When implementing APT as an asset pricing model, two problems arise with the implementation process: the sources of the factors and the number of the factors.

The theory fails to specify the source of the factors. Therefore, there can be a wide variety of factor sources that researchers can use when implementing the model.

Some of those sources can be trivial in nature but may be used since there is no restriction on the source of the factors.

The theory also does not state the number of factors. Therefore, researchers can use a large number of factors when implementing the model. The number of factors does not have a theoretical limit.

Empirical research has shown that the following five factors are viable factors: • • • • •

unexpected inflation, unexpected changes in the level of industrial production, unanticipated shifts in the market risk premiums, unanticipated corporate bond spread, and unanticipated changes in the structure of yields measured by the slope of the curve illustrating term structure of interest rates.

2. Fama–French 3-Factor Model. Describe the Fama–French 3-Factor model and what anomalies it was created to resolve. (LO 8–2) Answer: This might be an additional response - “The Fama–French Three-factor Model is an extension of the Capital Asset Pricing Model (CAPM). The Fama–French model aims to describe stock returns through three factors: (1) market risk, (2) the outperformance of small-cap companies relative to large-cap companies, and (3) the outperformance of high book-to-market value companies versus low book-tomarket value companies. The rationale behind the model is that high value and small-cap companies tend to regularly outperform the overall market.

Empirical studies in the finance literature provided evidence that average returns on common stocks are related to firm characteristics such as firm size, price-toearnings ratio, cash flow-to-price ratio, book-to-market ratio, past sales growth, long-term past return (long-term momentum), and short-term past return (shortterm momentum). CAPM does not explain those relationships. The Fama–French 3-

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

factor model uses the market portfolio return factor and adds two additional risk factors related to firm characteristics: the firm size and the book-to-market ratio to explain the average returns on common stocks.

The Fama–French 3-Factor model is:

(

)

R − R free = α + b1 Rm − R free + b2 (SMB) + b3 (HML) + ε

The equation explains the excess return on a stock or a portfolio in terms of an abnormal return (α), three risk factors, and their associated factor loadings. The b1 coefficient is interpreted like the CAPM beta. A positive b2 indicates the stock or portfolio is sensitive with small company returns. A negative value indicates it is sensitive to large company returns. A positive b3 indicates the firm’s return is sensitive to value stock returns, while a negative b3 means the firm returns moves with growth stocks.

3. 4-Factor Model. Describe the risk factors in the 4-Factor model and how they are constructed. (LO 8–3) Answer: The 4-Factor model is constructed by adding a momentum factor to the Fama– French 3-Factor model.

The first factor is the CAPM excess market portfolio return, which is constructed as the difference from the market portfolio, the no-risk portfolio called the risk-free asset.

The second factor is the firm size which, is referred to as the size premium. It is constructed by ranking all NYSE stocks by their market capitalization so that the midpoint is determined. Then all stocks trading in the NYSE, NASDAQ, and AMEX exchanges that are larger than that midpoint are combined to form a valueweighted portfolio called Big. The firms from the three exchanges that are smaller than the midpoint form a value-weighted portfolio called Small. The factor SMB (small minus big) is the return on the small portfolio minus the return on the big portfolio.

The third factor is the value premium or book-to-market ratio factor. It is constructed by sorting all NYSE firms into three groups by their book-to-market (B/M) ratio to find the 70th and 30th percentiles. The book is the accounting book value of their equity, while the market is their market capitalization. The firms from all three exchanges with B/M ratios higher than the 70th percentile breakpoint are designated for the value portfolio while the firms with B/M ratios smaller than the 30th percentile breakpoint form the growth portfolio. The HML (high minus low) factor is the return on the value portfolio minus the return on the growth portfolio.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

The fourth factor is the Momentum factor, which is the factor that captures the good performance of the stocks in the past. The momentum factor was originally called UMD, which is the twelve months return of the equal weighted average of the 50% highest performing stocks minus the twelve months return of the lowest performing stocks, lagged one month. Another popular version of the Momentum factor found in Professor French’s Data Library is computed as the monthly MOM factor, where three portfolios are formed from the prior 2 to 12-month period. The breakpoints are the 30th and 70th percentile of past returns for NYSE stocks. The MOM factor is the high past return portfolio from the NYSE, NASDAQ, and AMEX exchange stocks less the low past return portfolio return.

The equation of the 4-Factor model with the MOM factor is the following:

(

)

R − R free = α + b1 Rm − R free + b2 (SMB) + b3 (HML) + b4 (MOM) + ε

4. Fama–French 5-Factor Model. Describe the risk factors in the Fama–French 5Factor model and how they are constructed. (LO 8–4) Answer: The 5-Factor model includes the original three factors and two additional factors called RMW and CMA. The first factor is the CAPM excess market portfolio return, which is constructed as the difference from the market portfolio, the no-risk portfolio called the risk-free asset.

The second factor is the firm size, which is referred as the size premium. It is constructed by ranking all NYSE stocks by their market capitalization so that the midpoint is determined. Then all stocks trading in the NYSE, NASDAQ, and AMEX exchanges that are larger than that midpoint are combined to form a valueweighted portfolio called Big. The firms from the three exchanges that are smaller than the midpoint form a value-weighted portfolio called Small. The factor SMB (small minus big) is the return on the small portfolio minus the return on the big portfolio.

The third factor is the value premium or book-to-market ratio factor. It is constructed by sorting all NYSE firms into three groups by their book-to-market (B/M) ratio to find the 70th and 30th percentiles. The book is the accounting book value of their equity, while the market is their market capitalization. The firms from all three exchanges with B/M ratios higher than the 70th percentile breakpoint are designated for the value portfolio while the firms with B/M ratios smaller than the 30th percentile breakpoint form the growth portfolio. The HML (high minus low) factor is the return on the value portfolio minus the return on the growth portfolio.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

The fourth factor RMW (robust minus weak) is the return spread between profitable firms and unprofitable firms. Operating profit is computed as annual revenues minus cost of goods sold, interest expense, and selling, general, and administrative expenses divided by book equity. A positive factor beta for RMW indicates the stock or portfolio is sensitive to the movement of profitable firms.

The fifth factor CMA (conservative minus aggressive) is the return spread between companies that invest conservatively and those that invest aggressively. Investment is the change in total assets divided by total assets. A positive factor beta for CMA indicates the stock or portfolio is sensitive to the returns of firms with lower capital investment.

The Fama–French 5-Factor model is:

(

)

R − R free = α + b1 Rm − R free + b2 (SMB) + b3 (HML ) + b4 (RMW ) + b5 (CMA) + ε

5. Competitive Markets. What are the three important characteristics of a perfectly competitive securities market? (LO 8–5) Answer: The perfect competitive market is a description of a market where no participants are large enough to have the market power to set the price of a homogeneous product; this is because the conditions set for perfect competition are strictly applied. Realistically speaking, there are very few, if any, perfectly competitive markets. The closes comparison would be the buyers and sellers in some auction markets or for financial assets, which approximate the concept. The perfect competitive market serves as a natural benchmark against which to contrast other markets.

The three important characteristics of a perfectly competitive securities market are the following: • • •

New information arrives at the marketplace in an independent and random fashion.

Current stock prices reflect all relevant risk and return information.

Investors rapidly adjust stock prices to reflect unexpected new information.

6. Efficient Market Hypothesis. Explain how the EMH forms relate potential stock price mispricing. (LO 8–6) Answer: The weak form of EMH states that current prices reflect all stock market information, which include past price and trading volume information. Therefore, it would not be possible to beat the market on a risk-adjusted basis by buying or

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

selling stocks on the premise that they should continue to rise or fall on price momentum or other price related notions. Therefore, studying past price behavior and other technical indicators of the market will not produce superior investment results.

The semistrong form of the efficient market hypothesis asserts that the current price of a stock reflects all publicly available information concerning the company.

Knowledge of the public information includes both the firm’s price and volume history and the information learned through studying a firm’s financial statements, its industry, and the general economic environment. According to the semistrong form, analysis of this material can’t be expected to produce market beating results.

The strong form of the efficient market hypothesis asserts that the current price of a stock reflects all known (i.e., public) information and all private or inside information concerning the firm. Thus, even access to inside information cannot be expected to result in superior investment performance.

7. Anomalies. What are investment anomalies, and how do they relate to the EMH and investment strategies? (LO 8–7) Answer: Investment anomalies are the exceptions to market efficiency. They represent a situation or strategy that cannot be explained away but would not be expected to happen if the EMH were true.

Some of the most important market anomalies are P/E effect, the small-firm effect, book-to-market (B/M) effect, January effect, and neglected-firm effect.

The P/E effect suggests that portfolios consisting of stocks with low price/earnings (P/E) ratios have a higher average return than portfolios with higher P/E ratios.

Further research showed that the book-to-market (B/M) ratio performed better than the P/E ratio. High B/M firms are known as value stocks, and low B/M firms are growth stocks. During the 1990s, the research using decades of data showed that value stocks outperformed growth stocks. Recent decades have shown the opposite.

The small-firm effect (or small cap for small capitalization) suggests that returns diminish as the size of the firm rises. Size is generally measured by the market value of its stock. If all common stocks on the New York Stock Exchange are divided into five groups, the smallest quintile (the smallest 20 percent of the total firms) has tended to earn a return that exceeds the return on investments in the stocks that compose the largest quintile, even after adjusting for risk.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Subsequent studies have found that the small-firm effect occurs primarily in January, especially the first five trading days. This anomaly is referred to as the January effect. The January effect is often explained by the fact that investors buy stocks in January after selling for tax reasons in December. And there is some evidence that, within a size class, those stocks whose prices declined the most in the preceding year tend to rebound the most during January.

The neglected-firm effect suggests that small firms that are neglected by large financial institutions (e.g., mutual funds, insurance companies, trust departments, and pension plans) tend to generate higher returns than those firms covered by financial institutions. By dividing firms into the categories of highly researched stocks, moderately researched stocks, and neglected stocks (based on the number of institutions holding the stock), researchers have found that the last group outperformed the more well-researched firms. This anomaly is probably another variation of the small-firm effect, and both the neglected-firm effect and the smallfirm effect suggest that the market gets less efficient as firms get smaller. Because large financial institutions may exclude these firms from consideration, their lack of participation reduces the market’s efficiency.

Over the years, scholars have determined that the B/M ratio effect (value versus growth) is actually a proxy for a systematic risk factor. The same is true for the size effect. These risk factors are now included as HML and SMB in the Fama–French 3Factor model.

Anomalies create opportunities to study and expand asset pricing models, because as more anomalies are discovered, more asset pricing models are created.

8. Data-Snooping. What is the data-snooping problem in investment research, and how does it relate to the back testing of strategies? (LO 8–8) Answer: Data-snooping in investment research is the act of investigating for statistical patterns in historical stock return data. This type of research requires numerous hours of statistical analysis of the historical stock return data to find some patterns or relations that may have some statistical significance.

In addition, after finding some statistical patterns, those same patterns are tested using the same historical stock return data. This is the problem of back testing, where the same data used to uncover for statistical patterns is used again to test for trading strategies using the statistical patterns found.

An investment strategy is useful only to the extent that it can be used to generate positive abnormal returns in the future. While it is important to back test a trading strategy, most strategies were “found” by examining the same historical data. Thus,

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

real back-testing needs to test trading strategies in different data sets than they were first identified, in order to assess their usefulness.

9. Financial Bubbles. What are financial asset bubbles, and what do they imply about efficient markets? (LO 8–9) Answer: A financial asset bubble is defined as tremendous inflation (increase) in prices and then followed by a dramatic decline in the price.

There are two types of financial asset bubbles: Rational and irrational bubbles and Irrational bubbles.

Rational bubbles are defined as an inflation and subsequent decline in prices that can be reasonably explained by the asset’s fundamentals. That is, prices are efficient in a bubble if they reflect all available information.

Irrational bubbles are defined as a stark deviation of prices from fundamental values. Irrational-bubble theory suggests that assets may go through periods of undervaluation and overvaluation due to episodes of widespread euphoric speculation and pervasive pessimistic panic.

In stock markets, irrational bubbles can occur if investors are sometimes overly optimistic in evaluating the potential for future profits. Stock market bubbles can be difficult to explain as rational and consistent with the market efficiency concept, especially when they occur in large, liquid markets.

10. EMH Investment Implications. Explain how the forms of the efficient market hypothesis frame the types of investment activities that might be worthwhile to investors. (LO 8–10) Answer: If the markets are not efficient, then all kinds of investment analysis may work to provide returns higher than expected given the level of risk taken.

If the markets are only weak form efficient, then prices already reflect the historical price and volume information; therefore, activities like charting and technical analysis would not provide superior results. However, conducting fundamental analysis could produce higher returns.

If the markets are semistrong form efficient, then prices reflect all public information. That includes historical prices and volume as well as accounting and economic information. In this case, not only would technical analysis not be useful, but neither would fundamental analysis using public information. You could use fundamental analysis with private information, if you had any.

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8

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

If the markets are strong form efficient, then prices reflect all public and private information. Thus, no fundamental or technical analysis would produce superior returns. All investments would earn their required risk adjusted return.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Problems 1. APT Return. The realized APT model factors in a 3-factor model are F1 = 0.5, F2 = 0.8, and F3 = −0.9. If the risk-free rate for the month is 0.03, what will the returns be of these three portfolios with associated APT factor betas be? (LO 8–1) a. alpha = 0.10, b1 = 0.9, b2 = 0.5, b3 = 0.2 b. alpha = 0.11, b1 = 1.1, b2 = −0.5, b3 = −0.9 c. alpha = 0.09, b1 = −1.4, b2 = 0.7, b3 = 0.3

alpha = b1 = b2 = b3 =

F1 = F2 = F3 =

0.5 0.8 −0.9

R-free = 0.03

A 0.1 0.9 0.5 0.2

B 0.11 1.1 −0.5 −0.9

C 0.09 −1.4 0.7 0.3

B 1.1

C −0.29

Answer: Return (%) =

A 0.8

The APT equation using three-factors is given below: ˆ + b1F1 + b2 F2 + b3F3 + ε R − R free = α

The alpha and b variables with “hat” signs are the estimated values of those variables. The beta estimates represent the sensitivities of the return to each of their respective factors F. The problems provides the values of the factors and the value of the risk-free rate.

In each of parts A, B and C, we replace the values given for the different betas and alpha and solve for the return. a) R = 0.03 + 0.10 + (0.9 × 0.5) + (0.5 × 0.8) + (0.2 × −0.9) = 0.80% b) R = 0.03 + 0.11 + (1.1 × 0.5) + (−0.5 × 0.8) + (−0.9 × −0.9) = 1.10% c) R = 0.03 + 0.09 + (−1.4 × 0.5) + (0.7 × 0.8) + (0.3 × −0.9) = − 0.29%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

2. APT Return. The estimated parameters of a 4-factor APT model are: (LO 8–1) R − R free = 0.7 − 0.4F1 + 0.2F2 + 0.5F3 + 0.1F4

If the risk-free rate is 0.025, what will the return be of this stock be when the realized factors are the following? a. F1 = 0.2, F2 = –0.3, F3 = 0.0, F4 = 0.2 b. F1 = 0.1, F2 = 0.5, F3 = −0.3, F4 = 0.3 c. F1 = −0.3, F2 = 0.2, F3 = −0.1, F4 = 0.4

F1 = F2 = F3 = F4 =

alpha = b1 = b2 = b3 = b4 =

0.7 −0.4 0.2 0.5 0.1

R-free = 0.025

A 0.2 −0.3 0 0.2

B 0.1 0.5 −0.3 0.3

C −0.3 0.2 −0.1 0.4

Answer: Return (%) =

A 0.605

B 0.665

C 0.875

This problem is similar to problem 1. In this example the estimated values of alpha and different betas are given, and in each of parts A, B and C, we have to use the factors given to solve for the return. a) R = 0.025 + 0.7 − (0.4 × 0.2) + (0.2 × −0.3) + (0.5 × 0) + (0.1 × 0.2) = 0.605% b) R = 0.025 + 0.7 − (0.4 × 0.1) + (0.2 × 0.5) + (0.5 × −0.3) + (0.1 × 0.3) = 0.665% c) R = 0.025 + 0.7 − (0.4 × −0.3) + (0.2 × 0.2) + (0.5 × −0.1) + (0.1 × 0.4) = 0.875% 3. Deviations from APT Model. The estimated parameters of a 3-factor APT model are: (LO 8–1) R − R free = 0.08 + 0.03F1 + 0.03F2 − 0.04F3

The risk-free rate is 0.01 and the realized factors are F1 = 0.2, F2 = −0.3, F3 = 0.0. What are the stock’s deviations from expected APT return if the realized return is the following?

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11

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

a. R = 0.09 b. R = 0.075 c. R = 0.08 F1 = F2 = F3 = alpha = b1 = b2 = b3 =

0.2 −0.3 0

R-free = 0.01

0.08 0.03 0.03 −0.04

APT Return = 0.087

Return =

A 0.09

B 0.075

C 0.08

Answer: Return Diff =

A B 0.003 −0.012

C −0.007

In this problem, we first solve for the expected return using the 3-factor APT model, using the factor values given. Then for each of the parts A, B and C, we find the difference between the realized return given, and the return provided by the APT model.

The return using the three-factor APT is: R = 0.01 + 0.08 + (0.03 × 0.2) + (0.03 × −0.3) − (0.04 × 0) = 0.087% a) The deviation is 0.09 − 0.087 = 0.003% b) The deviation is 0.075 − 0.087 = −0.012% c) The deviation is 0.08 − 0.087 = −0.007% 4. FF 3-Factor Model Return. The realized Fama–French 3-Factor model factors are Rm − Rfree = −4.37, SMB = 0.80, and HML = 5.09. If the risk-free rate for the month is 0.00 and the alpha is 0, what will the returns be of these three portfolios with associated factor betas? (LO 8−2) a. β = 1.1, bSMB = 0.5, bHML = −0.3 b. β = 0.9, bSMB = 1.5, bHML = 0.4 c. β = 1.2, bSMB = −0.3, bHML = 0.8

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12

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Rm–Rfree = −4.37 0.8 SMB = HML = 5.09 A alpha = beta = b-SMB = b-HML =

R-free = 0

B 0 0.9 1.5 0.4

0 1.2 −0.3 0.8

B −0.697

C −1.412

0 1.1 0.5 −0.3

C

Answer: Return (%) =

A −5.934

The Fama–French 3-Factor model is:

(

)

R − R free = α + b1 Rm − R free + b2 (SMB) + b3 (HML) + ε

In the problem the values of the three factors are given, along with the risk-free rate and the alpha values.

In each of parts A, B and C, we replace the values given for the different betas and solve for the return using the Fama–French 3 Factor model. a) R = 0.00 + 0 + (1.1 × −4.37) + (0.5 × 0.8) + (−0.3 × 5.09) = −5.934% b) R = 0.00 + 0 + (0.9 × −4.37) + (1.5 × 0.8) + (0.4 × 5.09) = −0.697% c) R = 0.00 + 0 + (1.2 × −4.37) + (−0.3 × 0.8) + (0.8 × 5.09) = −1.412% 5. FF 3-Factor Model Return. The estimated parameters of the monthly Fama–French 3-Factor model are: (LO 8–2) R − R free = 0.05 + 0.75(Rm − R free ) + 0.8(SMB) − 0.5(HML)

If the risk-free rate for the month is 0.20%, what will the return be of this stock be when the realized factors are the following? a. Rm – Rfree = −9.55%, SMB = −2.42%, HML = −1.90% b. Rm – Rfree = 8.41%, SMB = 2.90%, HML = −0.44% c. Rm – Rfree = 3.40%, SMB = 2.04%, HML = −2.68% alpha = Beta = b-SMB = b-HML =

0.05 0.75 0.8 −0.5

R-free = 0.2

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Rm – Rfree = SMB = HML =

A −9.55 −2.42 −1.9

B 8.41 2.9 −0.44

C 3.4 2.04 −2.68

A −7.8985

B 9.0975

C 5.772

Answer: Return (%) =

This problem is similar to problem 4. We will use the Fama–French 3-factor model.

In this problem the values of the alpha and betas are given.

In each of parts A, B and C, we replace the values given for the different factors and solve for the return using the Fama–French 3 Factor model. a) R = 0.2 + 0.05 +(0.75 × −9.55) + (0.8 × −2.42) − (0.5 × −1.9) = −7.8985% b) R = 0.2 + 0.05 +(0.75 × 8.41) + (0.8 × 2.90) − (0.5 × −0.44) = 9.0975% c) R = 0.2 + 0.05 +(0.75 × 3.40) + (0.8 × 2.04) − (0.5 × −2.68) = 5.772% 6. Deviations FF 3-Factor Model Return. The estimated parameters of the monthly Fama–French 3-Factor model are: (LO 8–2) R − R free = 0 + 0.7(Rm − R free ) + 1.2(SMB) + 1.1(HML)

The risk-free rate is 0.21% and the realized factors are Rm – Rfree = 3.96%, SMB = −1.74%, HML = 2.17%. What are the stock’s deviations from expected Fama–French 3-Factor model return if the realized return is the following? a. R = 3% b. R = 2.5% c. R = 3.5% Rm–Rfree = 3.96 SMB = −1.74 HML = 2.17

alpha = beta = b-SMB = b-HML =

R-free = 0.21

0 0.7 1.2 1.1

3-Factor Return

3.281

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14

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Return =

A 3

B 2.5

C 3.5

Answer: Return Diff =

A B −0.281 −0.781

C 0.219

In this problem, we first solve for the expected return using the Fama–French 3factor model, using the factor values given. Then for each of the parts A, B and C, we find the difference between the realized return given, and the return provided by the Fama–French model.

The return using the Fama–French model is: R = 0.21 + 0 + (0.7 × 3.96) + (1.2 × −1.74) + (1.1 × 2.17) = 3.281% a) The deviation is: 3 − 3.281 = −0.281% b) The deviation is: 2.5 − 3.281 = −0.781% c) The deviation is: 3.5 − 3.281 = 0.219% 7. Estimate FF 3-Factor Model Coefficients. Annual returns and risk premiums are in the data file, ch8_pr07.xlsx. Estimate the Fama–French 3-Factor model alpha and factor betas. (LO 8–2) Answer: Port - Rfree 12.11 −21.22 50.7 23.06 6.2 17.88 −7.72 −35.53 35.81 27.7 −6.36 19.21 47.57 6.55

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

−2.13 24.81 16.3 −12.2 24.37 12.76 In order to estimate the Fama–French 3-factor model, we use the regression function from the “Data Analysis” toolpak under the data tab in Excel.

The first step is to calculate the difference between the portfolio return and the riskfree rate. This difference is the return series that will be used to estimate the betas of the model and the alpha. The difference is calculated in column L in the Excel solution file.

When we select the “Regression” function in the “Data Analysis” toolpak, we see a box where we have to input the following: In the “Input Y Range” tab, we select the column where we calculated the difference between the portfolio return and the risk-free rate, which is column L in the Excel solution file.

In the “Input X Range” tab, we select the 3 columns where we have the returns of Mkt-Rf, SMB, and HML, so we have to select the 3 columns of data F, G, and H together and put it in this box.

Finally, in the “Output Range” tab, we select the cell where we want the output to appear; in the Excel solution, it is the N5 cell. You can select any cell you like for the output range.

The results provide the following estimated values: Alpha = 1.3816 Market factor beta = 1.0487 SMB factor beta = 0.7325 HML factor beta = 0.2879

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

8. Estimate FF 3-Factor Model Coefficients. Annual returns for the stock that make up the health care industry and risk premiums are in the data file ch8_pr08.xlsx.

Estimate the Fama−French 3-Factor model alpha and factor betas. What do the factor betas indicate about health care stocks? (LO 8–2) Answer: Health - Rfree −16.02 −24.22 20.39 −0.62 1.78 3.33 −0.87 −18.83 21.09 4.58 10.83 20.29 41.17 24.44 5.78 −2.05 21.4 3.01 18.06 17.87 This problem is similar to problem 7. We use the same approach to find for the values of betas and alpha. The difference between the health care returns and the risk-free rate is calculated in column L in the Excel file.

Following the same approach, we get: Alpha = 2.3228 Market factor beta = 0.7470 SMB factor beta = −0.3699 HML factor beta = −0.0396 The market beta of 0.7470 indicates that the health care industry is somewhat less risky than the overall market. The SMB beta being negative means that the health care industry is leaning towards large firms, and the value of the factor being −0.3699 so it is considered to be more somewhat sensitive to large firms. Finally, the

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17

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

HML beta being negative means the health care industry is leaning towards low book to market ratio or growth stocks; however, the value being −0.0396, which is virtually 0, means that the health care industry is not sensitive to this factor.

Note: In order to fully assess those sensitivity factors, we have to check the t-statistic and/or the p-values to check their significance. Only statistically significant factors should be considered. In this example, only market beta is significant, the SMB beta is significant at 10% level, while the HML beta is not significant.

9. 4-Factor Model Return. The realized 4-Factor model factors are Rm – Rfree = 2.37, SMB = 1.80, HML = −3.09, and MOM = 0.22. If the risk-free rate for the month is 0.02 and the alpha is 0, what will the returns be of these three portfolios with associated factor betas? (LO 8–3) a. β = 1.2, bSMB = 0.5, bHML = 0.3, bMOM = −0.2 b. β = 0.8, bSMB = 1.2, bHML = 0.4, bMOM = 0.3 c. β = 1.0, bSMB = −0.3, bHML = −0.8, bMOM = 0.7 Rm–Rfree = SMB = HML = MOM =

alpha = beta = b-SMB = b-HML = b-MOM =

2.37 1.8 −3.09 0.22

A 0 1.2 0.5 0.3 −0.2

R-free = 0.02

B 0 0.8 1.2 0.4 0.3

C 0 1 −0.3 −0.8 0.7

Answer: Return (%) =

A B 2.793 2.906

C 4.476

The 4-Factor model is:

(

)

R − R free = α + b1 Rm − R free + b2 (SMB) + b3 (HML) + b4 (MOM) + ε

In the problem the values of the four factors are given, along with the risk-free rate and the alpha values.

In each of parts A, B and C, we replace the values given for the different betas and solve for the return using the 4-Factor model.

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18

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

a) R = 0.02 + 0 + (1.2 × 2.37) + (0.5 × 1.80) + (0.3 × −3.09) + (−0.2 × 0.22) = 2.793% b) R = 0.02 + 0 + (0.8 × 2.37) + (1.2 × 1.80) + (0.4 × −3.09) + (0.3 × 0.22) = 2.906% c) R = 0.02 + 0 + (1.0 × 2.37) + (−0.3 × 1.80) + (−0.8 × −3.09) + (0.7 × 0.22) = 4.476% 10. 4-Factor Model Return. The estimated parameters of the monthly 4-Factor model are: (LO 8–3) R − R free = 0.05 + 0.75(Rm − R free ) + 0.9(SMB) − 0.3(HML) + 0.5(MOM)

If the risk-free rate for the month is 0.20%, what will the return be of this stock be when the realized factors are the following? a. Rm – Rfree = −2.50%, SMB = 2.42%, HML = 4.90%, MOM = 0.93% b. Rm – Rfree = 3.43%, SMB = 1.90%, HML = −0.44%, MOM = 2.45% c. Rm – Rfree = 5.40%, SMB = −2.04%, HML = −1.68%, MOM = −0.88%

Rm–Rfree = SMB = HML = MOM =

alpha = beta = b-SMB = b-HML = b-MOM =

0.05 0.75 0.9 −0.3 0.5

R-free = 0.2

A −2.5 2.42 4.9 0.93

B 3.43 1.9 −0.44 2.45

C 5.4 −2.04 −1.68 −0.88

A −0.452

B 5.8895

C 2.528

Answer: Return (%) =

This problem is similar to problem 9. We will use the 4-factor model. In this problem the values of the alpha and betas are given.

In each of parts A, B and C, we replace the values given for the different factors and solve for the return using the 4-Factor model. a) R = 0.20 + 0.05 + (0.75 × −2.50) + (0.90 × 2.42) + (−0.3 × 4.90) + (0.5 × 0.93) = −0.452% b) R = 0.20 + 0.05 + (0.75 × 3.43) + (0.90 × 1.90) + (−0.3 × −0.44) + (0.5 × 2.45) = 5.8895% c) R = 0.20 + 0.05 + (0.75 × 5.40) + (0.90 × −2.04) + (−0.3 × −1.68) + (0.5 × −0.88) = 2.528%

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19

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

11. Deviations 4-Factor Model Return. The estimated parameters of the monthly 4Factor model are: (LO 8–3) R − R free = 0 + 1.2(Rm − R free ) − 0.3(SMB) + 1.3(HML) + 0.9(MOM)

The risk-free rate is 0.32% and the realized factors are Rm – Rfree = 2.55%, SMB = 2.07%, HML = −1.22%, and MOM = 0.82%. What are the stock’s deviations from the expected 4-Factor model return if the realized return is the following? a. R = 2% b. R = 2.8% c. R = 1.8% Rm–Rfree = SMB = HML = MOM =

2.55 2.07 −1.22 0.82

R-free = 0.32

alpha = 0 beta = 1.2 b-SMB = −0.3 b-HML = 1.3 b-MOM = 0.9 4-Factor Return

Return =

1.911 A 2

B 2.8

C 1.8

A 0.089

B 0.889

C −0.111

Answer: Return Diff =

In this problem, we first solve for the expected return using the 4-Factor model, using the factor values given. Then for each of the parts A, B and C, we find the difference between the realized return given, and the return provided by the 4Factor model.

The return using the 4-Factor model is: R = 0.32 + 0 + (1.2 × 2.55) + (−0.3 × 2.07) + (1.3 × −1.22) + (0.9 × 0.82) = 1.911%

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20

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

a) The deviation is: 2 − 1.911 = 0.089% b) The deviation is: 2.8 − 1.911 = 0.889% c) The deviation is: 1.8 − 1.911= −0.111% 12. Estimate 4-Factor Model Coefficients. Annual returns and risk premiums are in the data file ch8_pr12.xlsx. Estimate the 4-Factor model alpha and factor betas.

(LO 8–3) Answer: Port - Rfree 4.46 −22.59 47.3 19.34 4.93 8.81 −7.12 −31.27 31.73 26.89 −1.34 15.48 40.44 4.28 −5.98 19.31 14.44 −9.78 19.79 20.83 This problem is similar to problems 7 and 8 as far as the approach to follow. The problem is asking to estimate the betas and the alpha using the 4-Factor model. We use the same approach to find for the values of betas and alpha. The difference between the Portfolio returns and the risk-free rate is calculated in column L in the Excel file.

Also, note in this problem, we have 4 factors located in columns F, G, H, and I, so we have to use all those 4 columns in the Input X range area.

Following the same approach, we get:

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21

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Alpha = − 0.1212 Market factor beta = 0.9342 SMB factor beta = 0.7540 HML factor beta = 0.0530 MOM factor beta = − 0.0035 13. Estimate 4-Factor Model Coefficients. Annual returns for the technology industry and risk premiums are in the data file ch8_pr13.xlsx. Estimate the 4-Factor model alpha and factor betas. What do the factor betas indicate about technology stocks?

(LO 8–3) Answer: Tech - Rfree −28.56 −39.87 47.55 3.6 −1.26 4.56 12.96 −44.13 58.04 15.24 −1.14 13.19 32.63 16.69 5.08 12.07 35.62 −1.58 41.75 46.58 This problem is similar to problem 12. We follow the same approach as in the problem 12.

Following the same approach, we get: Alpha = 1.5061 Market factor beta = 1.1237 SMB factor beta = − 0.1129 HML factor beta = −0.5181 MOM factor beta = −0.2760

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22

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

The market beta of 1.1237 indicates that the technology stocks are somewhat more risky than the overall market. The SMB beta being negative means that the technology stocks lean towards large firms not small firms, and the value of the beta being −0.1129, which is rather small, indicates some slight sensitivity to large firms.

The HML beta being negative means technology stocks lean towards low book to market ratio or growth stocks; the value being −0.5181 means that technology stocks are more sensitive to growth stocks. Finally, the MOM beta being negative means that technology stocks are not momentum stocks, and the value being −0.2760 suggests that technology stocks have some sensitivity towards not momentum stocks.

Note: In order to fully assess those sensitivity factors, we have to check the t-statistic and/or the p-values to check their significance. Only statistically significant factors should be considered. In this example, the SMB beta is not significant, while the other 3 betas are significant.

14. FF 5-Factor Model Return. The realized Fama–French 5-Factor model factors are Rm–Rfree = 3.37, SMB = 0.50, HML = 4.20, RMW = 3.26, and CMA = −0.68. If the riskfree rate for the month to is 0.05% and the alpha to is 0, what will the returns be of these three portfolios with associated factor betas? (LO 8–4) A. β = 1.0, bSMB = 0.5, bHML = −0.3, bRMW = 0.4, bCMA = 0.8 B. β = 0.85, bSMB = 1.2, bHML = 0.5, bRMW = −0.3, bCMA = −0.7 C. β = 1.2, bSMB = −0.3, bHML = 1.4, bRMW = 0.6, bCMA = 0.3

alpha = beta = b-SMB = b-HML = b-RMW = b-CMA =

Rm–Rfree = SMB = HML = RMW = CMA =

3.37 0.5 4.2 3.26 −0.68

R-free = 0.05

A 0 1 0.5 −0.3 0.4 0.8

B 0 0.85 1.2 0.5 −0.3 −0.7

C 0 1.2 −0.3 1.4 0.6 0.3

Answer: Return (%) =

A 3.17

B 5.1125

C 11.576

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23

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

The Fama–French 5-Factor model is:

(

)

R − R free = α + b1 Rm − R free + b2 (SMB) + b3 (HML) + b4 (RMW ) + b5 (CMA) + ε

In the problem the values of the five factors are given, along with the risk-free rate and the alpha values.

In each of parts A, B and C, we replace the values given for the different betas and solve for the return using the Fama–French 5-Factor model. a) R = 0.05 + 0 + (1 × 3.37) + (0.5 × 0.5) + (−0.3 × 4.20) + (0.4 × 3.26) + (0.8 × −0.68) = 3.17% b) R = 0.05 + 0 + (0.85 × 3.37) + (1.2 × 0.5) + (0.5 × 4.20) + (−0.3 × 3.26) + (−0.7 × −0.68) = 5.1125% c) R = 0.05 + 0 + (1.2 × 3.37) + (−0.3 × 0.5) + (1.4 × 4.20) + (0.6 × 3.26) + (0.3 × −0.68) = 11.576% 15. FF 5-Factor Model Return. The estimated parameters of the monthly Fama–French 5-Factor model are: (LO 8–4) R − R free = 0.04 + 1.2(Rm − R free ) + 0.6(SMB) + 0.5(HML) − 0.6(RMW) + 1.1(CMA )

If the risk-free rate for the month is 0.20%, what should be the return of this stock when the realized factors are the following? a. Rm – Rfree = −1.58%, SMB = −3.42%, HML = −0.55%, RMW = −0.65%, CMA = 1.22% b. Rm – Rfree = 4.63%, SMB = 2.75%, HML = −0.44%, RMW = 1.64%, CMA = 1.00% c. Rm – Rfree = 3.25%, SMB = 3.27%, HML = −3.08%, RMW = 0.25%, CMA = −0.69%

Rm–Rfree = SMB = HML = RMW = CMA =

alpha = beta = b-SMB = b-HML = b-RMW = b-CMA =

0.04 1.2 0.6 0.5 −0.6 1.1

R-free = 0.2

A −1.58 −3.42 −0.55 −0.65 1.22

B 4.63 2.75 −0.44 1.64 1

C 3.25 3.27 −3.08 0.25 −0.69

Answer: Return (%) =

A −2.251

B 7.342

C 3.653

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24

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

This problem is similar to problem 14, so we will use the Fama–French 5-factor model. In this problem the values of the alpha and betas are given.

In each of parts A, B and C, we replace the values given for the different factors and solve for the return using the Fama–French 5-Factor model. a) R = 0.2 + 0.04 + (1.2 × −1.58) + (0.6 × −3.42) + (0.5 × −0.55) + (−0.6 × −0.65) + (1.1 × 1.22) = −2.251% b) R = 0.2 + 0.04 + (1.2 × 4.63) + (0.6 × 2.75) + (0.5 × −0.44) + (−0.6 × 1.64) + (1.1 × 1.00) = 7.342% c) R = 0.2 + 0.04 + (1.2 × 3.25) + (0.6 × 3.27) + (0.5 × −3.08) + (−0.6 × 0.25) + (1.1 × −0.69) = 3.653% 16. Deviations FF 5-Factor Model Return. The estimated parameters of the monthly Fama–French 5-Factor model are: (LO 8–4) R − R free = 0 + 1.3(Rm − R free ) + 1.1(SMB) + 0.4 (HML) + 1.8(RMW) − 0.4 (CMA )

The risk-free rate is 0.15% and the realized factors are Rm–Rfree = 1.55%, SMB = 2.76%, HML = −0.94%, RMW = 0.54%, CMA = 2.24%. What are the stock’s deviations from expected Fama–French 5-Factor model return if the realized return was? a. R = 4% b. R = 4.5% c. R = 5% Rm–Rfree = SMB = HML = RMW = CMA = alpha = Beta = b-SMB = b-HML = b-RMW = b-CMA =

0 1.3 1.1 0.4 1.8 −0.4

5-Factor Return

4.901

Return =

A 4

1.55 2.76 −0.94 0.54 2.24

B 4.5

R-free = 0.15

C 5

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25

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Answer: Return Diff =

A −0.901

B −0.401

C 0.099

In this problem, we first solve for the expected return using the Fama–French 5Factor model, using the factor values given. Then for each of the parts A, B, and C, we find the difference between the realized return given, and the return provided by the Fama–French 5-Factor model.

The return using the Fama–French 5-Factor model is: R = 0.15 + 0 + (1.3 × 1.55) + (1.1 × 2.76) + (0.4 × −0.94) + (1.8 × 0.54) + (−0.4 × 2.24) = 4.901% a) The deviation is: 4 − 4.901 = −0.901% b) The deviation is: 4.5 − 4.901 = −0.401% c) The deviation is: 5 − 4.901 = 0.099% 17. Estimate FF 5-Factor Model Coefficients. Annual returns and risk premiums are in the data file ch8_pr17.xlsx. Estimate the Fama–French 5-Factor model alpha and factor betas. (LO 8–4) Answer: Port-Rfree −1.8 −21.32 44.03 17.29 2.15 10.99 3.02 −38.12 36.45 30.78 −4.89 18.34 41.9 5.31 −6.02 22.46 13.99 −14.44 23.72 30.18

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26

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

This problem is similar to problems 7, 8, 12, and 13 as far as the approach to follow.

The problem is asking to estimate the betas and the alpha using the Fama–French 5Factor model. We use the same approach to find for the values of betas and alpha.

The difference between the Portfolio returns and the risk-free rate is calculated in column M in the Excel file.

Also, note in this problem, we have 5 factors located in columns F, G, H, I, and J, so we have to use all those 4 columns in the Input X range area.

Following the same approach, we get: Alpha = −0.71110 Market factor beta = 1.0609 SMB factor beta = 0.7085 HML factor beta = −0.0473 RMW factor beta = 0.0632 CMA factor beta = −0.0178 18. Estimate FF 5-Factor Model Coefficients. Annual returns for the manufacturing industry and risk premiums are in the data file ch8_pr18.xlsx. Estimate the Fama– French 5-Factor model alpha and factor betas. What do the factor betas indicate about manufacturing stocks? (LO 8–4) Answer: Manuf-Rfree −10.3 −8.54 31.76 14.81 3.96 14.47 16.3 −41.86 34.78 25.68 −0.79 14.79 36.57 7.54 −6.61 16.57 30.19

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27

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

−13.91 24.21 14.13 This problem is similar to problems 17.

Following the same approach, we get: Alpha = −1.4378 Market factor beta = 1.1459 SMB factor beta = 0.0946 HML factor beta = 0.0286 RMW factor beta = 0.4581 CMA factor beta = 0.1373 The market beta of 1.1459 indicates that the manufacturing stocks are somewhat more risky than the overall market. The SMB beta being positive means that the manufacturing stocks lean towards small firms. The value of the beta is 0.0946, a very small value, which indicates manufacturing stocks are very slightly sensitive to small stocks, but not really much. The HML beta being positive means manufacturing stocks lean towards high book to market ratio or value stocks. The value being 0.0286, a very small number, means that manufacturing stocks are not really sensitive to value stocks. The RMW beta is positive, which means manufacturing stocks lean towards profitable firms, and the value being 0.4581, means that manufacturing stocks are sensitive to the profitable firms. Finally, the CMA beta is positive, which means manufacturing stocks lean towards conservative investing firms. The value being 0.1373 suggests that manufacturing stocks have very slight sensitivity to conservative investing firms.

Note: In order to fully assess those sensitivity factors, we have to check the t-statistic and/or the p-values to check their significance. Only statistically significant factors should be considered. In this example, the market beta is significant, the RMW beta is significant at 10% level, while the other betas are not significant.

19. Estimate 4-Factor Model Coefficients. 60 monthly returns for the energy industry and risk premiums are provided in the data file ch8_pr19.xlsx. Estimate the 4-Factor model alpha and factor betas. What do the factor betas indicate about energy stocks? (LO 8–3) Answer: Energy - Rfree −4.39 −2.9

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28

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

10.78 9.1 −0.62 2.58 −2.78 1.45 2.8 −2.82 9.34 2.07 −4.4 −2.44 −1.22 −2.71 −3.34 −0.14 2 −5.18 10.86 0.4 2.91 4.92 2.75 −10.85 2.85 9.87 3.29 0.41 0.96 −3 3.2 −12.06 −2.35 −13.21 10.11 2.28 1.8 0.04 −12.02 8.68 −2.86

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29

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

−8.9 3.53 −2.22 1.09 6.04 −12 −15.42 −34.61 32.38 0.51 −0.41 −4.81 −1.08 −14.91 −4.54 28.45 6.15 This problem is similar to problems 18.

Following the same approach, we get: Alpha = −1.3638 Market factor beta = 1.2754 SMB factor beta = 0.4910 HML factor beta = 0.5440 MOM factor beta = −0.3690 The market beta of 1.2754 indicates that the energy stocks are more risky than the overall market. The SMB beta being positive means that the energy stocks lean towards small firms. The value of the factor being 0.4910 means that energy stocks are rather sensitive to small stocks. The HML beta being positive means energy stocks lean towards high book to market ratio or value stocks. The value being 0.5440 means that energy stocks are sensitive to value stocks. Finally, the MOM beta being negative means that energy stocks are not momentum stocks, and the value being −0.3690 suggests that energy stocks are slightly sensitive towards not momentum firms.

Note: In order to fully assess those sensitivity factors, we have to check the t-statistic and/or the p-values to check their significance. Only statistically significant factors should be considered. In this example all the betas are significant. SMB and MOM are significant at 10%, HML is significant at 5%, and the market beta is significant at 1%.

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30

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

20. Estimate a 6-Factor Model. 60 monthly returns for the utility industry and risk premiums are provided in the data file, ch8_pr20.xlsx. Estimate a 6-Factor model alpha and factor betas by adding the momentum factor to the Fama–French 5Factor model. What do the factor betas indicate about utility stocks? (LO 8–3, 4) Answer: Utility − Rfree 4.65 1.73 7.84 −0.85 2.22 7.39 −0.21 −3.92 1.74 −0.61 −2.83 3.62 1.04 4.01 0.29 0.33 2.5 −1.95 2.91 2.11 −2.06 2.98 2.34 −5.11 −2.94 −4.63 3.08 2.63 0.07 2.47 1.57 0.75 −0.7 −0.25

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31

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

3.09 −4.94 5.2 3.44 3.13 0.81 −1.75 3.46 −1.18 3.28 3.74 −1.57 −2.27 3.99 4.7 −9.97 −13.13 5.07 4.55 −5.03 6.36 −2.26 −0.28 4.48 2.62 0.62 This is similar to problem 19 except that we have 6 different factors. We follow the same approach as the previous problems using the Regression function.

Following the same approach, we get: Alpha = 0.4505 Market factor beta = 0.4304 SMB factor beta = −0.0763 HML factor beta = 0.3093 RMW factor beta = 0.4094 CMA factor beta = −0.0662 MOM factor beta = 0.1989 The market beta of 0.4505 indicates that the utility stocks are much less risky than the overall market.

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32

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

The SMB beta is negative but has very low value, which indicates that utility stocks are not sensitive to the size premium.

The HML beta being positive means utility stocks lean towards high book to market ratio or value stocks. The value being 0.3093 means that utility stocks are slightly sensitive to value factor.

The RMW beta is positive with a value of 0.4094, which means utility stocks are sensitive to the profitability factor.

The CMA beta is negative with a value of −0.0662; the very small value suggests that utility stocks do not have sensitivity towards conservative investment firms.

The MOM beta is positive with value of 0.1989, which means utility stocks are slightly sensitive to the momentum factor.

Note: In order to fully assess those sensitivity factors, we have to check the t-statistic and/or the p-values to check their significance. Only statistically significant factors should be considered. In this example the market beta is significant at 1% and the HML beta is significant at 10%, while the other betas are not significant.

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33

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

Case Study International Asset Pricing The models described in this chapter are focused on asset pricing in the United States.

Each factor is constructed using the returns of the stocks trading on the NYSE, NASDAQ, and AMEX. If you are examining stocks from other countries, should you use these U.S. centric factors?

The answer is likely…no.

Ken French’s Data Library also includes factor data for asset pricing in developed and emerging markets. Note that for developed markets, Fama–French 3-Factor and 5-Factor data is available for all developed markets combined, Europe, Japan, and the Asia Pacific.

The momentum factor is also available for these markets.

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34

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

There is also data available for the Fama–French Factors and momentum for emerging markets. The data for emerging markets is less pervasive than for developed markets due to a lack of reliable data.

Consider the monthly returns for a portfolio of international (non-US) stocks The data are in the file, ch8_case_study.xlsx. a. Download the monthly factor data from the French Data Library for both the 5Factor model and the momentum factor for all developed markets. b. Download the monthly factor data from the French Data Library for both the 5Factor model and the momentum factor for emerging markets. c. Estimate a 6-Factor model with the Fama–French 5-Factors and momentum for this international portfolio using the developed market data. d. Estimate a 6-Factor model with the Fama–French 5-Factors and momentum for this international portfolio using the emerging market data. e. Which model seems to fit better?

The data downloaded from the French Data Library is in the Excel file. First we calculated the excess return by taking the difference of the international portfolio return minus the risk-free rate. The excess return is calculated under column S. The model estimates for the 6-Factor model using developed market data are as follows: Alpha Market factor beta SMB factor beta HML factor beta RMW factor beta CMA factor beta MOM factor beta

0.116393 0.987429 −0.053220 0.259245 0.039050 −0.356550 0.216215

The R square is 0.86714.

The model estimates for the 6-Factor model using emerging market data are as follows: Alpha Market factor beta SMB factor beta HML factor beta RMW factor beta

0.523817 0.857924 0.192633 −0.383810 −0.565370

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35

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

CMA factor beta MOM factor beta

0.004059 −0.101770

The R square is 0.86722 The R square values of the 2 estimates are virtually the same; therefore, both models fit well based on the R square value. However, the factor betas are different using each model, and with this difference each model provides a different characterization of the International Portfolio.

Based on the first model, the developed market data, the International Portfolio has the following characteristics: The market beta of 0.987429, which gives the portfolio about the same risk as the overall market.

The SMB beta is −0.05322, a very low value, which indicates virtually no sensitivity to the size premium.

The HML beta is 0.259245, which indicates rather slight sensitivity to value factor.

The RMW beta is 0.03905, a very low value, which indicates no virtually sensitivity to the profitability factor.

The CMA beta is −0.35655, which indicates opposite sensitivity to the conservative investment factor, and some sensitivity towards aggressively investing firms.

The MOM beta is 0.216215, which indicates some slight sensitivity to the momentum factor.

Based on the second model, the emerging market data, the International Portfolio has the following characteristics: The market beta of 0.857924, which gives the portfolio about somehow less risk than the overall market. The market risk is less compared to the first model.

The SMB beta is 0.192633, which indicates some small sensitivity to the size premium, towards small firms.

The HML beta is −0.38381, which indicates some slight sensitivity to growth factor, towards growth stocks.

The RMW beta is −0.56537, which indicates some sensitivity to the opposite of the profitability factor, sensitivity towards not profitable firms.

The CMA beta is −0.004059, virtually zero, so non sensitivity to the conservative investment factor.

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36

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 08: Asset Pricing Models and Efficient Markets

The MOM beta is −0.10177, which indicates some very slight sensitivity to the opposite of momentum factor, so slightly non momentum firms.

Although the R square values were identical, the portfolio characteristics were widely different according to the two different models. In order to use the correct model, we have to know whether this international portfolio belongs to developed markets or emerging markets.

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37

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 22

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Questions 1. Category Comparison. Harford MidCap Y is a mutual fund with a midcap growth focus. What indexes and fund categories might be used to assess its performance?

What data do you use to compare performance? (LO 9−1) Answer: There are several indexes for tracking mid-cap stocks. The most widely referenced is the S&P Mid-Cap 400, but others include the Russell Midcap and Wilshire US MidCap Index.

To perform category comparison, the performance of a portfolio is compared to other portfolios with similar objectives and style. Harford MidCap Y is a midcap fund with growth focus, therefore the indexes and fund categories that are best suited to assess its performance is Mid-Cap Growth category from the Broad U.S. Stock Portfolios of Morningstar.

To conduct a comparison, first identify the after-cost return of Harford MidCap Y fund. This is the return to the shareholders after accounting for expenses, fees, and trading costs. Second, identify the Morningstar fund category that matches the portfolio’s objective, which is the Mid-Cap Growth category. Once you have the return and the category, two comparisons are common: rank and average.

Comparison by rank refers to how the portfolio return ranks with all the mutual funds in that category. To perform comparison by rank, you will need to gather the return of MidCap Y fund for the most recent year, and the returns of all the mutual funds in the category and rank those returns to see where MidCap Y fund’s return will rank among all the mutual funds returns.

The average method compares the portfolio’s return to the average of the returns of the funds in the category. To perform the average method comparison, you find the average return of all the mutual funds in the category and compare the MidCap Y fund’s return to the average.

It is also common to do average performance analysis using 3-year, 5-year, and 10year average returns. And perform rank analysis for the last 10 years of returns.

These indexes do not include portfolio costs, thus a Morningstar category may be a better comparison.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

2. Alpha. Discuss the importance of selecting the asset pricing model when computing an alpha. (LO 9−2) Answer: The capital asset pricing model is by no means a perfect theory. But the spirit of CAPM is correct. It provides a useful measure that helps investors determine what return they deserve on an investment, in exchange for putting their money at risk on it. Alpha is a measurement of the performance of an investment as compared to an index such as the S&P 500. It is considered to be an investment’s active return and is used to understand how an investment is performing as compared to the market as a whole. An alpha number can be negative or positive, and the baseline value is zero. For example, if an investment has an alpha value of two, this means that it has outperformed the comparison market index or benchmark by two percent. By contrast, if an investment has a negative value of one, this means that it underperformed the market by -1 percent. Alpha can be used to determine how well a portfolio manager is actually performing.

3. Alpha. Describe how a portfolio manager’s performance can be assessed with just its alpha. (LO 9−2) Answer: Jensen’s alpha can be used to assess the performance of the portfolio manager on risk-adjusted basis by comparing the realized return of the manager to the required return of a portfolio given its level of risk using an asset pricing model. The required return of the portfolio gives the return the portfolio should earn given its level of risk, subtracting this required return from the realized return gives the value of the alpha. A positive alpha shows superior performance of the manager, a negative alpha shows inferior performance of the manager. The alpha measure can be used by itself to assess the performance of a manager without the need to compare it to any other measures.

4. Treynor Index. How can you compute the Treynor Index? Discuss the data and procedures you would use. (LO 9−3) Answer: The Treynor Index is calculated using the following formula: Treynor Index =

R − RFree

β

R is the realized return of the portfolio over a period of time. RFree is the risk-free rate over the same period of time, and β is the beta of the portfolio, measured using the CAPM, representing the systematic risk of the portfolio.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

In order to estimate the Treynor Index, first we select an estimation period and collect the portfolio returns and the risk-free rate returns over this period. Also, we need to collect the return of the market for the same period in order to estimate the beta. Once we have those three return series over a selected period of time, we can find an estimate for the beta using either regression analysis or slope function in Excel. To estimate the value of the Treynor Index, we calculate the average value of the portfolio return over the estimation period, as well as the average value of the risk-free rate. Finally, we use the formula above, and subtract from the average value of the portfolio the average value of the risk-free rate, and divide this difference with the estimated value of the beta.

5. Sharpe Ratio. What is the difference between the Sharpe ratio and Treynor Index?

When would you use one versus the other in evaluating a portfolio? (LO 9−4) Answer: The Sharpe ratio is calculated using the following formula: Sharpe ratio =

R − RFree

σ

The Treynor Index is calculated using the following formula: Treynor Index =

R − RFree

β

The numerator for both Sharpe ratio and Treynor Index is the same, which is the excess return of a portfolio, the return of the portfolio minus the risk-free return.

The denominator is what differs between those two ratios.

The Sharpe ratio uses the standard deviation of the returns as the measure of risk, while the Treynor Index uses the portfolio’s beta as the measure of risk. The standard deviation as measure of risk assumes the portfolio is not well diversified, while the beta as measure of risk assumes the portfolio is well diversified. When the portfolio is not fully diversified, the Sharpe ratio provides a better comparison.

When the portfolio is fully diversified, the Treynor Index provides a better comparison.

The Sharpe ratio is the Treynor ratio that uses a portfolio’s beta or correlation with the rest of the market. Beta is a measure of an investment's volatility and risk as compared to the overall market. The goal of the Treynor ratio is to determine whether an investor is being compensated for taking additional risk above the inherent risk of the market. The Treynor ratio formula is the return of the portfolio, minus the risk-free rate, divided by the portfolio’s beta. There are systematic risks such as inflation, interest rates, government policy, etc., which apply to the entire economy. Therefore, Sharpe is a good measure where the portfolio is not properly

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

diversified while Treynor is a better measure where the portfolios are well diversified.

6. Performance Attribution. What types of decisions might a portfolio manager make in order to achieve a return that deviates (hopefully greater) from the return expected? (LO 9−5) Answer: A portfolio manager can perform two types of decisions related to the portfolio that deviate from the benchmark in order to achieve higher returns. (1) The manager can select particular securities and overweigh or under weigh those securities in the portfolio more or less than the benchmark. This is called security selection, or (2) the manager can overweigh or under weigh some asset classes or market sectors relative to the benchmark. Both those decisions aim to achieve higher returns.

Performance attribution is the analytical process to assess the manager’s decisions provided the desired higher returns or not.

7. Security Selection. What are stock pickers trying to achieve? How likely is it that they can achieve it? (LO 9−6) Answer: A stock pick is when an analyst or investor uses a systematic form of analysis to conclude that a particular stock will make a good investment and therefore should be added to their portfolio. This is also known as active management. While it is certainly not impossible to beat the overall market by selecting individual stocks, the data suggests it is an extremely low probability. While it is tempting to believe you (or a financial advisor) can pick the big winners, the notion is simply contradicted by the research and data available.

8. Allocation Effect. How important is the asset allocation decision to the total portfolio realized return? (LO 9−7) Answer: Asset allocation decision is very important to the total portfolio realized return.

Asset allocation is dividing the investment among different asset classes. If the asset allocation of the portfolio follows the allocation of the benchmark, then most likely the realized return of the portfolio will match the return of the benchmark. Portfolio managers sometimes overweigh or under weigh certain asset classes relative to the benchmark in order to earn positive alpha. Also, sometimes they rotate between the asset classes or sectors depending on the economic environment in order to achieve higher returns. Market timing is another type of allocation decision where the manager changes the allocation between stocks and cash to experience the broad market rallies and avoid the bear market declines.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

9. Market Timing. Describe the tremendous potential and hazard of market timing.

(LO 9−8) Answer: Market timing is a strategy where the investor holds stocks during periods when the market is rising, and holds cash during periods of declining market. Market timing has the potential to achieve very high returns if the investor can time the entry to the market and the exit correctly. Because the investor will benefit from the rising market and earn the return, but will not be penalized when the market goes down.

However, if the investor is not able to time the market correctly, and enters and exits the market at incorrect times, then the investor can earn below market returns. The key to be successful is to enter the market at the cusp of the rising time, and exit the market before the market starts declining.

10. Active Investment Management. Describe the advantages and disadvantages of active management versus passive management. (LO 9−9) Answer: An active Investment management involves performing one or more of the following three strategies: 1) hold a non diversified portfolio and pick good stocks, or 2) over weight sectors that perform better, or 3) successfully time the market.

A passive investment approach is the opposite of the active investment approach, where none of the three strategies mentioned above are performed, instead it involves performing a buy-and-hold strategy in which assets are purchased and held for an extended period, those assets can be a well-diversified portfolio or a mutual fund/ETF tracking a broad market index.

Active management strategies provide the potential of earning higher returns than the passive management strategy, since passive management strategy will mostly earn the return of the market. Active management requires much more time to follow the market, analyze assets, sectors, and the economic factors, while passive management does not require the same amount of time and effort as the active management. Active management involves more trading than passive management thus transaction costs are higher. Finally, there is no guarantee that active management will be successful all the time, so there is the potential of earning returns lower than that of passively managed portfolios.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Problems 1. Category Comparison. A portfolio exclusively invests in energy companies (50%) and utilities (50%). The portfolio earned 11% last year. Create a benchmark portfolio from the Morningstar categories. By how much did the portfolio beat its benchmark? (LO 9−1) Morningstar Category Financials Consumer Cyclical Equity Energy Industrials Utilities Technology Large Blend

Return −3.5% 14% 10.5% 5% 10% 13% 11%

Answer: Choose a benchmark that is 50% Equity Energy and 50% Utility Portfolio return = Benchmark return = Alpha

11.00% 10.25% 0.75%

The benchmark portfolio should be constructed in such a way to match how the investment portfolio is constructed. Therefore, the benchmark constructed from the Morningstar categories should be composed of equally weighted categories of Equity Energy and Utilities.

The Benchmark return is RB = (0.5 × 10.5) + (0.5 × 10) = 10.25% The Portfolio return was 11% Therefore, the portfolio beat the benchmark by alpha = 11% − 10.25% = 0.75% 2. Jensen’s Alpha. The market return was 12.5% and the risk-free rate was 3.2%. What is the Jensen’s alpha for these three portfolios? (LO 9−2) a. Return = 11%, beta = 0.75 b. Return = 14%, beta = 1.25 c. Return = 12.5%, beta = 1.05

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Answer: a. b. c. market risk-free

Return 11% 14% 12.50% 12.50% 3.20%

beta 0.75 1.25 1.05

a. b. c.

alpha 0.82% −0.82% −0.47%

In order to calculate the Jensen’s alpha, first we have to calculate the required return based on the CAPM for each portfolio A, B, and C based on the beta values provided and then find the Jensen’s alpha by subtracting, the required return from the return of the realized portfolio.

The CAPM equation to calculate the required return is R = Rf + b × (Rm − Rf) a. Required return = 3.2 + 0.75 × (12.5 − 3.2) = 10.18% Alpha = 11 − 10.18 = 0.82% b. Required return = 3.2 + 1.25 × (12.5 − 3.2) = 14.83% Alpha = 14 − 14.83 = − 0.83% c. Required return = 3.2 + 1.05 × (12.5 − 3.2) = 12.97% Alpha = 12.5 − 12.97 = − 0.47% 3. Alpha. The realized Fama-French 3-Factor model factors are Rm−Rfree = 4.37, SMB = 0.70, and HML = 5.09. The risk-free rate for the month was 0.00. The portfolio realized returns and associated factor betas are shown below. What is each portfolio’s alpha? (LO 9−2) a. RP = 4%, β = 1.1, bSMB = 0.5, bHML = −0.3 b. RP = 6.5%, β = 0.9, bSMB = 1.5, bHML = 0.4 c. RP = 10%, β = 1.2, bSMB = −0.3, bHML = 0.8

Return = Beta = b-SMB = b-HML =

Rm − Rfree = 4.37 SMB = 0.7 HML = 5.09

R-free = 0

A 4 1.1 0.5 −0.3

C 10 1.2 −0.3 0.8

B 6.5 0.9 1.5 0.4

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Answer: Alpha (%) =

A 0.37

B −0.519

C 0.894

In order to calculate the alpha, first we have to calculate the required return based on the Fama−French 3-factor model for each portfolio A, B, and C based on the beta values provided for each factor and then find the alpha by subtracting the required return from the return of the realized portfolio.

The Fama−French 3-factor equation to calculate the required return is: R = Rf + b × (Rm − Rf) + bSMB × SMB + bHML × HML a. Required Return = 0 + (1.1 × 4.37) + (0.5 × 0.7) + (−0.3 × 5.09) = 3.63% Alpha = 4 − 3.63 = 0.37% b. Required Return = 0 + (0.9 × 4.37) + (1.5 × 0.7) + (0.4 × 5.09) = 7.02% Alpha = 6.5 − 7.02 = − 0.52% c. Required Return = 0 + (1.2 × 4.37) + (−0.3 × 0.7) + (0.8 × 5.09) = 9.11% Alpha = 10 − 9.11 = 0.89% 4. Treynor Index. If the return on the S&P 500 Index was 9.3% and the risk-free rate was 2.4%, what is the Treynor Index for the following? (LO 9−3) a. S&P 500 Index b. Portfolio with Return = 12%, beta = 1.25: is this better or worse than the index? c. Portfolio with Return = 10.5%, beta = 1.05: is this better or worse than the portfolio in B? Return Beta a.

9.3% 1 b.

12% 1.25 c.

10.5% 1.05 Risk-free 2.40% Answer: a. b. c.

Treynor Index 6.90% 7.68% better 7.71% better

The Treynor Index is calculated using the following formula: Treynor Index =

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R − RFree

β

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

a. Treynor index S&P 500 = (9.3 − 2.4) / 1 = 6.9%. The beta of S&P 500 is 1. b. Treynor index for Portfolio B = (12 − 2.4) / 1.25 = 7.68%, better than the index which is 6.9%. c. Treynor index for Portfolio C = (10.5 − 2.4) / 1.05 = 7.71%, better than the index which is 6.9%.

5. Sharpe Ratio. The risk-free rate was 2.7%. What is the Sharpe ratio for each of these three portfolios? (LO 9−4) a. S&P 500 Index with Return = 11.4% and standard deviation = 15.7% b. Portfolio with Return = 11.8% and standard deviation = 17.3%: is this better or worse than the index? c. Portfolio with Return = 10.9% and standard deviation = 16.2%: is this better or worse than the portfolio in B?

a. b. c.

Risk-free

Return 11.4% 11.8% 10.9% 2.7%

S.D. 15.7% 17.3% 16.2%

Answer: a. b. c.

Sharpe Ratio 0.55 0.53 worse 0.51 worse

The Sharpe ratio is calculated using the following formula: Sharpe ratio =

R − RFree

σ

a. Sharpe ratio S&P 500 = (11.4 − 2.7) / 15.7 = 0.55 b. Sharpe ratio for Portfolio B = (11.8 − 2.7) / 17.3 = 0.53; worse than the index which is 0.53. c. Sharpe ratio for Portfolio C = (10.9 − 2.7) / 16.2 = 0.51; worse than the index which is 0.53.

Use the data file, ch9_pr06_09.xlsx for problems 6 through 9.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

6. Jensen’s Alpha. Estimate the Jensen alpha of the portfolio. Is it good or bad?

(LO 9−2) Answer: In order to estimate Jensen’s Alpha using the data given for this problem, we can use the following equation: R − Rfree = α + β × (RM − Rfree ) The equation is estimated using linear regression analysis, where the dependent variable is the (R − Rfree), the return of the portfolio minus the risk-free rate. The independent variable is the market risk premium (RM − Rfree).

Alpha is estimated either by using regression analysis or the Intercept function in Excel. Both will give the same numerical value of the alpha. Regression analysis also provides the significance of the alpha statistics, which can be important to tell whether the value found is valid or not.

Note the data provided are in monthly terms, all the columns show monthly data.

First, we have to find the Excess return, the difference of the portfolio return minus the risk-free rate which is found in column H, in the Excel file. Next, we provide the solution of the Alpha using both the Intercept function and the Regression analysis.

In the Intercept function, you choose the y variable as the excess return, while the x variable as the market risk premium that is MKT-Rf data in column D. The same variables are chosen as the Y variable and x variable in the regression analysis.

Alpha = −0.035 A negative value indicates the alpha is bad, although small. However, looking at the significance level of alpha in the regression output shows that the t value is small and the p value is high, which tells us that this is not significant variable.

7. Alpha. Estimate the 4-Factor model alpha of the portfolio. Is it good or bad? (LO 9−2) Answer: In order to estimate Alpha using the 4-Factor model, we can use the following equation: R − Rfree = α + β × (Rm − Rfree) + bSMB × SMB + bHML × HML + bMOM × MOM The equation is estimated using linear regression analysis, where the dependent variable is the (R − Rfree), the return of the portfolio minus the risk-free rate. The independent variable is the market risk premium (RM − Rfree), SMB, HML, and MOM factors.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

In order to estimate the 4-Factor model alpha of the portfolio, we use the regression approach as we did in problem #6. In this case, the y variable is the excess return of the portfolio, while the x variables will be the four different factors, Mkt-Rf, SMB, HML, and MOM factors.

Solving for Alpha we get −0.34551, which is negative, indicating that the portfolio performed badly. Note, the t-stat and the p-value are not significant so the value provided by the Alpha measure should not be considered significant.

8. Treynor Index. Estimate the Treynor Index of the portfolio and of the market portfolio. Which is better? (LO 9−3) Answer: The Treynor Index is calculated using the following formula: Treynor Index =

R − RFree

β

In order to estimate the value of the Treynor Index, you need to estimate the value of the beta for the portfolio. The beta for the market is 1.

We can use the regression analysis or the Slope function in Excel to estimate the beta for the portfolio.

Note: In problem #6, the regression method already provided the value of the beta in the regression output, beta = 0.790 The Slope function gives us the same value for the beta. In the Slope function, you choose the y variable as the excess return, while the x variable as the market risk premium that is MKT-Rf data in column D. To estimate the Treynor Index value, we calculate the average values for the excess return of the portfolio and the Market risk premium to use in the numerator of the Treynor Index.

Treynor Index Portfolio = 0.9833 / 0.790 = 1.244 Treynor Index Market = 1.2882 / 1 = 1.288 The Treynor Index of the Portfolio is better.

9. Sharpe Ratio. Estimate the Sharpe ratio of the portfolio and of the market portfolio.

Which is better? (LO 9−4) Answer: The Sharpe ratio is calculated using the following formula: Sharpe ratio =

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R − RFree

σ

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

To estimate the Sharpe ratio, we calculate the average values for the excess return over the sample period, and divide it with the standard deviation of the portfolio returns. We do the same for the Sharpe ratio of the market.

We already calculated the average values of the excess return and the market risk premium in problem #8.

The standard deviation of the portfolio is 4.51%.

The standard deviation of the market is 4.674%.

Sharpe ratio Portfolio = 0.9833 / 4.51 = 0.218 Sharpe ratio Market= 1.2882 / 4.674 = 0.276 The Sharpe ratio of the market is better.

10. Performance Rankings. Calculate the Treynor Index and Sharpe ratio of each of these portfolios and rank order the portfolios from best to worst using each measure. (LO 9−3, 4) Portfolio Blue Green Red S&P 500

Excess Return 9 11 8 9.5

St. Dev. 20 22 19 18.5

Beta 0.95 1.2 0.8 1

Answer: Portfolio Blue Green Red S&P 500

Treynor 9.47 9.17 10.00 9.50

Sharpe 0.45 0.50 0.42 0.51

Treynor Order 3 4 1 2

Sharpe Order 3 2 4 1

Treynor Index Blue = 9 / 0.95 = 9.47 Treynor Index Green = 11/ 1.2 = 9.17 Treynor Index Red = 8 / 0.8 = 10 Treynor Index S&P 500 = 9.5 / 1 = 9.5 Ranking based on Treynor Index: Red, S&P 500, Blue, Green.

Sharpe ratio Blue = 9/20 = 0.45 Sharpe ratio Green = 11/22 = 0.5 Sharpe ratio Red = 8/19 = 0.42 Sharpe ratio S&P 500 = 9.5/18.5 = 0.51 Ranking based on Sharpe ratio: S&P 500, Green, Blue, Red

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

11. Security Selection. Estimate the security selection ability for stocks, bonds, and total for the following portfolio. (LO 9−6) Asset Class Stocks Bonds

Allocation Target 0.7 0.3

Allocation Actual 0.65 0.35

Benchmark Return 11.0% 3.5%

Fund Return 12.5% 3.6%

Answer: Stocks = 0.975% Bonds = 0.035% Total = 1.010% The security selection ability is calculated by multiplying the difference of the portfolio return in an asset class to the benchmark return for the class with the actual allocation weight in that asset class.

The total selection effect is calculated using the equation: Selection Effect =

 ω × (R − R ) i

Pi

Pi

Bi

The security selection ability is: Stocks: 0.65 × (12.5 − 11) = 0.975% Bonds: 0.35 × (3.6 − 3.5) = 0.035% Total: 0.975 + 0.035 = 1.01% (taking the sum of stocks selection and the bonds selection gives the total selection effect).

12. Security Selection. Estimate the security selection ability for the sectors and for the total portfolio. The data are in the file, ch9_pr12.xlsx. (LO 9−6) Answer: Sector Selection Ability 0.40% 0.26% 0.24% −0.22% 0.09% −0.09% −0.07% 0.00% 0.00% 0.03% 0.00%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

The security selection ability is calculated by multiplying the difference of the portfolio return in an asset class to the benchmark return for the class with the actual allocation weight in that asset class.

The total selection effect is calculated using the equation: Selection Effect =

 ω × (R − R ) i

Pi

Pi

Bi

We calculate the security selection ability for each section and then add them up to get the total selection effect.

Information Technology: 0.307 × (27.6 − 26.3) = 03991% Health Care: 0.154 × (17.1 −15.4) = 0.2618% Consumer Discretionary: 0.128 × (29.6 − 27.7) = 0.2432% Communication Services: 0.111 × (17.7 − 19.7) = −0.222% Financials: 0.105 × (3.4 − 2.5) = 0.0945% Industrials: 0.082 × (−2.5 + 1.4) = − 0.0902% Consumer Staples: 0.063 × (6.8 − 7.9) = − 0.0693% Utilities: 0 × (0 − 5.4) = 0% Materials: 0.015 × (−2.9 + 2.6) = − 0.0045% Real Estate: 0.035 × (7.4 − 6.5) = 0.0315% Energy: 0 × (0 + 15.7) = 0% Total Selection Effect = 03991% + 0.2618% + 0.2432% − 0.222% + 0.0945% − 0.0902% − 0.0693% + 0% − 0.0045% + 0.0315% + 0% = 0.6441% 13. Allocation Effect. Estimate the asset allocation ability for stocks, bonds, and total for the following portfolio. (LO 9−7) Asset Class Stocks Bonds

Allocation Target 0.5 0.5

Allocation Actual 0.55 0.45

Benchmark Return 9.5% 2.5%

Fund Return 10.0% 2.3%

Answer: Stocks = Bonds = Total =

0.175% 0.175% 0.35%

The asset allocation effect is calculated by taking the difference between the actual allocation minus the target allocation for each asset, multiplied by the difference between the actual benchmark return of the asset minus the total benchmark

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

return. The total allocation effect is the sum of each asset’s allocation effect, given by the formula below: Allocation Effect =

 (ω − ω ) × (R − R ) i

Pi

Bi

Bi

B

In order to use the equation, first calculate the Benchmark return RB. RB = (0.5 × 9.5) + (0.5 × 2.5) = 6% Stocks Allocation Effect = (0.55 − 0.5) × (9.5 − 6) = 0.175% Bonds Allocation Effect = (0.45 − 0.5) × (2.5 − 6) = 0.175% Total Allocation Effect = 0.175 + 0.175 = 0.35% 14. Allocation Effect. Estimate the asset allocation ability for the sectors and for the total portfolio. The data are in the file, ch9_pr14.xlsx. (LO 9−7) Answer: Sector Allocation Effect 0.38% −0.01% −0.05% −0.05% −0.01% 0.00% −0.01% 0.36% 0.24% −0.12% 0.38% The asset allocation effect is calculated by taking the difference between the actual allocation minus the target allocation for each asset, multiplied by the difference between the actual benchmark return of the asset minus the total benchmark return. The total allocation effect is the sum of each asset’s allocation effect, given by the formula below: Allocation Effect =

 (ω − ω ) × (R − R ) i

Pi

Bi

Bi

B

In order to use the equation, first calculate the Benchmark return RB. RB = (0.27 × 26.3) + (0.13 × 15.4) + (0.132 × 27.7) + (0.124 × 19.7) + (0.104 × 2.5) + (0.082 × −1.4) + (0.062 × 7.9) + (0.034 × 5.4) + (0.028 × −2.6) + (0.022 × 6.5) + (0.012 × −15.7) = 15.9026%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Information Technology: (0.307 − 0.27) × (26.3 − 15.9026) = 0.3847% Health Care: (0.154 − 0.13) × (15.4 − 15.9026) = − 0.0121% Consumer Discretionary: (0.128 − 0.132) × (27.7 − 15.9026) = −0.0472 % Communication Services: (0.111 − 0.124) × (19.7 − 15.9026) = −0.0494% Financials: (0.105 − 0.104) × (2.5 − 15.9026) = −0.0134% Industrials: (0.082 − 0.082) × (−1.4 − 15.9026) = 0% Consumer Staples: (0.063 − 0.062) × (7.9 − 15.9026) = −0.008% Utilities: (0 − 0.034) × (5.4 − 15.9026) = 0.3571% Materials: (0.015 − 0.028) × (−2.6 − 15.9026) = 0.2405% Real Estate: (0.035 − 0.022) × (6.5 − 15.9026) = −0.1222% Energy: (0 − 0.012) × (−15.7 − 15.9026) = 0.3792% The Total allocation effect = 0.3847% − 0.0121% − 0.0472 % − 0.0494% − 0.0134% + 0% − 0.008% + 0.3571% + 0.2405% − 0.1222% + 0.3792% = 1.1092% 15. Performance Attribution. Estimate the security selection and asset allocation effects for the following portfolio. (LO 9−5) Asset Class Stocks Bonds

Allocation Actual 0.35 0.65

Allocation Target 0.4 0.6

Benchmark Return 10.2% 5.7%

Fund Return 9.8% 6.5%

Answer: Security Selection = Allocation Effect =

0.38% −0.225%

The total selection effect is calculated using the equation: Selection Effect =

 ω × (R − R ) Pi

i

Pi

Bi

The total allocation effect is calculated using the equation: Allocation Effect =

 (ω − ω ) × (R − R ) i

Pi

Bi

Bi

B

Security Selection Effect = 0.35 × (9.8 − 10.2) + 0.65 × (6.5 − 5.7) = 0.38%.

To calculate the total allocation effect, first we need to calculate the return of the benchmark RB. RB = 0.4 × 10.2 + 0.6 × 5.7 = 7.5% Allocation Effect = (0.35 − 0.4) × (10.2 − 7.5) + (0.65 − 0.6) × (5.7 − 7.5) = − 0.225%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

16. Performance Attribution. Estimate the security selection and asset allocation effects for the following global portfolio. The data are in the file, ch9_pr16.xlsx.

(LO 9−5) Asset Class Japan Europe Emerging Market North America

Allocation Target 0.1 0.2 0.3 0.4

Allocation Actual 0.15 0.25 0.27 0.33

Benchmark Return 7.2% 6.7% 15.3% 9.4%

Fund Return 8.6% 6.3% 15.5% 9.5%

Answer: Security Selection = Allocation Effect =

0.20% −0.42%

This is a similar problem to problem #15. We use the same procedure as problem #15 to solve this problem.

Security Selection Effect = 0.15 × (8.6 − 7.2) + 0.25 × (6.3 − 6.7) + 0.27 × (15.5 − 15.3) + 0.33 × (9.5 − 9.4) = 0.197%.

The benchmark return RB = 0.1 × 7.2 + 0.2 × 6.7 + 0.3 × 15.3 + 0.4 × 9.4 = 10.41% Allocation Effect = (0.15 − 0.1) × (7.2 − 10.41) + (0.25 − 0.2) × (6.7 − 10.41) + (0.27 − 0.3) × (15.3 − 10.41) + (0.33 − 0.4) × (9.4 − 10.41) = −0.422% 17. Performance Attribution. Estimate the security selection and asset allocation effects for the following portfolio. The data are in the file, ch9_pr17.xlsx. (LO 9−5) Answer: Sector Selection Ability −0.19% −0.10% 0.07% 0.19% −0.16% 0.04% −0.02% 0.00% 0.02% 0.04% 0.00%

Sector Allocation Effect −0.14% 0.00% −0.03% 0.27% 0.07% 0.00% 0.00% 0.02% −0.04% 0.02% 0.02%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

This is a similar problem to problem #15 and #16. We use the same procedure as problems #15 and #16 to solve this problem.

Security Selection Effect = 0.236 × (17.5 − 18.3) + 0.139 × (7.9 − 8.6) + 0.135 × (5.6 − 5.1) + 0.102 × (−3.5 + 5.4) + 0.105 × (14.4 − 15.9) + 0.082 × (6.1 − 5.6) + 0.088 × (8.6 − 8.8) + 0.036 × (5.3 − 5.4) + 0.035 × (4.8 − 4.2) + 0.031 × (13.7 − 12.5) + 0.011 × (−2.4 + 2.2) = −0.1065% The return of the benchmark RB is: RB = (0.251 × 18.3) + (0.142 × 8.6) + (0.128 × 5.1) + (0.121 × −5.4) + (0.095 × 15.9) + (0.081 × 5.6) + (0.076 × 8.8) + (0.042 × 5.4) + (0.027 × 4.2) + (0.024 × 12.5) + (0.013 × −2.2) = 9.0584% Allocation Effect = (0.236 − 0.251) × (18.3 − 9.0584) + (0.139 − 0.142) × (8.6 − 9.0584) + (0.135−0.128) × (5.1 − 9.0584) + (0.102 − 0.121) × (−5.4 − 9.0584) + (0.105 − 0.095) × (15.9 − 9.0584) + (0.082 − 0.081) × (5.6 − 9.0584) + (0.088 − 0.076) × (8.8 − 9.0584) + (0.036 − 0.042) × (5.4 − 9.0584) + (0.035 − 0.027) × (4.2 − 9.0584) + (0.031 − 0.024) × (12.5 − 9.0584) + (0.011 − 0.013) × (−2.2 − 9.0584) = 0.2013% 18. Market Timing. What are the best and worst annual returns possible by market timing using the risk-free yield (annual return) and the S&P 500 Index monthly returns in file ch9_pr18.xlsx. (LO 9−8) Answer: Best Return = 22.87% Worst Return = −7.78% The best annual return will be achieved when the investor holds S&P 500 during the months when S&P 500 earned positive return, and during the months when S&P earned negative return the investor holds the risk-free asset. Based on the information provided, the best annual return will be achieved if the investor holds S&P 500 during months of March, April, May, July, August, September, November, and December, while holding the Risk-free asset during the rest of the months.

To calculate the best annual return, we multiply 1+ each monthly return together, and subtract 1.

Note, since the risk-free rate is given in annual terms, then we have to divide them by 12 to have the monthly rate.

Best Annual return = [(1 + 0.0001/12) × (1 + 0.0002/12) × (1+ 0.06962) × (1 + 0.00921) × (1 + 0.01781) × (1+ 0.0002/12) × (1 + 0.03952) × (1 + 0.00502) × (1 + 0.00252) × (1 + 0.0002/12) × (1 + 0.04861) × (1 + 0.01823)] − 1= 0.22875 or 22.875%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

The worst annual return is achieved if the investor could not time the market at all, and invested in S&P 500 during the months when the market was down and invested in the risk free during the months when the market was up. The worst annual return will be when the investor holds S&P 500 during months of January, February, June, and October, while holding the risk-free asset the rest of the months.

Worst Annual return = [(1 − 0.05769) × (1 − 0.00078) × (1 + 0.0002/12) × (1 + 0.0001/12) × (1 + 0.0001/12) × (1 − 0.00048) × (1 + 0.0002/12) × (1 + 0.0002/12) × (1 + 0.0002/12) × (1 − 0.02018) × (1 + 0.0001/12) × (1 + 0.0003/12)] − 1 = −0.07776 or −7.776% 19. Sector Rotation. Consider a strategy of a portfolio being completely invested in one sector and then rotating it to possibly a different sector the next year. The goal is to always own the best sector. See the five sectors and their annual returns shown in file ch9_pr19.xlsx. What would your annual return be if you succeeded in always owning the best sector? What annual return would you have if you always owned by the worst sector? (LO 9−8) Answer: Best = Worst =

25.17% −19.42%

This is a similar problem to problem #18. We follow similar approach to solve for the problem.

The data provides annual returns for five different sectors over 11 years. In order to achieve the best return possible, the investor should have invested in the sector that yielded the highest return per year.

Highest Return = [(1 + 0.3784) × (1 − 0.0862) × (1 + 0.2544) × (1 + 0.6915) × (1 + 0.1420) × (1 + 0.0476) × (1 + 0.3788) × (1 + 0.2549) × (1 − 0.1102) × (1 + 0.2596) × (1 + 0.9053)]^(1/11) − 1 = 0.2516 or 25.167% The lowest return is achieved if the investor invested in the sector that yielded the lowest return per year.

Lowest Return = [(1 + 0.2197) × (1 − 0.2399) × (1 − 0.1197) × (1 + 0.1978) × (1 − 0.3872) × (1 − 0.4698) × (1 − 0.1121) × (1 − 0.1254) × (1 − 0.3695) × (1 − 0.1800) × (1 − 0.2705)]^(1/11) − 1 = −0.19418 or −19.42% Note: there are 11 annual returns, to calculate an annual return, we multiply those 11 returns chain-linked then take the product to the power 1/11 to get the annualized value.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

20. Market Timing. Estimate the market parameter in Equation 9−7 for the portfolio in file ch9_pr20.xlsx. Is there evidence of market timing ability? (LO 9−8) Answer: Equation 9−7 is the following: RP − RFree = α + β (RM − RFree ) + c (RM − RFree ) + ε 2

We can estimate the market parameters for this equation by using the regression analysis feature of Excel.

In order to perform the estimation, first we need to calculate the value of (RM − RFree)2, which is done by taking the squared value of Column E, and the result is provided in column F. In the Regression analysis window, we select the y variable is the excess return of the portfolio, while the x variables will be both (RM − RFree) and (RM − RFree)2.

The output provides the value of c = 0.009572. The market timing parameter has a positive value; however, it is not significant based on the t-value and the p-value in the Regression output.

Since the c parameter is not significant, then there is no evidence of market timing ability.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

Case Study Performance Evaluation Download the following data files from the Kenneth French Data Library (https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html): • •

17 Industry Portfolios file (CSV format) Fama/French 3 Factors (CSV format)

Use five years of monthly data ending in December, 2021. For the (1) Retail and (2) Steel industries, compute the following: a. b. c. d. e. f.

Jensen’s alpha 3-Factor alpha Treynor Index Sharpe Ratio Market Timing ability Compare the results for the two industries.

The data collected from the Kenneth French library covers from December 2016 to November 2021, a total of 60 data points, covering 5-year period. The December 2021 data was not available yet when this solution was written. In the future, you can download from January 2017 to December 2021.

The data provided in the 17 Industry portfolio file contains equally weighted portfolios and value-weighted portfolios for each industry.

This solution provides the answers for both types of portfolio weightings.

We calculate the excess returns of the portfolios by subtracting the risk-free rate from the portfolio returns. The results are provided in columns M, N, O, and P. Also, we calculated the square of the market risk premium column for the market timing regression.

The results for using the value-weighted portfolios for Steel and Retail are shown below in the table.

Jensen's Alpha 3-Factor Alpha Treynor Index Sharpe Ratio Market Timing Ability

Value-Weighted Steel

Value-Weighted Retail

−1.00729 −0.1603 0.723577 0.11706 −0.0118

0.385523 0.026587 1.842929 0.333204 0.018335

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 09: Portfolio Performance Analytics

The retail value-weighted retail portfolio has better performance using all four riskmeasures than the value-weighted steel portfolio.

The market timing variable is positive but small for value-weighted retail portfolio and is significant having large value of t statistic and small p-value; while it is negative and small for value-weighted steel portfolio and is not significant. So there is some market timing in the retail portfolio.

The results for using the equally weighted portfolios for Steel and Retail are shown below in the table.

Jensen's Alpha 3-Factor Alpha Treynor Index Sharpe Ratio Market Timing Ability

Equally Weighted Steel −0.73588 0.208801 0.886521 0.14859 −0.02441

Equally Weighted Retail 0.600978 0.469663 −16.0867 0.06074 0.01606

The results here are mixed. The equally weighted retail portfolio has larger Jensen’s alpha and 3-Factor alpha. While the Equally weighted Steel portfolio has larger Treynor Index value and Sharpe ratio value. The market timing variable is insignificant for both portfolios, with the retail portfolio having positive value while the steel portfolio having negative value.

The beta for the equally weighted retail portfolio was −0.034, very low negative number which caused the Treynor index to have such a large negative value, also the standard deviation of the equally weighted retail portfolio was about twice as much as the standard deviation of the value-weighted retail portfolio. Most likely explanation is the weighting choice affected the values of the performance attribution variables.

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23

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 13

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

Questions 1. GDP. What is the impact on GDP if consumer spending increases? Would the answer be different if consumer spending were directed toward foreign goods? (LO 10-1) Answer: Gross domestic product (GDP) is the total dollar value of all final goods and services newly produced within the country’s boundaries with domestic factors of production. GDP is calculated by adding the expenditures of the sectors of an economy. These expenditures are personal consumption (C ), gross private domestic investment (I ), government spending (G ), and net exports (E ). The sum, GDP, is given by the following equation: GDP = C + I + G + E

If the consumer spending increases, then GDP will increase as well, because consumer spending is the personal consumption component C in the GDP equation.

If the consumer spending is directed toward foreign goods, which means local consumers are buying foreign goods and imports are increasing, that will impact GDP negatively and GDP will decrease.

2. Inflation. What differentiates inflation and deflation? If both GDP and unemployment were simultaneously rising, would this period be classified as a recession? (LO 10-2) Answer: Inflation is an increase in the general prices of goods and services in an economy.

Deflation, conversely, is the general decline in prices for goods and services, indicated by an inflation rate that falls below zero percent.

Recession is a period in an economy where GDP declines for at least two successive quarters. During a recession, unemployment may also rise. However, it is not a recession if both GDP and unemployment are rising. When GDP is rising, that means there is economic activity going on and the economy is still expanding, in this situation, unemployment may increase if it doesn't keep up with the pace of the GDP, which is the case. When an economy emerges from a recession, or a slowing period, the rise in employment usually lags. That is where we can see the phenomenon asked about in this question.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

3. Interest Rates. What factors, besides the expected rate of inflation, may affect the rate of interest a borrower pays? (LO 10-2) Answer: Demand for and supply of money, government borrowing, inflation, Central Bank's monetary policy objectives affect the interest rates are the four factors that may impact Interest rates The interest rate a borrower pays is affected by the following factors: the real riskfree rate, the expected rate of inflation, the riskiness of the borrower, the liquidity of the loan, and the term to maturity of the loan. The factors that affect an interest rate are on the right-hand side of the equation below. i = ir + pi + pd + pl + pt

The current nominal interest rate (i) is the sum of the real risk-free rate (ir) plus a series of premiums: the premium for expected inflation (pi), the premium for default risk (pd), the premium for liquidity (pl), and the premium for the term to maturity (pt).

4. Federal Reserve. What is the Fed? What are its economic goals? (LO 10-3) Answer: The Federal Reserve System, or the “Fed,” is the Central Bank of the United States.

The Fed’s goals are full employment, economic growth, and stable prices. The Fed has an effect on the level of economic activity because it changes interest rates.

Through its impact on the cost of credit, the Fed controls inflation or stimulates employment and economic growth. The Fed affects interest rates through its power to change the money supply by using the tools of monetary policy: the reserve requirements of banks, the discount rate, and open market operations.

The Federal Reserve System (FRS), often called simply the Fed, is the central bank of the United States and arguably the most powerful financial institution in the world.

It was founded to provide the country with a safe, flexible, and stable monetary and financial system.

5. Monetary Policy. How does the Fed pursue its economic goals? How may the tools of monetary policy affect securities prices? (LO 10-4) Answer: The Fed pursues its economic goals through its impact on the supply of money and the cost of credit. Monetary policy refers to changes in the supply of money and credit. When the Fed wants to increase the supply of money and credit to help expand the level of income and employment, it follows an easy monetary policy.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

When it wants to contract the supply of money and credit to help fight inflation, it pursues a tight monetary policy.

The Fed affects interest rates through its power to change the money supply by using the tools of monetary policy: the reserve requirements of banks, the discount rate, and open market operations.

Changes in monetary policy affect stock prices. This impact may be the result of a change in the required return used to discount future cash flows. For example, in the capital asset pricing model, a higher risk-free rate would lead to a higher required return and lower stock valuations. Monetary policy may also affect stock prices through its effect on a firm’s earning capacity. An easy monetary policy that reduces the cost of credit may increase earnings, resulting in higher dividends and more growth through the retention of earnings. A tight monetary policy should have the opposite impact. Higher interest rates should reduce earnings, which reduces the firm’s ability to expand and pay dividends.

6. Discount Rate. What is the difference between the discount rate and the target federal funds rate? (LO 10-3) Answer: The fed funds rate is the interest rate that depository institutions—banks, savings and loans, and credit unions—charge each other for overnight loans. The discount rate is the interest rate that Federal Reserve Banks charge when they make collateralized loans—usually overnight—to depository institutions.

The discount rate is the interest rate the Fed charges depository institutions for borrowing reserves. When banks borrow from the Fed, they receive excess reserves.

When these reserves are loaned, they expand the supply of money and credit.

Depository institutions may also borrow from the Fed when they determine that they have insufficient reserves to meet their reserve requirements. In that case, borrowing the required reserves would not expand the supply of money and credit, because the expansion had already occurred at the time the loans were made.

The federal funds rate is the interest charged by banks when they lend reserves to each other. Banks with excess reserves can put those funds to work by lending them to other banks in the federal funds market, and the bank in need of reserves acquires them without having to borrow from the Fed. The Fed uses open market operations to control the target federal funds rate. Open market operations are buying and selling of Treasury bills by the Fed, which results in adjusting the short-term rates to its target federal funds rate.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

7. Monetary Supply. What are M1 and M2? How does the Fed alter M1 and M2?

(LO 10-5) Answer: M1 and M2 are two different definitions of money supply. M1 is the sum of currency, coins, and checking accounts (including interest-bearing checking accounts) in the hands of the public. M2 adds savings accounts to this definition.

Thus, if individuals shift funds from savings accounts to checking accounts, the money supply is increased under the narrow definition of M1 but is unaffected under the broader definition of M2. The Fed controls the money supply and uses its monetary policy tools to either increase or decrease it.

8. Monetary Supply. Do the fundamental economic goals of fiscal policy differ from those of monetary policy? If the Fed finances the federal government’s deficit, what will happen to the supply of money? (LO 10-6) Answer: Fiscal policy is taxation, expenditures, and debt management by the federal government. Monetary policy refers to changes in the supply of money and credit.

They both can be used to pursue the economic goals of price stability, full employment, and economic growth.

If the Fed were to finance the federal government’s deficit, the impact would be the same as if the Fed had purchased securities through open market operations. In either case, the money supply would be increased. In effect, when the Fed buys the securities issued to finance the federal government’s deficit, it is monetizing the debt because new money is created. This is essentially what occurred during the period of the Fed’s quantitative easing, which followed the financial crisis. The federal government ran a sizable deficit that had to be financed. Federal government securities were sold in the financial markets virtually every week and were also sold to the Fed. The Fed’s buying of the securities increased the supply of money and created liquidity, which reduced interest rates.

9. Recessions. What are the primary differences between the recession stemming from the housing bubble in 2007−2008 and that arising from the COVID-19 pandemic? (LO 10-7) Answer: Both the recession stemming from the housing bubble in 2007−2008 and that arising from the COVID-19 pandemic resulted in the federal government’s taking unprecedented steps designed to stimulate economic activity. At the same time, the Fed also took similar actions to stimulate the economy. The Fed pursued a highly

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

expansionary monetary policy by driving interest rates to historic lows in both cases.

The Fed used open market operations to buy Treasury securities as well as a variety of other debt instruments. Such purchases had the effect of increasing the money supply.

The U.S. government also enacted new legislation to provide support and stimulus to the economy. The major difference is in the size of the stimulus package provided by the U.S. government: the COVID-19 pandemic package was much larger than the one provided for the financial crisis.

10. Inflation. How does expanding the monetary supply encourage inflation? (LO 10-7) Answer: Increasing the money supply faster than the growth in real output will cause inflation. The reason is that there is more money chasing the same number of goods. Therefore, the increase in monetary demand causes firms to put up prices.

Expansionary monetary policy aims to increase growth by reducing interest rates and expanding the money supply to make cheaper credit available. One of the drawbacks of such a policy is its impact on rising inflation. Expanding the money supply encourages inflation because as more money is available to the economy, and more and cheaper credit is available, the availability of goods and services does not follow the same pace. This leads to an increase in the prices of those goods and services. This is what happened during the COVID-19 pandemic. Both the Fed and the U.S. government made extremely large amounts of money available in the economy, but because of supply shortages and issues with the supply chain, goods and services did not grow as fast as the growth of the money, and that caused inflation to increase.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

Problems 1. GDP. If U.S. personal consumption were $12,147,400 million, government spending were $2,805,200 million, gross private domestic investment were $5,345,400 million, and net exports were $1,645,200 million, what would GDP be? (LO 10-1) Answer: Personal consumption Government spending Gross private domestic investment Net exports GDP

$12,147,400 $2,805,200 $5,345,400 $1,645,200 $21,943,200

The gross domestic product (GDP), which is the total dollar value of all final goods and services newly produced within the country’s boundaries with domestic factors of production, can be found using the following relationship: GDP = C + I + G + E

Where C is the personal consumption, I is the gross private domestic investment, G is the government spending, and E is the net exports, which is the difference between a country's exports and imports.

In the example, we have: C = $12,147,400 million I = $5,345,400 million G = $2,805,200 million E = $1,645,200 million GDP = $12,147,400 + $5,345,400 + $2,805,200 + $1,645,200 = $21,943,200 million 2. Inflation. If GDP were $17,147,400 million, government spending were $2,805,200 million, personal consumption were $15,312,000 million, and gross private domestic investment were $5,345,400 million, what would net exports be? (LO 10-1) Answer: Personal consumption Government spending Gross private domestic investment Net exports GDP

$15,312,000 $2,805,200 $5,345,400 $6,315,200 $17,147,400

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

The gross domestic product (GDP) can be found using the following relationship: GDP = C + I + G + E

Where C is the personal consumption, I is the gross private domestic investment, G is the government spending, and E is the net exports, which is the difference between a country's exports and imports.

In this example, the GDP is given, and the question is asking to find the value of the net exports, E. We solve for E: E = GDP − C − I − G E = $17,147,400 − $15,312,000 − $5,345,400 − $2,805,200 = −$6,315,200 million The value of net exports being negative means that, for this country, the value of the imports were higher than the value of the exports.

3. Interest rates. If GDP were $18,204,700 million, net exports were −$2,805,200 million, personal consumption were $15,312,000 million, and gross private domestic investment were $5,345,400 million, what would government spending be? (LO 10-1) Answer: Personal consumption Government spending Gross private domestic investment Net exports GDP

$15,312,000 $352,500 $5,345,400 $2,805,200 $18,204,700

The gross domestic product (GDP) can be found using the following relationship: GDP = C + I + G + E

Where C is the personal consumption, I is the gross private domestic investment, G is the government spending, and E is the net exports, which is the difference between a country's exports and imports.

In this example, the GDP is given, and the question is asking to find the value of government spending, G. G = GDP − C − I − E G = $18,204,700 − $15,312,000 − $5,345,400 + $2,805,200 = $352,500 million Note: Because the net exports were negative, the sign changes to addition in the equation.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

4. Federal Reserve. If the CPI rose from 242.459 to 244.205, what would be the percentage change in the CPI on an annualized effective basis? (LO 10-2) Answer: Starting CPI Ending CPI Percentage change Annualized basis

242.459 244.205 0.7201% 8.99%

The CPI rose from 242.459 to 244.205 over a one-month period. Therefore, the monthly nominal percentage change is the following: 244.205 / 242.459 − 1 = 0.00720, or 0.720% To find the annualized effective rate from the monthly nominal rate, we can use the following formula: Annual Effective Rate = (1 + Monthly Nominal Rate)12 − 1 Annual Effective Rate = (1 + 0.00720)12 − 1 = 0.08992, or 8.992% 5. Fiscal policy. If the CPI rose from 242.459 to 244.205, what would be the percentage change in the CPI on an annualized nominal basis? (LO 10-2) Answer: Starting CPI Ending CPI Percentage change Nominal annual change

242.459 244.205 0.720% 8.64%

The CPI rose from 242.459 to 244.205 over a one-month period. Therefore, the monthly nominal percentage change is the following: 244.205 / 242.459 − 1 = 0.00720, or 0.720% The annualized nominal rate is found by multiplying the monthly nominal rate by 12.

Annualized Nominal Rate = 12 × 0.720% = 8.64%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

6. Discount rate. If the CPI fell from 257.314 to 254.205, what would be the percentage change in the CPI on an annualized effective basis? (LO 10-2) Answer: Starting CPI Ending CPI Percentage change Annualized basis

257.314 254.205 −1.208% −13.5706%

The CPI fell from 257.314 to 254.205 over a one-month period. Therefore, the monthly nominal percentage change is the following: 254.205 / 257.314 − 1 = −0.01208, or −1.208% To find the annualized effective rate from the monthly nominal rate, we can use the following formula: Annual Effective Rate = (1 + Monthly Nominal Rate)12 − 1 Annual Effective Rate = (1 − 0.01208)12 − 1 = −0.135706, or −13.5706% 7. Monetary supply. If the CPI fell from 257.314 to 254.205, what would be the percentage change in the CPI on an annualized nominal basis? (LO 10-2) Answer: Starting CPI Ending CPI Percentage change Nominal annual change

257.314 254.205 −1.208% −14.496%

The CPI fell from 257.314 to 254.205 over a one-month period. Therefore, the monthly nominal percentage change is the following: 254.205 / 257.314 − 1 = −0.01208, or −1.208% The annualized nominal rate is found by multiplying the monthly nominal rate by 12.

Annualized Nominal Rate = 12 × −1.208% = −14.496% Note: In Problem 6, the effective rate was calculated. The nominal rate was calculated in this problem. The effective rate is always larger or at least equal to the nominal rate but never smaller, because the effective rate includes the compounding effect. −13.57% is larger than −14.50%, so the relationship holds with negative numbers as well.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

8. Monetary supply. If the quoted nominal annual rate on a bond is 9.00%, but the real risk-free rate is 1.50%, the premium for expected inflation is 1.75%, the liquidity premium is 1.25%, and the maturity premium is 2.00%, what is the default premium for the bond? (LO 10-2) Answer: Nominal annual rate Real risk-free rate Inflation premium Liquidity premium Maturity premium Default premium

9.00% 1.50% 1.75% 1.25% 2.00% 2.50%

The nominal interest rate can be expressed by the following equation: i = ir + pi + pd + pl + pt

Where i (i) is the nominal interest rate, which is given by the sum of the real risk-free rate (ir) plus a series of premiums: the premium for expected inflation (pi), the premium for default risk (pd), the premium for liquidity (pl), and the premium for the term to maturity (pt).

In this example, the question is asking to find the premium for default risk. pd = 9.00% − 1.50% − 1.75% − 1.25% − 2.00% = 2.50% 9. Recessions. If the quoted nominal annual rate on a bond is 11.50%, but the real risk-free rate is 1.50%, the premium for expected inflation is 1.75%, the default premium is 1.25%, and the maturity premium is 2.00%, what is the liquidity premium for the bond? (LO 10-2) Answer: Nominal annual rate Real risk-free rate Inflation premium Liquidity premium Maturity premium Default premium

11.50% 1.50% 1.75% 5.00% 2.00% 1.25%

The nominal interest rate can be expressed by the following equation: i = ir + pi + pd + pl + pt

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

Where i is the nominal interest rate, which is given by the sum of the real risk-free rate (ir) plus a series of premiums: the premium for expected inflation (pi), the premium for default risk (pd), the premium for liquidity (pl), and the premium for the term to maturity (pt).

In this example, the question is asking to find the liquidity premium for the bond. pl = 11.50% − 1.50% − 1.75% − 1.25% − 2.00% = 5.00% 10. Inflation. If the default premium on a bond is 3.00%, but the real risk-free rate is 1.50%, the premium for expected inflation is 1.75%, the liquidity premium is 1.25%, and the maturity premium is 2.00%, what should be the quoted nominal annual rate for the bond? (LO 10-2) Answer: Nominal annual rate Real risk-free rate Inflation premium Liquidity premium Maturity premium Default premium

9.50% 1.50% 1.75% 1.25% 2.00% 3.00%

The nominal interest rate can be expressed by the following equation: i = ir + pi + pd + pl + pt

Where i is the nominal interest rate, which is given by the sum of the real risk-free rate (ir) plus a series of premiums: the premium for expected inflation (pi), the premium for default risk (pd), the premium for liquidity (pl), and the premium for the term to maturity (pt). i = 1.50% + 1.75% + 3.00% + 1.25% + 2.00% = 9.50%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 10: The Macroeconomic Environment for Investment Decisions

Case Study Dealing with Inflation Suppose that the current trend in the U.S. economy toward increased inflation continues. a. What actions could you expect the U.S. government to take to try and head off this inflation? b. Assuming you expected the government to be unsuccessful at staving off inflation, how would that affect your investment strategies? Why? c. How would your answers to a and b above change if you expected variants of COVID-19 to continue to have an effect on health, and hence economic stability, in the United States?

Answers: a. The Fed would be expected to purse a contractionary monetary policy to increase the interest rates to try to reduce the inflation. One of the Fed’s goals is to keep prices stable. Increasing inflation in the U.S. economy results in the opposite of this goal; therefore, the Fed will react by using monetary tools to increase interest rates and reduce inflation.

The government can also take measures to reduce inflation by reducing spending and/or increasing taxes. However, the Fed is usually the first to act. b. If the government is unsuccessful at staving off inflation, would someone change their investment strategy? Investment strategies usually depend on the particular investor and their risk and return objectives, any constraints they may have, their time horizon, etc. However, one particular strategy that would be beneficial is to invest in TIPS if inflation persists. TIPS, Inflation Protected Treasury Securities, are issued by the U.S. government, so they provide some protection in a high inflationary environment. In addition, investors usually shift their investment focus toward commodities—gold, in particular—during periods of high inflation (whether gold is an inflation hedge or not is debatable). c. If the COVID-19 pandemic persists, and new variants emerge that require lockdowns and impact economic activity—which will eventually keep inflation high—similar strategies can be used as in part b. Stocks will still be a good choice: even though the stock market will be affected in the short run by inflationary fears and fears from COVID-19 health effects, it will rebound and stocks will climb in the long run.

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13

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 20

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Questions 1. Distribution of Dividends. Describe the timing dynamics of a company announcing and paying a cash dividend. (LO 11-1) Answer: The firm’s board of directors meets and declares a dividend. Two important dates are established. The first date determines who is to receive the dividend. On the date of record, everyone who owns stock in the company at the end of that day receives the dividend. The second important date when a dividend is declared is the day on which the dividend is paid, or the distribution date. The distribution date may be several weeks after the date of record, as the company must determine who the owners were as of the date of record and process the dividend checks.

There is also another important date established by the market, the ex-dividend date. The stock is traded ex-dividend, for the price of the stock does not include the dividend payment. This ex-dividend date is two trading days prior to the date of record, because the settlement date for a stock purchase is three working days after the transaction. In order to receive the dividend, you must purchase the stock one day before the ex-dividend day.

2. Dividend Payments. How do stock dividends differ from cash dividends? How do stock dividends differ from stock splits? (LO 11-2) Answer: Cash dividends: When investors and other financial experts use the word “dividend,” they’re usually referring to cash dividends. When a profitable company distributes dividend to its shareholders by way of cash, it is known as a cash dividend.

Stock dividends: When a company, whether profitable or not, decides to distribute its own stocks to its equity shareholders in exchange for their investment in the company, it is said to have distributed stock dividends Stock dividend and stock splits: Cash dividend means dividend that is paid to shareholders in Cash/Bank. When a company doesn’t have cash for payment of dividends, it gives dividends in the form of equity or additional shares of the company are allotted to the shareholder. This term is called a stock dividend.

Stock split is one of the forms of Corporate Action. Stock split and stock dividend are different and cannot be used interchangeably. Let’s understand the Stock Split. As the name itself tells the meaning, a stock split means splitting of stock or equity shares. Stock splits are splitting of already issued shares to increase the number of shares of the company.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

3. Ratio Analysis. What do the liquidity ratios, activity ratios, profitability ratios, leverage ratios, and coverage ratios tell you about a firm? (LO 11-3) Answer: Liquidity is the ease with which assets may be quickly converted into cash without the firm’s incurring a loss. If a firm has a high degree of liquidity, it will be able to meet its debt obligations as they become due. Therefore, liquidity ratios provide information about the liquidity position of the firm and its ability to pay its shortterm obligations.

Activity ratios indicate at what rate the firm is turning its inventory and accounts receivable into cash. The more rapidly the firm turns over its inventory and receivables, the more quickly it acquires cash. High turnover indicates that the firm is rapidly receiving cash and is in a better position to pay its liabilities as they become due.

Profitability ratios are measures of performance that indicate the amount the firm is earning, i.e., generating profit relative to some base, such as sales, assets, or equity.

Higher profitability ratios indicate better performance.

Leverage ratios measure the amount of debt financing the firm uses to finance its assets. High leverage ratios indicate high use of debt, which could be a source of potential financial risk. Because debt financing increases risk, each of these ratios is extremely valuable in analyzing the financial position of the firm. The most used capitalization ratios are the debt-to-equity ratio and the debt-to-total assets ratio.

Coverage ratios measure the ability of the firm to service its debt and preferred stock. For debt, the ratios indicate to creditors and bondholders how much the firm is earning from its operations relative to what is owed. The coverage for interest payments is called times interest earned.

4. Statement of Cash Flows. What does the statement of cash flows add to the analyst’s knowledge of the firm? (LO 11-4) Answer: A cash flow analysis determines a company's working capital — the amount of money available to run business operations and complete transactions. That is calculated as current assets (cash or near-cash assets, like notes receivable) minus current liabilities (liabilities due during the upcoming accounting period). It is a financial statement that summarizes the amount of cash and cash equivalents entering and leaving a company. The CFS measures how well a company manages its cash position, meaning how well the company generates cash.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

The cash flow is widely believed to be the most important of the three financial statements because it is useful in determining whether a company will be able to pay its bills and make the necessary investments.

5. Future Price. Under what circumstances might you use the constant growth rate model compared to the PE model to estimate a future price? (LO 11-5) Answer: The constant growth model can be used to estimate the future value of a company if the company is assumed to be growing at a constant rate, starting sometime in the future. This method works well for companies that don’t have a constant growth rate now but may be expected to in the future. You could estimate dividends each year until the mature growth rate starts and then estimate the future price at that year.

The PE model can be used to estimate the future price of a stock if the PE multiple can be estimated accurately and the firm’s earnings in the future can be estimated accurately as well. So, if you knew the PE multiple of a stock years from now and knew the company earnings, you could compute the stock’s price.

6. Dividend Discount Model. What inputs are needed to value a stock using the dividend discount model? (LO 11-6) Answer: The general form of the dividend discount model is the following: P0 =

D1 1

(1 + r )

+

D2 2

(1 + r )

+

D3 (1 + r )

3

++

Dn (1 + r )

n

+

Pn (1 + r )n

The model has infinite life, since stocks are assumed to have infinite life. It is not easy to estimate the dividends that a stock will pay over infinite period. Therefore, in order to value a stock using this model, you need to estimate the dividends that the stock will pay over a finite period of time, for example five years, and estimate the terminal value of the stock at the end of this finite period, using either the constant growth model or the PE multiple. Also, you need an estimate of the required return that is used as the discount rate.

Therefore, the inputs needed are the dividends over a period of time, the terminal value, and the required return.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

7. Analysts. Why do you see sell-side analyst forecasts but not buy-side analyst forecasts? What incentives may each offer? (LO 11-7) Answer: Sell-side analysts work for investment banks and brokerage firms. Their forecasts are public. Sell-side analysts try to generate interest in stocks that leads to trading through their employer. This type of analyst is commonly seen on CNN and other business outlets, and their forecasts are reported publicly. They commonly report a price target, earnings estimates, growth estimates, and a recommendation as to whether to buy, sell, or hold. The typical sell-side analyst focuses on one or two industries in order to become an expert in those firms. Sell-side analysts have been criticized as a group for having a positive bias. The criticisms come because they work for investment banks, who have a business relationship with the companies being examined. Because of that business relationship, the analysts will often stop providing forecasts rather than recommend a “sell” type rating. The Sarbanes–Oxley Act of 2002 attempted to eliminate the incentives for biased analyst recommendations, which has helped but not solved the problem.

The buy-side analyst works for an institutional investor, like a mutual fund, hedge fund, or pension fund. The forecasts of this type of analyst are private recommendations to the fund about what they should buy, sell, or hold. You will not see their recommendations. Therefore, all analyst forecasts that are publicly reported are from sell-side analysts.

8. PE ratios. What are the differences between the PE ratio, forward PE ratio, and Shiller PE ratio? (LO 11-8) Answer: The Price-to-earnings (PE) ratio is defined as the price of a stock divided by the earnings per share. Unless otherwise stated, the earnings are measured from the past 12 months. The PE ratio can be used to calculate the value of a stock by taking the product of the earnings per share and the PE multiple.

The forward PE ratio is defined as the current price divided by the expected earnings in the next 12 months. Therefore, the forward PE ratio uses the expected earnings in the next 12 months as the denominator, while the PE ratio uses the past earnings.

The Shiller PE ratio, named after the Nobel laureate Robert Shiller, is defined as the current stock price divided by the average of 10 years of inflation-adjusted earnings.

Because of the long period, the price and earnings are adjusted for inflation. This ratio is usually referred to as the Shiller PE ratio, or the CAPE ratio (cyclically

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

adjusted price-to-earnings). The Shiller PE ratio is used for the stock market most often, while the PE ratio and the forward PE ratio are used for individual stocks.

9. PEG ratio. What does a PEG ratio tell you? (LO 11-9) Answer: The PEG ratio is defined as the PE ratio divided by the earnings growth rate.

The PEG ratio standardizes PE ratios for growth. It gives a relative measure of value and facilitates comparing firms with different growth rates. If the growth rate exceeds the PE ratio, the numerical value is less than 1.0 and suggests that the stock is undervalued. If the PE ratio exceeds the growth rate, the PEG ratio is greater than 1.0. The higher the numerical value, the higher the valuation and the less attractive is the stock. A PEG of 1.0 to 2.0 may suggest the stock is reasonably valued, and a ratio greater than 2.0 may suggest the stock is overvalued.

10. PEG ratio. What are the value and growth investment strategies? Which is better?

(LO 11-10) Answer: Value investing is an investment strategy focusing on investing in securities that are considered to be undervalued or unpopular for various reasons. Growth-stock investing is an investment strategy focusing on investing in securities that are expected to have above-average rates of growth in sales and earnings.

In both cases, investors seek to find stocks that are selling at prices below their actual value, or intrinsic value. In value investing, bargains are typically described in terms of a market price that is below its value of assets in place or future discounted cash flows. In growth-stock investing, bargains are defined in terms of securities selling for prices below the value of future growth opportunities.

It is hard to say one is better than the other, as each strategy can work if applied correctly. Analyzing the historical data, there were time periods where value investing worked better than growth investing, and other times when the opposite was true.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Problems 1. Payout. What are the payout ratio and retention ratio of the three companies?

(LO 11-2)

Company A Company B Company C

Earnings per share $0.52 $2.66 $3.65

Dividends per share $0.76 $1.64 $1.60

Answer:

a. b. c.

Payout Retention Ratio Ratio 146% −46% 62% 38% 44% 56%

The payout ratio is calculated by dividing the dividends per share with the earnings per share.

The retention ratio is equal to 1 − the payout ratio, since the retention ratio represents the part of the earnings that is not paid out as dividends, but rather retained in the company.

Payout ratio company A = 0.76 / 0.52 = 1.4615 or 146.15% Payout ratio company B = 1.64 / 2.66 = 0.6165 or 61.65% Payout ratio company C = 1.60 / 3.65 = 0.4384 or 43.84% Retention ratio A = 1 − 1.4615 = − 0.4615 or − 46.15% Retention ratio B = 1 − 0.6165 = 0.3835 or 38.35% Retention ratio C = 1 − 0.4384 = 0.5616 or 56.16% 2. Stock Splits. You own 200 shares of a stock priced at $80 per share. How many shares of stock would you own and what is the stock price after each of these scenarios? (LO 11-2) a. 2-for-1 stock split b. 4-for-1 stock split c. 1-for-4 stock split Shares = 200 Price = $80

A. B. C.

Split 2 4 1

for 1 1 4

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Answer: Shares 400 800 50

a. b. c.

Price $40 $20 $320

After the stock split, the price of the stock will be divided by the split ratio, while the number of shares will be multiplied by the same split ratio. a. After a 2-for-1 stock split, the price will be 80 / (2/1) = $40; the number of shares will be 200 × (2/1) = 400 shares. b. After a 4-for-1 stock split, the price will be 80 / (4/1) = $20; the number of shares will be 200 × (4/1) = 800 shares. c. After a 1-for-4 stock split, the price will be 80 / (1/4) = $320; the number of shares will be 200 × (1/4) = 50 shares.

3. DRIPs. You own 350 shares of a stock priced at $75 per share. If the stock has a dividend reinvestment program and pays a $0.45 per share dividend, how many shares of stock would you get and how much cash would be remaining? (LO 11-2) Stock Price = Dividend = Number of Shares =

$75.00 $0.45 350

Answer: Total Cash = Shares Purchased = Remaining Cash =

$157.50 2 $7.50

At $0.45 per share dividend, you will receive a total of 350 × 0.45 = $157.50, which will be used in the DRIP. The stock is valued at $75 per share, therefore, you can buy two shares worth $150 (2 × 75), and there will be $7.5 (157.5 − 150) cash remaining in the account.

Use the balance sheet and income statement, provided in the data file, ch11_pr04_10.xlsx to answer Problems 4 to 10:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

4. Liquidity Ratios. Given the balance sheet and income statement, compute the current ratio and the quick ratio for 20X1 and 20X0. Which year is better for each?

(LO 11-3) Answer: Current Ratio Quick Ratios

20X1 1.67 1.20

20X0 1.55 1.13

Better 20X1 20X1

The current ratio is defined as the current assets divided by the current liabilities.

The quick ratio is defined as the current assets minus inventories divided by the current liabilities.

For 20X0: Current ratio = 2089.10 / 1351.10 = 1.55 Quick ratio = (2089.10 − 556.60) / 1351.10 = 1.13 For 20X1: Current ratio = 2270.70 / 1361.60 = 1.67 Quick ratio = (2270.70 − 639.60) / 1361.60 = 1.20 The ratios for year 20X1 are better.

5. Activity Ratios. Given the balance sheet and income statement, compute the inventory turnover for 20X1 using both net sales and COGS. Also compute the average collection period and receivables turnover for 20X1 and 20X0. Which year is better for each? (LO 11-3) Answer: Inv Turn −- NS Inv Turn−- cogs ACP Receivables Tur

20X1 10.29 5.78 24.92 14.44

20X0

Better

25.19 14.29

20X1 20X1

The inventory turnover ratio is calculated using either net sales or COGS in the numerator and dividing it by the average inventory. Average inventory is calculated by taking the average value of the inventory account over two consecutive periods.

The average collection period (ACP) is calculated by dividing receivables with sales per day.

The receivables turnover is calculated by dividing the annual credit sales with accounts receivables.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

For 20X1: Inventory turnover using net sales = 6157.20 / (639.60 + 556.60)/2 = 10.29 times Inventory turnover using COGS = 3458.60 / (639.60 + 556.60)/2 = 5.78 times For 20X1: Average collection period (ACP) = 426.30 / (6157.20/360) = 24.92 days Receivables turnover = 6157.20 / 426.30 = 14.44 times For 20X0: Average collection period (ACP) = 410.00 / (5859.30/360) = 25.19 days Receivables turnover = 5859.30 / 410.00 = 14.29 times The collection of receivables is better in 20X1.

6. Activity Ratios. Given the balance sheet and income statement, compute the fixedasset turnover and total asset turnover for 20X1 and 20X0. Which year is better for each? (LO 11-3) Answer: Fixed Asset Turn Total Asset Turn

20X1 3.82 1.30

20X0 3.90 1.32

Better 20X0 20X0

The fixed-asset turnover ratio is calculated using annual sales in the numerator and dividing it by the fixed assets.

The total asset turnover ratio is calculated using annual sales in the numerator and dividing it by the total assets.

For 20X1: Fixed-asset turnover = 6157.20 / 1612.20 = 3.82 times Total asset turnover = 6157.20 / 4724.80 = 1.30 times For 20X0: Fixed-asset turnover = 5859.30 / 1502.10 = 3.90 times Total asset turnover = 5859.30 / 4425.60 = 1.32 times The ratios for year 20X0 are better.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

7. Profitability Ratios. Given the balance sheet and income statement, compute the gross profit margin, operating profit margin, and net profit margin for 20X1 and 20X0. Which year is better for each? (LO 11-3) Answer: Gross Profit Margin Operating Profit Margin Net Profit Margin

20X1 43.8% 17.7% 10.4%

20X0 44.2% 17.2% 10.0%

Better 20X0 20X1 20X1

The gross profit margin is calculated by taking the difference of sales minus COGS and dividing it by sales.

The operating profit margin is calculated by dividing the operating earnings by the sales.

The net profit margin in calculated by dividing the earnings after tax by the sales.

For 20X1: Gross profit margin = (6157.20 − 3458.60) / 6157.20 = 0.4383 or 43.83% Operating profit margin = 1090.50 / 6157.20 = 0.1771 or 17.71% Net profit margin = 639.80 / 6157.20 = 0.1039 or 10.39% For 20X0: Gross profit margin = (5859.30 − 3268.40) / 5859.30 = 0.4422 or 44.22% Operating profit margin = 1010.40 / 5859.30 = 0.1724 or 17.24% Net profit margin = 588.84 / 5859.30 = 0.1005 or 10.05% The values between the two years are very close and did not change substantially.

The gross profit margin is a little bit better in 20X0, while the operating profit margin and the net profit margin were slightly better in 20X1.

8. Profitability Ratios. Given the balance sheet and income statement, compute the return on assets and return on equity for 20X1 and 20X0. Which year is better for each? (LO 11-3) Answer: Return on Assets Return on Equity

20X1 13.5% 64.2%

20X0 13.3% 60.9%

Better 20X1 20X1

The return on assets is calculated by dividing the earnings after tax by total assets.

The return on equity is calculated by dividing the earnings after tax by total equity.

For 20X1:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Return on assets = 639.80 / 4724.80 = 0.135 or 13.5% Return on equity = 639.80 / 997.3 = 0.642 or 64.2% For 20X0: Return on assets = 588.84 / 4425.60 = 0.133 or 13.3% Return on equity = 588.84 / 967.6 = 0.609 or 60.9% The ratios for year 20X1 are better.

9. Leverage Ratios. Given the balance sheet and income statement, compute the debt to equity and debt to total assets for 20X1 and 20X0. Which year is riskier for each?

(LO 11-3) Answer: Debt to Equity Debt to Total Assets

20X1 3.74 0.79

20X0 3.57 0.78

Riskier 20X1 20X1

The debt to equity ratio is calculated by dividing the total debt by the total equity.

The debt to total assets ratio is calculated by dividing the total debt by the total assets.

For 20X1: Debt to equity = 3727.50 / 997.3 = 3.74 Debt to total assets = 3727.50 / 4724.80 = 0.79 For 20X0: Debt to equity = 3458.00 / 967.6 = 3.57 Debt to total assets = 3458.00 / 4425.60 = 0.78 The ratios for 20X0 are better; there is less financial risk. The ratios for 20X1 are higher, so there is more financial risk.

10. Coverage Ratios. Given the balance sheet and income statement, compute the times interest earned for 20X1 and 20X0. Which year is better? (LO 11-3) Answer:

Times Interest Earn

20X1 10.27

20X0 9.67

Better 20X1

The times interest earned ratio is calculated by dividing the earnings before interest and tax by the annual interest expense.

For 20X1: Times interest earned = 1090.50 / 106.20 = 10.27 times For 20X0:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Times interest earned = 1010.40 / 104.50 = 9.67 times The ratio for 20X1 is better.

11. Cash Flow. Do each of the following activities lead to a net outflow or inflow of the cash position? (LO 11-4) a. b. c. d. e.

Increase in accounts receivables Increase in accounts payables Purchase of plant and equipment Pay dividends Repurchase shares

Answer: a b c d e

Outflow Inflow Outflow Outflow Outflow

Increase in accounts receivables is an increase in assets, so it is an outflow.

Increase in accounts payables is an increase in liabilities, so it is an inflow.

Purchase of plant and equipment is an increase in assets, so it is an outflow.

Paying dividends is a decrease in equity, so it is an outflow.

Repurchase shares is a decrease in equity so it is an outflow. (Treasury stock will be negative, which will reduce equity.)

12. Perpetuity Model. If a security pays a dividend of $2.40 per share per year that will not change over time and the required rate of return is 7%, what is the value of the security? If the required rate changes to 7.5%, what is the price change? (LO 11-5) Div = $2.40 Required Rate 7% New Rate7.50% Answer: Value = $34.29 New Value = $32.00 Change = ($2.29) A security that pays the same dividend forever can be valued using the perpetuity model, which divides the annual dividend by the required return to find the value of the security.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Value of security = 2.4 / 0.07 = $34.29 If the required return increases, the price will decrease, and the new price will be 2.4 / 0.075 = $32.

Therefore, the price change is 34.29 − 32 = $2.29 decrease.

13. Constant Growth Model. A security paid a dividend of $1.25 per share for the year.

Its required rate is 9.8%. If the dividend is expected to grow at the constant rates shown below, what is the value of the security? A new announcement is made that changes the growth expectation. If the growth changes as noted, what is the price change? (LO 11-5) a. b. c. d.

Growth at 7%, then increases by 0.5% Growth at 7%, then decreases by 0.5% Growth at 6%, then increases by 0.5% Growth at 8%, then decreases by 0.5%

Answer: a. b. c. d.

Dividend $1.25 $1.25 $1.25 $1.25

Req Rate 9.80% 9.80% 9.80% 9.80%

Growth 7% 7% 6% 8%

Change 0.50% −0.50% 0.50% −0.50%

A. B. C. D.

Value $47.77 $47.77 $34.87 $75.00

New Value $58.42 $40.34 $40.34 $58.42

Change $10.65 $(7.43) $5.47 $(16.58)

The constant growth model values a security by dividing the next period’s expected dividend by the difference between the required return and the constant growth rate. The formula for the constant growth model is: P0 =

D1 r−g

=

D0 × (1 + g ) r−g

D0 = 1.25 and the required return r = 9.8%. For each of the parts A, B, C, and D, we find the value of the stock using the given constant growth and the associated changed value of the constant growth. a. g = 7%; P0 = (1.25 × 1.07) / (0.098 − 0.07) = $47.77 g = 7.5% P0 = (1.25 × 1.075) / (0.098 − 0.075) = $58.42 The price change is 58.42 − 47.77 = $10.65 b. g = 7%; P0 = (1.25 × 1.07) / (0.098 − 0.07) = $47.77 g = 6.5% P0 = (1.25 × 1.065) / (0.098 − 0.065) = $40.34 The price change is 40.34 − 47.77 = − $7.43 c. g = 6%; P0 = (1.25 × 1.06) / (0.098 − 0.06) = $34.87 g = 6.5% P0 = (1.25 × 1.065) / (0.098 − 0.065) = $40.34 The price change is 40.34 − 34.87 = $5.47

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

d. g = 8%; P0 = (1.25 × 1.08) / (0.098 − 0.08) = $75.00 g = 7.5% P0 = (1.25 × 1.075) / (0.098 − 0.075) = $58.42 The price change is 58.42 − 75.00 = −$16.58 14. Future Price Constant Growth Model. A security paid a dividend of $2.75 per share for the year. The dividend is expected to grow by $0.05 per year for five years.

Afterwards, the dividend will grow at a constant 4% forever. Its required rate is 8.8%.

What is the expected price in five years? (LO 11-5) Div = div grow = Growth Rate = Required Rate =

$2.75 $0.05 4% 8.80%

Answer: Dividend in 5 years Price in 5 years

$3.00 $65.00

The question is asking to find the price of the stock in five years; at that time, the stock is expected to grow at the constant rate of 4% forever.

First, we find the expected dividend in five years.

D5 = 2.75 + (5 × 0.05) = $3.00 Using the constant growth model at time 5, we find the price at time 5 as: P5 = D6 / (r − g) = 3 × 1.04 / (0.088 − 0.04) = $65.00 15. PE Model. A security earned $4.16 per share for the year and has a price of $75 per share. Earnings are expected to grow at 12% annually for the next five years. If the PE multiple is expected to increase 10% between now and five years, what is the forecasted price of the stock in five years? (LO 11-5) EPS Price growth PE change Years

$4.16 $75 12% 10% 5

Answer: Future Price =

$145.39

The current PE ratio is 75/4.16 = 18.0288.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

The PE ratio is expected to increase by 10% between now and five years; therefore, the expected value of the PE ratio in five years is 18.0288 × 1.1 = 19.8317.

The earnings are expected to grow by 12% annually for the next five years, we can calculate the expected earnings in five years as follows: Earnings in five years = 4.16 × (1 + 0.12)5 = $7.3313 The price of the stock in five years is expected to be 19.83 × 7.33 = $145.39.

16. Dividend Discount Model. In three years, a company is expected to pay its first dividend of $1.44 per share per year. At that point, the dividend is expected to grow at 7% per year indefinitely. If the required rate of return is 9.4%, what is the value of the stock? (LO 11-6) Dividend growth Required Rate

$1.44 7% 9.40%

Answer:

Cash flow Value =

Year 0 1 0 0 $50.13

2 0

3 $1.44

3 $64.20

The stock price in three years can be found using the constant growth model. The value of the stock today is the present value of the sum of the price in three years plus the dividend $1.44, discounted at the required return.

P3 = 1.44 × 1.07 / (0.094 − 0.07) = $64.20 P0 = (64.20 + 1.44) / (1 + 0.094)3 = $50.13 17. Dividend Discount Model. A company will pay a $0.88 per-share-per-year dividend next year. It is expected to increase that dividend by $0.04 each year for three years (to year four). In year four, the PE ratio of the firm is expected to be 21. Earnings were $2.10 per share last year are expected to grow at 8% each year to year four. If the required rate of return is 8.7%, what is the value of the stock? (LO 11-6) D1 = Increase = future PE E0 = growth = Required Rate

$0.88 $0.04 21 $2.10 8% 8.70%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Answer: Year 0 Div = Price = Cash Flow = Value =

1 $0.88

2 $0.92

3 $0.96

$0.88

$0.92

$0.96

4 $1.00 $60.00 $61.00

$46.03

The information provides the values of the dividends that the firm will pay up to year four, and also it provides the PE ratio for year four. We can estimate the terminal value of the company at year four using the PE ratio, and then find the value of the stock today but discounting the cash flows the firm will have over four years.

D1 = $0.88 D2 = $0.92 D3 = $0.96 D4 = $1.00 Expected earnings at year 4 is E4 = 2.10 × (1 + 0.08)4 = $2.857.

Price of the stock at year 4 is P4 = 21 × 2.857 = $60.00.

P0 = 0.88/(1.087) + 0.92/(1.087)2 + 0.96/(1.087)3 + (1+60)/(1.087)4 = $46.03 18. Dividend Discount Model. A company paid a $1.78 per-share-per-year dividend last year. It is expected to increase at an annual 9% growth rate to year five. After year five, the dividend will growth at 6% per year indefinitely. If the required rate of return is 10.2%, what is the value of the stock? (LO 11-6) D0 = $1.78 1st Growth 9% 2nd Growth 6% Required Rate 10.20% Answer: Year Div = Price = Cash Flow = Value =

0 $1.78

1 $1.94

2 $2.11

3 $2.31

4 $2.51

$1.94

$2.11

$2.31

$2.51

5 $2.74 $69.12 $71.86

$51.14

This is similar to Problem 17. Here, we first have to calculate the values of the dividends and then use the constant growth model to find the terminal value of the

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

company at year five. Finally, discount the five cash flows to the present using the required return.

D1 = 1.78 × 1.09 = $1.94 D2 = 1.94 × 1.09 = $2.11 D3 = 2.11 × 1.09 = $2.30 D4 = 2.31 × 1.09 = $2.51 D5 = 2.52 × 1.09 = $2.73 P5 = (2.73 × 1.06) / (0.102 − 0.06) = $68.90 P0 = 1.94/(1.102) + 2.11/(1.102)2 + 2.30/(1.102)3 + 2.51/(1.102)4 + (2.73+68.90)/(1.102)5 = $51.00 The solution in the Excel file gives the answer without any decimal rounding errors.

19. Price Multiples. Consider the data below from the financial statements. If the stock price of the company is $75 per share, what are the PE ratio, price-to-cash flow ratio, PS ratio, and PB ratio? (LO 11-8) (in 000) $ 6,157.20 $ 639.80 $ 711.95 $ 997.30 220

Net Sales Net Income Cash Flow Book Value # Shares Answer: PE ratio P to CF ratio PS ratio PB ratio

25.8 23.2 2.7 16.5

PE ratio is the price per share divided by the earnings per share. Earnings per share is the net income divided by the number of shares.

PE ratio = 75 / (639.80/220) = 25.79 Price-to-cash flow ratio is the price divided by the cash flow per share. The cash flow per share is the cash flow divided by the number of shares.

Price-to-cash flow ratio = 75 / (711.95/220) = 23.18 PS ratio is the price per share divided by the sales per share. Sales per share is the net sales divided by the number of shares.

PS ratio = 75 / (6157.2/220) = 2.68

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

PB ratio is the price per share divided by the book value per share. Book value per share is the book value divided by the number of shares.

PB ratio = 75 / (997.3/220) = 16.54 20. PEG ratio. Compute the PEG ratio for the three firms below. Which is a more attractive PEG ratio to a GARP investor? (LO 11-9) Company A Company B Company C

$ $ $

Price 85.00 75.00 90.00

EPS $2.56 $2.75 $0.56

Growth (%) 11.0 8.0 15.0

Answer: a. b. c.

Best =

PEG Ratio 3.02 3.41 10.71 A.

The PEG ratio is calculated by dividing the PE ratio by the earnings growth rate.

PE ratio company A = (85/2.56) / 11 = 3.02 PE ratio company B = (75/2.75) / 8 = 3.41 PE ratio company C = (90/0.56) / 15 = 10.71 The three companies have PEG ratios above 1. The most attractive PEG ratio to a GARP investor will be the one with the lowest PEG ratio, and that is company A.

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19

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Case Study Fundamental Analysis Conduct a fundamental analysis on Appaloosa, a clothes manufacturer. Appaloosa specializes in preteen clothes and produces only a modest amount of clothes for other age groups. Its sales of preteen clothes account for one-third of the total preteen market, both domestic and abroad. Appaloosa’s balance sheets and income statements for the past two years are presented in Exhibit 1. Appaloosa’s per-share earnings and dividends are given in Exhibit 2. Except for the most recent year, 20X9, and 20X8, per-share earnings have steadily increased, and dividends have risen every year for the past 10 years. This pattern of earnings and dividend growth is impressive.

For Appaloosa to be a good investment, it should have strong fundamentals and be financially sound. Analyze Appaloosa using ratios to analyze the firm’s financial statements.

You can compare the two years and compare to the industry averages given in Exhibit 3.

Currently, Appaloosa’s stock sells for $50. You could invest in U.S. Treasury bills that yield 3.5%, but the stock market is expected to earn an annual 9.5%. The data are in the file, ch11_case_study.xlsx. Should you buy Appaloosa stock? Answer the following questions: 1. Compute the ratios shown in Exhibit 3 for both years of Appaloosa. What is your conclusion?

2. What is the firm’s current payout ratio compared to its historical payout ratio?

3. What are the annual growth rates in the earnings per share and the dividend per share? Why is the growth rate in the dividend not sustainable?

4. Is there any reason to believe that the firm has changed its dividend policy?

5. Compute the PE ratio, PS ratio, and PB ratio. (Note that you can infer the number of outstanding shares from net income/EPS.) Does Appaloosa’s PE, PS, and PB ratios suggest the firm is undervalued?

6. If a dividend growth rate of 4% can be sustained, is the stock a good purchase if the required return is 9.5%?

1. The ratios for Appaloosa for years 20X9 and 20X8.

Selected Ratios for Appaloosa Current ratio Quick ratio Average collection period Inventory turnover (sales/average inventory) Fixed-asset turnover Debt ratio (debt/total assets) Times interest earned Net profit margin Return on assets Return on equity

20X9 3.66 1.69 43.11 5.57 3.34 19.15% 19.67 4.79% 7.57% 9.36%

20X8 3.34 1.68 56.22 6.19 4.15 22.52% 28.33 6.44% 11.38% 14.69%

Industry Averages 3.2:1 1.6:1 55 days 3.7 a year 4.5 a year 33% 10.3 3.30% 4.50% 7.00%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

Note: The inventory turnover is calculated as sales divided by inventory value. In this case the value of the inventory for the two years is about the same.

Overall, Appaloosa is doing very well and has better ratios than the industry in almost all categories. There are improvements in some ratios between 20X8 and 20X9, while some other ratios went down. The current ratio and the quick ratio improved over the year period and are higher than the industry averages. Appaloosa’s liquidity position is very good.

The average collection period improved between 20X8 and 20X9. However, the inventory turnover and fixed asset turnover slightly decreased.

The debt ratio is much lower than the industry. Appaloosa does not use much debt financing: the annual interest expense was $3000 only. They are generating 20 times EBIT on average to pay for the interest, which is very good.

Finally, Appaloosa’s profitability and performance is very good—much better than the industry averages.

2. The current payout ratio is 37.5%. Table 1 below shows the historical payout ratios.

Table 1: Historical payout ratio, EPS growth rate and dividend growth rate 20X9 20X8 20X7 20X6 20X5 20X4 20X3 20X2 20X1 20X0 20Y9

Payout ratio 37.48% 22.68% 24.03% 25.76% 20.00% 19.39% 18.89% 27.89% 34.81% 38.35% 50.00%

EPS growth rate −33.45% 17.76% 20.61% −8.00% 37.76% 23.43% 58.17% 58.86% 18.80% 33.00% NA

Dividend growth rate 10.00% 11.11% 12.50% 18.52% 42.11% 26.67% 7.14% 27.27% 7.84% 2.00% NA

We notice that the payout ratio was high, decreased over time, and then started increasing.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 11: Valuing Common Stock

3. The current dividend growth rate between 20X8 and 20X9 is 10%. This is a very high growth rate. Also, we notice that the growth rate of the dividends was much higher but decreased with time. Over time, the company will not be able to grow rapidly and generate sales as it once did; more competitors will enter the market, and a 10% growth rate will not be sustainable.

4. The company’s payout ratio increased to 37.5% in 20X9 from 22.68% in 20X8. This increase is most likely due to the fact that earnings went down from 20X8 to 20X9 and therefore the ratio increased. However, there is no indication that there is a change in payout policy.

5. For 20X9, the number of shares outstanding can be calculated by dividing the NI with EPS: # of shares = 32,000 / 5.87 = 5,451 shares The PE ratio = 50 / 5.87 = 8.52 The PB ratio = 50 / (342,000 / 5,451) = 0.80 The PS ratio = 50 / (668,000 / 5,451) = 0.41 Both PB and PS ratios are less than 1, which may indicate the stock being undervalued.

The PE ratio is 8.52, which is relatively low compared to the general stock market’s PE ratio.

6. If the dividend growth rate of 4% is sustainable, then we can assume the 4% growth will continue forever, and we can use the constant growth model to value the company’s stock.

The current dividend is $2.20 P0 = 2.2 × 1.04 / (0.095 − 0.04) = $41.60 The stock price is $41.60, under the assumption that dividends will grow by 4% next year and onward. The market value is $50, so the stock price is overvalued and is not a good buy.

Overall, the company’s financial statements depict the company’s very strong position, while PB and PS ratios suggest some undervaluation of the stock. Perhaps a growth rate above 4% can be sustainable.

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22

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 19

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

Questions 1. Preferred Stock. Why would someone invest in preferred stock? What features would appeal to them, and why? (LO 12-1) Answer: Most shareholders are attracted to preferred stocks because they offer more consistent dividends than common shares and higher payments than bonds.

However, these dividend payments can be deferred by the company if it falls into a period of tight cash flow or other financial hardship.

2. Change in Yield. What effect would an increase in the required rate of return have on the price of an existing share of preferred stock? Why? (LO 12-1) Answer: The price of a preferred stock can be found using the following formula: P0 =

D k

Where D is the annual dividend and k is the discount rate or the required rate of return.

The required rate of return is in the denominator; therefore, an increase in the required rate of return will decrease the price of an existing share of preferred stock, assuming the dividend is unchanged. Further, if the opposite happens, and the required return decreases, keeping the dividend unchanged, the price will increase. Therefore, the relationship between the price of preferred stock and the required return is inverse. This inverse relationship exists because in the valuation formula above, the price is inversely related to the required return (the required return is in the denominator).

3. Finite Lives. Would a finite-lived preferred stock sell for more or less than a perpetual preferred stock? Why? (LO 12-2) Answer: The value of a perpetual preferred stock is the ratio of the fixed dividend divided by the required return. The fixed dividend is usually calculated using a fixed rate times the par value. The price of the preferred stock then will be the product of this fixed dividend rate times the par value divided by the discount rate.

In the case of a finite-lived preferred stock, the stock will pay the same dividend using the same method as above; however, it will have finite life, and at the end of the life, the preferred stock will also pay a final amount to the shareholders, which is set at above the par value (or can sometimes be equal to par). So, the value of the

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

finite-live preferred stock is the present value of the dividends discounted at the required return over its life plus the present value of the final amount also discounted at the required return.

The value of the finite-lived preferred stock compared to perpetual preferred stock will be dependent upon the dividend rate and the required return.

If the dividend rate is greater than the required return, the perpetual preferred stock will have higher value.

If the dividend rate is less than or equal to the required return, the finite-lived preferred stock will have higher value.

When the required return is very large or the life of the finite-lived preferred stock is very large, the two values converge and become equal.

4. Conversion Ratio. What effect should you expect a common stock split to have on the conversion ratio for convertible preferred shares? Why? (LO 12-3) Answer: The conversion ratio represents the number of common shares that shareholders may receive for every convertible preferred share. For example, if the conversion ratio is 5, this means that the shareholder will receive five shares of common stock for every convertible preferred stock.

A stock split is a corporate event where the management decides to reduce the value of the company and increase the number of shares. The stock split does not have any impact on the wealth of shareholders. For example, in a 2-to-1 split, the number of shares of the company will double while the share value will be reduced by half.

Since the split is a corporate event, and it doesn’t affect the wealth of the shareholders, the conversion ratio of the preferred stock should be adjusted in order to account for the stock split. Following up with the examples above, if the conversion ratio is 5, and the company’s common stock has a 2-to-1 split, the conversion ratio should be adjusted by the split value and become 10. This way, the shareholder will not be affected by the split and the wealth resulting from the conversion of the preferred stock will remain the same as pre-split value.

The conversion ratio can also be found by taking the bond's par value, which is generally $1,000, and dividing it by the share price. A stock trading for $40 has a conversion ratio equal to $1,000 divided by $40, or 25. When convertible preferred stockholders choose to convert their stocks to common stocks, the stocks they receive are newly issued. This increases the total number of common shares.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

Because the number of common shares increases while the value of the company remains the same, the value of existing shares goes down.

5. Floating Preferred Shares. Why do floating preferred shares generally sell for close to par? (LO 12-4) Answer: Preferred shares are issued with a face value, but this is effectively an arbitrary price chosen by the issuing company. Because preferred shares pay steady dividends, but lack voting rights, they will typically trade in the market for a value different from the same firm's common shares.

In a floating rate preferred stock, the dividend is reset or adjusted at specific time periods to match changes in the going yield (current market rate) on equivalent securities. Because of this reset in dividends, the price tends to remain close to the issue price or par.

6. Noncumulative Preferred Shares. What would keep firms from permanently skipping dividends on noncumulative preferred shares? (LO 12-5) Answer: Two factors that affect the decision of firms not to permanently skip dividend payments on noncumulative preferred shares are as follows: 1) The preferred shareholders would not remain shareholders and sell those shares if the firm does so; and 2) skipping dividend on preferred stocks also doesn’t allow the firm to pay dividends on its common stock, which will not be perceived positively by the common stockholders. They may end up selling their common stock as well if it persists.

7. Participating Preferred Shares. Explain how participating preferred shares could be used as part of a poison pill strategy. (LO 12-6) Answer: A poison pill is a type of defensive strategy that can be used by a firm when it is subject to a hostile takeover. The basic principle of a poison pill is to create a situation where the firm becomes less desirable to be acquired by the hostile acquirer. Preferred stocks can be used as part of a poison pill strategy in a variety of ways; the basic idea is to provide the current shareholders with a means to deter a hostile takeover situation. One method is to have the preferred stock become convertible into common stock with voting rights whenever the firm is subject to a hostile takeover. When the preferred stock has this feature, it can become a poison pill because during a hostile takeover, all the preferred stocks can be converted into

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

common stocks, which will increase the difficulty of the acquisition. A variation of this strategy is to have the preferred stock be convertible into a large number of common stocks in case of a hostile takeover.

8. Preferred Share Options. Intuitively, how would you value callable, puttable preferred shares? (LO 12-3) Answer: The value of a callable or puttable preferred stock can be found by taking the value of otherwise similar non-callable or non-puttable preferred stock and adding or subtracting the value of the option.

The callable preferred stock is a type of preferred stock where the issuer has the right to call (buy back) the preferred stock from the investor; therefore, in this case, since the call option is held by the issuer, we subtract the value of the call option.

Value of Callable PS = Value of Non-callable PS − Value of Call The puttable preferred stock is a type of preferred stock where the investor has the right to sell the preferred stock back to the issuer; therefore, in this case, the put option is held by the investor, so we add the value of the put option.

Value of Puttable PS = Value of Non-puttable PS + Value of Put The issuing corporation can redeem “callable” preferred for a predetermined price on or after one or more call dates. “Puttable” preferred shareholders can force the corporation to buy back the shares, once again at a preset price. Owners of callable preferred don’t reap any capital appreciation beyond that garnered at the call price.

Preferred shares may be cumulative or noncumulative—this feature is unrelated to whether they are redeemable convertible preference shares. Even though both common shareholders and preferred shareholders own a part of the company, only the common shareholders have voting rights. Preferred shareholders do not have voting rights. For example, if there were a vote on the new board of directors. A board of directors is a panel of people elected to represent shareholders.

9. DRD. Explain how a change in the DRD to only allow corporations to exclude 35% of dividends from other corporations would affect the price of preferred shares.

(LO 12-7) Answer: DRD is a rule followed by the IRS that allows corporations to exclude part of the dividends received from other corporations when they calculate their taxes. The current rules allow corporations to exclude from 50% to 65% of the dividends subject to ownership requirements. If the DRD changes and lowers the exclusion amount to only 35% of dividends received from other corporations, then the tax

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5

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

advantage of investing in other companies’ preferred stocks is reduced, which would most probably lead to reduction of those investments as well. Therefore, companies may end up selling part of their investments in preferred stocks in other companies, which will affect the price of those preferred shares negatively.

10. Non-Preferred Shares. If we wanted to create a class of common stock that could be called “non-preferred shares,” how would we go about doing so? What features discussed in this chapter would such shares have? (LO 12-1) Answer: A class of common stock that could be called “non-preferred shares” can be created by forming a new class of shares with characteristics opposite to preferred shares.

Several common characteristics of preferred shares discussed in this chapter would be reversed in the new class. This new class of non-preferred shares would include the following features: 1. Voting rights 2. No fixed dividend payment; instead, the dividend payments would follow a similar pattern to the dividends on the common stock. The dividends can be even lower than those on the common stock.

3. No priority on dividend payments; instead, the dividends would be paid after payments were made to common stockholders. Also, in the case of liquidation, the non-preferred stockholders would be paid after the common stockholders.

4. No cumulative feature

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

Problems 1. Stock price. If a newly issued preferred stock will have an annual dividend of $3 and a dividend yield of 7%, what will the price of each share be? (LO 12-1) Answer: Dividend Dividend yield Price

$ 3.00 7% $42.86

The price of a preferred stock can be found using the following formula: P0 =

D k

Where D is the annual dividend and k is the discount rate or the dividend yield at time 0.

P0 = 3 / 0.07 = $42.86 2. Dividend yield. If a newly issued preferred stock will have an annual dividend of $1.23 and a price of $25.25, what will the dividend yield be? (LO 12-1) Answer: Dividend Price Dividend yield

$ 1.23 $25.25 4.87%

The dividend yield can be found using the following formula: k=

D P0

Where D is the annual dividend and P0 is the price of the preferred stock. k = 1.23 / 25.25 = 0.0487, or 4.87% 3. Stock price. If a newly issued preferred stock will have a quarterly dividend of $1.05 and a dividend yield of 4.23%, what will the price of each share be? (LO 12-1) Answer: Dividend Dividend yield Price

$ 1.05 4.23% $99.29

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7

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

The price of a preferred stock can be found using the following formula: P0 =

D k

Where D is the quarterly dividend and k is the quarterly discount rate or the quarterly dividend yield at time 0.

The quoted dividend yields are usually given in annual terms; therefore, the quarterly dividend yield is: 4.23% / 4 = 1.0575%.

The price of the preferred stock is: P0 = 1.05 / 0.010575 = $99.29.

4. Quarterly dividend. If a company wants to price a new preferred stock issue at $50 and needs to offer an effective annual yield of 5.5%, what should they set the quarterly dividend to? (LO 12-1) Answer: Price Annual yield Quarterly dividend

$ 50 5.5% $0.67

First, we find the nominal annual dividend yield using the following formula: Rnominal = n × [(REffective + 1)1/ n − 1]

Rnominal = 4 × [(0.055+1)1/4 − 1] = 0.0539, or 5.39% The dividend amount can be calculated using the following formula: P0 =

D k

After rearranging the formula to calculate the amount of the annual dividend, we have: D = P0 × k D = 50 × 0.0539 = $2.695 The quarterly dividend becomes: 2.695 / 4 = $0.67.

5. Preferred stock price. Suppose that a preferred stock is paying an annual dividend of $4.25, has a 6% rate of return, and is callable in 10 years at a price of $250. What should the price of each share be? (LO 12-2) Answer: Dividend n Discount rate at time 0

$

4.25 10 6%

Pn

$

250

P0

$170.88

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

The price of a preferred stock can be found using the following formula: 1− P0 = D ×

1

(1+ k ) + n

k

Pn

(1+ k )

n

Where Pn represents the amount that is returned to the stockholder when the preferred stock is retired after n number of periods, k is the discount rate, D is the annual dividend, and n is the number of periods until the preferred stock is called.

1− P0 = 4.25 ×

1 250 (1 + 0.06)10 + = $170.88 0.06 (1 + 0.06)10

You can also use the PV() function in Excel to get the same answer.

6. Preferred stock price. Suppose that a preferred stock is paying a quarterly dividend of $1.27, has a 5.5% effective annual rate of return, and is callable in 15 years at a price of $75. What should be the price of each share? (LO 12-2) Answer: Dividend n Discount rate at time 0

$ 1.27 15 5.5%

Pn

$

P0

$85.63

75

We can use the same formula and procedure as in Problem 5 to solve this problem.

First, we have to calculate the nominal annual rate of return from the effective rate of return given in the problem.

We find the nominal annual rate of return using the following formula: Rnominal = n × [(REffective + 1)1/ n − 1]

Rnominal = 4 × [(0.055+1)1/4 − 1] = 0.0539 or 5.39% The quarterly rate then is 5.39% / 4 = 1.3475%.

Since the preferred stock is paying quarterly dividends, we use the formula in such a way to have quarterly compounding; therefore, convert the number of periods into quarters and use the quarterly dividend.

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9

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

The price of the preferred stock is calculated as follows: 1− P0 = 1.27 ×

1 75 (1 + 0.013475)60 + = $85.63 0.013475 (1 + 0.013475)60

Note: If you use the discount rate with two decimal values in the formula above, you may have a slightly different answer due to rounding effects.

You can also use the PV() formula in Excel to solve the problem: follow the same approach as for quarterly compounding by finding the nominal rate first and then determining the quarterly rate.

7. Conversion price. If a preferred share is selling for $31.30 and has a conversion ratio of 1.5, what is the conversion price? (LO 12-3) Answer: P0 Conversion ratio Conversion price

$31.30 1.5 $20.87

The conversion price can be found using the following formula: Conversion Price =

P0 Conversion Ratio

Where the conversion ratio represents the number of common shares that shareholders may receive for every convertible preferred share and P0 represents the price of the preferred stock.

Conversion Price = 31.30 / 1.5 = $20.87 8. Conversion price. If a preferred share is selling for $125 and has a conversion ratio of 5, what is the conversion price? (LO 12-3) Answer: P0 Conversion ratio Conversion price

$ 125 5 $25.00

As this is similar to Problem 7, the same approach is used: Conversion Price = 125 / 5 = $25.00

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10

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

9. Floating preferred. You are considering buying a floating preferred share slated to pay an annual dividend of $2.50 one year from now. The preferred’s dividends will reset to LIBOR + 2.3%, and the current LIBOR rate is 0.7%. If the shares have a par value of $25, what price should you expect to pay today? (LO 12-4) Answer: Dividend n Discount rate at time 0

$ 2.50 1 3.0%

Pn

$

P0

$26.70

25

The problem can be solved using a modified version of the following formula: 1− P0 = D ×

1

(1+ k ) + n

k

Pn

(1+ k )

n

Where n is set equal to the length of time until the next dividend adjustment and Pn is set equal to the issue price or par.

The LIBOR rate of 0.7% is the annual LIBOR rate; therefore, the discount rate of 3.0% is in annual terms.

1− P0 = 2.50 ×

1

(1+ 0.03) + 1

0.03

25

(1+ 0.03)

1

= $26.70

You can also use the PV() formula in Excel to solve the problem: follow the same approach as in earlier problems. In this example, n = 1.

10. Floating preferred. You are considering buying a floating preferred share slated to pay a quarterly dividend of $0.75 one quarter from now. The preferred’s dividends will reset to LIBOR + 1.5%, and the current LIBOR rate is 0.7%. If the shares have a par value of $50, what price should you expect to pay today? (LO 12-4) Answer: Dividend n Discount rate at time 0

$ 0.75 1 2.2%

Pn

$

P0

$50.47

50

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11

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

The discount rate is LIBOR + 1.5 = 0.7 + 1.5 = 2.2%. The LIBOR rate of 0.7% is the annual LIBOR rate; therefore, the discount rate is in annual terms. The quarterly rate is 2.2% / 4 = 0.55%.

1− P0 = 0.75 ×

1

(1+ 0.0055) + 1

0.0055

50

(1+ 0.0055)

1

= $50.47

You can also use the PV() formula in Excel to solve the problem: follow the same approach as in earlier problems. You will have to change the annual rate into quarterly first.

11. Floating preferred. You are considering buying a floating preferred share slated to pay a quarterly dividend of $0.50 each quarter over the next year. The preferred’s dividends will reset to LIBOR + 3.25%, but only annually and, in this case, at the end of the coming year. If the current LIBOR rate is 0.5% and the shares have a par value of $37.50, what price should you expect to pay today? (LO 12-4) Answer: Dividend n Discount rate at time 0

$ 0.50 4 3.75%

Pn

$37.50

P0

$38.08

In this example, the floating preferred pays quarterly dividends, but the reset happens at the end of the year, or after four quarterly dividends are paid.

Therefore, we have four payments of $0.50 that happen before the next reset.

The discount rate is LIBOR + 3.25 = 0.5 + 3.25 = 3.75%. The LIBOR rate of 0.5% is the annual LIBOR rate therefore, the discount rate is in annual terms. The quarterly discount rate is 3.75% / 4 = 0.9375%.

1− P0 = 0.50 ×

1

(1+ 0.009375) + 4

0.009375

37.50

(1+ 0.009375)

4

= $38.08

You can also use the PV() formula in Excel to solve the problem: follow the same approach as in earlier problems. You will have to change the annual rate into quarterly first. Make sure to use n = 4, since there are four dividend payments.

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12

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

12. Noncumulative preferred. You own a floating, noncumulative preferred share that normally pays dividends quarterly. The firm has announced that, due to current economic conditions, it will not be paying dividends for the next year but expects to restart dividends one quarter into next year, paying the promised rate of LIBOR + 2.2%. If the current LIBOR rate is 0.5% and the shares have a par value of $37.50, what price should you expect to pay today? (LO 12-5) Answer: − 4 2.7%

Dividend n Discount rate at time 0

$

Pn

$37.50

P0

$36.50

The discount rate is LIBOR + 2.2 = 0.5 + 2.2 = 2.7%. The LIBOR rate of 0.5% is the annual LIBOR rate; therefore, the discount rate is in annual terms. The quarterly discount rate is 2.7% / 4 = 0.675%.

The next reset will happen one year from now, so that the firm starts paying dividends one quarter into the next year. To find the value of the preferred stock today, we just need to find the present value of the par, with quarterly discounting.

We can also use the formula that we used in Problems 10 and 11.

1− P0 = 0 ×

1

(1+ 0.00675) + 4

0.00675

37.50

(1+ 0.00675)

4

= $36.50

Note: The first part of the formula is equal to 0 since it is the product of 0 and another value. Therefore, the formula becomes effectively the present value of the par only.

You can also use the PV() formula in Excel to solve the problem: follow the same approach as in earlier problems. You will have to change the annual rate into quarterly first. Make sure to use n = 4 and select 0 for the payments, as there are no dividend payments.

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13

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

13. Noncumulative preferred. You own a share of noncumulative preferred stock that normally pays a quarterly dividend of $1. If the appropriate rate of return is 6% per year, but the company has announced that it will be suspending dividends for the next two quarters, what price should the stock be selling for right now? (LO 12-5) Answer: Dividend Discount rate Price

$

1 6% $64.71

The company will suspend the dividend for the next two quarters, which means the next expected dividend of $1 will be three quarters from now. To find the value of the stock today, first we find the value of the stock at the end of the second quarter, assuming $1 of perpetual dividends. Then, find the present value of the value at the end of the second quarter, over two quarters.

Quarterly Rate = 6% / 4 = 1.5% The value of the preferred stock at the end of two quarters from today = 1 / 0.015 = $66.67.

The value of the stock today is the present value of $66.67 over two quarters.

Value of Preferred Stock Today = 66.67 / (1 + 0.015)2 = $64.71 14. Preferred interest rate. A share of noncumulative preferred stock that normally pays a dividend of $1.25 per quarter but which has had its dividend halted for the next year is selling for a price of $33.45. What is the appropriate interest rate for this stock? (LO 12-5) Answer: Dividend Price Annual rate of return

$ 1.25 $ 33.45 13.14%

Time 0 1 2 3 4 5

CF $(33.45) $ − $ − $ − $ − $ 1.25

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14

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

The preferred stock will not pay any dividends for one year and will then resume quarterly dividends next year. The value of this preferred stock at the end of one year from now can be found by using the perpetual valuation of the preferred stock: Value of Preferred Stock 1 Year from Now = 1.25 / k; where k is the quarterly discount rate.

The value of the stock today is $33.45, which is equal to the present value of the value one year from now, discounted over four quarters.

33.45 = (1.25 / k) / (1 + k)4 Rearranging this equation, we get: k × (1 + k)4 = 1.25 / 33.45 = 0.037369.

To solve for k, we can use the solver function in Excel that was introduced in the textbook earlier.

First, we set the value of k to an arbitrary number. You can choose any value; for example, 1%. We set the cell G4 to 1%.

Then in a cell, solve for the equation k × (1 + k)4 using that arbitrary value for k. In cell G6, the solution of the equation is written.

With the Solver function, set the objective function to cell G6 so that the solver solves for its value. In the next line, select “value of” and write in the white box the value 0.0373692; the more decimal values you input, the closer the answer will be to its true value. In the cell “by changing the variables cell,” select cell G4. This way, the solver will make the value of the equation equal to 1.25 / 33.45 = 0.0373692 by finding the quarterly value of k that will do so.

We find the quarterly k = 3.28%.

Therefore, the annual interest rate is 4 × 3.28% = 13.12%, not 13.14%.

The second method for solving the problem is shown in the Excel sheet under columns A and B. Use 0 for the value of the dividend for the first four quarters and then 1.25 for several quarters in the future (the more quarters you provide value for, the more accurate the answer will be), and solve for IRR and find the annual IRR.

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15

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

15. Participating preferred. A share of participating preferred stock offers a guaranteed $5 annual dividend and has an appropriate rate of return of 8%.

What should the stock be selling for? (LO 12-6) Answer: Dividend Discount rate Price

$

5 8% $62.50

The price of a preferred stock can be found using the following formula: P0 =

D k

Where D is the annual dividend and k is the discount rate at time 0.

P0 = 5 / 0.08 = $62.50 16. Participating preferred. A share of participating preferred stock offers a guaranteed $1.50 quarterly dividend and has an appropriate rate of return of 5%.

What should the stock be selling for? (LO 12-6) Answer: Dividend Discount rate Price

$1.50 5% $ 120

The price of a preferred stock can be found using the following formula: P0 =

D k

Where D is the quarterly dividend and k is the quarterly discount rate at time 0.

The rate of return provided of 5% is in annual terms; therefore, the quarterly discount rate is 5% / 4 = 1.25%.

P0 = 1.5% / 0.0125 = $120 17. Conversion option. Suppose a share of convertible preferred stock was selling for $27.50 when an otherwise equivalent share of preferred stock for the same company was selling for $19.73. What would be the value of the conversion option?

(LO 12-3) Answer: Share with option Share without option Value of option

$27.50 $19.73 $ 7.77

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16

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

The value of the conversion option will be the difference between the two prices.

The text explains that the price of the convertible preferred stock is the sum of the price of an otherwise regular preferred stock and the value of the conversion option. The equation below represents this relationship. Pc is the price of the convertible preferred stock, P is the price of the regular preferred stock, and Vo is the value of the option.

Pc = P + Vo Vo = 27.50 − 19.73 = $7.77 18. Conversion option. Suppose a share of convertible preferred stock was selling for $10.50 when an otherwise equivalent share of preferred stock for the same company was selling for $13.00. What would be the value of the conversion option?

(LO 12-3) Answer: Share with option Share without option Value of option

$10.50 $13.00 $(2.50)

As this is similar to Problem 17, we can use the same relationship: Pc = P + Vo Pc is the price of the convertible preferred stock, P is the price of the regular preferred stock, and Vo is the value of the option.

Vo = 10.50 − 13.00 = −$2.50 19. Preferred after-tax yield. A corporation owning preferred shares in another corporation earns a before-tax dividend yield of 6.7% on those shares. If the receiving corporation faces a corporate tax rate of 21.0%, what is the effective aftertax yield on those shares if the corporation owns 35.0% of the dividend-paying firm?

(LO 12-7) Answer: Before-tax yield Corporate tax rate After-tax yield

6.7% 21.0% 6.2%

The corporation owns 35.0% of the dividend-paying firm, which means the corporation can benefit from a dividend received deduction (DRD) on the amount of dividends that taxes must be paid on, amounting to 65.0%.

The After-Tax yield then will be calculated by the following formula:

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17

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

After-Tax Corporate Yield if Ownership

≥ 20% and < 80% = k × 1− 0.21 × (1− 0.65) = 0.9265k

Therefore, the after-tax yield = 6.7 × [1 − 0.21 × (1 − 0.65)] = 6.7 × 0.9265 = 6.2% 20. Preferred after-tax yield. An individual owning preferred shares in another corporation earns a before-tax dividend yield of 8.2% on those shares. If they face a personal tax rate of 22.0%, what is their effective after-tax yield on those shares? (LO 12-7) Answer: Before-tax yield Individual tax rate After-tax yield

8.2% 22.0% 6.4%

For the individual owning preferred shares, the after-tax yield is calculated using the following formula: After-Tax Individual Yield = k × (1 − t) Where k is the before-tax yield and t is the personal tax rate.

After-Tax Yield = 8.2 × (1 − 0.22) = 6.4%

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18

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

Case Study Preferred share issue On June 22, 2021, LifeMD filed a prospectus with the U.S. Securities and Exchange Commission (SEC) for an issue of preferred shares. That prospectus is available at https://www.sec.gov/Archives/edgar/data/948320/000149315221024380/form424b5. htm. You may also find current pricing information on these shares at Yahoo! Finance by searching for “LFMDP” on http://finance.yahoo.com. Refer to these sources to answer the following questions: A. Using the prospectus, what are the details of the preferred issue (how many shares, par value, etc.) and which, if any, of the special features discussed in this chapter does this issue have?

B. How much will the dividends be, and how often will they be paid?

C. Based on the current market price, what is the dividend yield on these shares?

Answer: A. The prospectus of LifeMD lists detailed information about the preferred shares as well as other details about the company. According to the prospectus, the preferred shares have the following characteristics: Cumulative perpetual preferred stock with fixed dividend amount, dividends to be paid quarterly. The original issue size is 1,400,000 shares, with an option for the underwriters to buy an additional 210,000 shares within 30 days of the issue.

The dividend rate is set at 8.875% fixed, out of the $25.00 liquidation preference per-share value. The liquidation preference represents the amount to be paid in case the company liquidates its assets. In addition, the offering price is set to be $25. The prospectus also provides the amount of commission to be paid to the underwriting group and the net proceeds the company will receive from the sale of those shares.

Also, the prospectus notes that the company will establish a segregated account to pre-fund eight quarterly dividend payments.

The prospectus also contains information about when the company will be able to call those shares. The prospectus lists the date after which the company can redeem the shares and the redemption value if the company chooses to redeem the shares. This is the call feature discussed in the chapter.

The prospectus also explains the convertibility option available to those shares and the conversion ratio that is applicable.

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19

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 12: Valuing Preferred Stock

B. The amount of the dividend will be 8.875% of 25. Therefore, the amount is 0.08875 × 25 = $2.21875 per share each year.

The dividends are going to be paid on a quarterly basis, and the dates of those payments will be the 15th day of January, April, July, and October of each year.

C. On November 11, 2021 (the date when the solution for this case was written), the preferred stock had a value of $22.52. On the Yahoo! Finance website, enter the ticker symbol LFMDP to see the most recent price for the preferred stock.

Based on the amount of fixed dividend that the company will pay per year ($2.21875), the current dividend yield = 2.21875 / 22.52 = 9.852%.

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20

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 27

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Questions 1. Interest and Maturity. Explain why interest and maturity are the two most important attributes of a bond driving its valuation. (LO 13-1) Answer: Bond valuation consists of finding the present value of the cash flows that will be paid by the bond, over its life, discounted at a rate of return that is available on similar bonds with similar risks. This discount rate is called the yield to maturity (YTM).

The interest rate impacts the bond valuation in two distinct ways. First, when a bond is issued, the coupon rate on the bond is based on the prevailing interest rates in the market. For most bonds, this coupon rate is fixed; therefore, over the life of the bond, the coupon payments are based on the interest rate that was prevailing at the time the bond was issued. Even for variable rate bonds, the coupon payments vary with some factor that is linked to the prevailing interest rates. Second, the prevailing interest rate, or the YTM, is the rate that is used as the discount rate to do the bond valuation. Each coupon payment and the principal payment at maturity are discounted at the YTM to the present to find the value of the bond.

The maturity (or life) of the bond impacts its valuation because the bond is valued over its lifetime by taking the cash flows that the bond pays over its maturity to the present at YTM. Therefore, we can see that those two variables are really the two important attributes that drive the bond valuation.

2. Bond Risk. Explain what would cause the spread between different rankings of bonds to increase. How would this affect your portfolio investment strategy?

(LO 13-2) Answer: The spread between different rankings of bonds increases due to worsening economic conditions, which in turn affects the supply and demand of bonds with different rankings. In general, when the economic situation deteriorates, there is a trend that is called flight to quality: investors tend to sell low-quality bonds and buy high-quality bonds. This action will cause the price of low-quality bonds to decrease and their rates to increase, which will increase the spread.

Investors may use the spread as a guide for an investment strategy. When the spread increases, the investor sells the quality debt and purchases the lower-quality debt. The process would be reversed if the spread diminished. Essentially, the spread must be sufficient to compensate for the additional risk. Even if only 5% of

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2

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

the bonds were to default, the total loss on each bond may offset a substantial proportion of the yield advantage.

3. Purchasing Bonds. Why would you buy a flat bond? (LO 13-3) Answer: A flat bond is a bond that is trading without the accrued interest. This happens when the issuer of the bond is having financial difficulty and has suspended the coupon payments on the bond. Those bonds are considered to be in default, and the letter F is placed next to them in the transactions. A flat bond is a speculative type of investment. This bond is in default; however, if the financial situation of the issuer improves and they resume coupon payments, the return from buying this type of bonds becomes substantial. Basically, this is a very high-risk strategy.

4. Corporate Bond Types. What types of firms would be able to sell debentures? Why would they want to do so versus selling some type of secured bond issue? (LO 13-4) Answer: A debenture is an unsecured promissory note supported by the general creditworthiness of the firm. A debenture does not have any type of collateral to support the debt issue. This type of debt involves more risk than bonds that are supported by collateral. In the case of default or bankruptcy, the unsecured debt is redeemed only after all secured debt has been paid off. In addition, some debentures are subordinated, and these involve even more risk, for they are redeemed after the other general debt of the firm has been redeemed.

Firms with good credit ratings and sound financial conditions will be able to sell debentures. Because these bonds are among the riskiest debt instruments issued by firms, they usually have higher interest rates or other attractive features, such as convertibility into the stock of the company, to compensate the lenders for assuming the increased risk.

Because the debentures are general obligations of the company, they do not tie up its specific assets. If the firm needs additional funds, it can use specific assets as collateral to secure additional debt. If the assets had been previously pledged, the firm would lack this flexibility in financing.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

5. Accrued Interest. Why are zero coupon bonds taxed on interest accrual instead of interest payment? (LO 13-5) Answer: Zero coupon bonds do not pay any interest over their life. A zero coupon bond is a type of bond that is sold at discount. Its price is lower than its par value, and the zero coupon bond will pay the par value only at maturity. The interest on zero coupon bonds accrues until it is received when the bond matures. Since there is no interest payment, zero coupon bonds are taxed on accrued interest rather than on actual interest payment.

6. Bond Retirement. Why does a sinking fund make a bond safer for investors?

(LO 13-6) Answer: Sinking funds are generally employed to ease the retirement of long-term corporate debt. A sinking fund is a periodic payment to retire part of the debt issue. When a debt issue has the sinking fund feature, the risk of this debt is less compared to an identical debt issue without a sinking fund. The early retirement of debt associated with a sinking fund makes the issue less risky because the firm will pay off the debt over time rather than paying the whole amount at maturity.

7. Bond Pricing. Why might some argue that bonds are easier to price than stocks?

(LO 13-7) Answer: Valuation of both stocks and bonds involves finding the present value of the future cash flows discounted at an interest rate reflecting the risk of the asset.

Bonds are easier to price than stocks mainly because of the following factors: Bonds have finite maturities, while stocks do not have a maturity date. It is easier to value a security with a finite maturity than one with an infinite maturity.

Bonds make periodic coupon payments. Most bonds have fixed coupon payments over their lifetime, while some bonds have variable coupon payments. In either case, the complete description of the coupon rate and how the coupon rate may vary is written in the contract of the bond. Therefore, there is not much uncertainty about the cash flows that the bond will pay over its lifetime. Stocks, on the other hand, do not have any contractual agreements to pay dividends. The dividend payment is a managerial decision.

The discount rate used to value bonds can be estimated with more accuracy than the discount rate used to value stocks. The discount rate is the prevailing market

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4

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

rate on similar risk securities, which can be determined by calculating the YTM on bonds with similar characteristics. The discount rate to value stocks is not as easy to estimate as the YTM calculation.

For these three reasons, the argument that bonds are easier to value than stocks seems logical.

8. Yields. When would an investor want to focus on current yield instead of YTM? Why? (LO 13-8) Answer: The current yield is the return that the investor earns annually from coupon payments. It is calculated as the annual coupon payment divided by the price of the bond.

The yield to maturity is the return that the investor earns over the life of the bond from all the cash flows that the bond makes.

The current yield is important because it gives the investor an indication of the current return that will be earned on the investment. Investors who seek high current income prefer bonds that offer a high current yield.

9. Duration and Convexity. Why is a convexity-adjusted calculation of bond price changes in response to changes in interest rate more accurate than one done using only duration? (LO 13-9) Answer: The percentage change in a bond’s price for a change in the yield to maturity, using the duration variable, is given by the following formula: Δ PB = −D ×

Δ YTM ×P 1 + YTM B

The bond price change formula above assumes there is a linear relationship between the price change and the change in interest rate. In reality, this relationship is not linear; it is a convex function. Because of this convex relationship between the changes in the price with respect to the change in the interest rate, the convexityadjusted calculation gives a more accurate estimation for the price change.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

10. Bond Portfolio Management. Suppose you expected bond rates to go up in the next few years. What type of strategy would you want to adopt regarding your bond portfolio? Why? (LO 13-10) Answer: If you expect interest rates to go up in the next few years, you want to adopt a strategy where the bonds mature during the next few years so that you can reinvest them in new bonds with higher coupon payments and earn higher reinvestment rates.

Your strategy should be to buy short-term bonds. The bond portfolio should have a short duration over the next few years. A bond portfolio with short duration, and that has short-term bonds, does not decrease its value by much when interest rates rise. Also, because those bonds will mature within the next few years, the proceeds can be used to invest in higher yielding bonds after interest rates rise.

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Problems 1. Consol bond. What price would a consol bond paying $75 per year trade for if the YTM were 5%? (LO 13-7) Answer: Coupon i

$

75 5%

PB

$1,500

A consol bond is a perpetual bond that does not have a maturity date. The price of a perpetual bond can be found using the following equation: P=

PMT i

Where PMT is the periodic interest payment and i is the periodic interest earned on alternative investments with similar risk, which is given by the yield to maturity.

Price = 75 / 0.05 = $1,500 2. Annual coupon. What price would a 10% annual coupon bond with maturity of 17 years and a face value of $1,000 sell for if the current YTM were 12.3%? (LO 13-7) Answer: FV Coupon n i

$ 1,000 $ 100 17 12.3%

PB

$839.03

The value of a bond with a finite life is the present value of its cash flows (interest and principal repayment), which is given by the sum of the present value of the annuity of interest payments (PMT) plus the present value of the lump sum face value (FV) discounted by i, which is the periodic interest earned on alternative investments with similar risk, which is given by the yield to maturity.

The formula to calculate the price is as follows: 1− PB = PMT ×

1

(1+ i ) + n

i

FV

(1+ i )

n

PMT is the annual coupon payment, FV is the principal payment, n is the number of years to maturity, and i is the YTM.

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7

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

1− PB = 100 ×

1

(1+ 0.123)

17

0.123

+

1,000

(1+ 0.123)

17

= $839.03

3. Seminannual coupon. What price would an 8% semiannual coupon bond with maturity of eight years and a face value of $1,000 sell for if the current YTM were 6.5%? (LO 13-7) Answer: FV Coupon n i

$ $

1,000 80 8 6.5%

PB

$1,092.43

The value of the bond with semiannual coupon can be calculated in a similar manner as in Problem 2, with the additional change of having semiannual compounding. In order to account for the semiannual compounding, the following equation is used: 1− PB =

PMT × c

1  i 1 +  c   i c

n×c

+

FV  i 1 +   c

n×c

Where c is the frequency of compounding, while the rest of the variables are the same as in Problem 2.

1− PB =

80 × 2

1  0.065  1 +  2   0.065 2

8×2

+

1,000  0.065  1 +  2  

8×2

= $1,092.43

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8

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

4. Zero coupon. How much would a zero coupon bond with a face value of $10,000 and eight years to maturity sell for if the YTM were 7%? (LO 13-7) Answer: FV Coupon n i

$ $

10,000 − 8 7%

PB

$5,820.09

A zero coupon bond does not distribute any coupon payments over its lifetime.

Therefore, the PMT value is 0. We can use the same equation as in Problem 2 to solve for the value of the zero coupon bond.

1− PB = PMT ×

1− PB = 0 ×

1

(1+ i ) + n

i

FV

(1+ i )

n

1

(1+ 0.07) + 10,000 = $ 5,8 2 0 .0 9 8 0.07 (1+ 0.07) 8

By setting the value of PMT to 0, the price of the zero coupon bond is simply the present value of the principal or the face value, discounted by the YTM over the remaining life of the bond.

5. Split coupon. A split coupon bond with a face value of $1,000 pays $0 in interest during the first 10 years, then $200 annually for the next 10 years, and matures after 20 years. How much would an investor pay if the required return were 13%?

(LO 13-7) Answer: FV Coupon n i

$ $

1,000 200 10 13%

P10

$1,379.84

PB

$ 406.48

To find the value of a split coupon bond, we have to use a two-step approach.

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9

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

As the first step, we can find the value of this bond 10 years from now, when it will be a bond paying an annual coupon of $200 per year during each of the subsequent 10 years and a principal value of $1,000 at the end of those 10 years.

The value of the bond 10 years from now is calculated as follows: 1− P10 = 200 ×

1

(1+ 0.13)

10

+

0.13

1,000

(1+ 0.13)

10

= $1,379.84

This is the value of this bond 10 years from now.

To find the value of the bond today, we just need to find the present value of $1,379.84 over 10 years, discounted at the YTM of 13%.

PB =

1,379.84

(1 + 0.13)

10

= $406.48

6. Current yield. What would the current yield on an 8% annual coupon bond with maturity of 14 years and a face value of $1,000 be if it were selling for $1,137? (LO 13-8) Answer: Annual interest

$

80

PB Current yield

$1,137 7.04%

The current yield is the percentage that the investor earns annually. It is calculated using the following formula: Current Yield =

Annual Interest Payment Price of the Bond

Current Yield = 80 / 1137 = 0.0704, or 7.04% 7. Current yield. What would the current yield on a 7% semiannual coupon bond with maturity of four years and a face value of $1,000 be if it were selling for $987?

(LO 13-8) Answer: Annual interest

$ 70

PB Current yield

$987 7.09%

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10

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

The current yield is calculated using the equation below. We use the annual interest payment in the numerator, so when the bond pays semiannual coupons, we double the coupon payment in the numerator.

Current Yield =

Annual Interest Payment Price of the Bond

Current Yield = (35 + 35) / 987 = 0.0709, or 7.09% 8. YTM. What would the YTM yield on an 8.5% annual coupon bond with maturity of 12 years and a face value of $1,000 be if it were selling for $987? (LO 13-8) Answer: PB Annual interest FV Call penalty n Time 0 1 2 3 4 5 6 7 8 9 10 11 12

$ 987 $ 85 $1,000 0 12

YTM YTM

8.68% 8.68%

CF $ 987.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $ 85.00 $1,085.00

The YTM can be calculated using the same formula as for the price. In this case, the price will be known and the formula will be used to calculate the interest i. However, this calculation is very tedious; it takes a long time because you have to start by guessing an interest rate and then make several adjustments until the price of the bond matches the market price.

1− PB = PMT ×

1

(1+ i ) + FV n i (1+ i ) n

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

However, the calculation of the YTM becomes very simple if we use Excel. There are several approaches for using Excel to solve for the YTM. The simplest approach is to use the RATE function as it is shown in the Excel solutions.

Within the RATE function, you will input the following values, in the following order: nper, PMT, PV, FV; where nper is the number of periods to maturity, PMT is the periodic coupon payment, PV is the current value of the bond (here you have to make sure to enter this value as negative) and FV is the value you will get at maturity.

Using the RATE function, you get YTM = 8.68%.

Another approach is to use the IRR function to calculate the YTM, which is explained in the textbook and illustrated in the Excel solutions as well.

9. YTM. What would the YTM yield on a 7.25% semiannual coupon bond with maturity of 16 years and a face value of $1,000 be if it were selling for $1,034? (LO 13-8) Answer: PB Annual interest FV Call penalty n

$1,034 $72.50 $1,000 0 16

Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CF $1,034.00 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25

YTM (6 months) YTM (annual) YTM

3.45% 6.90% 6.90%

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12

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

$ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $ 36.25 $1,036.25

This problem is similar to Problem 8, except the bond is paying a semiannual coupon. To solve the problem, we can use the RATE function in Excel or the IRR function.

Remember to convert the problem into a semiannual basis in order to solve it correctly.

Semiannual Coupon Payment PMT = 36.25 The number of payments is n = 32.

FV = 1,000 PV = −1,034 Note: When we input those values into the RATE function in Excel, the answer is an interest rate given in semiannual terms. As we have to find the YTM on an annual basis, we multiply by 2 to get the annual YTM. YTM = 6.90% Another approach is to use the IRR function to calculate the YTM, which is explained in the textbook and illustrated in the Excel solutions.

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13

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

10. YTC. What would the YTC on an 8.5% annual coupon bond with maturity of 12 years and a face value of $1,000 be if it were selling for $987, carried a call penalty of $85, and you expected it to be called in three years? (LO 13-8) Answer: PB Annual interest FV Call penalty n Time 0 1 2 3

$ −987 $ 85 $1,000 85 3

YTC YTC

11.57% 11.57%

CF $ 987 $ 85 $ 85 $1,170

This problem is similar to Problems 8 and 9: the bond is paying an annual coupon.

To solve the problem, we can use the RATE function in Excel or the IRR function.

To solve for the YTC, we have to use the following values: Annual Coupon Payment PMT = 85 The number of payments until the bond is called is n = 3.

The value to be received when the bond is called including the call penalty is FV = $1,085.

Price of Bond PV = $−987 YTC = 11.57% Another approach is to use the IRR function to calculate the YTM, which is explained in the textbook and illustrated in the Excel solutions.

11. Macaulay duration. What would the Macaulay duration of a bond be with an annual 6% coupon rate, seven years until maturity, and a YTM of 7.3%? (LO 13-9) Answer: Annual coupon rate Yield Settlement date n Maturity date Payments per year Basis

6% 7.3% 28-04-2022 7 28-04-2029 1 0

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14

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

The Macaulay duration can be calculated using the Excel function DURATION as it is explained in the chapter. Using the DURATION function is the simplest and quickest way to find the value of the Macaulay duration. In order to use the DURATION function, we need to have the settlement date. The chapter explains how to use the TODAY function in Excel to get the settlement date.

The following should be used when using the DURATION function in Excel: Settlement Date = TODAY (This will set the value of the settlement date as the day you will be solving the problem.) n = 7 (number of years to maturity) Maturity Date = Date [Year(date given by today) + n, Month(date given by today), Day(date given by today)] [You are adding to the year part of the date given by the TODAY() function, the number of years of maturity the bond has.]

Coupon = 6% (The coupon should be in percentage terms.)

Yield = 7.3% (yield to maturity) Frequency = 1 (The frequency is where you specify whether it is an annual paying bond or semiannual paying bond; use 1 for annual and 2 for semiannual.)

Basis = 0 (You can usually leave this blank or use 0.)

Value of Duration = 5.87 years You can also use another approach explained in the chapter to calculate the duration, but it takes a longer time.

Period 1 2 3 4 5 6 7

Amount per Period $ 60.00 $ 60.00 $ 60.00 $ 60.00 $ 60.00 $ 60.00 $1,060.00

PV of Amount $ 55.92 $ 52.11 $ 48.57 $ 45.26 $ 42.18 $ 39.31 $647.30 $930.65

Product Period × PV $ 55.92 $ 104.23 $ 145.70 $ 181.06 $ 210.92 $ 235.89 $4,531.12 $5,464.84

Duration

5.87

Note: These amounts are off by a few cents due to rounding.

The column “Period” includes the values for each period until maturity. In this problem, as the maturity of the bond is seven years and the bond is an annual coupon bond, there are seven periods (1–7).

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15

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

The column “Amount per Period” includes the values that the bond will pay every period. Note that for year 7, the bond will pay the coupon payment and the principal.

The column “PV of Amount” is the present value of each periodic payment discounted by the yield to maturity.

The “Product Period × PV” is the product of the PV of Amount column and the Period column.

When we take the sum of the PV of Amount column, that sum is the value of the bond. In this example, the bond’s value is $930.65.

To calculate the duration, we have to take the sum of the Product Period × PV column and divide it by the bond’s value.

Duration = 5464.84/930.65 = 5.87 years 12. Macaulay duration. What would the Macaulay duration of a bond be with a semiannual 5% coupon rate, 17 years until maturity, and a YTM of 5.3%? (LO 13-9) Answer: Annual coupon rate Yield Settlement date n Maturity date Payments per year Basis

5% 5.3% 28-04-2022 17 28-04-2039 2 0

This is similar to Problem 11. The only difference is that the bond pays a semiannual coupon. To solve this problem using the DURATION function in Excel, follow the exact same approach as in Problem 11. The only difference is to set the frequency value to 2. The following should be used for the DURATION function in Excel: Settlement Date = TODAY (This will set the value of the settlement date as the day you will be solving the problem.) n = 17 Maturity Date = Date [Year(date given by today) + n, Month(date given by today), Day(date given by today)] [You are adding to the year part of the date given by the TODAY() function, the number of years of maturity the bond has.]

Coupon = 5% Yield = 5.3%

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16

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Frequency = 2 (The frequency value of 2 is for semiannual coupon payments.)

Basis = 0 Duration = 11.54 years The second approach that was used in Problem 11 can also be used here. This approach is very similar; the only difference is to convert the problem into a semiannual basis.

Therefore, there will be 34 periods, and the coupon payment will be $25. To find the present value of each amount, you need to discount them at 2.65%, which is the YTM/2.

Finally, to calculate the value of the duration, we use the following: Duration = (22,316.47 / 2) / 966.66 = 11.54 years Period Amount per Period 1 $ 25.00 2 $ 25.00 3 $ 25.00 4 $ 25.00 5 $ 25.00 6 $ 25.00 7 $ 25.00 8 $ 25.00 9 $ 25.00 10 $ 25.00 11 $ 25.00 12 $ 25.00 13 $ 25.00 14 $ 25.00 15 $ 25.00 16 $ 25.00 17 $ 25.00 18 $ 25.00 19 $ 25.00 20 $ 25.00 21 $ 25.00 22 $ 25.00 23 $ 25.00 24 $ 25.00 25 $ 25.00 26 $ 25.00

PV of Amount $ 24.35 $ 23.73 $ 23.11 $ 22.52 $ 21.94 $ 21.37 $ 20.82 $ 20.28 $ 19.76 $ 19.25 $ 18.75 $ 18.27 $ 17.79 $ 17.33 $ 16.89 $ 16.45 $ 16.03 $ 15.61 $ 15.21 $ 14.82 $ 14.43 $ 14.06 $ 13.70 $ 13.35 $ 13.00 $ 12.67

Product Period × PV $ 24.35 $ 47.45 $ 69.34 $ 90.07 $ 109.68 $ 128.21 $ 145.72 $ 162.24 $ 177.81 $ 192.46 $ 206.25 $ 219.19 $ 231.32 $ 242.68 $ 253.31 $ 263.22 $ 272.45 $ 281.03 $ 288.98 $ 296.34 $ 303.12 $ 309.36 $ 315.07 $ 320.28 $ 325.02 $ 329.29

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

27 28 29 30 31 32 33 34

$ 25.00 $ 25.00 $ 25.00 $ 25.00 $ 25.00 $ 25.00 $ 25.00 $1025.00

$ 12.34 $ 12.02 $ 11.71 $ 11.41 $ 11.11 $ 10.83 $ 10.55 $421.23 $966.66

$ 333.13 $ 336.55 $ 339.57 $ 342.21 $ 344.49 $ 346.42 $ 348.02 $14,321.82 $22,316.47

Duration

11.54

Note: Most amounts in this column are off by a few cents due to rounding.

13. Portfolio future value. Consider a portfolio manager who needs $1,200 at the end of three years and purchases at par a 6% annual coupon bond that matures at the end of three years. If the yield immediately changes to 8.5%, how much will the investor have at the end of three years if he can reinvest the coupons at 8.5%?

(LO 13-9) Answer: YTM Annual coupon Face value n FV

8.5% 60 1,000 3 $1,195.73 $ $

The problem is asking you to determine how much money the portfolio manager will have if every coupon payment is reinvested at 8.5% over three years. To solve this problem, we have to find the future values of the coupon payments and add them to the principal that will be received at maturity.

We can use the following formula to solve for this problem:  (1 + r )n − 1 FV = Principal + PMT ×   r    (1 + 0.085)3 − 1 FV = 1,000 + 60 ×   = $1,195.73 0.085  

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18

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

14. Modified duration. What would the modified duration of a bond be with an annual 7% coupon rate, 12 years until maturity, and a YTM of 4%? (LO 13-9) Answer: Annual coupon rate Yield Settlement date n Maturity date Payments per year Basis

7% 4% 28-04-2022 12 28-04-2034 1 0

The modified duration can be calculated using the Excel function MDURATION as it is explained in the chapter. Using the MDURATION function is the simplest and quickest way to find the value of the modified duration.

If you have already calculated the Macaulay duration, then you can calculate the modified duration with the following formula: D* =

D 1 + YTM

Where D is the Macaulay duration and YTM is the yield to maturity. The calculation process for finding the Macaulay duration is provided in Problems 11 and 12.

To solve for the modified duration, we have to input the following settings into the MDURATION FUNCTION in Excel: Settlement Date = TODAY() n = 12 Maturity Date = Date [Year(date given by today) + n, Month(date given by today), Day(date given by today)] Coupon = 7% Yield = 4% Frequency = 1 Basis = 0 Modified Duration = 8.60 years

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19

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

15. Modified duration. What would the modified duration of a bond be with a semiannual 4% coupon rate, 12 years until maturity, and a YTM of 7%? (LO 13-9) Answer: Annual coupon rate Yield Settlement date n Maturity date Payments per year Basis

4% 7% 28-04-2022 12 28-04-2034 2 0

This is very similar to Problem 14. The bond in this problem pays a semiannual coupon.

To solve for the modified duration, we have to input the following settings into the MDURATION function in Excel: Settlement Date = TODAY() n = 12 Maturity Date = Date [Year(date given by today) + n, Month(date given by today), Day(date given by today)] Coupon = 4% Yield = 7% Frequency = 2 Basis = 0 Modified Duration = 8.91 years 16. Convexity. Calculate the convexity of a 15-year, 8.2% annual coupon bond with a YTM of 8.8%. (LO 13-9) Answer: FV Coupon n YTM Convexity

$1,000 $ 82 15 8.8% 99.10

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20

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

The convexity is calculated using the following formula: Convexity =

n

 P × 1 + YTM 1

B

(

(t + t ) 1 + YTM CFt

) t =1 ( 2

2

)

t

The formula is not straightforward and requires very long and tedious calculations if done manually. With the help of Excel, the calculations become much more manageable.

The bond pays an annual coupon of $82, and at maturity in 15 years, it will also pay the principal of $1,000. The current price of this bond is $951.06.

The table below provides the information necessary to calculate the value of the convexity. t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CF 82 82 82 82 82 82 82 82 82 82 82 82 82 82 1,082

PV(CF) $ 75.37 $ 69.27 $ 63.67 $ 58.52 $ 53.79 $ 49.44 $ 45.44 $ 41.76 $ 38.38 $ 35.28 $ 32.43 $ 29.80 $ 27.39 $ 25.18 $305.35

Sum

$951.06

t2 + t 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240

PV(CF) × (t2 + t) $ 150.74 $ 415.63 $ 764.03 $ 1,170.38 $ 1,613.58 $ 2,076.30 $ 2,544.48 $ 3,006.87 $ 3,454.59 $ 3,880.77 $ 4,280.26 $ 4,649.34 $ 4,985.51 $ 5,287.23 $ 73,283.31 $111,563.02

Note: Most amounts in this column are off by a few cents due to rounding.

The first column represents the number of payments the bond will make until maturity, which is 15.

The second column provides the value of each payment every period. Note that for the 15th payment, the bond will pay the coupon plus the principal.

The third column is the present value of each payment from the second column, discounted at the rate of YTM, which is 8.8%. Taking the sum of all those present

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

values gives us the current price of the bond, which is $951.06. This is the price that we should use to calculate the convexity, PB, in the formula above.

The fourth column gives us the value of (t2 + t) for each value of the periods up to maturity.

The fifth column gives us the product of the third and the fourth columns, which is the product of the present value of each cash flow times the value of (t2 + t). This column represents the following portion of the convexity formula for every period:

(t + t ) 1 + YTM CFt

(

2

)

t

We have to take the sum of column 5 to find the value of the following portion of the formula: n

 t =1

(t + t ) = $111,563.02 1 + YTM CFt

(

2

)

t

Finally, to calculate the convexity, we find the following product: Convexity =

1 951.06 × (1 + 0.088)2

× 111,563.02 = 99.10

17. Expected price change. What would the expected price change be using a convexity-adjusted estimate if the YTM on a 10-year, 7% annual coupon bond changed from 6.5% to 7.2%? (LO 13-9) Answer: FV Coupon n YTM Convexity t 1 2 3 4 5 6 7

$1,000 $70 10 6.5% 66.11 CF 70 70 70 70 70 70 70

Coupon rate Settlement date Maturity date Frequency Basis

PV(CF) $ 65.73 $ 61.72 $ 57.95 $ 54.41 $ 51.09 $ 47.97 $ 45.05

t2 + t 2 6 12 20 30 42 56

7% 28-04-2022 28-04-2032 1 0

PV(CF) × (t2 + t) $ 131.46 $ 370.30 $ 695.39 $ 1,088.25 $ 1,532.75 $ 2,014.88 $ 2,522.54

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

8 9 10

70 70 1,070

$ 42.30 $ 39.71 $570.02

Sum

$1,035.94

72 90 110

$ 3,045.33 $ 3,574.33 $62,701.85 $77,677.08

Note: Most amounts in this column are off by a few cents due to rounding.

In order to calculate the expected price change using the convexity-adjusted estimate, we use the following formula: Δ PB = ( −D* × Δ YTM +

1 × Convexity × Δ YTM 2 ) × PB 2

Where D* is the modified duration, Convexity is the value of the convexity measure, PB is the price of the bond, and ΔYTM is the change in the yield.

We need to calculate the values of the modified duration and the convexity, using YTM = 6.5%. (The details to calculate the modified duration and convexity are explained in other problems.)

The price of this bond when the YTM is 6.5% is $1,035.94.

The value of the convexity is 66.11.

The modified duration is 7.10.

The change in the YTM is 0.007 (the difference between 7.2% and 6.5%).

The convexity-adjusted price change is calculated as follows: ΔPB = [−7.10 × 0.007 + 0.5 × 66.11 × (0.007)2] × 1,035.94 = −$49.81 The new price becomes: New PB = 1,035.94 − $49.81 = $986.13 If you calculate the actual price of this bond using the new YTM of 7.2%, the price is $986.08. This shows that the convexity-adjusted price calculation gives very accurate results.

18. Straight ladder. Suppose you use a $500,000 bond portfolio to construct a straight ladder over the next 10 years. How much would you invest in bonds maturing in each year of the ladder? (LO 13-10) Answer: Portfolio n Amount invested each year

$500,000 10 $ 50,000

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

A straight ladder strategy involves investing in bonds with maturities that span the number of years of the investment. A straight ladder portfolio could be constructed by investing $50,000 worth of bonds that mature for each of the next 10 years. The width of each step is the same, and the distance between each step is the same.

The amount invested is calculated by dividing the total portfolio value by the investment horizon.

Amount = 500,000 / 10 = $50,000 Bonds worth $50,000 will mature in 1 year, $50,000 worth of bonds that will mature in 2 years, etc., up to $50,000 worth of bonds will mature in 10 years.

19. Barbell. Suppose you use a $250,000 bond portfolio to construct a barbell strategy over the next 20 years. How much would you invest in bonds maturing in year 20?

(LO 13-10) Answer: Portfolio n Amount invested each year

$250,000 10 $125,000

A barbell strategy involves investing in two types of bonds: half the amount is invested in very short maturity bonds, and the other half is invested in very long maturity bonds.

The amount invested in each type is half the value of the portfolio, which is 250,000 / 2 = $125,000.

In this example, you can invest $125,000 in bonds with short maturities (e.g., six months to a year) and $125,000 to purchase 20-year bonds.

20. Expected price. What would the expected new price be using a convexity-adjusted estimate if the YTM on a 30-year, 6% annual coupon bond selling at par increased by one basis point? (LO 13-9) Answer: FV Coupon n YTM Convexity

$1,000 $ 60 30 6% 294.57

Settlement date Maturity date Coupon rate Frequency Basis

28-04-2022 28-04-2052 6% 1 0

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

CF 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 1,060

PV(CF) $ 56.60 $ 53.40 $ 50.38 $ 47.53 $ 44.84 $ 42.30 $ 39.90 $ 37.64 $ 35.51 $ 33.50 $ 31.61 $ 29.82 $ 28.13 $ 26.54 $ 25.04 $ 23.62 $ 22.28 $ 21.02 $ 19.83 $ 18.71 $ 17.65 $ 16.65 $ 15.71 $ 14.82 $ 13.98 $ 13.19 $ 12.44 $ 11.74 $ 11.07 $ 184.56

Sum

$1,000.00

t2 + t 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 812 870 930

PV(CF) × (t2 + t) $ 113.21 $ 320.40 $ 604.53 $ 950.51 $ 1,345.06 $ 1,776.50 $ 2,234.59 $ 2,710.42 $ 3,196.25 $ 3,685.41 $ 4,172.16 $ 4,651.63 $ 5,119.72 $ 5,572.99 $ 6,008.62 $ 6,424.31 $ 6,818.25 $ 7,189.05 $ 7,535.70 $ 7,857.48 $ 8,153.99 $ 8,425.05 $ 8,670.73 $ 8,891.23 $ 9,086.95 $ 9,258.40 $ 9,406.21 $ 9,531.10 $ 9,633.86 $171,637.77 $330,982.07

This is similar to Problem 17. The purpose is to find the convexity-adjusted price change for the bond for 1 basis point change in YTM. When the bond is selling at par, then at that time we know that the YTM is equal to the coupon rate of 6%. So, the initial YTM is 6%.

One basis point change is equivalent to a 0.01% change. The problem does not specify how the change is going to happen: it can go either up or down by 0.01%,

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

which is a very low change. Therefore, we can expect the price of this bond not to change by much.

Similar to the solution method provided in Problem 17, we can calculate the following: Current Price of Bond Is Par = $1,000 The value of the convexity is 294.57.

The modified duration is 13.76.

The change in the YTM is 0.0001 (this can be either up or down).

The convexity-adjusted price change is $1.38.

Therefore: If the YTM increases by one basis point, the price will decrease by $1.38 and become $998.62.

If the YTM decreases by one basis point, the price will increase by $1.38 and become $1,001.38.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Case Study Changes in Yield On March 18, 2020, the yield on Moody’s Aaa-rated bonds with maturities from 20 years and longer went from 3.40 to 3.92%, the largest jump since the Federal Reserve started tracking such ranked yields in 1983.

Using this 3.92% figure as the YTM for a 20-year bond issue that was selling at par the day before, graph expected bond prices as a function of future YTMs on that date using the convexity adjustment.

Answer: The bond with 20 years of maturity was selling at par on March 17, 2020; therefore, the coupon rate must be 3.40% in order for this bond to sell at par on this day. The next day, the yield jumps to 3.92%.

Using this information, we can calculate the values of the Macaulay duration, modified duration, and convexity, and then find the price change for this bond for a range of YTM from 0 to 20%.

The Excel file shows the solution for this case. The graph shows the convexity-adjusted bond price in blue, while the actual bond price is in red. We notice that the convexityadjusted price is providing fairly accurate estimations up to a YTM of 10%. When the YTM is above 10%, the error between the convexity-adjusted price and the actual price increases.

This high error can be attributed partly to the low coupon rate that this particular bond has: 3.40%. In addition, even with a convexity adjustment, when the interest rate changes become higher and higher, more errors will be introduced between the convexity-adjusted price versus the actual price.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 13: Valuing Corporate Bonds

Estimated Bond Price with Convexity Adjustment vs.

Actual Bond Price $2,000.00 $1,800.00 $1,600.00 $1,400.00 $1,200.00 $1,000.00 $800.00 $600.00 $400.00 $200.00 $0.00 0%

5%

10%

Convexity Adjusted Bond Price

15%

20%

25%

Actual Bond Price

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28

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 18

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

Questions 1. Government Bonds. What distinguishes Series EE bonds from Treasury bills?

(LO 14-1) Answer: Savings bonds now come in two versions: Series EE and Series I. Series EE bonds carry a fixed rate and are investments that are guaranteed to double in value over 20 years and expire after 30 years. The newer Series I bonds have both a fixed rate and a variable rate to keep up with inflation. The better-known Series EE bond is a direct descendant of the Series E savings bond. The original Series E was known as the War Bond and helped finance the American participation in World War II. Series EE bonds can be purchased with a face value of as little as $25. Face values are also available in penny increments over the base $25. So you could buy a bond for $25.32 if you desired. The maximum amount that one buyer can purchase in a year is $10,000. The bonds are issued to a single owner and cannot be sold in the secondary market. Treasury bills (or T-bills) are short-term securities that mature in one year or less from their issue date. T-bills are purchased for a price less than or equal to their par (face) value, and when they mature, Treasury pays their par value.

2. STRIPS. Explain why STRIPS are well suited to be held in retirement accounts.

(LO 14-2) Answer: STRIPS are well suited to be held in retirement accounts because they are basically zero coupon bonds. They do not pay interest, but the interest earned on a zero coupon bond is taxed as it accrues. STRIPS pay all the funds (i.e., principal and accrued interest) in one lump sum at maturity. Because any tax on a retirement account is paid when the funds are withdrawn, the tax disadvantage of zero coupon bonds is circumvented. The investor can purchase issues that mature at a desired date to meet retirement needs. STRIPS can be used to create a laddered bond strategy, where the bonds mature and the funds are received after retirement. At that time, they would replace the individual’s earned income that ceases at retirement.

3. TIPS. How are TIPS adjusted for inflation? (LO 14-3) Answer: TIPS yields are based on their current amount of principal. When inflation rises, the principal of TIPS adjusts higher, and the payments go up along with it. TIPS are a form of U.S. Treasury bond designed to help investors protect against inflation. They are indexed to inflation, have U.S. government backing, and pay investors a fixed interest rate as their par value adjusts with the inflation rate.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

4. Asset-Backed Bonds. What different types of assets back the debt of the government agencies discussed in this chapter? What were the objectives behind the creation of such agencies? (LO 14-4) Answer: Several government agencies were created to provide debt financing for specific groups or individuals. The Government National Mortgage Association (GNMA or Ginnie Mae), a division of the Department of Housing and Urban Development (HUD), issues securities that are backed by a pool of FHA/VA guaranteed mortgages.

(FHA and VA are the Federal Housing Administration and Department of Veterans Affairs, respectively.) The mortgages are originated by private lenders, such as savings and loan associations and other savings institutions, and packaged into securities that are sold to the general public and guaranteed by GNMA. The Student Loan Marketing Association (Sallie Mae) was created in 1972 to provide liquidity to the insured student loans made under the Guaranteed Student Loan Program by commercial banks, savings and loan associations, and schools that participate in the program. Sallie Mae became private in 2004. Student loans were the assets that back the debt issued by Sallie Mae. The Banks for Cooperatives used to provide subsidized loans to farm cooperatives to help purchase supplies.

The objectives behind creating such agencies are to facilitate the lending process in those particular sectors, to guarantee loans made in those sectors, and to provide liquidity to those markets.

5. CMOs. Explain the advantage of CMOs over Ginnie Maes for investors. (LO 14-4) Answer: A collateralized mortgage obligation (CMO) consists of debt securities, Ginnie Maes, and other federal government-supported mortgages. When a CMO is created, it is subdivided into classes (called tranches). For example, a $100 million CMO may be divided into four tranches of $25 million each. The principal repayments received by the CMO are initially paid to the first class until that tranche has been entirely retired. Once the first tranche has been paid off, mortgage principal repayments are directed to the holders of the CMOs in the second tranche. This process is repeated until all the tranches have been repaid. No principal repayments are made to the next tranche until all the funds owed by the first tranche are paid.

Ginnie Mae securities serve as a conduit through which the interest and principal repayments are received from the homeowners and distributed to investors. The investor acquires part of the Ginnie Mae pool. As interest and principal repayments are made to the pool, the funds are channeled to the Ginnie Mae’s owners. The

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

investor receives a monthly payment that is their share of the principal and interest payments received by the pool.

The advantage of the CMOs over Ginnie Maes is that the uncertainty of the timing of monthly payments are very high in Ginnie Maes, while this uncertainty is much less with the CMO structure. The uncertainty arises when the principal payments are accelerated and investors suffer from reinvestment risk.

6. Munis. Munis offer tax advantages to investors. Is this advantage of equal value to all investors? Why, or why not? (LO 14-5) Answer: The tax advantage offered by municipal bonds is not of equal value to all investors.

Municipal bonds are tax-exempt at the federal level; however, this tax exemption advantage is dependent on the investor’s federal income tax bracket. The higher the investor’s federal income tax bracket, the higher the tax savings are, which translates into higher tax advantage.

In addition, if the investor lives in a state that taxes income, then municipal bonds issued by municipalities within those states offer additional tax advantage to investors resident in those states by exempting the interest payments from municipal bonds from state income taxes. Therefore, some investors can earn double tax exemptions from municipal bonds.

7. M/T Ratio. Why might the M/T ratio go close to or even over 1.0? (LO 14-5) Answer: The yields on municipal bonds are often expressed using the municipal/Treasury (M/T) ratio, a comparison of the current yield of municipal bonds to U.S. Treasuries calculated by comparing the yield on an index of AAA-rated municipal bonds with the yield on the equivalent Treasury note.

The M/T ratio can get close to 1.0 if the rates on Treasury notes are lower than the rates on municipal bonds. One way this can happen is if the Federal Reserve adopts a highly expansionary monetary policy for a long period of time and keeps the rates very low. Another way for the ratio to go above 1.0 is when the municipal bonds yields are very high compared to the Treasury notes. This situation happened during the early months of the COVID-19 pandemic: investors dumped municipal bonds, which led to prices going down and yields going up, which resulted in very high M/T ratios above 1.0 for several months.

Most of the time, though, the M/T ratio stays near 80% to 90%.

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4

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

8. State Tax Exemption. Is Equation 14.6 assuming that munis in a given state are exempt from state taxes, or not exempt? (LO 14-6) Answer:

(

)

Equation 14.6 is the following: ic 1 − t f − t s = im This equation assumes that the investor lives in a state that taxes income; therefore, the equation includes the impact of the local tax given by the term ts. The term tf is the federal tax rate.

This equation incorporates the impact of both federal and state taxes to determine the equivalent yields on tax-exempt bonds and nonexempt bonds.

9. Exchange Rate Risk. If an investor invests in the debt of a foreign government that uses the U.S. dollar as the basis of their currency, will there still be exchange rate risk? Why or why not? (LO 14-7) Answer: If the debt of a foreign government is issued in U.S. dollars, the interest payments and the principal payment will be made in U.S. dollars. In this situation, an American investor will not be subject to foreign exchange risk, since the return on the investment does not require conversion back to U.S. dollars. An American investor will simply transfer the dollars to the United States.

However, a non-American investor will still be subject to foreign exchange risk, since they will have to convert U.S. dollars into their domestic currency.

10. Mutual Funds. Explain why individual investors may wish to invest in government securities through a mutual fund rather than purchasing such securities themselves.

(LO 14-8) Answer: There are several specific reasons investors turn to mutual funds instead of managing their own portfolio directly. The primary reasons why an individual may choose to buy mutual funds instead of individual stocks are diversification, convenience, and lower costs.

Some government and agency securities do not have active secondary markets; the spread between the bid and ask prices can be substantial, especially for small issues or if the individual acquires small denominations, such as a $5,000 face amount.

Financial information about some government and agency securities is not readily available. Municipal bonds are not registered with the SEC. Information on many issues is not readily available. Prices are not quoted, and though bond values may

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

be provided by brokers on the investor’s monthly statements, the values are at best approximations and are not indicative of actual trades or available bid prices.

Government and agency securities do not have a standard size of the unit of trading, and a minimum size to trade varies from one security to another. For example, Ginnie Mae bonds are sold in units of $25,000, and municipal bonds are sold in units of $5,000.

Finally, diversification may not be possible, as it requires the purchase of a variety of issues, which in turn requires a substantial amount of money to invest.

Those issues are resolved if the investor purchases a mutual fund that invests in government securities.

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

Problems 1. Bid vs. asked. Suppose a $10,000 T-bill is quoted with bid and ask prices of 2.37 and 2.34, respectively. At what price would you be able to buy a bond? (LO 14-1) Answer: Face value Bid Ask Price

$10,000 2.37% 2.34% $ 9,766

You will buy the T-bill at the ask price. The quote shows the ask discount yield of 2.34%. There is no maturity value shown in the problem; therefore, we can assume it is a one-year T-bill. Therefore, the price will be: (10,000 − Price) / 10,000 = 0.0234 10,000 − Price = 234 Price = 10,000 − 234 = $9,766 2. Bid vs. asked. Suppose a $10,000 T-bill is quoted with bid and ask prices of 2.75 and 2.73, respectively. At what price would you be able to sell a bond? (LO 14-1) Answer: Face value Bid Ask Price

$10,000 2.75% 2.73% $ 9,725

You will sell the T-bill at the bid price. The quote shows the bid discount yield of 2.75%. There is no maturity value shown in the problem; therefore, we can assume it is a one-year T-bill. Therefore, the price will be: (10,000 − Price) / 10,000 = 0.0275 10,000 − Price = 275 Price = 10,000 − 275 = $9,725

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

3. Discount yield. What will the discount yield of a five-month $10,000 Treasury bill selling for $9,800 be? (LO 14-1) Answer: Par value Price Number of days to maturity id

$10,000 $ 9,800 150 4.8%

The discount yield is calculated using the following formula: id =

Par Value − Price 360 × Par Value Number of Days to Maturity

The maturity of the T-bill is five months; using 30 days in a month for the discount yield, we have 5 × 30 = 150 days to maturity. id = (10,000 − 9,800) / 10,000 × (360 / 150) = 0.048, or 4.8% 4. Annualized yield. What will the annualized yield of a seven-month $10,000 Treasury bill selling for $9,550 be? (LO 14-1) Answer: Par value Price Number of days to maturity ia

$10,000 $ 9,550 210 8.19%

The annualized yield is calculated using the following formula: ia =

Par Value − Price 365 × Price Number of Days to Maturity

The maturity of the T-bill is seven months; using 30 days in a month for the yield, we have 7 × 30 = 210 days to maturity. ia = (10,000 − 9,550) / 9,550 × 365 / 210 = 0.0819, or 8.19% 5. Annualized yield. Suppose the discount yield on a four-month T-bill is 3.40%. What will the annualized yield be? (LO 14-1) Answer: id Number of days to maturity

3.40% 120

ia

3.487%

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8

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

The annualized yield can be calculated from the discount yield using the following formula: ia =

365 × id

360 − (id × Days to Maturity )

The maturity of the T-bill is four months; using 30 days in a month for the yield, we have 4 × 30 = 120 days to maturity. ia = 365 × 0.0340 / [360 − (0.0340 × 120)] = 0.03487, or 3.487% 6. Annual compound return. If you earn a simple annualized rate of 6.3%3 on a fourmonth $10,000 T-bill selling for $9,723, what will the annual compound return be?

(LO 14-1) Answer: Par value Price Number of days to maturity

$10,000 $ 9,723 120 8.92%

ic

The formula to calculate the compound interest is as follows: ic = n

Par Value −1 Price

The maturity of the T-bill is four months; using 30 days in a month for the yield, we have 4 × 30 = 120 days to maturity. ic = (10,000 / 9,723)365 / 120 − 1 = 0.0892, or 8.92% 7. Bond quotes. If a $10,000 Treasury bond is quoted as 105:09–105:12, what price would you pay to buy the bond? (LO 14-1) Answer: Face value Bid Pct Bid 32s Ask Pct Ask 32s Price

$

10,000 105 9 105 12 $10,537.50

You will buy the Treasury bond at the ask price. Treasury bonds are quoted in 32nds. The ask price of 105:12 is equal to 105 12 / 32 as percent of the par value.

The price you pay will be 105.375 × 10,000 / 100 = $10,537.50

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

8. Bond quotes. If a $10,000 Treasury bond is quoted as 95:09–95:11, at what price would you be able to sell the bond? (LO 14-1) Answer: Face value Bid Pct Bid 32s Ask Pct Ask 32s Price

$ 10,000 95 9 95 11 $9,528.13

You will sell the Treasury bond at the bid price. Treasury bonds are quoted in 32nds.

The bid price of 95:09 is equal to 95 9 / 32 as percent of the par value.

The price you pay will be 95.28125 × 10,000 / 100 = $9,528.13 9. Age in bonds. According to the “age in bonds” calculation, what percentage of their portfolio should a 57-year-old have invested in stocks? (LO 14-1) Answer: Age Percentage in stocks

57 43

According to the “age in bonds” calculation, a 57-year-old should have 57% of their portfolio in bonds, which leaves 43% in stocks.

10. Age minus 20. According to the “age minus 20 in bonds” calculation, what percentage of their portfolio should a 43-year-old have invested in stocks? (LO 14-1) Answer: Age Percentage in stocks

43 77

According to the “age minus 20 in bonds” calculation, a 43-year-old should have 23% of their portfolio invested in bonds, which leaves 77% in stocks.

11. (Age minus 40)*2. According to the “[(age−40)*2]” calculation, what percentage of their portfolio should a 53-year-old have invested in stocks? (LO 14-1) Answer: Age Percentage in stocks

53 74

According to the “[(age−40)*2]” calculation, a 53-year-old should have 26% of their portfolio invested in bonds, which leaves 74% in stocks.

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10

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

12. Yield change. Suppose you buy both a $1,000, 4% annual coupon bond with a maturity of eight years and a zero coupon bond with a maturity of eight years. The yield is 6.25% when you buy them but changes to 5.50%. What will the new prices of the bonds be? (LO 14-2) Answer: Initial yield New yield FV of both bonds Coupon on coupon bond Term of both bonds Price of coupon bond at initial yield Price of zero at initial yield Price of coupon bond at new yield Price of zero at new yield

6.25% 5.50% $ 1,000 4% 8 $861.65 $615.70 $904.98 $651.60

The zero coupon bond will pay the par value at maturity. The price of the zero coupon bond is the present value of the par over the life of the bond, discounted at the prevailing interest rates.

Initial Price of Zero Coupon = 1,000 / (1 + 0.0625)8 = $615.70 New Price of Zero Coupon = 1,000 / (1 + 0.055)8 = $651.60 The price of a coupon paying bond can be found using the following formula from Chapter 13: 1− PB = PMT ×

1−

Initial Price of Bond = 40 ×

1−

New Price of Bond = 40 ×

1

(1+ i ) + n

i

FV

(1+ i )

n

1

(1+ 0.0625) + 8

0.0625

1,000

(1+ 0.0625)

8

= $861.65

1

(1+ 0.055) + 8

0.055

1,000

(1+ 0.055)

8

= $904.98

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11

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

13. Yield change. Suppose you buy both a $1,000, 4% annual coupon bond with a maturity of 10 years and a zero coupon bond with a maturity of 10 years. The yield is 4% when you buy them but changes to 5%. How much more or less will the price of the zero go down than the price of the coupon bond? (LO 14-2) Answer: Initial yield New yield FV of both bonds Coupon on coupon bond Term of both bonds Price of coupon bond at initial yield Price of zero at initial yield Price of coupon bond at new yield Price of zero at new yield Change in price of coupon bond Change in price of zero Change in price of zero − change in price of coupon bond

4% 5% $ 1,000 4% 10 $ 1,000 $675.56 $922.78 $613.91 −$ 77.22 −$ 61.65 $ 15.57

The zero coupon bond will pay the par value at maturity. The price of the zero coupon bond is the present value of the par over the life of the bond, discounted at the prevailing interest rates.

Initial Price of Zero Coupon = 1,000 / (1 + 0.04)10 = $675.56 New Price of Zero Coupon = 1,000 / (1 + 0.05)10 = $613.91 The price of a coupon paying bond can be found using the following formula from Chapter 13: 1− PB = PMT ×

1

(1+ i ) + n

i

FV

(1+ i )

n

The initial price of the bond is $1,000 since the yield was equal to 4%, which is same as the coupon rate.

1−

New Price of Bond = 40 ×

1

(1+ 0.05)

10

0.05

+

1,000

(1+ 0.05)

10

= $922.78

The change in the price of the zero coupon bond was $613.91 − $675.56 = −$61.65.

The change in the price of the coupon bond was $922.78 − $1,000.00 = −$77.22.

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12

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

The coupon bond decreased by $77.22 − $61.65 = $15.57 more than the zero coupon bond.

14. Inflation-indexed. Assume you buy a 10-year inflation-indexed bond having a real interest rate of 3.625% when the CPI was 260.229. If, one year later, the CPI had risen to 277.948, how much interest would you receive? (LO 14-3) Answer: Real interest rate CPI at purchase CPI at time of interest payment Interest

3.625% 260.229 277.948 $38.72

The change in the CPI in one year is equal to: Change in CPI = 277.948 / 260.229 − 1 = 0.06809, or 6.809% Since the inflation-indexed bonds adjust the par value for any changes in inflation, the par value will increase by 6.809%. Assuming the bond has a par value of $1,000, the new par value will be 1,000 × 1.06809 = $1,068.09 The interest that will be received is 1,068.09 × 0.03625 = $38.72.

15. Mortgage interest. If you purchase a $290,000 30-year mortgage carrying an interest rate of 3.697%, how much interest will you receive during the first year (i.e., from the first 12 payments)? (LO 14-4) Answer: Loan amount Interest rate Term (years) Payment Number of Payment 1 2 3 4 5 6 7 8 9

$ 290,000 3.697% 30 $1,334.33 Interest Payment $ 893.44 $ 892.08 $ 890.72 $ 889.35 $ 887.98 $ 886.61 $ 885.23 $ 883.85 $ 882.46

Principal Repayment $440.89 $442.25 $443.61 $444.97 $446.35 $447.72 $449.10 $450.48 $451.87

Balance of Loan $289,559.11 $289,116.87 $288,673.26 $288,228.29 $287,781.94 $287,334.22 $286,885.12 $286,434.64 $285,982.77

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13

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

10 11 12

$ 881.07 $ 879.67 $ 878.27 $10,630.73

$453.26 $454.66 $456.06

$285,529.50 $285,074.84 $284,618.78

Note: Numbers may be slighty off due to rounding.

To calculate the amount of interest from the first 12 payments of the mortgage, Excel can be used to create the payment schedule for the first 12 months of the mortgage life.

The mortgage will pay monthly payments; therefore, to solve the problem, we have to convert it to monthly terms.

N = 360; there will be 360 monthly payments.

I = 3.697 / 12 = 0.30808%, the monthly interest rate Using the (PMT) function in Excel, you calculate the monthly payment, by inserting the monthly rate of 0.30808%, 360 payments, and 290,000. The monthly payment is $1,334.33.

The table provided in the Excel file calculates the proportion of the payment that is interest and the proportion that is the principal.

The interest amount per month is calculated by multiplying the beginning balance by the monthly interest rate.

The principal amount per month is calculated by subtracting the interest amount from the monthly payment.

The ending balance is calculated by subtracting the principal amount from the beginning balance.

The ending balance at the end of the first month is the beginning balance at the beginning of the second month and so forth.

Following the same procedure for the first 12 months, we get the total amount of interest paid of $10,630.73.

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14

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

16. CMO. Suppose a CMO has five tranches. Each tranche consists of a $200,000 loan ($1,000,000 total outstanding), $100,000 of which is retired each year. Interest is paid annually on the amount of the loan outstanding in each tranche. The rate of interest varies with the expected life of each tranche. The interest rates start at 5% for tranche A and rise to 9% for tranche E. How much total interest across all tranches will be paid in year 5? (LO 14-4) Answer: Tranche A interest Tranche B interest Tranche C interest Tranche D interest Tranche E interest Year

5% 6% 7% 8% 9%

A

$200,000 $200,000 $200,000 $200,000 $200,000

B

C

D

E

Interest

Principal

Interest

Principal

Interest

Principal

Interest

Principal

Interest

Principal

1

$10,000

$100,000

$12,000

0

$14,000

0

$16,000

0

$18,000

0

2

$ 5,000

$100,000

$12,000

0

$14,000

0

$16,000

0

$18,000

0

3

0

0

$12,000

$100,000

$14,000

0

$16,000

0

$18,000

0

4

0

0

$ 6,000

$100,000

$14,000

0

$16,000

0

$18,000

0

5

0

0

0

0

$14,000

$100,000

$16,000

0

$18,000

0

6

0

0

0

0

$ 7,000

$100,000

$16,000

0

$18,000

0

7

0

0

0

0

0

0

$16,000

$100,000

$18,000

0

8

0

0

0

0

0

0

$ 8,000

$100,000

$18,000

0

9

0

0

0

0

0

0

0

0

$18,000

$100,000

10

0

0

0

0

0

0

0

0

$ 9,000

$100,000

Total Interest Year 5

$48,000

The Excel solution provides the interest payments and principal payments for each tranche per year. Starting with tranche A, every year $100,000 will be retired.

In year 5, tranche A and tranche B are already retired. There will be $100,000 retired of tranche C at the end of year 5.

Total interest will be based on the loans outstanding in tranches C, D, and E only.

The interest will be paid on the outstanding balances in year 5, which is $200,000 in each of tranches C, D, and E. Interest Amount in Year 5 = (0.07 × 200,000) + (0.08 × 200,000) + (0.09 × 200,000) = $48,000 The detailed interest and principal payment schedule is shown in the Excel file.

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15

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

17. Equivalent municipal yield. An investor faces a federal tax rate of 24% and can buy a corporate bond yielding 2.71%. What would the equivalent municipal yield be?

(LO 14-6) Answer: Federal tax rate Corporate yield Equivalent muni yield

24% 2.71% 2.06%

The relationship between the yield on corporate bonds, municipal bonds, and federal taxation is given by the following formula:

ic (1 − t ) = im The equivalent municipal yield is 2.71 × (1 − 0.24) = 2.06%.

18. Equivalent corporate yield. An investor faces a federal tax rate of 24% and can buy a muni bond yielding 4.08%. What would the equivalent corporate yield be?

(LO 14-6) Answer: Federal tax rate Muni yield Equivalent corporate yield

24% 4.08% 5.37%

The relationship between the yield on corporate bonds, municipal bonds, and federal taxation is given by the following formula: ic (1 − t ) = im

The equivalent corporate yield is 4.08 / (1 − 0.24) = 5.37%.

19. Equivalent municipal yield. An investor lives in a state that taxes income and faces a state tax rate of 6% and a federal tax rate of 24%. If they can buy a corporate bond yielding 2.71%, what would the equivalent municipal yield be? (LO 14-6) Answer: State tax rate Federal tax rate Corporate yield Equivalent muni yield

6% 24% 2.71% 1.90%

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16

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

The relationship between the yield on corporate bonds, municipal bonds, state income taxes, and federal taxation is given by the following formula:

(

)

ic 1 − t f − t s = im

The equivalent municipal yield is 2.71 × (1 − 0.24 − 0.06) = 1.90%.

20. Equivalent corporate yield. An investor lives in a state that taxes income and faces a state tax rate of 6% and a federal tax rate of 24%. If they can buy a muni bond yielding 4.25%, what would the equivalent corporate yield be? (LO 14-6) Answer: State tax rate Federal tax rate Muni yield Equivalent corporate yield

6% 24% 4.25% 6.07%

The relationship between the yield on corporate bonds, municipal bonds, state income taxes, and federal taxation is given by the following formula:

(

)

ic 1 − t f − t s = im

The equivalent corporate yield is 4.25 / (1 − 0.24 − 0.06) = 6.07%.

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17

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 14: Valuing Government Securities

Case Study M/T Ratio In 2021, M/T ratios hit a historic low. Explain what factors were behind it. What does this mean for yields on munis?

Answer: In 2021, investors heavily bought municipal bond funds, and bonds issued by municipalities across the United States saw a very high demand. The state agencies and municipalities were in much better shape in 2021 than they were in 2020, partly because the fears that arose at the start of the COVID-19 pandemic in 2020 were reduced, tax collections were better than expected for most of the states, and the government provided stimulus funds to states and municipalities.

With the high demand for municipal bonds, their prices went up, which resulted in their yields going down. This is the reason behind low M/T ratio values for 2021 following the historic highs in 2020 after the pandemic. The M/T ratio for the 10-year maturities went down to a low 60% range.

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18

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 18

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Questions 1. Options. How is an option’s minimum (or intrinsic value) determined? How does arbitrage ensure that the price of an option will not be less than the option’s intrinsic value? If you saw that the price of a share of stock was $20, the exercise price of an option to buy the stock was $10, and the price of the option was $5, what would you do? (LO 15-1) Answer: An option is a financial instrument that gives its holder the right to buy or to sell an underlying asset at a specified price, called the strike price, within a specified time period. At the end of the time period, the option expires on its expiration date. A call option is the right to buy the underlying asset, while a put option is the right to sell the underlying asset.

A European-type option can be exercised only on the expiration date, while an American type option can be exercised any time over its time period until expiration.

For a call option, the intrinsic value is the difference between the price of the stock and the strike price of the option. For a put option, the intrinsic value is the difference between the strike price and the stock price.

Arbitrage is the act of simultaneously buying and selling a commodity or security in two different markets to make a profit from the different prices offered by the markets. In the case of an option, the two markets are the market for the stock and the market for the option. The essence of the arbitrage position is a short sale in the stock and a long position (i.e., a purchase) in the option. After these transactions are enacted, the arbitrageur will exercise the option. Then the shares acquired by exercising the call will be used to cover the short position in the stock. Because of the presence of arbitrage, the option value will never be below its intrinsic value.

If the price of the stock is $20 and the strike price of the option is $10, then the option has an intrinsic value of $10. If the current market price of the option is $5, you can buy the option by paying $5 and use it to buy the stock for the strike price of $10. The market value of the stock is $20. You are profiting by $5 with this transaction because the total cost of purchasing the stock is $15, and it is worth $20 in the market.

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2

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

2. Leverage. Why may an option be considered a speculative investment? (LO 15-2) Answer: Options provide a source of leverage because they can be quite a bit cheaper to purchase in comparison to the actual stock. This allows a trader to control a larger position in options, compared with owning the underlying stock.

Leverage, however, works in both directions. Although it may increase the investor’s potential return, it may also increase the potential loss if the price of the stock declines.

An option may be considered a speculative investment because of the opportunity it provides, as described above. If the investor is thinking that the value of the stock may change (increase or decrease), and invests in options in order to benefit from this change in the stock price, plus benefit from the additional leverage that the options provide to magnify the return, then this is considered speculation.

3. Covered vs. naked calls. Why do some individuals buy call options while others write calls? (LO 15-3) Answer: An investor in a naked call position believes that the underlying asset will be neutral to bearish in the short term. A covered call provides downside protection on the stock and generates income for the investor.

A naked call writing is a type of strategy where the investor sells the call without owning the stock. This strategy exposes the investor for a much greater risk than the covered call because when the call is exercised by its buyer, the option writer must buy the stock at the higher market price in order to supply it to the buyer. This will result in higher losses.

Investors buy call options if they anticipate that the underlying stock will increase in value over the duration of the option contract. This anticipated price increase will be the potential source of profit for the investors who buy call options.

Investors sell call options if they anticipate a decline or at least no increase in the price of the underlying stock over the duration of the option contract. In this case, the option premium is the income that they receive as profit.

4. Put vs. short sale. Why? (LO 15-4) Answer: Both buying a put option and short selling stocks can be used when investors anticipate the price of the stock is going to decline.

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3

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

However, the put option offers the investor two major advantages over selling short.

First, the amount of potential loss is less because when you purchase a put, the maximum you can lose is the value of the put purchased, while if you short sell the stock, and the stock price increases, then there is no limit on the amount of loss that you can have. Second, puts may offer a greater return on the investor’s capital because of their leverage. Short selling requires much larger capital in order to execute the trade, while the put requires much less capital to purchase. The only disadvantage that put options have is their limited time, while a short sale can remain open indefinitely.

5. Term premium. That is, why is the premium for an option always more than its intrinsic value as long as there is time left on the option until expiration? (LO 15-5) Answer: An option has a specific expiration period. Once the option expires, its value is its intrinsic value only. This can be either 0, or for the call the stock price minus the strike price, or for a put the strike price minus the stock price. The expressions for the intrinsic values are as follows: Intrinsic Value of Call = max (St − K, 0) Intrinsic Value of Put = max (K − St, 0) Over the life of the option, the value of the option can be either higher than its intrinsic value or at least equal to the intrinsic value, but never less.

The reason the value or premium of an option will always be more than its intrinsic value, and never less, is because the time premium is the price of the possibility that the option will be profitable. The only way this possibility can be realized is if the option is not expired. As long as the option is alive, the option has the potential to be profitable. This is the reason behind the expression “Worth more alive than dead.”

6. Warrants vs. calls. What is the major difference between warrants and call options? (LO 15-6) Answer: The one major difference between call options and warrants is the fact that when warrants are exercised, the company that issued the warrants receives the proceeds and has to issue new shares to give them to the warrant holders. Therefore, exercising the warrant impacts the company’s number of shares because the company has to issue more shares and sell them to the holder of warrants at the strike price. So there will be more shares after the warrants are exercised.

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4

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

When call options are exercised, the number of shares of the company is not affected and the company does not have to issue new shares. There is no impact on the number of shares outstanding.

Due to this difference between warrants and calls in terms of how they affect the outstanding number of shares, their prices will be different, even if all other terms (number of shares, etc) are the same. The price difference will be affected by the ratio of the existing number of shares to the new total number of shares after the warrants are exercised. Since this ratio is less than 1.0 (because more shares will become available after the warrants are exercised), warrants typically cost less than call options.

7. Futures vs. forwards. Who might prefer a forward contract, and why? (LO 15-7) Answer: Futures and forward contracts are very similar. They are both contracts that allow one party to buy and the other party to sell an underlying asset at a future date for an agreed-upon price in the contract.

The major difference between the two is the fact that futures are standardized contracts created by and traded on an exchange, while forward contracts are private, customized contracts that are not traded on an exchange. Futures contracts require an initial margin to be posted with the exchange and are marked to market on a daily basis. Forward contracts typically do not have any initial cost and are executed at maturity of the contract. There is no marking to market on a daily basis.

A forward contract might be preferred by a company or an investor who may have specific requirements that cannot be available in a standard futures contract.

Because forward contracts are customized contracts, any details and specifications can be negotiated between the two parties of the contract and included in the contract requirements. Therefore, the forward contract provides more flexibility than a standard futures contract.

8. Margin call. If you were a farmer who had entered into a futures contract to sell your wheat harvest, what changes in the spot price of wheat would generate a margin call for you? Why? (LO 15-8) Answer: If the farmer entered into the futures contract to sell the wheat harvest at a specified price in the futures contract, the farmer will benefit if the spot price of the wheat goes down but lose if the spot price of the wheat goes up. If the futures market is marking the contracts to market on a daily basis, and the price of the wheat increases, then the futures position of the farmer will start generating losses.

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5

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Once the amount of the loss reduces the margin account value to below the maintenance level requirement, then the farmer will get a margin call.

9. Naked call vs. futures. How are the positions of a naked call writer and the seller in a futures contract different? (LO 15-9) Answer: The naked call writer sells the call option and receives the premium of the call as compensation. By selling the option, the naked call writer gives up the right that the call provides to the other party. The other party, who purchased the call, holds the right to exercise the call whenever it is in their interest. The call will be exercised only when the underlying stock is trading above the strike price, and only then will the holder of the call exercise it. The seller is obligated to provide the underlying stock by buying it in the market and receives the strike price for it. If the underlying stock does not trade higher than the strike price over the life of the call, then the call will not be exercised and the seller pockets the premium.

The seller of the futures contract, on the other hand, enters the futures contract as the short position, to sell the underlying asset, at the future date, at the agreedupon price in the futures contract. When the contract expires, the seller has the obligation to sell the underlying asset and receive the agreed-upon price. No matter what the underlying asset’s price in the market is at the time the contract expires, the seller has to sell that asset at the agreed-upon price in the futures contract.

This is the difference between the seller of the call and the seller of the futures contract.

10. Hedging. Suppose you have a futures contract to exchange U.S. dollars for euros in six months. What aspect(s) of your business would have led you to enter into this contract as a hedge? (LO 15-11) Answer: A company with business activities in Europe that has an obligation to pay a large sum of money in euros in six months would be interested in hedging for the foreign exchange rate risk and enters into such a contract as the long party to buy euros in six months. This way, the company hedges the foreign exchange rate risk and does not worry about what will happen to the exchange rate of the euro relative to dollars. It has already locked in the price of the euros with the futures contract.

Similarly, a U.S. company that has a subsidiary in Europe and expects to receive a large sum of money from that subsidiary would want to hedge the foreign exchange rate risk and enter into the futures contract as the short position. It would sell the euros in six months at the futures price. This way, the company is hedging the foreign exchange risk.

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6

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Problems 1. Put exercising. Suppose you buy a long put on a stock with a strike price of $37 and a premium of $3. What is the highest stock price at which you would exercise the put? (LO 15-1) Answer: Strike price Premium Price

$37 $ 3 $37

The put option gives its holder the right to sell the underlying stock for the strike price, which is $37. This is the highest value the holder of the put will be able to sell the stock for when the stock is trading below $37. Even when the stock price goes to $0, the put option allows its holder to sell the stock for $37.

2. Call exercising. Suppose you buy a long call on a stock with a strike price of $23 and a premium of $2.50. What is the lowest stock price at which you would exercise the call? (LO 15-1) Answer: Strike price Premium Price

$ 23 $2.50 $ 23

The call option gives its holder the right to buy the stock for the strike price, which is $23. This is the lowest value the holder of the call will be able to purchase the stock for when the stock is trading above $23. The call will be exercised when the stock is trading above $23, and no matter what the value of the underlying stock is above $23, the holder of the call can buy the stock for the strike price of $23.

3. Call intrinsic value. You bought a call with a strike price of $20 for $2, and the underlying asset is now selling for $15. What is the intrinsic value of the call?

(LO 15-1) Answer: Strike price Premium Stock price Intrinsic value

$ 20 $ 2 $ 15 $ −

The intrinsic value of the call is calculated as the underlying stock price minus the strike price, or zero if this difference is a negative number. In this example, the strike price is $20, and the underlying stock is selling for $15. The difference then is 15 − 20 =

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7

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

−$5. Because this difference is a negative number, the call has an intrinsic value of zero.

Note: The lowest intrinsic value for the call option is zero and never a negative number.

4. Call intrinsic value. You bought a call with a strike price of $10 for $2, and the underlying asset is now selling for $18. What is the intrinsic value of the call?

(LO 15-1) Answer: Strike price Premium Stock price Intrinsic value

$10 $ 2 $18 $ 8

The intrinsic value of the call is calculated as the underlying stock price minus the strike price, or zero if this difference is a negative number. In this example, the strike price is $10, and the underlying stock is selling for $18. The difference then is 18 − 10 = $8. The intrinsic value of the call is $8.

5. Put intrinsic value. You bought a put with a strike price of $20 for $2, and the underlying asset is now selling for $15. What is the intrinsic value of the put?

(LO 15-1) Answer: Strike price Premium Stock price Intrinsic value

$20 $ 2 $15 $ 5

The intrinsic value of the put is calculated as the strike price minus the underlying value of the stock, or zero if this difference is a negative number. In this example, the strike price is $20, and the underlying stock is selling for $15. The difference then is 20 − 15 = $5. The intrinsic value of the put is $5.

Note: The lowest intrinsic value for the put option is zero and never a negative number.

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8

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

6. Put intrinsic value. You bought a put with a strike price of $10 for $2, and the underlying asset is now selling for $18. What is the intrinsic value of the put?

(LO 15-1) Answer: Strike price Premium Stock price Intrinsic value

$10 $ 2 $18 $ −

The intrinsic value of the put is calculated as the strike price minus the underlying value of the stock, or zero if this difference is a negative number. In this example, the strike price is $10, and the underlying stock is selling for $18. The difference then is 10 − 18 = −$8. Because this difference is a negative number, the put has an intrinsic value of zero.

7. Call profit. You bought a call with a strike price of $27 for $2.50. At what price of the underlying stock will you start to make a profit on your investment? (LO 15-1) Answer: Strike price Premium Break-even price

$ 27 $ 2.50 $29.50

The premium paid for the call is $2.50. The strike price is $27. The call option will be in the money when the stock price is trading above $27. In order for the investment to start being profitable, the stock price needs to be traded above $29.50, because of the $2.50 paid to purchase the call initially.

Therefore, because the call will be exercised once the stock price is above its strike, in order for the investment to start making a profit, the stock price needs to include this additional premium that was paid initially when the call was purchased. Thus, 27 + 2.50 = $29.50.

8. Put profit. You bought a put with a strike price of $27 for $2.50. At what price of the underlying stock will you start to make a profit on your investment? (LO 15-1) Answer: Strike price Premium Break-even price

$ 27 $ 2.50 $24.50

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

The premium paid for the put is $2.50. The strike is $27. The put option will be in the money when the stock price is trading below $27. In order for the investment to start being profitable, the stock price needs to be below $24.50, because of the $2.50 paid to purchase the put initially.

Therefore, because the put will be exercised once the stock price is below its strike, in order for the investment to start making a profit, the stock price needs to be reduced by this additional premium that was paid initially when the put was purchased. Thus, 27 − 2.50 = $24.50.

9. Call premium. Suppose you buy a call option with a $27 strike price on a stock that is currently trading for $30. What is the minimum premium you would expect to have to pay to purchase this option? (LO 15-1) Answer: Strike price Stock price Intrinsic value

$27 $30 $ 3

The minimum premium expected on this call is its intrinsic value, which is $3.

However, the premium will probably be higher than $3. The minimum value that a call option can have is its intrinsic value, which is $3 in this example. (The underlying stock price minus the strike price is the intrinsic value.)

10. Call exercising. You bought a call with a strike price of $27 for $2.50. At what price of the underlying stock would the call go out of the money? (LO 15-1) Answer: Strike price Premium

$ 27 $2.50

The call option is out of the money if the underlying stock trades just below $27.

If the stock trades at $27, the call will be at the money.

If the stock trades above $27, the call will be in the money.

If the stock trades below $27, the call will be out of the money.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

11. Call profit. You can purchase a three-month call option that gives you the right to buy stock at $20. Currently, the stock is selling for $22 and the call is selling for $5.

You are considering buying 100 shares of the stock ($2,200) or one call option ($500, giving you the right to buy 100 shares). If the price of the stock rose to $29 within three months, what would the profits or losses be on each position? (LO 15-1) Answer: Strike price Call premium Current stock price Stock price after change Profit on 100 shares Profit on call on 100 shares Pct profit on 100 shares Pct profit on call on 100 shares

$ 20 $ 5 $ 22 $ 29 $700 $400 31.82% 80.00%

If you buy 100 shares of the stock, when the stock is trading for $22, the total amount needed is $2,200. In three months, when the stock price rises to $29, the value of the 100 shares become $2,900.

The profit is 2,900 − 2,200 = $700, and the return on the investment will be 700 / 2,200 = 31.82%.

If you buy one call option, which gives you the right to purchase 100 shares of the underlying stock for the strike price of $20, the total amount needed is $2,000.

Because the call is selling for $5 per underlying share, and it gives you the right to buy 100 shares, the total amount needed to purchase the call is $500. After three months, when the stock price is $29, you can exercise the call to purchase 100 shares for $20 each, for a total value of $2,000. You can sell those shares immediately in the market for $29 each, for a total of $2,900, earning a profit of $900 from exercising the call.

The profit is 900 − 500 = $400, and the return on the investment will be 400 / 500 = 80.00%.

Purchasing the call provided less dollar profit, but the return on the investment was more than double than purchasing the stocks.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

12. LEAPS time premium. A LEAPS call with an expiration date of two years is an option to buy stock at $24. The current market price of the stock is $35, and the market price of the LEAPS is $15. What is the time premium paid for the LEAPS? (LO 15-3) Answer: Strike price Stock price Premium Intrinsic value Time premium

$24 $35 $15 $11 $ 4

The market value of any option is the sum of its intrinsic value and its time value.

The expression of the market value is as follows: Market Value of Option = Intrinsic Value of Option + Time Value of Option In this example, the stock price is $35, and the strike price of the option is $24.

Therefore, the intrinsic value of the call option is 35 − 24 = $11.

The market price of the option is $15. Therefore, using the expression above, the time value is as follows: Time Value of Option = Market Value of Option − Intrinsic Value of Option The time value of the option is 15 − 11 = $4.

13. Warrant conversion. You have a warrant that gives you the right to buy 0.75 share of a stock for $25 that is currently selling for $3. How many such warrants are necessary to buy one share of stock? (LO 15-6) Answer: Number of shares conveyed Warrant premium Warrant strike price Warrants needed to buy one share of stock

0.75 $ 3 $25 1.33

The warrant gives you the right to buy 0.75 share of a stock. That is one warrant = 0.75 share. To buy one share of a stock, you will need to have 1 / 0.75 = 1.33 warrants.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

14. Per-share strike price. You have a warrant that gives you the right to buy 0.25 share of a stock for $25 that is currently selling for $3. What is the per-share strike price? (LO 15-6) Answer: Number of shares conveyed Warrant premium Warrant strike price Per-share strike price

0.25 $ 3 $ 25 $100

The warrant gives you the right to buy 0.25 share of a stock for $25. To buy one share of stock, you will need 1 / 0.25 = 4 warrants. Since one warrant is worth $25, four warrants are worth $100. Therefore, the per-share strike price is $100, because four warrants will give you the right to purchase one full share at the cost of $100.

15. Futures profit or loss. Assume that you buy a futures contract on corn at $4.00 a bushel for 5,000 bushels. If the spot price of corn at the settlement of the contract is $3.75, how much will you make or lose? (LO 15-7) Answer: Contracted price Spot price Contract amount in bushels Profit (loss) per bushel Profit (loss) for 5,000 bushels

$ 4.00 $ 3.75 5,000 $ 0.25 −$1,250

You buy a futures contract on corn to purchase at $4.00 a bushel. Therefore, you are the long position in this futures contract. At the settlement of the contract, the spot price is $3.75, so the price went down. The long position will lose when the price goes down. Therefore, the loss will be $0.25 per bushel for the long position.

If the futures contract for corn is for 5,000 bushels, then the total loss will be 5,000 × −0.25 = −$1,250.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

16. Futures margin. You expect the stock market to decline, but instead of selling stocks short, you decide to sell a stock index futures contract based on an index of NYSE common stocks. The index is currently 700, and the contract has a value that is 250 times the amount of the index. The margin requirement is $2,000, and the maintenance margin requirement is $1,000. When you sell the contract, how much must you put in the margin account? (LO 15-8) Answer: Index value Contract value Margin requirement Maintenance margin requirement Initial deposit in margin account

700 250 $2,000 $1,000 $2,000

Because the margin requirement is $2,000, you need to post this amount in your account in order to be able to enter the futures contract as the short position.

Therefore, the amount you need to put in the margin account is $2,000.

17. Price discovery. One use for futures markets is “price discovery”; that is, the futures price mirrors the current consensus of the future price of the commodity. The current price of gold is $1,827, but you expect the price to rise to $2,000. If the futures price were $1,990 per ounce for a contract for 100 ounces, what would you do? If your expectation is fulfilled, what is your profit? (LO 15-10) Answer: Spot price of gold Futures price of gold Expected future price of gold Profit per contract on 100 ounces

$1,827 $1,990 $2,000 $1,000

The investor expects the future price of gold to be $2,000, but the price of the futures contract is only $1,990. Therefore, in order to profit from their expectation, the investor can buy the futures contract and enter into the contract as the long position to buy gold in the future. When the contract expires, and the price of gold turns out to be $2,000, then the investor will make a profit of $10 per ounce on this contract. The investor will use the futures contract to buy the gold for $1,990 and then sell it in the market for $2,000, earning the $10 profit per ounce.

The futures contract on the gold is for 100 ounces. Therefore, the investor’s total profit from this transaction will be 10 × 100 = $1,000.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

18. Swap cash flows. Two institutional investors execute a swap agreement for $10,000,000 in which party A agrees to remit payments to counterparty B based on the EAFE, an index of European, Australasian, and Far Eastern stocks. Counterparty B agrees to remit payments based on the return on the S&P 500 to party A. During the next four time periods, the returns on the two indexes are as follows. What are the cash flows between the two parties for each time period? (LO 15-12) Answer: Party A will pay to party B the return on the EAFE. Party B will pay to party A the return on S&P 500.

Since the notional principal is $10,000,000, both parties will pay in terms of U.S. dollars, and only net cash flows will end up being paid.

The following table shows the cash flows that each party will pay, along with the net cash flow and its direction.

Basis of swap

$10,000,000

Period S&P 500 1 4% 2 −3% 3 15% 4 −2%

EAFE 10% 8% 0% −5%

Cash Flow A −> B Cash Flow B −> A Net A −> B $1,000,000 $ 400,000 $ 600,000 $ 800,000 −$ 300,000 $1,100,000 $ 0 $1,500,000 −$1,500,000 −$ 500,000 −$ 200,000 −$ 300,000

The first two columns in the table below represent the cash flow that each party is going to pay to the other party based on the return of the EAFE and S&P 500, respectively. Those cash flows are calculated by multiplying the notional principal of $10,000,000 with the return of EAFE and S&P 500 for each period.

When the cash flow is negative, it means that the party with the negative cash flow will receive that amount from the other party.

The net cash flow represents the net amount that one party will end up making and the direction of the cash flow.

Note that in the second period, party B has a negative cash flow. This means that party B will receive $300,000 from party A. Because party A will pay party B $800,000, the net becomes $1,100,000 from A to B. In period 4, because the two cash flows were negative, party A will receive $500,000 from party B and party B will receive $200,000 from A. The net is $300,000 from B to A.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Party A Will Pay $1,000,000 $ 800,000 $ 0 $ (500,000)

Party B Will Pay $ 400,000 $ (300,000) $1,500,000 $ (200,000)

Net Cash Flow Net Cash Flow Direction $ 600,000 From A to B $1,100,000 From A to B $1,500,000 From B to A $ 300,000 From B to A

19. Position investment. An investor buys a stock for $37. At the same time, a sixmonth put option to sell the stock for $34 is selling for $2. If the investor also purchases the put (i.e., constructs a protective put), what is the combined cash outflow? (LO 15-3) Answer: Stock price Put premium Put option contract size Combined cash outflow per share basis Total cash outflow

$ $

37 2 100 $ 39 $3,900

The investor buys the stock for $37 per share.

The put option is selling for $2 per share.

The total amount needed per share basis is 37 + 2 = $39.

The put option contract is for 100 shares. Therefore, to construct the protective put position correctly, the investor needs to buy 100 shares of the stock and one put contract.

The total value to buy the shares will be 37 × 100 = $3,700.

The total value of the option contract will be 2 × 100 = $200.

The total cash outflow to construct this protective put will be $3,900.

20. Position profits. Suppose you buy a call with a strike price of $25 for $3 and a put with a strike price of $20 for $2, both on the same underlying stock. At what price(s) will you start making a profit on this position? (LO 15-2) Answer: Call strike price Call premium Put strike price Put premium Price will start making profit on call Price will start making profit on put

$25 $ 3 $20 $ 2 $30 $15

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

You are buying two options here, one call with strike $25 for $3 and one put with strike $20 for $2. Therefore, the initial investment needed to buy both the call and the put is $5.

With those two options, it is possible to make profit if the underlying stock price decreases or increases. When the stock price decreases, only the put will become profitable once the stock price is below the put strike (the call will not be). When the stock price increases above the strike price of the call, only the call will become profitable (the put will not be).

To become profitable when the stock price decreases, the put can be exercised once the underlying stock is below $20. However, the overall position will not be profitable until the underlying stock price goes below $15, which is after including the initial $5 paid to buy both options.

To become profitable when the stock price increases, the call can be exercised once the underlying stock is above $25, but the overall position will not be profitable until the underlying stock price goes above $30, which is after including the initial $5 paid to buy both options.

This particular strategy is called strangle.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

Case Study Options Quotes Versus Intrinsic Values Go to the CBOE options page for AMD stock and obtain the quotes for the calls and puts on AMD that are expiring the soonest. Compare the intrinsic values of these calls and puts with the premiums (“asks”) being quoted. What patterns do you see?

Answer: You can go to the following website, https://www.cboe.com/delayedquotes/, and enter AMD in the search box to get the information about the AMD stock.

Once the information appears, click on the “Options” tab to get the information about the option chains available on AMD stock.

The following screen illustrates what you will see on the CBOE website when you select the Options tab.

Notice that this screenshot was taken on March 12, 2022. Therefore, the options in the screen above expired on Friday, March 11, the day before. If you look further down, you will see the options chain with expiration dates on Friday, March 18, and Friday, March 25.

Note: Option exchanges have been creating options with weekly expirations as long as there has been a demand for such options. Below is an example of the breadth of options offered on AMD.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

The middle column shows the strike price for each option: on the left side are the call options, and on the right side are the put options for a particular strike price.

You can change the “Options Range” tab from “Near the Money” as is shown in the screenshot to “All” to see all the options available on AMD for a particular expiration date. Also, the CBOE website allows you to download the information for those options into an Excel file. Scroll down to the bottom of the page to the “Download CSV” tab.

Look at the first line of the screenshot for the expiration of Friday, March 18, 2022.

The strike price of this option is $101. There are two different option contracts on that line: one is the call, and the other is the put. The ask price of the call is $5.7, while the ask price of the put is $2.4. The price of the AMD stock last traded on Friday, March 11, was $103.83, which is shown in the first screenshot.

The following screenshot provides information for call and put options from a strike price of $80 to a strike price of $114. We can identify the relationship between the intrinsic value of the call and the put and their premiums in terms of the ask price to see if there are any patterns.

The intrinsic value of the call is the stock price minus the strike, while for the put, it is the strike price minus the stock price. In this example the stock price is $103.83.

For the strike $80, the call has ask price of $25.55, the put has ask price of $0.32.

The intrinsic value of the call is 103.83 – 80 = $23.83, while the intrinsic value of the

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 15: An Introduction to Futures Contracts and Options

put is $0 (80 – 103.83 is negative). We can find the time premiums: for the call it is $1.72, while for the put it is $0.32.

We notice that for the call option, as the strike price increases, the value of the call, the ask price decreases. While for the put option, as the strike price increases, the value of the put, the ask price of the put increases. Those patterns confirm the explanation provided in the text.

For the call option, since its intrinsic value is the stock price minus the strike, when the strike price increases, the intrinsic value decreases, and once the option becomes out of the money, the intrinsic value is zero, and the ask price then only reflects the time premium of the option. When the strike price is very high, we notice that the option premium is very low as well. When the strike price is very low, then in this case the option premium is almost equals to the intrinsic value.

Therefore, the patterns detected in the pricing chart below confirm the explanation provided in the text.

The intrinsic value of the put option is the strike price minus the stock price. So, when the strike price increases, the intrinsic value also increases. When the strike price is very high, the ask price is almost equal to the intrinsic value, and the time premium is low. When the strike price is very low, then the intrinsic value is zero, and the ask price is almost zero; it shows as 0.01 for the low values of strike prices in the following screenshot. The patterns detected again confirm the explanation provided in the text.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 7 Case Study ....................................................................................................................................... 24

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Questions 1. Black-Scholes sensitivity. According to the Black–Scholes option valuation model, what is the relationship between the value of a call option and each of the following? (LO 16-1) a. Risk as measured by the variability of the underlying stock’s return b. Interest rates c. The term of the option (i.e., the length of time to expiration) Answer: The Black–Scholes option valuation model is given below.

Vo = Ps × N ( d1 ) −

Pe e rT

× N ( d2 )

a. In the Black–Scholes model, the relationship between the value of the call and risk measured by the variability of the underlying stock’s return is positive. That is, an increase in the variability of the stock (an increase in σ) increases the value of a call option. Decreased variability decreases the value of an option. The variability of the stock, given by its standard deviation value σ, is included in the d1 part of the equation. b. In the Black–Scholes model, the relationship between the value of the call and interest rates is positive. An increase in interest rates (an increase in r) increases the value of a call option. Higher interest rates are associated with higher call option valuations. c. In the Black–Scholes model, the relationship between the value of the call and time is positive. An increase in the time to expiration (an increase in T ) increases the value of a call option. As time diminishes and the option approaches expiration, its value declines.

2. Put-call parity. According to the Black–Scholes option valuation and put–call parity, what will happen to the value of a call option if interest rates decline? (LO 16-1) Answer: The Black–Scholes option valuation model is given below.

Vo = Ps × N ( d1 ) −

Pe e rT

× N ( d2 )

According to the Black–Scholes option valuation model and the put–call parity, if interest rates decline, the value of the call option will also decline. The interest rate is positively related to the value of the call option. To see why this is the case, in the Black–Scholes model, the interest rate is in the exponential term, Pe/erT; when the

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

interest rate declines, the exponential value of the interest rate will be lower, but Pe divided by a lower value will become higher. Therefore, everything else remaining constant, we are subtracting a higher term from the Ps × N(d1) term, which will lower the value of the option.

A similar argument can be made for the put–call parity equation, which is given below.

Ps + Pp = Pc +

Pe

(1 + i )

n

The interest rate is in the denominator, so a decrease in its value will increase the Pe/(1+i)n factor, which in turn will decrease the value of the call, all else being constant.

3. Risk inference. How might the Black–Scholes option valuation model be used to determine the risk associated with the underlying stock? (LO 16-1) Answer: The Black–Scholes option valuation model can be used to solve for the standard deviation of the returns rather than for the value of the call option as long as we have the stock price, strike price, option price, option term, and interest rate. In this case, the value found for the standard deviation is called the implied volatility.

4. Straddle exposure. An investor expects the price of a stock to remain stable and writes a straddle. What is this individual’s risk exposure? How may the investor close the position? (LO 16-5) Answer: Writing a straddle means the investor is selling both the put and the call options on the same stock, with the same strike price. If the investor expects the price of a stock to remain stable, then writing a straddle will generate an income, which is the value of the two premiums from the call and the put that the investor will receive.

The investor will choose the call and the put option with a strike price as close as possible to the underlying stock price at the time of the trades. The risk exposure to the investor arises if the underlying stock’s price is not stable and moves either up or down by a large amount. In that case, the investor will experience losses. The investor can close the positions by entering in “buy to close” trades for both the call and put options. The investor must have initially entered into the trade by making “sell to open” positions for both the call and the put.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

5. Bull spread. Why would an investor use a bull spread instead of just buying a call?

(LO 16-5) Answer: The investor will save on the amount needed to establish the position. The bull spread is created by buying a call option with a lower strike price and selling a call option with a higher strike price. This may require a small initial amount, as the investor will pay the premium for the option purchased but receive the premium of the option sold. The difference is the amount needed to open the bull spread position. When buying a call option, the investor has to purchase the call, which normally will require a higher initial amount than the bull spread. Obviously, the call will provide a higher return than the bull spread because for the bull spread, the maximum return is limited. However, the investor will incur less loss if the strategy doesn’t work the way it was intended, as the initial investment need for the bull spread is less than the call.

6. Put-call parity. How would you use put–call parity to value a stock? (LO 16-2) Answer: The relationship between the prices of a put and a call, the price of the underlying stock, and the option’s strike price is referred to as put–call parity. The expression of the put–call parity and the expression of the stock price are given in the two equations below.

Ps + Pp = Pc + Ps = Pc +

Pe

(1 + i )

Pe

(1 + i )

n

n

− Pp

From the put–call parity equation, we can find the price of the stock by taking the sum of the value of the call and the present value of the strike price and subtracting the value of the put from the sum, as shown in the second equation.

7. Risk mitigation. You sell a stock short. How can you use an option to reduce your risk of loss should the price of the stock rise? (LO 16-5)

Answer: You can use a protective call when you sell a stock short, but you want to reduce your risk of loss should the stock price rise instead. The protective call strategy involves buying a call combined with a short in the stock. The protective call limits the possible loss from an increase in the price of the stock. To achieve this increased safety, the investor forgoes some possible profit on the short in the stock. The

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

investor will profit when the stock price falls, which is why the short position in the stock, and in this case the call option, expires out of the money. However, if the stock price rises, the call option value will rise as well. The call will give the investor the right to buy the stock at the strike, so this strategy reduces losses if the stock price rises.

8. Straddle. If you thought a stock was fairly valued and its price would not change, how could you use a straddle to take advantage of your valuation? (LO 16-5)

Answer: If the investor thought a stock was fairly valued and its price would not change, the investor could write a straddle to take advantage of the valuation. Writing a straddle means the investor is selling both the put and the call options on the same stock, with the same strike price. If the investor expects the price of a stock to remain stable, writing a straddle will generate an income, which is the value of the two premiums from the call and the put that the investor will receive. The investor will choose the call and put options with a strike price as close as possible to the underlying stock price at the time of the trades.

9. Risk management. How do collars, the hedge ratio, the protective call, and the protective put help investors manage risk? (LO 16-5)

Answer: A collar is constructed when an investor who owns a stock wants to hedge against a movement in the stock’s price. The investor constructs a collar by selling a call at a higher strike price and buying a put at a lower strike price. Because this strategy involves both a purchase and a sale, the cash flows offset each other, resulting in either a small cash inflow or, at worst, a modest cash outflow. With the collar, the investor is protecting the downside risk by the put option. If the stock price increases, the investor will lose some of that upside potential. However, a collar is generally constructed to protect from the downside risk.

The hedge ratio can be used to protect the portfolio of stock from price fluctuations by selling call options. If an investor or a portfolio manager wants to exactly offset price changes by using options, they can use the reciprocal value of the hedge ratio to know the exact number of call options that should be sold for each 100 shares purchased.

The protective call can be used to protect the investor from rising stock prices if the investor has sold the stock short. The protective call strategy involves buying a call combined with a short in the stock. The protective call limits the possible loss from an increase in the price of the stock.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

The protective put can be used to protect the investor who owns stock from a price decrease. The investor owns some stock and buys a put option on those stocks to protect from the downside risk. If the stock prices decreases, the investor can use the put to sell the stock for the strike price.

10. Volatility impact. Explain what effect an increase on volatility in the underlying stock would have on a call option. (LO 16-1)

Answer: An increase in the variability of the stock (an increase in σ) increases the value of a call option. A speculator will find an option on a volatile stock more attractive than an option on a stock whose price tends to be stable. The increase volatility increases the value of the call because higher volatility means the stock price will fluctuate more. With higher proportions for the option on that stock, the high volatility means that if the option were out of the money, there is a greater possibility that the option becomes in the money, as the underlying stock is moving more frequently now and with larger increments.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Problems 1. Call valuation. A stock sells for $28. What is the value of a one-year call option to buy the stock at $25, if debt currently yields 10% and the standard deviation of stock returns is 15%? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ 28 $ 25 100% 10% 15%

d1 d2

1.49719 1.34719

V0

$5.51

The Black–Scholes options pricing model can be used to find the value of the call option. Ps is the value of the stock, Pe is the value of the strike, r is the risk-free rate, σ is the standard deviation of the stock returns, and T is the time to expiration.

In order to use the Black–Scholes model to find the value of the call option, first we have to calculate the values of d1 and d2 using the equations provided below. Then we find the values for the cumulative normal probability distribution, N(d1) and N(d2), to solve for the value of the call.

Vo = Ps × N ( d1 ) −

Pe e rT

× N ( d2 )

P   σ2  ln  s  +  r + T Pe   2   d1 = σ T

d2 = d1 − σ T In this example: Ps = 28 Pe = 25 r = 0.1 σ = 0.15

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

T=1 With those values, we solve for d1 and d2.

d1 =

 28   0.152  + + ln  0.1  ×1   2   25   0.15 × 1

= 1.49719

d2 = 1.49719 − 0.15 × 1 = 1.34719 Once we have those values, we can use the NORMSDIST() function in Excel to find the values of N(d1) and N(d2).

N(d1) = 0.93283 N(d2) = 0.91104 Vo = 28 × 0.93283 −

25 × 0.91104 = $5.5107 e 0.1×1

Note: You can also use the option pricing template Excel file provided by the book to solve for the value of the option.

2. Call valuation. A stock sells for $32. What is the value of a three-month call option to buy the stock at $35, if debt currently yields 8% and the standard deviation of stock returns is 15%? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ $

32 35 25% 8% 15%

d1 d2

−0.89066 −0.96566

V0

$0.24

This is similar to Problem 1. The question is asking to find the value of the call option for the following given information: In this example: Ps = 32 Pe = 35

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

r = 0.08 σ = 0.15 T = 0.25 With those values, we solve for d1 and d2.

d1 =

 32   0.152  ln  +  0.08 +  × 0.25  2   35   0.15 × 0.25

= −0.89066

d2 = −0.89066 − 0.15 × 0.25 = −0.96566 Once we have those values, we can use the NORMSDIST() function in Excel to find the values of N(d1) and N(d2).

N(d1) = 0.18656 N(d2) = 0.16711 Vo = 32 × 0.18656 −

35 e

0.08×0.25

× 0.16711 = $0.23688

Therefore, the value of the call is about $0.24.

3. Put valuation. A stock sells for $28. What is the value of a one-year put option to buy the stock at $25, if debt currently yields 10% and the standard deviation of stock returns is 15%? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ 28 $ 25 100% 10% 15%

d1 d2

1.497191 1.347191

V0

$5.51

Pp

$0.24

The problem is asking to find the value of the put option. In order to find the value of the put option using the put–call parity, first we have to find the value of the call

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

option, using the Black–Scholes method, then use the put–call parity to find the value of the put option.

The value of the call was calculated in Problem 1.

Pc = $5.5107 The put–call parity is given by the following equation:

Ps + Pp = Pc +

Pe

(1 + i )

n

Ps = 28 Pc = 5.5107 Pe = 25 i = 0.1 n=1 Solving for the price of the put option, Pp, we get the following: Pp = 5.5107 + 25/1.1 – 28 = $0.23797 The value of the put is about $0.24.

4. Put valuation. A stock sells for $32. What is the value of a three-month put option to buy the stock at $35, if debt currently yields 8% and the standard deviation of stock returns is 15%? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ $

32 35 25% 8% 15%

d1 d2

−0.89066 −0.96566

V0

$0.24

Pp

$2.57

This is similar to Problem 3. The value of the call was found in Problem 2.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Pc = 0.23688 Ps = 32 Pe = 35 i = 0.08 n = 0.25 Solving for the price of the put option, Pp, we get the following: Pp = 0.23688 + 35/1.080.25 – 32 = $2.5699 The value of the put is about $2.57.

5. Hedge ratio. One useful piece of information derived from the Black–Scholes model for the valuation of a call option is the hedge ratio, which gives the slope of the line relating the change in the price of an option to the change in the price of the stock.

If the delta is 0.7 and the investor owns 600 shares of stock, how may the investor use call options to hedge the position? (LO 16-4)

Answer: Delta Shares owned

0.7 600

Call options needed to hedge

8.57

The reciprocal value of the hedge ratio gives the number of call options that should be sold for each 100 shares of stock purchased. The hedge ratio has a value of 0.7.

The reciprocal value is 1/0.7 = 1.4286.

So, the investor needs to sell 6 × 1.4286 = 8.57 call option contracts for the 600 shares owned to have a perfect hedge (as each contract is for 100 shares of stock).

However, the investor cannot sell a fractional number of call options; therefore, one call option contract can be sold for 70 shares. Eight call option contracts will cover 560 shares; one additional contract will cover 630 shares, which is more than what the investor owns. In reality, the investor will not be able to have the perfect hedge due to the limitation in the size of call option contracts.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

6. Put-call parity. Put–call parity basically says that the combination of a stock and a put produces the same return as the comparable position in a call and a risk-free bond. If not, at least one market is in disequilibrium. The resulting arbitrage alters the securities’ prices until the value of the stock plus the put equals the prices of the call and the bond. However, put–call parity only holds at the current stock price: things will have to readjust if the stock price changes. If the price of a stock is currently $100 while the price of a call option at $100 is $9, the price of the put option at $100 is $3, and the price of a discounted bond is $94, show that put–call parity holds at the current stock price of $100, but wouldn’t hold if all else remained the same but the stock price changed to $90, $95, $105, or $110. (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Pc Pp Price of discounted bond

Ps 90 95 100 105 110

$100 $100 $ 9 $ 3 $ 94 Payoff on Short Stock $ 10 $ 5 $ − −$ 5 −$ 10

The put–call parity equation is the following:

Ps + Pp = Pc +

Pe

(1 + i )

n

From this form of the parity equation, we can find the expression for the value of the stock, which is:

Ps = Pc +

Pe

(1+ i )

n

− Pp

From the expression derived for the value of the stock, we can see that a long position in a stock is equivalent to a long position in call, a long position in bond, and a short position in put option.

To get the expression for the short position in stock, we just take the negative of the long stock expression, which gives us the following for the short position in stock:

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

−Ps = −Pc −

Pe

(1 + i )

n

+ Pp

As we can see from the expression above, a short position in stock is equivalent to a short position in call option, a short position in bond, and a long position in put option. When we create a security using the three other securities from the put–call parity equation, the name usually given is synthetic. In this example, the last expression is the synthetic short stock expression.

When the stock price is $100, and you short this stock, you will get $100. You can achieve the same amount by selling the call, selling the bond, and buying the put.

Selling the call will result in $9, selling the bond will result in $94, and buying the put will require $3; therefore, the sum becomes $9 + $94 – $3 = $100, which is the amount received from selling the stock short.

7. Put strategy. Currently, a stock that sells for $57 has a put option at $55 and another at $60. The prices of the options are $6 and $3, respectively. What would you do? (LO 16-2)

Answer: Put Exercise Price $55 $60

Put Premium $6 $3

Intrinsic Value $− $3

The stock is selling at $57.

The first put option, which is out of the money, has a strike price of $55 and is selling for $6.

The second put option, which is in the money, has a strike price of $60 and is selling for $3.

You can sell the first put option with strike $55, as it is out of the money and is selling for $6, a much higher price than its intrinsic value of $0. Simultaneously, you buy the put option with strike $60, which is in the money for $3. Thus, you will make at least $3 for sure no matter what happens to the stock. At expiration, if the stock price closes below $55, the profit will be $8. If the stock price closes in the range $56 to $60, the profit will decline from $7 to $3, and if the stock price closes above $60, the profit will be $3.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

8. Call valuation. A stock sells for $25. What is the value of a one-year call option to buy the stock at $28, if debt currently yields 10% and the standard deviation of stock returns is 15%? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ 25 $ 28 100% 10% 15%

d1 d2

−0.01386 −0.16386

V0

$1.34

The Black–Scholes options pricing model can be used to find the value of the call option. Ps is the value of the stock, Pe is the value of the strike, r is the risk-free rate, σ is the standard deviation of the stock returns, and T is the time to expiration.

In order to use the Black–Scholes model to find the value of the call option, first we have to calculate the values of d1 and d2 using the equations provided below. Then we find the values for the cumulative normal probability distribution, N(d1) and N(d2), to solve for the value of the call.

Vo = Ps × N ( d1 ) −

Pe e rT

× N ( d2 )

P   σ2  ln  s  +  r + T Pe   2   d1 = σ T

d2 = d1 − σ T In this example: Ps = 28 Pe = 25 r = 0.1 σ = 0.15 T=1

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

With those values, we solve for d1 and d2.

d1 =

 28   0.152  + + ln  0.1  ×1   2   25   0.15 × 1

= 1.49719

d2 = 1.49719 − 0.15 × 1 = 1.34719 Once we have those values, we can use the NORMSDIST() function in Excel to find the values of N(d1) and N(d2).

N(d1) = 0.93283 N(d2) = 0.91104 Vo = 28 × 0.93283 −

25 × 0.91104 = $5.5107 e 0.1×1

Note: You can also use the option pricing template Excel file provided by the book to solve for the value of the option.

9. Hedge ratio. One useful piece of information derived from the Black–Scholes model for the valuation of a call option is the hedge ratio, which gives the slope of the line relating the change in the price of an option to the change in the price of the stock.

If the delta is 0.66 and the investor owns 1,300 shares of stock, how may the investor use call options to hedge the position? (LO 16-4)

Answer: Delta Shares owned

0.66 1,300

Put options needed to hedge

19.70

The reciprocal value of the hedge ratio gives the number of call options that should be sold for each 100 shares of stock purchased. The hedge ratio has a value of 0.66.

The reciprocal value is 1/0.66 = 1.5152.

So, the investor needs to sell 13 × 1.5151 = 19.70 call option contracts for the 1,300 shares owned to have a perfect hedge (as each contract is for 100 shares of stock).

However, the investor cannot sell a fractional number of call options; therefore, one call option contract can be sold for 66 shares. Nineteen call option contracts will cover 1,254 shares, and one additional contract will cover 1,320 shares, which is more than what the investor owns. In reality, the investor will not be able to have the perfect hedge due to the limitation in the size of call option contracts.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

10. Position payoff. Suppose an investor sells a stock short and sells a put on the stock with a strike price of $35. What will be the net payoff to their total position if the stock price is at $30 at option expiration? (LO 16-5)

Answer: Stock price Exercise price

$30 $35

Payoff at expiration

$ 0

Net payoff

$0 + price sold put for

The investor sells the stock short and also sells a put option with strike $35. This is a covered put position, which has a limited amount of profit and a potential for large losses. The investor will be profitable as long as the value of the stock remains below the strike price of $35. Since the price is $30 at expiration, which is below the strike $35, then the investor will have some profit. This position has a payoff pattern similar to a short call position.

11. Position payoff. You short shares of ABM at $20 and buy a call on ABM with an exercise price of $23. What will be your total payoff if the stock is selling for $25 at option expiration? (LO 16-5)

Answer: Initial stock price shorted Stock price Exercise price

$20 $25 $23

Payoff at expiration

−$ 3

The investor short sells ABM at $20 and buys a call option with an exercise price of $23. The investor is creating a protective call strategy, which has basically the same payoff diagram as a long put.

The investor will receive $20 from selling the stock short and will pay the value of the call. The strategy will be profitable if the stock price decreases; however, the investor will lose if the stock price rises. This loss will be limited.

At expiration, the stock price rises to $25. The investor has to cover the short stock position. The call option will allow the investor to buy the stock for only $23 when it is trading at $25 in the market, so the investor will exercise the call and buy one stock for $23 and cover the short. Since the investor had $20 from shorting the stock and has to pay $23 to buy the stock using the call, the payoff is −$3.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

(The value of the call that was paid will be deducted to calculate the net payoff of the investor, which will increase the loss a little more.)

12. Straddle payoff. Suppose you enter into a straddle with an exercise price of $37.

What will your payoff be at a price of $41? (LO 16-5)

Answer: Stock price Exercise price

$41 $37

Payoff at expiration $ 4 The investor enters into a straddle with an exercise price of $37. This means the investor purchased both a call and a put option on the same stock, with the same expiration, and the same strike price of $37. Purchasing both the call and the put will require some initial investment to cover the value of the call and the put options.

At expiration, the stock price is $41, so only the call will be exercised by the investor, not the put. The payoff to the investor will come from exercising the call, which is in the money by $4 ($41 – $37). The payoff is $4. However, the initial cost to create the straddle will reduce the final net profit to the investor.

13. Straddle payoff. Suppose you enter into a straddle with an exercise price of $21.

What will your payoff be at a price of $18? (LO 16-5)

Answer: Stock price Exercise price

$18 $21

Payoff at expiration

$ 3

The investor enters into a straddle with an exercise price of $21. This means the investor purchased both a call and a put option on the same stock, with the same expiration, and the same strike price of $21. Purchasing both the call and the put will require some initial investment to cover the value of the call and the put options.

At expiration, the stock price is $18, so only the put will be exercised by the investor, not the call. The payoff to the investor will come from exercising the put, which is in the money by $3 ($21 – $18). The payoff is $3. However, the initial cost to create the straddle will reduce the final net profit to the investor.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

14. Bull spread profit. You enter into a bull spread by purchasing a call with a strike price of $79 and selling a call with a strike price of $90. If the first call costs $10 and the second call sells for $3, at what underlying stock price will you break even?

(LO 16-5)

Answer: Call purchased strike price Call purchased premium Call sold strike price Call sold premium

$79 $10 $90 $ 3

Break-even price

$86

Buy the call with strike $79 for $10, so there will be an outflow of $10.

Sell the call with strike $90 for $3, so there will be an inflow of $3.

The initial amount needed to choose this strategy is $7, an outflow.

The bull spread will be profitable if the underlying stock price increases. The breakeven value will occur when the stock price is at $86. At this value of the underlying stock, the option purchased will be in the money by $7; the option sold will be out of the money, so the position will break even.

If the stock price is below $79, there will not be any profit and the loss will be −$7: the initial investment.

If the stock price is above $90, the profit will be $4.

15. Bull spread strategy. You enter into a bull spread by purchasing a call with a strike price of $29 and selling a call with a strike price of $40. If the first call costs $7 and the second call sells for $3, what is the lowest price you will exercise the first call at?

(LO 16-5)

Answer: Call purchased strike price Call purchased premium Call sold strike price Call sold premium

$29 $ 7 $40 $ 3

Lowest price to exercise purchased call at

$29

Buy the call with strike $29 for $7, so there will be an outflow of $7.

Sell the call with strike $40 for $3, so there will be an inflow of $3.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

The initial amount needed to choose this strategy is $4, an outflow.

The call options become valuable and are exercised when they are in the money.

The first call option that was purchased has the lowest strike and can be exercised once it becomes in the money. When the stock price is right above $29, the first call will be exercised. Therefore, the first call can be exercised when the stock price reaches $29.01 and above.

16. Bull spread profit. You enter into a bull spread by purchasing a call with a strike price of $47 and selling a call with a strike price of $50. If the first call costs $7 and the second call sells for $3, what is the most profit you can make from this strategy?

(LO 16-5)

Answer: Call purchased strike price Call purchased premium Call sold strike price Call sold premium

$47 $ 7 $50 $ 3

Lowest price to exercise purchased call at

−$ 1

Buy the call with strike $47 for $7, so there will be an outflow of $7.

Sell the call with strike $50 for $3, so there will be an inflow of $3.

The initial amount needed to choose this strategy is $4, an outflow.

The first call will be exercised once the stock is above $47, and the second call will be exercised once the stock is above $50. When both calls are exercised, the difference between the two strike prices, $50 – $47 = $3, is the maximum payoff of the bull spread. However, since the initial cost of the strategy was $4, this bull spread will not give any profit, and there will be a loss of −$1.

17. Bull spread strategy. You enter into a bear spread by selling a call with a strike price of $47 and buying a call with a strike price of $50. If the first call sells for $7 and the second call costs $3, what is the most profit you can make from this strategy? (LO 16-5)

Answer: Call purchased strike price Call purchased premium Call sold strike price Call sold premium

$50 $ 3 $47 $ 7

Lowest price to exercise purchased call at

$ 4

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Sell the call with strike $47 for $7, so there will be an inflow of $7.

Buy the call with strike $50 for $3, so there will be an outflow of $3.

The initial amount resulting from this strategy is $4, an inflow.

The initial amount of $4 is the most that can be made from this strategy. This will happen if the underlying stock remains below $47.

18. Collar profit. You enter into a collar by selling a call with a strike price of $47 for $4 and buying a put with a strike price of $35 for $3 when you already own the stock.

What is the most profit you can make from this strategy? (LO 16-5)

Answer: Put purchased strike price Put purchased premium Call sold strike price Call sold premium

$35 $ 3 $47 $ 4

Lowest price to exercise purchased call at

$ 1

You sell a call option with a strike price of $47.

You buy a put option with a strike price of $35.

Also, you own the stock. Therefore, this is a collar strategy, which has a very small cost. Both put and call options have the following purposes. The purchase of the put protects from decreasing stock prices, while selling the call will provide the income to purchase the put. The cost of the collar is minimal but will reduce the profit if the stock price increases.

If the stock price decreases substantially, the investor will be able to sell the shares owned at the strike $35 by exercising the put option.

If the stock price increases above the strike of the call, the investor will be forced to sell the stock for $47 and will not benefit from increasing stock prices above that price.

Of course, you need to know the price paid initially for the stock that you own. Most of the time that price can be very low, as you purchased those stocks some time ago and received capital gains on them.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

19. Implied standard deviation. A stock sells for $28 and a one-year call option on the stock with a $37 exercise price sells for $5.70. If debt currently yields 10%, what is the implied annual standard deviation in stock returns? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ 28 $ 37 100% 10% 67.90%

d1 d2

0.076312 −0.6027

V0

$5.70

This question is asking us to calculate for the implied annual standard deviation in the stock returns given the value of the call option.

Such calculation is not possible manually: we must use Excel.

We can use the Solver tool or the Goal Seek tool under What-If Analysis in Excel to do this calculation. We will illustrate use of the Goal Seek tool.

The process to solve for the implied volatility is as follows: Each of the formulas below needs to be calculated in Excel and kept as formula in order for the Goal Seek tool to find the solution. P   σ2  ln  s  +  r + T Pe   2   d1 = σ T

d2 = d1 − σ T Vo = Ps × NORMSDIST (d1) −

Pe e rT

× NORMSDIST (d2 )

It is important to start by calculating the values of d1 and d2 and then use them in the Black–Scholes formula to calculate the value of the call option as shown above using the NORMSDIST() function in Excel.

In this example: Ps = 28

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Pe = 37 r = 0.1 T=1 We must select an arbitrary value for the standard deviation to solve the problem.

We can select any initial value: in this example, we will use 15%. σ = 0.15 With those values, we solve for d1 and d2.

d1 =

 28   0.152  +  0.1+ ln   ×1  2   37   0.15 × 1

= −1.11642

d2 = −1.11642 − 0.15 × 1 = −1.26642 Then we use the Black–Scholes formula as follows: Vo = 28 × NORMSDIST ( −1.11642) −

37 × NORMSDIST ( −1.26642) = $0.26 e 0.1×1

Keep in mind that in Excel, each value should be referenced by its cell location.

The value provided for the call is not the answer we are seeking; rather, it is just the solution for the standard deviation for which we selected 15%.

To find the implied volatility, we use the Goal Seek tool, which is under the “What-If Analysis” tab. Once you open the Goal seek tool, you will see three areas to fill in.

In the first tab, called “Set Cell”: select the location of the cell where the value of the call is calculated with the Black–Scholes formula. In the Excel solution, that is cell B12.

In the second tab, called “To value”: enter the number 5.7, as this is the value of the call in this problem.

In the third tab, called “By changing cell”: select the location of the cell where the standard deviation value was stored. In the Excel solution, that is cell B7.

After you click ok, Excel will find the solution of the implied volatility to be 67.90%.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

20. Implied standard deviation. A stock sells for $67 and a three-month call option on the stock with a $73 exercise price sells for $3.70. If debt currently yields 8%, what is the implied annual standard deviation in stock returns? (LO 16-2)

Answer: Current stock price (Ps) Exercise price (Pe) Time until expiration (% of year) (T) Continuously compounded risk-free rate (r) Standard deviation of underlying stock returns (σ)

$ 67 $ 73 25% 8% 41.26%

d1 d2

−0.21564 −0.42194

V0

$3.70

This is similar to Problem 19. The same approach should be followed to solve for the implied annual standard deviation.

In this example: Ps = 67 Pe = 73 r = 0.08 T = 0.25 The value of the call is $3.70.

Using the same approach as above, you will get the value of the implied annual standard deviation of 41.26%.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

Case Study Option Valuation Got to www.cboe.com and retrieve the latest ask price for the call option on Amazon (AMZN) with the highest strike price maturing the soonest. Download the last five years’ worth of monthly prices for AMZN from finance.yahoo.com and use the adjusted closing prices to estimate annual standard deviation in returns. Use that standard deviation, along with other applicable information from the CBOE option quote, to calculate the Black– Scholes valuation for the option. How does it compare to the actual quoted ask price?

Answer: The solution for this case was written in early April 2022. Therefore, the earliest maturity for Amazon options is April 14, 2022. Note in the screenshot below that there are options on Amazon with different expiration dates, both calls and puts, with different strike prices. On this day, when the solution was written, the stock price of Amazon closed at $3,155.69.

To retrieve the latest ask price for the call option on Amazon (AMZN) with the highest strike price maturing the soonest, we select the expiration date that is the closest to the day we are going to solve the case: April 14, 2022.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

The screenshot below shows the call option with the largest strike price for Amazon.

The largest strike price is $5,400. The fourth column shows the call option’s ask price of $0.02 per share.

The CBOE website also provides the values of the implied volatility, the delta, and the gamma of each option contract.

The Black–Scholes equation for the call option is given below.

Vo = Ps × N ( d1 ) −

Pe e rT

× N ( d2 )

P   σ2  ln  s  +  r + T Pe   2   d1 = σ T

d2 = d1 − σ T In order to estimate the Black–Scholes value of this call option on Amazon, the following needs to be collected: The stock price Ps, which is $3,155.69 on the day the solution is written.

The strike price Pe, which is $5,400.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 16: Derivative Valuation and Strategies

The time to expiration, T, which is seven days from the day the solution is written to April 14. The time to expiration is calculated as a percentage of the year. Using 252 as the average number of trading days per year, we get T = 7/252 = 0.028.

Two more variables remain: the annual risk-free rate and the annual standard deviation of the Amazon stock.

For the annual standard deviation of returns, we will use the last five years’ worth of monthly adjusted closing prices downloaded from Yahoo!. The Excel file where the calculation for the annual standard deviation is shown is attached to this case solution. Using the monthly average standard deviation of returns, we calculate the annualized standard deviation of returns by multiplying it by the square root of 12.

This yields an estimate of the annual standard deviation of 28.34%.

For the risk-free rate, we use the three-month T-bill rate as the risk-free rate, also taken from Yahoo!. On the day the solution was written, the three-month T-bill rate was 0.66%. (To get this rate, search for the ticker symbol ^IRX on Yahoo!.)

With the input provided, we estimate the value of the call option using the Black– Scholes equation to be $0. This is very close to the actual value of $0.02.

Note that this is a predicted value, as the strike price is much higher than the stock value, so the option is deep out of the money and will not have any value.

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26

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Solution and Answer Guide Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Table of Contents Questions .......................................................................................................................................... 2 Problems ........................................................................................................................................... 8 Case Study ....................................................................................................................................... 22

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1

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Questions 1. Technical Analysis. What is the purpose of technical analysis? What are the underlying forces it is trying to measure and assess? (LO 17-1) Answer: Technical analysis analyzes price and volume information to detect changes in the short-run supply and demand for a stock and make buy/sell decisions based on those changes. Technical analysis does not study the intrinsic or economic value of a stock, as fundamental analysis does. Technical analysts try to understand, measure, and predict the forces of supply and demand. Technical analysts use different types of charts and graphs to detect patterns from the price and volume information to make decisions about when to buy or sell a stock. Technical analysis is a trading tool used to guide short-term buy and sell decisions.

Technical analysis is one of the most popular techniques, used in trading systems design. While it is considered by many a simplified approach to trading on the financial markets, based on identifying trends and looking for patterns on charts, it has evolved to something much more than that. There has always been an opposing camp of people who are skeptical about the predictive power of the technical analysis. A lot of academic research suggests that price movements are close to a random walk. Many analysts support the thesis that prices are formed by the balance of supply and demand and are driven only by fundamental and economic data. As prices move only in response to the latest available information or news release and it is impossible to predict their move only by looking at a chart.

2. Moving Averages. Explain the importance of moving averages and moving average crossovers in technical analysis. When is a moving average crossover bullish or bearish? (LO 17-2) Answer: The 50-day price moving average (MA) is the average price over the previous 50 trading days (roughly two calendar months). The 200-day moving average is the average price over the previous 200 trading days (roughly one year of trading activity). Because moving averages calculate the average value of the price over past several trading days, it has less volatility than the actual price graph.

Moving averages are used to detect trends in the price data and determine a buy/sell decision. From a visual perspective, technical analysts see that the price trend is reversing itself when the actual price line crosses over an important moving average. When the actual price line crosses from below to above its moving average, a bull trend has started, and a buy signal is generated. Similarly, when the actual price crosses the moving average from above to below, the new trend is bearish, and the signal is to sell.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

3. Charts. What are the different type of charts used by technicians, and what are they used for? (LO 17-3) Answer: The two most widely used charts by technicians are the bar graph and the candlestick graph.

A bar graph shows the high for the day, the low for the day, and the closing price. A vertical line represents the range of the stock’s price (i.e., the high and the low prices), and the horizontal line represents the closing price.

A candlestick graph requires one additional piece of data: the opening price. Like the bar graph, a thin line connects the high and low prices. The body of the candlestick connects the opening and closing prices. If the opening price exceeds the closing price, indicating that the price fell, the body of the candlestick is filled in with black or red. If the opening price is less than the closing price (the price rose), the body is filled in as clear or with green. Dark or red candlesticks (especially long sticks, which indicate a large decline from the opening to the closing price) are bearish indicators, while light or green candlesticks are bullish.

4. Chart Patterns. In technical analysis terms, what is a head and shoulders trading pattern? Is such a pattern bullish or bearish? (LO 17-4) Answer: A popular chart price pattern is known as the head and shoulders. Candlesticks can be used to graph head and shoulder patterns. As its name implies, the head and shoulders pattern is made up of a left shoulder, head, right shoulder, and neckline.

The following paragraph describes the head and shoulders pattern.

While still in an uptrend, the left shoulder forms a peak that marks the high point of the current trend. After making this peak, a decline ensues to complete the formation of the shoulder. The low of the decline usually remains above the trend line, keeping the uptrend intact. From the low of the left shoulder, an advance begins that exceeds the previous high and marks the top of the head. After peaking, the low of the subsequent decline marks the second point of the neckline. The low of the decline usually breaks the uptrend line, putting the uptrend in jeopardy. The right shoulder peak is lower than the head (a lower high) and usually in line with the high of the left shoulder. While symmetry is preferred, sometimes shoulders can be out of whack. The decline from the peak of the right shoulder should break the neckline. The neckline forms by connecting low points from the formation of each shoulder prior to the formation of the head. Depending on the relationship between the two low points, the neckline can slope up, slope down, or be horizontal. The slope of the neckline will affect the pattern's degree of bearishness—a downward

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

slope is more bearish than an upward slope. During a bull market trend, the formation of the head and shoulders pattern signals a reversal to a bear market trend. A sell signal occurs when the price falls below the neckline after the right shoulder forms.

5. Volume. Why is trading volume important in technical analysis, and how is it used?

(LO 17-5) Answer: Stock price movements aren’t always what they appear. Beneath the surface of a move higher or lower, trends may be forming—or fizzling into a reversal. That’s why traders look for other indications of enthusiasm when they want to confirm or refute a price signal. Trading volume, which measures the number of shares traded during a particular time period, can help. While swings in trading volume may not be enough on their own to reveal changes in a trend, they can give you a sense of how much strength there is behind a move.

6. Market Breadth and Imbalance. What are the indicators for market breadth and imbalance, and how are they interpreted? (LO 17-6) Answer: Market breadth measures how many issues are rising relative to the number of issues that are declining. Some of the most widely used market breadth measures are based on advance−decline data. At the end of the trading day, each trading venue reports the number of stocks that advanced in value, declined, and remained unchanged. The advance−decline ratio for a particular market is the number of firms that advanced in price divided by the number that declined during a day. The advance−decline ratio is considered by technical analysts as good measure of the overall market's direction. Technicians consider it bullish if the advance−decline ratio is greater than 1 and bearish if the ratio is less than 1.

A common indicator of market imbalance is called the trading index (TRIN) ratio. The TRIN ratio is an indicator used to detect overbought and oversold levels in the market. The idea of the TRIN ratio is to detect market emotions on a small, daily scale.

The TRIN ratio combines advance and decline data with upside and downside volume information. The ratio is computed as TRIN =

# Advancing Stocks /# Declining Stocks UpVolume / DownVolume

TRIN provides a look at the volume that is trading in the advancing and declining stocks. If the number of advancing issues equals the number of declining issues and

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

total up volume equals total down volume, the TRIN ratio is 1.0. Ratios less than 1.0 are considered bullish, while ratios over 1.0 are considered bearish. Technical analysts consider a TRIN < 0.65 as very bullish, 0.65 < TRIN < 0.90 as bullish, 0.90 < TRIN < 1.10 as neutral, 1.10 < TRIN < 1.35 as bearish, and a TRIN > 1.35 as very bearish.

7. Investor Demand. Is an increase in odd-lot trading and mutual fund inflows considered bullish or bearish, and why? (LO 17-7) Answer: Individual investors are the biggest investors in mutual funds and do most of oddlot trading. Therefore, when odd-lot purchases are greater than odd-lot sales, then individual investors are buying. When odd-lot sales are greater than odd-lot purchases, then individual investors are selling. Similarly, mutual fund flow indicators that show mutual fund inflows, outflows, and credit balance information illustrate the actions of individual investors.

Technical analysts believe institutional investors represent “smart money,” whereas individual investors symbolize the overly emotional crowd. Therefore, odd-lot trading and mutual fund inflows are considered a contrary indicators, so the increase in both of them is taken as bearish sign by technical analysts.

8. Sentiment. What is investor sentiment, and why do technical analysts value it? How is it measured? (LO 17-8) Answer: Investor sentiment is the mood or feeling that Wall Street and individual investors have about the stock market and the economy. There are many surveys available that measure the investors’ sentiment. Among the more widely followed surveys used to gauge investor sentiment are the following: •

•

•

AAII Investor Sentiment Survey: The American Association of Individual Investors (AAII) Sentiment Survey measures the percentage of individual investors who are bullish, bearish, and neutral on the stock market in the short term. People are polled on a weekly basis from the AAII website (www.aaii.com).

Consumer Confidence Index: The Consumer Confidence Survey is based on a representative sample of thousands of U.S. households. It seeks to gauge consumer attitudes, buying intentions, vacation plans, and expectations for inflation, stock prices and interest rates. The monthly survey is conducted by The Conference Board (www.conference-board.org).

University of Michigan Consumer Sentiment: The Index of Consumer Sentiment (ICS) is based on consumer survey questions regarding spending and savings plans (www.sca.isr.umich.edu).

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

•

•

Bank of America Merrill Lynch Sell Side Indicator: This monthly indicator gauges the bullishness on Wall Street by surveying strategists about what percentage of assets they recommend that clients allocate to equities.

Robert Shiller’s Stock Market Confidence Indexes: Yale University Professor Robert Shiller compiles four different indexes based on surveys of individual and institutional investors: One-Year Confidence Index, Buy on Dips Confidence Index, Crash Confidence Index, and Valuation Confidence Index.

Technical analysts value results of sentiment-related surveys because statistical studies have found that investor sentiment and stock prices tend to move together.

When sentiment gets too extreme, technical analysts use sentiment as a contrary indicator. Excessive optimism on the part of the public and market professionals almost always coincides with market tops. Acute pessimism tends to coincide with market bottoms.

9. Momentum. What is price momentum, and how is it measured? (LO 17-9) Answer: The rate of change (ROC) indicator is a price momentum. The ROC shows the amount prices have changed over the given period, often over 10 to 12 days. A rising ROC indicates expanding momentum, which is a bullish signal, while a falling ROC is a bearish signal of declining momentum. An extremely low ROC suggests the stock is oversold and a recovery is likely. An extremely high ROC suggests that the market is overbought. ROC is interpreted as a leading indicator of a change in price trend. ROC is calculated with this formula:  Current Price  − 1 × 100 ROCN =   Price N Days Ago 

One of the most popular momentum indicators is the moving average convergence−divergence (MACD) indicator. It has two aspects. The first, called the MACD line, is calculated by subtracting the value of a 26-period exponential moving average from the value of a 12-period exponential moving average. The second is determined by calculating a 9-day exponential moving average of the MACD. The MACD trading rule is to sell when the MACD line falls below its 9-day moving average and to buy when the MACD line rises above the 9-day moving average. The MACD crossing above zero is considered bullish, while crossing below zero is bearish. Secondly, when the MACD turns up from below zero, it is considered bullish. When it turns down from above zero, it is considered bearish.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

10. Technical Analysis. What are the major challenges to technical analysis validity?

(LO 17-10) Answer: The major challenge to the validity of technical analysis is the efficient market hypothesis (EMH), which asserts that the current market price is the best available estimate of the intrinsic value of the firm. It also explains that short-run fluctuations in price and volume information appear to be essentially random in nature.

Therefore, the EMH concludes that trading rules based on historical price and volume information are fruitless in a perfectly efficient market.

Furthermore, there is no convincing evidence that technical analysis and technical trading rules can be consistently profitable. In addition, technical analysis does not provide precise trading rules, and sometimes the buy or sell signals can be opposite using different technical indicators.

Finally, even if sometimes traders make a profit using some technical rules, it is difficult to assess the return on those trades on a risk-adjusted basis.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Problems 1. Moving Average. Compute the 5-day moving average for days, 0, −1, and −2. (LO 17-2) Answer: Date Today, T = 0 −1 −2 −3 −4 −5 −6

Price 217.25 221.72 223.84 220.01 221.40 225.83 224.47

Each point on a 5-day moving average shows the average price over the previous 5 trading days, starting with the day listed.

The 5-day moving average (MA) for day 0 will include the prices from time 0 to −4.

The 5-day moving average (MA) for day −1 will include the prices from time −1 to −5.

The 5-day moving average (MA) for day −2 will include the prices from time −2 to −6.

5-day MA for day 0 = (217.25 + 221.72 + 223.84 + 220.01 + 221.40)/5 = 220.844 5-day MA for day −1 = (221.72 + 223.84 + 220.01 + 221.40 + 225.83)/5 = 222.56 5-day MA for day −2 = (223.84 + 220.01 + 221.40 + 225.83 + 224.47)/5 = 223.11 It will be much more efficient and less time consuming to do the calculation of MA with Excel, especially when we have 10 or more days.

2. Moving Average. Compute the 10-day moving average for days, 0, −1, and −2. The data are in the file, ch17_pr02.xlsx. (LO 17-2) Answer: Date Today, T = 0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11

Price 228.86 234.17 231.95 231.44 231.91 227.92 224.91 224.1 221.01 217.74 220.07 219.19

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Each point on a 10-day moving average shows the average price over the previous 10 trading days, starting with the day listed.

The 10-day moving average (MA) for day 0 will include the prices from time 0 to −9.

The 10-day moving average (MA) for day −1 will include the prices from time −1 to −10.

The 10-day moving average (MA) for day −2 will include the prices from time −2 to −11.

It will be best to use Excel to the calculation when we are dealing with 10 or more values.

10-day MA for day 0 = 227.401 10-day MA for day −1 = 226.522 10-day MA for day −2 = 225.024 You can use Excel to do the average value calculation, which is provided in the Excel file.

3. Moving Average. On what day does this stock price, provided in the file, ch17_pr03.xlsx, cross its 10-day moving average? Is it a cross from above or from below? (LO 17-2) Answer: To see on what day the stock price crossed its 10-day moving average, first we have to calculate all the possible 10-day MA values that we can use the data provided above.

Each point on a 10-day moving average shows the average price over the previous 10 trading days, starting with the day listed. We can calculate MA day 0 to MA day −10 using the data provided.

The table provides the calculated values of the 10-day MA for days 0 to −10, and the difference between the actual price and its 10-day MA for those days.

Date 0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10

Price 224.47 227.55 227.42 230.78 231.35 228.86 234.17 231.95 231.44 231.91 227.92

10-Day MA 229.99 230.34 230.07 229.74 228.76 227.40 226.52 225.02 224.16 223.49 223.97

Difference −5.52 −2.78 −2.65 1.04 2.59 1.46 7.65 6.93 7.28 8.42 3.95

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

When the difference has a positive value, it means the price of the stock is above its 10-day MA. As we you can see in the table, the difference turned negative on day −2.

On that day, the price crossed its 10-day MA from above to below.

4. Advance−Decline Ratio. What is the advance−decline ratio for this day for the NYSE and the NASDAQ? Is this bullish or bearish for each market? The data are in the file, ch17_pr04.xlsx. (LO 17-6) Answer: NYSE

NASDAQ

Issues Advancing

2,461

3,204

Declining

892

1,444

Unchanged

141

263

Total

3,494

4,911

Issues At New Highs

96

45

New Lows

57

172

Share Volume Advancing

3,417,259

3,354,742

Declining

659,203

992,125

The advance−decline ratio for a given trading day is the number of firms that advanced in price divided by the number that declined. The advance−decline ratio is considered by technical analysts as a good measure of the overall market's direction. Technicians consider it bullish if the advance−decline ratio is greater than 1 and bearish if the ratio is less than 1.

Advance−decline ratio NYSE = 2,461/892 = 2.76 Advance−decline ratio NASDAQ = 3,204/1,444 = 2.22 Both are much larger than 1, so they show bullish signals for both markets.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

5. Advance−Decline Ratio. What is the advance−decline ratio for this day for the NYSE and the NASDAQ? Is this bullish or bearish for each market? The data are in the file, ch17_pr05.xlsx. (LO 17-6) Answer: NYSE

NASDAQ

Issues Advancing

1,218

1,597

Declining

2,133

3,126

Unchanged

178

267

Total

3,529

4,900

Issues At New Highs

95

87

New Lows

205

740

Share Volume Advancing

1,742,692

2,403,016

Declining

2,715,391

2,708,862

Advance−decline ratio NYSE = 1,218/2,133 = 0.57 Advance−decline ratio NASDAQ = 1,597/3,126 = 0.51 Both are lower than 1, so they show bearish signals for both markets.

6. Trading Index Ratio. What is the TRIN for this day for the NYSE and the NASDAQ? Is this very bearish, bearish, neutral, bullish, or very bullish for each market? The data are in the file, ch17_pr06.xlsx. (LO 17-6) Answer: NYSE

NASDAQ

Issues Advancing

2,461

3,204

Declining

892

1,444

Unchanged

141

263

Total

3,494

4,911

Issues At New Highs

96

45

New Lows

57

172

Share Volume Advancing

3,417,259

3,354,742

Declining

659,203

992,125

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11

Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

The TRIN ratio is an indicator used to detect overbought and oversold levels in the market. The idea of the TRIN ratio is to detect market emotions on a small, daily scale. The TRIN ratio is calculated using the following formula: TRIN =

# Advancing Stocks /# Declining Stocks UpVolume / DownVolume

Technical analysts consider a TRIN < 0.65 as very bullish, 0.65 < TRIN < 0.90 as bullish, 0.90 < TRIN < 1.10 as neutral, 1.10 < TRIN < 1.35 as bearish, and a TRIN > 1.35 as very bearish.

NYSE TRIN = (2,461/892)/(3,417,259/659,203) = 0.53, the TRIN value is less than 0.65, which is very bullish indicator for the NYSE market.

Nasdaq TRIN = (3,204/1,444)/(3,354,742/992,125) = 0.66, the TRIN value is between 0.65 and 0.9, slightly above 0.65, so this is also a bullish indicator for the NASDAQ market.

7. Trading Index Ratio. What is the TRIN for this day for the NYSE and the NASDAQ? Is this very bearish, bearish, neutral, bullish, or very bullish for each market? The data are in the file, ch17_pr07.xlsx. (LO 17-6) Answer: NYSE

NASDAQ

Issues Advancing

1,218

1,597

Declining

2,133

3,126

Unchanged

178

267

Total

3,529

4,900

Issues At New Highs

95

87

New Lows

205

740

Share Volume Advancing

1,742,692

2,403,016

Declining

2,715,391

2,708,862

NYSE TRIN = (1,218/2,133)/(1,742,692/2,715,391) = 0.89, the TRIN value is between 0.65 and 0.9, which is bullish indicator for the NYSE market.

Nasdaq TRIN = (1,597/3,126)/(2,403,016/2,708,862) = 0.58, the TRIN value is less than 0.65, which is very bullish indicator for the NASDAQ market.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

8. Confidence Index. Compute the Confidence Index for each week with the yields provided. Does the trend suggest a prediction of a stronger or weaker economy?

The data are in the file, ch17_pr08.xlsx. (LO 17-7) Answer: Week T=0 −1 −2 −3 −4 −5 −6

Best Grade Bond 2.45 1.89 1.8 1.69 1.58 1.55 1.42

Interim Grade Bond 2.90 2.46 2.44 2.48 2.55 2.65 2.70

The Barron’s Confidence Index (0 to 100%) is measured by the ratio of the yield to maturity on Barron’s Best Grade Bonds (index of 10 bonds) to Barron’s Intermediate Grade Bonds (index of 10 bonds).

The bond market Confidence Index will be low if a weak economy and a poor stock market environment are expected and high if a robust economy and favorable stock market are anticipated.

The table below shows the values of the Confidence index for each week.

Week T=0 −1 −2 −3 −4 −5 −6

Confidence Index 84.48% 76.83% 73.77% 68.15% 61.96% 58.49% 52.59%

The Confidence Index value has been increasing steadily from week −6 to week 0, which is a sign of the economy getting stronger and that the stock market is anticipated to get better.

9. Put−Call Ratio. Using the put option volume and call option volume below, what day does the option market start signaling optimism for the stock market? The data are in the file, ch17_pr09.xlsx. (LO 17-7) Answer: The put−call ratio is calculated as the put−option trading volume divided by call−option trading volume. A high put−call ratio indicates that option traders are pessimistic. A low put−call ratio means that option traders are optimistic. Typically,

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

this ratio falls in a range between 0.6 and 0.4. When the put−call ratio moves outside this range, technicians take notice.

The table below provides the value of the put−call ratio for each days.

Date T=0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11

Put−call ratio 35.51% 32.74% 36.91% 32.35% 48.44% 40.46% 48.29% 46.98% 51.89% 46.29% 43.32% 52.71%

As you can see in the table, for days −3, −2, −1 and 0, the put−call ratio has a value below 0.4, which is an optimistic signal about the stock market. The optimism started at day −3.

10. Put−Call Ratio. Using the put option volume and call option volume below, what day does the option market start signaling pessimism for the stock market? The data are in the file, ch17_pr10.xlsx. (LO 17-7) Answer: The table below provides the value of the put−call ratio for each day.

Date T=0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11

Put−call ratio 72.68% 75.01% 66.82% 63.31% 71.90% 66.89% 62.14% 76.71% 63.01% 57.27% 56.82% 58.36%

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

As the table shows, the put−call ratio value is above 0.6 on day −8, and remains above that level until day 0, which shows pessimism about the stock market.

11. AAII Sentiment. Using the monthly AAII sentiment survey results below for 12 months, in what month does the survey first show bullish optimism by individual investors? The data are in the file, ch17_pr11.xlsx. (LO 17-8) Answer: The American Association of Individual Investors Sentiment Survey measures the percentage of individual investors who are bullish, bearish, and neutral on the stock market. The value of bullish percentage minus the bearish percentage can be positive or negative. Positive values indicate individual investors are net bullish, while negative values indicate they are net bearish.

The table below calculates the difference and provides how investors feel each month.

Month T=0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11

Bull−Bear 6.75% 19.90% 15.74% 13.35% 17.68% 19.93% −9.47% −11.37% −15.29% −20.05% −7.36% −2.62%

Sentiment Bullish Bullish Bullish Bullish Bullish Bullish Bearish Bearish Bearish Bearish Bearish Bearish

Investors started feeling bullish at month −5.

12. AAII Sentiment. Using the monthly AAII sentiment survey results below for 12 months, in what month does the survey first show bearish pessimism by individual investors? The data are in the file, ch17_pr12.xlsx. (LO 17-8) Answer: The table below calculates the difference and provides how investors feel each month.

Month Bull−Bear Sentiment T=0 −14.89% Bearish −1 −6.46% Bearish −2 19.32% Bullish

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

−3 −4 −5 −6 −7 −8 −9 −10 −11

12.93% 4.60% 2.80% 12.87% 10.00% 6.61% 16.48% 22.03% 1.13%

Bullish Bullish Bullish Bullish Bullish Bullish Bullish Bullish Bullish

Investors started feeling bullish at month −1.

13. Rate of Change. Calculate the 10-day rate of change (ROC) for days 0, −1, −2, −3, −4, and −5. Do the results imply a bullish or bearish signal? The data is in the file, ch17_pr13.xlsx. (LO 17-9) Answer: The ROC shows the amount prices have changed over the given period, over 10 days. A rising ROC indicates expanding momentum, which is a bullish signal, while a falling ROC is a bearish signal of declining momentum. An extremely low ROC suggests the stock is oversold and a recovery is likely. An extremely high ROC suggests that the market is overbought.

ROC is calculated with this formula:

 (Current Price)  − 1 × 100 ROCN =   Price N Days Ago    Where N = 10 in this problem.

ROC10 for day 0 = (372.00/415.01 − 1) × 100 = −10.36 ROC10 for day −1 = (386.98/409.94 − 1) × 100 = −5.60 ROC10 for day −2 = (389.40/410.84 − 1) × 100 = −5.22 ROC10 for day −3 = (386.67/406.22 − 1) × 100 = −4.81 ROC10 for day −4 = (387.46/404.09 − 1) × 100 = −4.12 ROC10 for day −5 = (393.61/397.07 − 1) × 100 = −0.87 The results indicate a declining trend in the ROC, which is a bearish signal.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

14. Rate of Change. Calculate the 12-day rate of change (ROC) for days 0, −1, −2, −3, and −4. Do the results imply a bullish or bearish signal? The data is in the file, ch17_pr14.xlsx. (LO 17-9) Answer: The ROC is calculated with this formula:

 (Current Price)  − 1 × 100 ROCN =   Price N Days Ago    Where N = 12 in this problem.

ROC12 for day 0 = (363.12/328.12 − 1) × 100 = 10.67 ROC12 for day −1 = (356.75/325.13 − 1) × 100 = 9.73 ROC12 for day −2 = (356.52/328.50 − 1) × 100 = 8.53 ROC12 for day −3 = (353.55/326.91 − 1) × 100 = 8.15 ROC12 for day −4 = (348.97/335.54 − 1) × 100 = 4.00 The results indicate an increasing trend in the ROC, which is a bullish signal.

15. Exponential Moving Average. Calculate the 12-period EMA for days 0, −1, −2, and −3.

The data is in the file, ch17_pr15.xlsx. (LO 17-9) Answer: The equation for the EMA is:

EMAN =

2 (Closing Price − Previous EMA) + Previous EMA N +1

The EMA illustrates how much the closing price deviates from the previous day’s EMA, scaled by 2 ÷ (N + 1), and added to the previous day’s EMA. N = 12 for this problem.

EMA (12) for day −3 = 2/13 × (187.67 − 183.60) + 183.60 = 184.23 EMA (12) for day −2 = 2/13 × (190.91 − 184.23) + 184.23 = 185.26 EMA (12) for day −1 = 2/13 × (189.63 − 185.26) + 185.26 = 185.93 EMA (12) for day 0 = 2/13 × (188.21 − 185.93) + 185.93 = 186.28

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

16. Exponential Moving Average. Calculate the five-period EMA for days 0 through −6.

The data is in the file, ch17_pr16.xlsx. (LO 17-9) Answer: Day T=0 −1 −2 −3 −4 −5 −6 −7 −8 −9 −10

Price 174.45 162.11 159.63 158.43 158.83 157.33 155.58 154 154.16 151.03 151.34

The equation for the EMA is:

EMAN =

2 (Closing Price − PreviousEMA) + PreviousEMA N +1

The EMA illustrates how much the closing price deviates from the previous day’s EMA, scaled by 2 ÷ (N+1), and added to the previous day’s EMA. To get started, the simple average is used for the first EMA. N = 5 in this problem.

We start by calculating the first EMA as the simple average for day − 6.

EMA (5) for day − 6 = (155.58 + 154 + 154.16 + 151.03 + 151.34)/5 = 153.22 EMA (5) for day − 5 = 2/6 × (157.33 − 153.22) + 153.22 = 154.59 EMA (5) for day − 4 = 2/6 × (158.83 − 154.59) + 154.59 = 156.00 EMA (5) for day − 3 = 2/6 × (158.43 − 156.00) + 156.00 = 156.81 EMA (5) for day − 2 = 2/6 × (159.63 − 156.81) + 156.81 = 157.75 EMA (5) for day − 1 = 2/6 × (162.11 − 157.75) + 157.75 = 159.20 EMA (5) for day 0 = 2/6 × (174.45 − 159.20) + 159.20 = 164.28 17. MACD. Calculate the MACD for this day when price is $149.10, EMA (12) is $150.95, and EMA (26) is 154.71. (LO 17-9) Price 149.10

EMA(12) EMA(26) 150.95 154.71

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Answer: The MACD is calculated by subtracting the value of a 26-period exponential moving average from the value of a 12-period exponential moving average.

MACD = EMA(12) − EMA(26) MACD = 150.95 − 154.71 = −3.76 18. MACD. Calculate the MACD for each day. On what day is there a trade signal, and what is the signal? The data is in the file, ch17_pr18.xlsx. (LO 17-9) Answer: MACD = EMA(12) − EMA(26) For each day, we subtract the EMA (26) from EMA (12) in the table below.

Day T=0 −1 −2 −3 −4 −5 −6 −7 −8 −9

MACD −0.68 −0.75 −0.89 −0.60 −0.32 0.10 0.54 0.98 1.76 2.32

The MACD is positive on day −9, and starts going down and turns negative by day −4, and remains negative with decreasing in value further. On day −4, there was a bearish turn, which is a sell signal.

19. MACD. Calculate the 9-day moving average MACD for days 0, −1, and −2. The data is in the file, ch17_pr19.xlsx. (LO 17-9) Answer: Each point on a 9-day moving average shows the average MCAD value over the previous 9 trading days, starting with the day listed.

The 9-day moving average (MA) for day 0 will include the MCAD values from time 0 to −8.

The 9-day moving average (MA) for day −1 will include the prices from time −1 to −9.

The 9-day moving average (MA) for day −2 will include the prices from time −2 to −10.

9-day MA for MCAD day 0 = 1.28 9-day MA for MCAD day −1 = 1.47

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

9-day MA for MCAD day −2 = 1.60 You can use Excel to do the average value calculation, which is provided in the Excel file.

20. MACD. Given the six months of price data provided in the file, ch17_pr20.xlsx, compute the EMA(12), EMA(26), MACD, and MACD 9-day moving average. Report these four statistics for the last day, January 21. (LO 17-9) Answer: The Excel file provides the calculations for the problem.

The equation for the EMA is:

2 (Closing Price − Previous EMA) + Previous EMA N +1 The EMA illustrates how much the closing price deviates from the previous day’s EMA, scaled by 2 ÷ (N + 1), and added to the previous day’s EMA. To get started, the simple average is used for the first EMA. EMAN =

The problem asks to calculate both EMA (12) and EMA (26) in order to be able to calculate MACD, which is given by: MACD = EMA(12) − EMA (26) To calculate EMA(12), N = 12, and we have to start by calculating the first EMA by taking the simple average of the first 12 price data.

The EMA(12) for August 6 is the simple average, which has a value of 516.87.

For August 9 to January 21, we can calculate the EMA(12) values using the equation above.

We do similar calculation for EMA(26).

To calculate EMA(26), N = 26, and we have to start by calculating the first EMA by taking the simple average of the first 26 price data.

The EMA(26) for August 26 is the simple average, which has a value of 524.27.

For August 27 to January 21, we can calculate the EMA(26) value using the equation above.

MACD can be calculated from August 26 to January 21 by taking the difference between EMA(12) and EMA(26), using the equation above.

Finally, the MACD 9-day moving average can be calculated by taking the average MCAD value over the previous 9 trading days, starting with the day listed.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

The MACD 9-day MA can be calculated from September 8 to January 21.

The values for January 21 are the following: EMA(12) = 515.74 EMA(26) = 552.84 MACD = −37.10 MACD 9-day MA = −25.73

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

Case Study Charts Use an online financial website, like Yahoo! Finance, to obtain specific charts for Amazon.com, Inc. (AMZN).

Use the one-year date range of January 22, 2021, to January 21, 2022, of daily data. a. Obtain and interpret a candlestick chart.

Interestingly, it looks like a head and shoulders pattern was forming from April to October, but the price didn’t convincingly break the neckline after the right shoulder. If so, it would have been a sell signal. The price did eventually break hard to the downside in January.

By the way, the large price break shown at the end of July is called a gap. Technical analysis believes that the price must go back up to fill in this gap before going down further. It took four months to fill it back in, but the price did continue its down trend afterward.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

b. Obtain a line graph with 50-day MA and 200-day MA and assess the crossovers.

The 50-day MA (in purple) shows many buy and sell signals throughout the year, possibly over 25! The 200-day moving average has fewer signals. However, since it is so flat, few profits can be made from it. For example, there is a crossover to the upside in early June, which is a buy signal. The price climbs to its peak. However, the price falls back. By the time it crosses the 200-day MA to the downside in August for the sell signal, the price is nearly back to the buy signal price. Thus, little in profit is made.

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Solution and Answer Guide: Adair/Nofsinger, Foundations of Investments, 1e, Chapter 17: Technical Analysis

c. Obtain a line graph with the MACD and evaluate momentum signals.

The MACD turns positive in early April, early June, early July, late August, and mid-October. These do appear to be good times to buy AMZN. The times that it turns negative, like in mid-February, early May, mid-July, late September, and late November, also appear to be good sell opportunities. The horizontal movements of stocks confuse the MACD, as it usually hovers near zero.

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