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Table of Content

006 Risk Management at the Top . . . . . . . . . . . . . . . . .

Go to chapter

015 The Valuation of Financial Companies . . . . . . . . .

Go to chapter

030 Mezzanine Financing . . . . . . . . . . . . . . . . . . . . . . .

Go to chapter

Mark Laycock Chapter 1: Introduction

Mario Massari, Gianfranco Gianfrate & Laura Zanetti Chapter 1: Bank Business Models

Luc Nijs Chapter 1: Introduction

041 Mathematics and Statistics for Financial Risk Management, 2nd Edition . . . . . . .

Go to chapter

Michael B. Miller Chapter 1: Some Basic Steps

056 Mathematical Methods for Finance . . . . . . . . . . .

Go to chapter

Sergio M. Focardi, Frank J. Fabozzi & Turan G. Bali Chapter 1: Basic Concepts

069 Risk Management and Financial Institutions, 3rd Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Go to chapter

John Hull Chapter 1: Introduction

084 Counterparty Credit Risk and Credit Value Adjustment, 2nd Edition . . . . . . . . . .

Go to chapter

091 Emerging Markets in an Upside Down World . . .

Go to chapter

108 Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Go to chapter

Jon Gregory Chapter 1: Introduction

Jerome Booth Chapter 1: Globalisation and the Current Global Economy

Matthew Hudson Chapter 1: Introduction to Funds

Some of these chapters are from advance uncorrected first proofs and are subject to change. All information and references must be checked against final bound books.

5


Risk Management at the Top A Guide to Risk and its Governance in Financial Institutions Mark Laycock 978-1-118-49742-5 • Hardback • 336 pages • January 2014

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2

Risk Management at the Top

In the years since the 2007–2009 financial crisis, a number of expectations and requirements for financial institutions have changed and been published. Alongside technical issues, such as changes to capital requirements, stakeholders have outlined their expectations for revitalised oversight of risk issues by the Board. This book is intended to support Non-Executive Directors (NEDs) in their oversight of risks to which the firm is exposed. While some NEDs will specialise in particular topics, such as risk, the Board has overall responsibility for risk oversight. This oversight of risk is part of the Board’s responsibility for supervising the activities of the Executive and establishing boundaries within which they act. To promote an effective dialogue there needs to be shared terminology and concepts, which in turn lead to improved communication and appreciation between the NEDs, the Executive and the risk managers.

1.1 INTRODUCTION The topic of risk oversight at the Board level and the materialisation of risk issues have a higher profile since the financial crisis. In response to expectations of NEDs and risk, some firms have established a Boardlevel Risk Committee, while others may nominate one or more NEDs to be the risk specialist representing the Board on the Enterprise or Group Risk Committee. Risk is an aspect of many, if not all, discussions at Board meetings. For example, risk is expected to feature in the discussions on compensation, business tactics and strategy. Over the past 30 years the discussion of risk has become increasingly technical. This evolution has been stimulated by initiatives of regulators of the financial sector. Basel I, II and III, European Directives and Dodd– Frank are examples of these initiatives. Very often, these initiatives are transposed into national requirements, each with their own variations that correspond to national priorities or perspectives. For firms that operate in many countries, the complexity generated by national differences can substantially expand the details that affect the Executive and influence Board decisions. In the post-financial crisis landscape some firms are winners. The winners were either lucky or had something that provided competitive advantage. Unfortunately, luck is not reproducible. A perceived aspect of the competitive advantage through the financial crisis is risk management. There are tales of firms reducing their exposure to particular activities or changing their long/short positions before others and

7


Introduction

3

weathering the crisis better than others. Whilst some firms got through the financial crisis, the winners were able to grasp opportunities. This competitive advantage through risk management did not arise by accident; it developed over time and is an integral part of how these firms operate. Not all firms are the same, not all firms face the same risks to the same extent and so a single template is not appropriate. Nevertheless, there will be common themes such as the risk appetite, monitoring compliance with the risk appetite, risk and return, and the variety of risks with different emphases. Pro-active oversight of risk by the Board is now an expectation of many powerful stakeholders to prevent crises and reinforce the competitiveness of the firm. To meet this objective the Board needs to have a meaningful dialogue on risk with the Executive. With the technical evolution of risk, this is not a simple objective. Some risk management queries are universal, but will only take the risk oversight and challenge dialogue so far: (a) (b) (c) (d) (e)

What can go wrong? How likely is it to go wrong? How badly wrong can it go? What is the relative upside versus downside? What can be done to manage the downside and change the ratio to the upside?

The Board, and their designated risk specialists, need sufficient knowledge to enable a productive dialogue with the Chief Risk Officer (CRO) or their risk specialists, such as the Chief Credit Risk Officer (CCRO), but without replicating the full extent of their knowledge. Risk is also expected to be an integral part of the Board’s dialogue on strategy with heads of businesses and countries or regions. Without going into extensive detailed technicalities, this book supports that productive dialogue. The rest of this chapter looks at: 1.2 Boards 1.3 Why Now? 1.4 Rest of the Book

1.2 BOARDS Irrespective of the jurisdiction in which it operates, one of the Board’s responsibilities is the oversight of risk.

8


4

Risk Management at the Top

In non-legal terms, the Board has a number of responsibilities:

∙ ∙ ∙ ∙

strategy formulation, policy making, oversight of Executives, and accountability to the owners of the company.

Risk is a subtext to all of these responsibilities. The expectation is that the NEDs on the Board will be able to provide “constructive challenge to the decisions and effective oversight” of the Executive.1 The European Banking Authority (EBA) expectation is that NEDs “should be able to demonstrate that they have, or will be able to acquire, the technical knowledge necessary to enable them to understand the business of the credit institution and the risks that it faces sufficiently well”. One approach to meeting this objective is to have a NED who has the role of being more expert than others on risk issues. Nevertheless, the Board has shared responsibility, even in the presence of specialists. The optimal attributes required of a risk specialist NED have been grouped into the following categories:2

∙ ∙ ∙ ∙

risk management acumen personal attributes business acumen education.

Each of these categories is supported by subcategories such as “an understanding of how incentive and compensation design influence risk taking”. Alongside these headings is the necessary experience, for example having been a CRO and experienced a complete business cycle. These attributes, when considered as a set, are challenging. As not all firms are the same, so the importance of meeting certain attributes will vary by firm. Depending upon the exact role, the variety of experience may be more important than its duration, for example 20 years’ practical knowledge of a narrow aspect of banking may be of limited value. The suitability of experience needs to be proportional to the firm’s activities in terms of scope, scale and complexity. 1

European Banking Authority (November 2012), paragraph 14.6. The Directors and Chief Risk Officers Group, “Attributes of a qualified risk director” – these are intended to be broadly applicable. 2

9


Introduction

5

1.3 WHY NOW? Following the 2007–2009 financial crisis there were many initiatives by:

∙ ∙ ∙ ∙

governments, trans-government bodies (such as the G20), financial regulators (national and international), and industry bodies.

These initiatives are intended to prevent reoccurrence of an equally grave crisis and fall into two broad categories – governance and technical. The initial rush of initiatives appears to be over and the focus is upon migrating from concept to rules and requirements. Firms are implementing various processes in response to these rules and requirements and are being “encouraged” by regulators, regulatory groups (such as the Basel Committee) and politicians with deadlines. 1.3.1

Governance Expectations

Stakeholder expectations on governance have been published, including:

∙ ∙ ∙

the Walker Report,3 documents from the Financial Reporting Council4 and the International Corporate Governance Network,5 and the UK Report of the Parliamentary Commission on Banking Standards.

In some instances the expectations and requirements apply to the entire corporate sector, in others they relate specifically to banks and other financial institutions. The EBA has produced a set of guidelines to focus on the experience of individuals on the Board and key Executive functions.6 These guidelines apply to unitary as well as two-tier Boards. These functions can also be known as significant influencing functions (SIFs). Several national regulators had SIF regimes established before the publication of the EBA guidelines. These regulators were able to raise their expectations 3

HM Treasury (November 2009). http://www.frc.org.uk/Our-Work/Codes-Standards/Corporate-governance/UK-CorporateGovernance-Code.aspx 5 https://www.icgn.org/ 6 European Banking Authority (November 2012). 4

10


6

Risk Management at the Top

and implement the new standards almost immediately. In some cases, this has been accompanied by greater assertiveness by the regulators about SIFs meeting these expectations. These guidelines were adopted by EU banking regulators in May 2013. For regulators that already had a SIF regime, the interviews may, originally, only have been conducted pre-appointment. A satisfactory outcome influenced whether the appointment could proceed. With the changed environment, it is expected that these interviews with regulators will occur on a regular basis when the individual has been in position for a period of time. Some regimes are expected to go beyond the SIF interview prior to appointment and these “in-position” inverviews.7 The UK regime has a proposal that SIFs, “in a case of failure, should demonstrate that they took all reasonable steps to prevent or mitigate the effects of a specified failing”.8 This obligation is reinforced by the suggestion that a criminal offence should be created for SIFs “carrying out their professional responsibilities in a reckless manner”. It is not clear if other jurisdictions will adopt similar expectations and sanctions. 1.3.2

Technical Changes

In addition to changes in expectations on governance, the post-financial crisis technical changes are adding complications and complexity for the firms. Some of these technical changes are expected to amend the business models as they have implications for return on capital. Other changes will affect the organisational structure of firms. These changes have consequences for Board-level oversight of risk and effective challenge of the Executive. Amongst the complicating factors is the characterisation of some financial firms as systemically important financial institutions (SIFIs) by the Financial Stability Board (FSB).9 The designation of SIFI means that the firm is important to the smooth operation of domestic and global financial systems.10 The implication of being a SIFI means that the firm 7

UK Report of the Parliamentary Commission on Banking Standards, p. 10. The Parliamentary Commission on Banking Standards refers to “Senior Persons”. 9 Financial Stability Board (2011, 2012). 10 The FSB plans to review the list of SIFIs on an annual basis, possibly moving firms between categories of SIFIs, adding or deleting firms from the list. The FSB is also considering whether some insurance companies, and other parts of the financial sector, should be given a SIFI designation. 8

11


Introduction

7

needs a sophisticated approach to risk management and its oversight, as well as holding additional capital. In some regimes the technical changes are likely to result in different business models for banks. The changes that fall into this category include:

∙ ∙ ∙ ∙

the Volker proposals, in the Dodd–Frank Act in the USA, the Vickers Report in the UK, “Living Wills” – resolution and recovery plans, and liquidity risk requirements.

These initiatives will affect proprietary trading, the separation of retail from wholesale banking, the distribution of capital within a group, guarantees provided to subsidiaries and sources of funding, as well as internal transfer pricing for funding. While the scope of some initiatives will be national, their consequences may be international. For example, a reduction in proprietary trading may affect the liquidity of individual securities with consequences for their use as collateral to mitigate credit risk. These technical changes add complexity to the Board’s oversight of existing risks. In addition, responding to these regulatory initiatives is expected to alter the risk profile of the firm. While some risks may diminish – the underlying purpose of these technical changes – other risks can be expected to raise their profile, and potentially new risks may be added.

1.4 REST OF THE BOOK The rest of the book is in three parts (see Figure 1.1): Risk Oversight, Specific Risks and Regulatory Environment. Part I describes the main elements of the risk management and oversight apparatus. A challenge is to arrive at a conceptual description of the various elements and practical implications. Most of the chapters in this part contain sections on terminology. This terminology, when combined with the description of the risk oversight apparatus, will support a dialogue, including challenge, as opposed to engaging in a monologue with the potential to be confused and frustrated. The organisational and human aspects, for example risk culture and biases, which can affect decision making are also covered in this section.

12


8

Risk Management at the Top

Risk Management at the Top Ch. 1: Introduction

Part I: Risk Oversight Ch. 2: Risk – An Overview

Ch. 3: Risk Oversight

Ch. 4: Risk Management

Ch. 5: Risk Appetite

Ch. 6: Risk Culture

Part II: Specific Risks Ch. 7: Credit Risk

Ch. 8: Market Risk

Ch. 9: Operational Risk

Ch. 10: Liquidity Risk

Ch. 11: Other Risks

Ch. 12: Risk Interactions

Part III: Regulatory Environment Ch. 13: Regulatory Environment

Figure 1.1

Book overview

Risk management, appetite and culture are all part of the risk consciousness of the organisation. For a portion of these topics the Board needs to perform a comparison between where the firm is and where the Board wants it to be, communicating any changes to the Executive for implementation. Part II covers risk types that are common to financial firms. Other risk types, such as underwriting risk or investment risk, may be specific to subsections of finance such as insurance. Some second-order effects are described, where one risk source can influence the severity of another risk source. This interaction presents a challenge for risk oversight and management. Part III looks at the regulatory environment. The regulatory framework is influential on the firm’s risk management through the creation of technical requirements and governance expectations, for example “principles for enhancing corporate governance”. The technical requirements have consequences for the amount and composition of capital of the firm. In turn, this has consequences for various stakeholders, for example the impact on dividends.

13


Introduction

9

FURTHER READING Basel Committee on Banking Supervision (October 2010) Principles for Enhancing Corporate Governance. http://www.bis.org/publ/bcbs176.pdf European Banking Authority (November 2012) Guidelines on the Assessment of the Suitability of Members of the Management Body and Key Function Holders. http://eba.europa.eu/cebs/media/Publications/Standards%20and %20Guidelines/2012/EBA-GL-2012-06–Guidelines-on-the-assessmentof-the-suitability-of-persons-.pdf Financial Stability Board (4 November 2011) Policy Measures to Address Systemically Important Financial Institutions. http://www.financialstability board.org/publications/r_111104bb.pdf Financial Stability Board (1 November 2012) Update of Global Systemically Important Banks. http://www.financialstabilityboard.org/publications/ r_121031ac.pdf HM Treasury (November 2009) A Review of Corporate Governance in UK Banks and Other Financial Industry Entities – Final Recommendations [the Walker Report]. http://www.hm-treasury.gov.uk/d/walker_review_ 261109.pdf The Directors and Chief Risk Officers Group (5 June 2013) Qualified Risk Director Guidelines. http://www.thegoverenancefund.com/DCRO/PDF/ Qualified_Risk_Director_Guidelines.pdf UK Report of the Parliamentary Commission on Banking Standards (June 2013) Changing Banking for Good. http://www.parliament.uk/documents/ banking-commission/Banking-final-report-volume-i.pdf

14


The Valuation of Financial Companies Tools and Techniques to Measure the Value of Banks, Insurance Companies and Other Financial Institutions Mario Massari, Gianfranco Gianfrate & Laura Zanetti 978-1-118-61733-5 • Hardback • 256 pages • February 2014

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1 Bank Business Models

TE

D

MA

TE RI

AL

From an economic point of view, banks carry out the crucial role of intermediating between individuals and/or organizations (corporations, financial institutions, national and local governments, and non-profit entities) with financial surpluses and those suffering from (temporary) money deficits. Such a definition is quite general and falls short of fully representing the complexity and articulation of an industry that is essential for economic development and national growth. When the banking system does not work properly the costs for the economy may be severe as the last financial crisis has made painfully clear. To sketch the main features of the banking business, we will segment the industry into a few categories in order to identify the different business models’ economics, profitability drivers, and, eventually, valuation metrics. Nevertheless, it’s worth underlining that, as Paul Volcker,1 former Federal Reserve Chairman used to say, fiduciary responsibility is at the very core of every banking organization, regardless of the specific activities carried out.

1.1 ECONOMICS OF BANKING

CO

PY RI

GH

Bank valuation can build only on a sound understanding of what banking business involves, what the different business models are over time, and now coexist in most countries. For valuation purposes, we will identify the main revenue-generating activities that a bank may carry and outline the business models behind such activities. While some banks are “mono-business” in the sense that they offer solely one type of service, most actually are “multi-business” with a wide array of financial products and services. When the portfolio of financial products is wide and encompasses both commercial and investment banking services the bank is usually referred to as “universal”. Table 1.1 introduces the relationship between business models and types of revenues that we will analyze in detail in the next paragraphs. The nature and mechanics of the insurance business will be presented in Chapter 6. Historically the core source of revenues for commercial banks has been the issue of loans to customers (individuals and/or corporate) and the gathering of money in the form of deposits. Net interest income is typically the difference between the interest earned from loans and interest paid to depositors, in this sense commercial 1 From the “Statement before US Senate, Committee on Banking, Housing, and Urban Affairs, January 21, 1987,” Federal Reserve Bulletin.

16


2

The Valuation of Financial Companies

Table 1.1

Types of banking revenues and business models

Types of revenues

Business model

Net interest income Fee and commission income

Commercial banking Commercial banking. Investment banking. Asset management Investment banking Bank assurance

Trading income Premium underwriting

banking is a “spread business”. Net interest income also includes earned and paid interest on other financial instruments. Collecting deposits and lending money are not value creating activities per se, but they are so if two more aspects are taken into account:

Commercial banks usually perform a maturity-transformation activity: in fact, they receive short-term financing (deposits are usually regarded as short-term debt although money invested in most of them can be generally withdrawn upon request so they are “on demand debt”) and issue long-term loans. Therefore, if the yield curve is upward sloping, part of the spread is due to the difference in the maturity of the instruments. There is a certain amount of risk embedded in the loans issued. Deposits, on the contrary, tend to have a very low risk (risk premium is generally assumed close to 0).

The second major source of revenue in the industry is fee and commission income. Services such as underwriting and placement of securities (mostly associated with investment banking), trust services and securities brokerage are commonly charged a fee or commission. The main difference between commercial and investment banks consists of the targeted segments of clients that commercial and investment banks strive to serve: while investment bank clients are usually large corporations to be served with tailored (costly) advisory services (especially related to extraordinary financial events such as IPO, seasoned equity offerings or M&A), commercial bank customers are individuals and small/medium enterprises for which less customized (expensive) services are provided. Typical fee-based services offered by banks are:

∙ ∙ ∙

Asset Management. Banks typically earn a management fee, as a fixed percentage of the Assets Under Management. Risk of financial investments carried out by the funds is held by clients. Private Banking. Banks provide advice to wealthy individual customers (including specialized advice on taxation) managing their financial assets. Corporate Advisory. Such services cover the entire spectrum of the events in the life of a company. So, they vary from risk management services (e.g.,

17


Bank Business Models

3

hedging foreign currency risk) and decisions on the optimal financial structure to the choice of issuing new securities, both debt and equity capital, and M&A transactions. In this sub-category, we consider the fees banks earn both for the piece of advice they provide to their clients and the fees earned to compensate for the risk involved in underwriting a security issue. Debt origination and specific advisory (e.g., project finance) is offered to sovereign, local governments and municipalities. Brokerage and Dealership. Commissions on trades are earned by banks in the secondary market. It’s important to underline that the recent trend originated by an increasing competition and Internet-based trading has both augmented the volume of trades and reduced the per unit commission.

It’s worth noting that banks’ activities earning fees and commissions have different economics and value drivers from those that generate interest income, as the former are typically based on limited asset positions and minimal risk capital. The third possible source of revenues is trading, which is mostly an investment banking activity even though commercial banks tend to have some exposure to that business. Proprietary trading involves trading of a wide variety of securities (in the name of the bank) on exchanges and OTC. For investment banks (an example is presented in Section 1.3) trading has always represented a large portion of total revenues, although trading results are quite volatile and predictable only under certain assumptions. As a fourth source of income, we refer to non-banking activities, which range from real estate development to insurance activities and minority investment in non-banking companies. Universal banks, generally, cover most of this non-typical business.

1.2 COMMERCIAL BANKS Commercial banks constitute the kind of banks people usually have in mind every time they speak of banks. They are basically engaged in the business of receiving money from their customers in the form of deposits and providing them with money in the form of loans. Even though these two activities are certainly the main part of the commercial banking business (in terms of the weight they have on the Balance Sheets of these organizations), both commercial banks’ liabilities and assets are broader in range and don’t fit such a narrow definition. Furthermore, commercial banks are also involved in providing their clients with trust services, namely managing their assets, and investment or financial advice. 1.2.1

Structure of the Industry in the US

In 2012, the number of institutions registered as commercial banks in the US was 6168, sub-divided by the value of their assets in commercial banks with assets

18


4

The Valuation of Financial Companies 1% 8%

Commercial banks with assets less than $100M (#2034 out of 6168)   Commercial banks with assets $100M to $1B (#3608 out of 6168)  Commercial banks with assets more than $1B (#526 out of 6168) 

91%

Figure 1.1 Structure of the US commercial banking business by assets Source: Federal Deposit Insurance Corporation (2012), www.fdic.gov.

lower than $100M, commercial banks with assets ranging between $100M and $1B and those ones with assets more than $1B according to Figure 1.1. Even though in terms of their number, large banks (with assets over $1B) represent 8.53% of the total, they manage 91% of the total assets in the industry, as shown in Figure 1.1. Specifically, we have community banks, which are small banks (under $1B) specializing in retail and consumer banking. Therefore, what they do is simply receive money from their local customer base and lend this money out to consumers. Savings banks, although commonly regarded as different entities to commercial banks, can technically be considered as just banks offering a higher interest rate in order to attract money. However, they can choose not to lend any money as long as they invest the collected deposits and earn, with a certain degree of safety, a return high enough to repay their depositors. The bulk of assets are held by regional or superregional banks. Big banks carry out activities that are generally more complex and variegated than community banks and also have access to markets for purchased funds, for example, interbank or federal funds market. Currently, five big players are also referred to as money center banks. In alphabetical order, they are: Bank of New York Mellon, Citigroup, Deutsche Bank, HSBC, and JPMorgan. It’s worth noting that this title is not awarded because of the asset size of those banks (in fact, Bank of America or Wells Fargo are not included in the list and they are both larger in terms of assets than Bank of New York Mellon). Being considered a money center bank is the result of both reliance on non-deposit sources of funding and of geographic location (Chicago or New York). Although the number of banks is currently shrinking and the assets are concentrated in the hands of the few largest players, it’s unlikely that community banks will disappear. Even in a mature industry like US banking, there are several ways of competing successfully and niche business models (from a geographical and product offering point of view) may coexist.

19


Bank Business Models

1.2.2

5

Overview of the US Regulation

The current number of US banks is a direct reflection of intense merger and bankruptcy waves recorded in the industry in the past two decades. The US financial regulation, which, until some years ago, restricted the geographic expansion of players in the market, is commonly regarded as the main source for the consolidation trend. We will first analyze the rules about the gulf between commercial and investment banking, and then the regulations concerning the constraints on geographic extension. In the early 1930s, after about 10 000 commercial banks went bankrupt in US, the Glass–Steagall Act was eventually promulgated (1933). Its goal was to rigidly separate commercial banks and investment banks. The distinction between investment and commercial banks is a peculiarity of the US banking history shared only with the Japanese one and some smaller contexts: in fact, in the rest of the world the universal banking model has been predominant for most of the twentieth century. The letter and spirit of Glass–Steagall Act were maintained intact for some decades. However, in the 1960s, after commercial banks somehow got involved in underwriting securities such as commercial papers and municipal bonds and in managing mutual funds, the rigid separation, hoped for by the original legislator, started losing de facto relevance. In 1987, commercial bank holdings were allowed by the Federal Reserve Board to establish investment bank affiliates (Section 20 affiliates) and all those “gray area” activities mentioned previously were transferred to these subsidiaries. Finally, a revolutionary change occurred in 1997. In that year, first the Federal Reserve and then US Congress, through the Financial Service Modernization Act, eliminated the barrier between commercial and investment banks for good. As a consequence, looking from a commercial bank strategic standpoint, many commercial banking players (such as the Bank of America) entered the investment banking business in force. Nevertheless, investment banks, which were generally not subject to Federal Reserve rules and capital requirements, maintained their leading position in that business segment. However, some new changes occurred after the recent crisis in 2008. Among the five big independent players (Merrill Lynch, Morgan Stanley, Goldman Sachs, Bear Sterns, and Lehman Brothers), just two companies survived and they all eventually applied to change their status into one of a Bank Holding Company (BHC).2 Today, they all actually look very similar to commercial banks from a regulatory requirements point of view, as they have to comply with stricter rules and capital regulation, and higher levels of disclosure.

2 A BHC, as provided by the Bank Holding Company Act of 1956 can be broadly defined as “any company that has control over a bank”. The bank holding company status makes it easier for the firm to raise capital than as a traditional bank, allowing better and quicker access to liquidity and funding. The downside includes responding to additional regulatory authorities: e.g., all BHCs in the US are required to register with the Board of Governors of the Federal Reserve System.

20


6

The Valuation of Financial Companies

As far as restrictions on interstate banking are concerned, the major piece of legislation shaping the industry until 1997 was the McFadden Act, which dated from the early 1930s. While state chartered banks were already generally constrained to state borders nationally chartered banks were also prohibited to expand. However, the potential loophole arising from this Act was that while a bank could not create a branch in a different state, subsidiaries could be established. The following period in fact, saw the growth of multi-bank holding companies (MBHCs) possessing subsidiaries in more than one state. Aware of that loophole, the Congress passed a law in 1956 constraining MBHCs from acquiring subsidiaries to only the extent allowed by the law of the target bank’s state of. This is why we observe a huge growth in interstate banking pacts – namely agreements between states to outline the conditions for entrance for out-of-state banks – in that period. In 1997, the enactment of the Riegle–Neal Act, which allowed interstate banking in US, immediately triggered the consolidation wave that featured hundreds of mergers in the industry. It’s also worth underlining that the US banking system can be defined as dual. In fact, it is a system in which nationally chartered and state-chartered banks do coexist. Banks, instead of being nationally chartered by the Office of the Comptroller of the Currency (OCC), a sub-agency of the US Treasury, can be chartered by one of the 50 state bank regulators. Finally, while all the nationally chartered banks are automatically members of the Federal Reserve System, just about 20% of all state chartered banks have decided to get membership.

1.2.3

Commercial Banks’ Balance Sheets

The Balance Sheets of a commercial bank, unlike that of other financial institutions (e.g., insurance companies), can be considered as both asset- and liability-driven. Commercial banks, in order to become a major player in the industry, have to compete and succeed in both attracting money (for instance, in the form of deposits) and lending money (generally, issuance of loans). As shown in Figure 1.2, the ability to attract deposits at a cost sustainably lower than the return from the assets is the core of bank profitability. Table 1.2 shows the consolidated balance sheet items for all the US commercial banks as of December 2012. On the asset side, as expected, loans and leases net of loan loss provisions (a balance sheet item generally related to the estimates of loan losses) account for the majority of the assets (51.5%). The other two main asset categories, with weights of almost 21% and 10% respectively, are securities (which don’t include securities held in trading accounts) and cash (including due from depository institution). As to the liability side, deposits represent about 83% of the total liabilities, while federal funds purchased and securities sold under the agreement to repurchase are close to 4%. Equity capital is not higher than 11.5% of total

21


Bank Business Models ×

Interest rate for assets

=

Interest income

Deposits and other × interest-bearing liabilities

Interest rate for liabilities

=

Interest expenses

Loans, mortgages and other investments

7

= Net interest income Cost/Income ratio

– Operating expenses – Loan loss provisions – Taxes = Net income /

Capital requirements

Equity = Return on Equity

Figure 1.2

Cost of Equity

=

Value created (destroyed)

The determinants of retail banking profitability

funding. We will discuss the structure of bank financial statements in detail in the next chapter.

1.3 INVESTMENT BANKS We are investment bankers, not commercial bankers, which means that we underwrite to distribute, not to put a loan on our balance sheet. Matt Harris, Managing Director, Chase Securities

At the bare minimum, investment banking involves helping corporations and governments to raise debt and equity securities in the market. Despite recent criticism, from an historical perspective, the financial intermediation role of investment banks has been crucial to the development of most developed countries’ financial systems and economies. All large corporations have always relied on those organizations in order to find investors and, therefore, continue their “expansion”. Investment banking activities range from the origination to the underwriting and placement of the issued securities. With the term underwriting, we refer to the practice of purchasing securities from the issuer and then selling them in the market (underwrite to distribute). When issuing securities, investment banks usually

22


8

The Valuation of Financial Companies

Table 1.2

Balance Sheet for all FDIC-Insured Commercial Banks (in $000s)

Total assets

$13 390 970

Net loans and leases of which: Loans secured by real estate Commercial & industrial loans Loans to individuals Farm loans Other loans & leases Less: Unearned income Less: Reserve for losses

51.50% 26.99% 10.84% 9.22% 0.48% 5.11% 0.01% 1.14%

Securities Other real estate owned Goodwill and other intangibles All other assets

20.54% 0.26% 2.62% 25.08%

Total liabilities and capital

$13 390 970

Non-interest-bearing deposits Interest-bearing deposits Other borrowed funds Subordinated debt All other liabilities Equity capital

19.23% 55.55% 9.04% 0.88% 4.08% 11.22%

Off-balance-sheet derivatives

16.73x

Source: Federal Deposit Insurance Corporation (www.fdic.gov), as of Dec. 2012.

distinguish between best effort practice and firm commitment. With firm commitment, investment banks underwrite the issuance, thus guaranteeing the full proceeds to the issuer regardless of the actual demand (the service so conceived tends to be very expensive for issuers). In case of best efforts, banks simply put these into selling the securities, not underwriting the issuance, so with no money commitment, which implies less risk for the bank and a lesser fee for issuing clients. Investment banks are also involved in the stages following placement, which supports these securities in the secondary market through brokerage or dealing services and/or market making. Finally, the other two main activities of investment banks consist of advising their customers during M&A (mergers and acquisitions) transactions and corporate restructurings (not just liquidation) in exchange for a fee. Such services clearly do not involve any Balance Sheet commitment for the bank, unless some form of direct financing is attached to the transaction. Investment banks also usually engage in proprietary trading (also known as “prop trading�), which consists of systematic trading activities in stocks, bonds, currencies,

23


Bank Business Models Net trading assets × Risk-adjusted = (trading assets - trading liabilities) return on trading

Trading income

Assets Under Management (AUM)

×

Management fee

Assets Under Management performance

×

Performance related fee

+

– Operating expenses

Taxes

Operating expenses

=

Net income Capital requirements

9

Taxes

/

=

Equity =

Net income /

Return on Equity

Equity = Return on Equity

Figure 1.3

The determinants of profitability in asset management and trading

commodities, their derivatives, or other financial instruments. With proprietary trading, the firm’s own money, as opposed to its customers’ money, is invested and exposed to market related risks. The profitability of such activities depends therefore, not just on their return, but also on the level of risk associated with the trades (see Figure 1.3) as well as asset management of various securities (shares, bonds, and other financial instruments) and assets (e.g., real estate) in order to meet specified investment goals for the benefit of the investors. Usually the fees for asset management mandates are partly related to the volumes of managed assets and partly to the actual performance of the assets themselves (Figure 1.3).

1.3.1

Structure of the US Banking Industry

By segmenting the industry in few categories of investment banks, which differ from each other in size and shape, we can neatly distinguish between boutiques, regional, sub-majors, major, and bulge bracket firms. The distinguishing characteristic does not depend simply on the geographical scope or number of employees. Bulge bracket firms are the largest global and most profitable investment banks. They are referred to as the bulge bracket because of the tendency for these companies to be reported in large and bold characters in “tombstones” (written announcements placed during a security offering). Major and sub-major bracket banks are second and third tier banks, respectively, while regional banks are usually smaller institutions with operations limited to specific regions. Boutique firms, as opposed to one-stop shops (that offer the entire spectrum of investment banking services), are very specialized in terms of services provided (so, as they affirm, “avoiding the conflicts of interests naturally arising in larger firms”) and/or geographic area.

24


10

1.3.2

The Valuation of Financial Companies

Typical Balance Sheet for an Investment Bank

As an example of the main structure of an investment bank’s economics, Table 1.3 shows the balance sheet of Morgan Stanley (as of December 2011). Unlike commercial banks – for which there is a significant investment in assets, typically loans, funded through deposits – investment banks do not require any significant investment in assets to run most operations. Even for securities trading, an activity usually run by investment banks and for corporate finance services, a huge medium-/long-term investment in assets is not necessary. As a consequence, the asset volume is often not an indication of the value of the bank. Deposits represent a very low portion of total funding (8.76%) compared to standard commercial banks. The bank applied for the BHC status with the FED in the aftermath of Lehman’s collapse (2008), but along with Goldman Sachs who made the same move, it essentially remains an investment bank. For Morgan Stanley, the major categories of funding are represented by longterm borrowings, financial instruments sold and not yet purchased, securities sold under agreements to repurchase, and payables representing respectively 24.5, 15.5, 14 and 16.5% of the total funding. Financial instruments sold and not yet purchased are, generally speaking, securities involved in transactions where the bank borrowed those securities in order to sell them and the position has not been covered yet: they represent obligations for the seller. This category, together with the “securities sold under repurchase agreement”, has always connoted the privileged source of funding in the investment banking business model. With the term payables (receivables), we are generally referring to payables to (receivables from) brokers, dealers, and clearing organizations. They include amounts payable (receivable) for securities not received (delivered) by Morgan Stanley by the settlement date (“fails to deliver”), payables to clearing organizations (margin deposits), commissions, and net receivables/payables arising from unsettled trades. On the asset side, securities purchased under agreement to resell represent a relevant asset for Morgan Stanley and is a feature shared with other investment banking players. The last point we would like to stress, as far as an investment bank Balance Sheet is concerned, is that securities borrowed or loaned require the two parties (lender and borrower) to exchange securities with an amount of cash collateral. The amount of cash advanced or received is recorded as securities borrowed and securities loaned, respectively. Finally, “other assets” for an investment bank generally means a portion of prepaid expense. Interest Income and Interest Expense in the Income Statement (Table 1.4) are constituted by interest earnings and expenses deriving from financial instruments owned and financial instruments sold, not yet purchased, securities available for sale, securities borrowed or purchased under agreements to resell, securities loaned or sold under agreements to repurchase, loans, deposits, commercial paper, and other short-term and long-term borrowings. The major expenses in an investment

25


26

Source: Morgan Stanley, December 2011.

127 074 48 669 15 369 4832 6457 6686 4285 12 106 749 898

15 944 184 234 679 820 70 078 749 898

Other liabilities and accrued expenses Long-term borrowings Total liabilities Total equity TOTAL LIABILITIES AND EQUITY

123 615

Payables (to customers, brokers, interest and dividends)

Securities loaned

20 719

30 462

Securities sold under agreements to repurchase

Other secured financings

104 800

Obligation to return securities received as collateral, at fair value

30 495 11 651 130 155

15 394

Total Financial instruments sold, not yet purchased, at fair value

63 449 29 059 68 923 47 966 48 064 8195 9697 275 353

Securities available for sale, at fair value Securities received as collateral, at fair value Federal funds sold and securities purchased under agreements to resell Securities borrowed Receivables (from customers, brokers, fees, others) Loans Other investments Premises, equipment and software costs Goodwill Intangible assets Other assets TOTAL

116 147

Deposits Commercial paper and other short-term borrowings

76 766

Cash and due from banks (including interest bearing deposits and cash deposited with clearing organization) Financial instruments owned, at fair value: US Government and agency securities Other sovereign government obligations Corporate and other debt Corporate equities Derivative and other contracts Investments Physical commodities Total Financial instruments owned, at fair value

65 662 2843

Liabilities and Equity

Morgan Stanley’s 2011 Balance Sheet (in $ M)

Assets

Table 1.3


12

The Valuation of Financial Companies

Table 1.4

Morgan Stanley’s Consolidated Statement of Income (in $ M) Consolidated Statements of Income

Investment banking Trading Investments Commissions and fees Asset management, distribution and administration fees Other Total non-interest revenues Interest income Interest expense Net interest Non-interest expenses: Compensation and benefits Occupancy and equipment Brokerage, clearing and exchange fees Information processing and communications Marketing and business development Professional services Other Total non-interest expenses Income from continuing operations before income taxes

4991 12 392 573 5379 8502 209 32 046 7264 6907 357 16 403 1564 1652 1815 602 1803 2450 26 289 6614

Source: Morgan Stanley, December 2011

bank are due to compensation and benefits to employees: human capital, in fact, is assumed to be the key success factor in the industry.

1.3.3

The Banking Industry outside the US

The strong development of the US economy and financial system has, over time, conferred global primacy to the US banking industry, and especially the US investment banking sector. To date, Europe is second to the US in terms of banking industry development. Similar to the US, most of the financial assets in Europe are concentrated in the hands of the few largest players. The segmentation provided by the European Central Bank (ECB) is similar from the point of view of the items recorded but differs regarding size ranges for categorizing banks (Figure 1.4). Banks with more than 0.5% of the total European consolidated banking assets are considered large, those ones with assets ranging between 0.5 and 0.005% are defined medium, and those with assets lower than 0.005% of total consolidated assets are considered small. In terms of concentration, 14.33% of the banks hold 97.1% of total assets held by European domestic banks, and just the top 1% of banks control 74.28% of total assets.

27


Bank Business Models

13

3%

23%

Large banks Medium banks Small banks

74%

Figure 1.4 Structure of European banking business by assets Source: European Central Bank, June 2012, www.ecb.int/stats

Consolidated Balance Sheet data for European commercial banks is not available, because six countries (including Germany and the UK), still apply local Generally Accepted Accounting Principles (GAAP) instead of International Financial Reporting Standards (IFRS). Since IFRS and local GAAP differ substantially, the aggregation of IFRS and non-IFRS data would prove meaningless in some cases. This element already signals some difficulties faced by analysts who have to deal with relative valuation of banks that use different accounting principles. Just as a rough indication of the values at play in the European financial system, loans represent about 56% of the total assets, debt instruments (which for the most part are governmental debt securities) about 15%, while equity is circa 5% of total assets (Table 1.5). In Chapter 4 we will further elaborate on the regulatory capital requirements in the US and Europe, and on why European banks apparently look relatively undercapitalized. As it happens, in other industries globalization is opening up the financial services markets and new players are emerging challenging the secular leadership

Table 1.5

The European Banking assets

Assets IFRS and Non-IFRS reporting banks

In â‚Ź B

Total loans and advances

20 053

Total debt instruments

522

Total equity instruments

558

Total assets

Liabilities IFRS and Non-IFRS reporting banks Total deposits from credit institutions Total deposits (other than from credit institutions) Total debt certificates (including bonds) Total liabilities Total equity

35 901

28

In â‚Ź B 3 348 14 154 6050 34 107 1793


14 Table 1.6

The Valuation of Financial Companies The largest Chinese and Japanese banks

Institution name

Total assets ($ M)

Industrial & Commercial Bank of China (ICBC) Mitsubishi UFJ Financial Group China Construction Bank Corporation Agricultural Bank of China Japan Post Bank Bank of China Mizuho Financial Group Sumitomo Mitsui Financial Group

2 822 334 2 382 911 2 248 062 2 130 857 2 104 219 2 040 160 1 820 416 1 518 478

Source: data from original financial statements. Exchange rates as of March 29, 2013.

of US and European banks. In Asia, for example, along with the leading Japanese financial institutions, four Chinese banks have assets worth more than $2 trillion (Table 1.6). However, the new emerging banking groups have so far adopted the same business models as Western banks. Therefore, the valuation frameworks presented in the next chapters easily apply to banks outside the US and Europe.

29


Mezzanine Financing Tools, Applications and Total Performance Luc Nijs 978-1-119-94181-1 • Hardback • 528 pages • November 2013

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1 Introduction

MA

TE RI

AL

For as long as some sort of trade-centered economy and society has existed for mankind, people have been financing those activities, either directly or through the sort of intermediaries that we now know as banks or financial institutions. Historically, there have always been two types of financing available for businesses which are trying to raise capital to fund their activities. That sounds somewhat simplistic but ‘debt’ and ‘equity’ have always been the fundamental financing classes tapped into by businesses, despite the many investment vehicles most businesses have access to. We begin this section by looking at the characteristics of debt and equity and then conclude by defining the scope of the mezzanine product group.

D

1.1 THE BI-POLAR WORLD OF FINANCE

CO

PY RI GH

TE

There are many different ways in which businesses can raise money, the primary ones being ‘debt’ and ‘equity.’ As I mentioned above, that sounds somewhat basic, and I guess it is, looking at the many product choices firms have these days. However, the two groups point at a fundamental difference as we know it in corporate finance. Let’s first look at the characteristics of both groups and then at the individual products that are included in these groups. After that, we will look more closely at the hybrid or mezzanine product group. Although debt and equity are often characterized by referring to the products that feature their characteristics, i.e., stocks and bonds, the true nature of the difference lies much deeper; in the nature of the cash flow claims of each product. The first big distinction has to do with the debt claim, which entitles the holder to a contractual set of cash flows to finance the repayment of the principal amount as well as the interests on a period-to-period basis. An equity claim, on the other hand, only holds a residual claim on the cash flows of the firm, i.e., after all expenses and other commitments are honored. This is the fundamental difference, although the tax code and legal qualifications have contributed to the creation of further distinctive characteristics between both groups. The second distinction, which can be seen as a direct consequence of the first distinction, is a logical result of the contractual claim that debt holders have versus the residual cash flow claim of equity holders. Debt claims have priority over equity claims, hence the qualification of equity owners as residual cash flow owners. That is true for both the principal amount and interest payments, and is valid until the instrument reaches maturity, even in the case of a bankruptcy or liquidation of the firm (claim by the debt holders on the firm’s assets). The tax laws in most countries make a distinction between the tax treatment of interest versus dividends. Interests paid are tax deductible when paid by the borrowing firm and are therefore cheaper on a net (after tax) basis. Dividends, however, are not tax deductible, as they are considered to be paid out of net cash flows.

31


2

Mezzanine Financing

Additionally, debt instruments have a fixed maturity, i.e., the principal amount becomes due at a certain point in time, together with the interests which have not yet been paid. (We will ignore, for the time being, perpetual bonds, which are, in essence, 99/100 year renewable instruments). Equity instruments are perpetual or infinite, i.e., they continue to exist until the firm decides to buy them back and retire them, or to liquidate the firm completely. Lastly, because equity owners are the residual cash flow owners, they are given control over the assets of the firm and its operational direction. Debt investors usually have a more passive role, often with no power of veto over major decisions in the firm. However, in recent years debt owners have done a pretty good job of getting their foot in the door, by using positive and negative covenants in their loan agreements to have (some level of) control over major transactions that would impact their position in the firm, often by making their investment more risky (i.e., due to increased leverage) or by damaging their chances of being repaid. In short, debt is characterized by a contractual claim on the firm, benefiting from taxdeductible interest payments, with a finite lifetime and a priority claim on cash flows in both going concern situations and bankruptcy or liquidations. Equity, on the other hand, has a residual cash flow claim on the firm, is an infinite security, where dividend payments do not come with tax deductibility, has no priority, but provides control over the management and assets of the firm (in theory). Securities that have characteristics of both are termed hybrid or mezzanine capital, a definition which we will refine later in this chapter. Figure 1.1a brings the categories and characteristics together but requires some explanation. Starting from the debt and equity positions we have already discussed (which make up boxes 1 and 3), the figure substantiates those two financing classes by indicating which types of instruments can be classified as being either debt or equity and further introduces the hybrid capital category (box 2) with an indicative set of products included. For the sake of completeness, and to provide a level playing field, I will review most of the products mentioned at this stage. Additionally, all terms are explained in the glossary, which can be found at the end of this book, and which includes a review of all technical terms used in this book, regardless of whether they have already been explained in the core text. Box 1, which reflects the debt products, includes the following instruments: (1) Bank debt or loans which are fixed-income instruments with a fixed or floating interest rate and a pre-determined maturity. Often these loans are secured and therefore repayment is secured by collateral. (2) Leasing, which is a form of asset financing where banks or specialized leasing institutions provide the financing for a specific (im)movable asset. The asset also serves as collateral in case the lessee (the person who has requested the finance) is unable to meet the lease payments. Two main categories exist, i.e., financial (or capital) and operational leases. In an operational lease, the lessor (or owner) transfers only the right to use the property to the lessee. At the end of the lease period, the lessee returns the property to the lessor. In case of a financial lease, the lessee has an option to acquire the asset (often at the end of the lease contract). Technical criteria distinguish operational from financial leases, and there are numerous accounting implications that are beyond the scope of this book. The distinction is also under review by the IASB (accounting body governing IFRS/IAS statements) which has been in its final phase for some time now (at the time of publication). For our purposes the distinction matters less as both types involve the lessee making payments to the lessor, which include a repayment of the loan underlying the asset

32


Introduction

3

Figure 1.1a The financial spectrum

purchase by the lessor. The lease payments include much more, i.e., insurance, depreciation, maintenance costs etc. (3) Commercial paper: when companies want to raise debt they traditionally have two options, they raise bank debt or issue a corporate bond (which can be listed or raised through a private placement). In both cases the firm will face significant costs, either because of the fees that come with bank debt or in terms of the capital raising fees it will have to pay to the investment bankers raising capital for the company. In case of bank debt those expenses can be as significant as 3–6% of the amounts looked for. In the case of a bond this can be anywhere between 3 and 7% depending on the investment bank one uses, the region where capital is raised and the amount sought. A cheaper alternative for organizations is to raise debt directly in the market through commercial paper. Commercial paper is

33


4

Mezzanine Financing

an unsecured instrument that allows companies to raise short-term debt (quite often the maturity will not exceed 270 days or nine months) often to finance current assets such as inventory, account receivables and other short-term liabilities. Because this type of instrument is unsecured, it can only be used by significantly creditworthy companies. In practice, the instrument is open to companies with an A credit rating or higher. (4) The next category in box 1 is junior debt, which can be qualified as those instruments that are ‘junior’ to other debt obligations a company has. That is, they are ranked lower on the repayment schedule than the more ‘senior’ debt instruments a company has committed to. They are also often unsecured. (5) Subordinated debt: Subordinated debt (which is mostly unsecured) is debt that is ranked lower than other debt instruments a company is committed to. In that sense they are also ‘junior’ as a debt instrument and aren’t backed by a security. Subordination can happen in two ways: the first is contractually – the loan contract will explicitly indicate that the interest and principal of this instrument will only be repaid after all other senior instruments have been repaid first. The subordination can also happen structurally – when the conditions and maturity of the loan have been structured in such a way that all other loans will be repaid before the structurally subordinated loan will be repaid. That can happen because the maturity of the loan is further in the future than all other loans and/or the interest is rolled up towards the instrument’s maturity. In the meantime, all other senior lenders will be repaid. (6) High-yield bonds (aka junk bonds) are debt instruments with a poor credit rating (in practice a non-investment grade rating which comes down to BB+ (S&P and Fitch), Ba1 (Moody) or lower categories. In box 3, which is the equity box, one can find common equity, the mother of all equity instruments. Equity provided by private equity firms and venture capital firms fits into this category as well. Warrants, once converted, entitle the holder to a certain pre-determined stake, in most cases, in the equity of the firm which issued the warrants. A warrant can therefore be qualified as an instrument that entitles the holder to purchase or receive common equity in the warrant’s issuing company. Contingent value rights are like an option where the holder of the rights is entitled to buy additional shares in the issuing company when certain events happen, under pre-determined conditions and pricing. This often happens after an acquisition or restructuring, where shareholders of the target company can acquire additional shares in the acquiring company (if, for example, the value of the shares of the acquirer drops below a certain point before a certain date). Finally, in category two, the instruments that have characteristics of both debt and equity either simultaneously or subsequently are listed. In Chapter 2 we will discuss extensively each of these instruments and compare their technical characteristics. For now it is sufficient to understand that each of the products included in box 2 will have, with varying degrees of intensity, characteristics of debt and equity and consequently their risk profile will be very different. Some will be hardly any different from a normal debt instrument as included in box 1 and others will show extreme similarities with the equity product group in box 3. What is striking, though, is that almost all are packaged in what qualifies legally as a debt instrument (with the exception of preferred stock), despite their significantly higher risk profile, a risk profile that sometimes hardly differs from an equity instrument. In the wider context of financing options, mezzanine qualifies as an external source of funding as categorized in Figure 1.1b.

34


Introduction

5

Forms of financing Internal financing

External financing

Funds from business Funds from the release of capital: activities:

Equity:

Debt:

Capital contribution from existing equity holders Capital contribution from new equity holders Private equity Public equity (IPO, Secondary offering)

•Banks (loans) •Capital goods leases •Suppliers (credits) •Customer (advances) •Bonds

•Retained profits •D&A •Reversal of provisions

•Sales of assets (divestitures)

Mezzanine financing

Figure 1.1b Financing options for companies Source: Credit Suisse economic research

1.2 DEMARCATION OF THE PRODUCT GROUP Now that we have the categories in place, we are left with the grueling task of finding the demarcation line as precisely as possible and defining it as accurately as possible. We could do that by looking at the reality of how the instruments are used, positioned or otherwise, but that would prove to be a mixed bag as well, and further, would not really help us develop a clearer picture of the product group. Looking at the legal qualification would force us to drag many hybrid instruments back into either the debt or the equity category, mostly the former, hence the need for a separate category of hybrid capital. The above issues have left those wishing to define the product group in the difficult position of having to describe the product group by its characteristics. Though I don’t want to go out on a limb here, I will take on the challenge of breaking down the individual characteristics, to see where the rough edges are or question marks could be placed. By looking at the mezzanine product group as a whole, the following characteristics can be identified:

• •

The individual products are all unsecured products, i.e., there is no collateral and/or firm lien on some or all assets of the borrowing firm. Second lien loans are an exception to this criterion, but aren’t strictly part of the mezzanine group. All the products carry a compensation scheme which includes the provision that (at least part of) the compensation is dependent on the future profitability of the firm (or, by extension, the return on equity or economic value creation of the firm). This one raises some additional

35


6

• •

Mezzanine Financing

questions. Products like junior debt, subordinated debt or unsecured debt all tend to be unsecured in their positions, but otherwise do enjoy the equity kicker that many other mezzanine products do. So some discretionary judgment is needed. On the one hand, these products are legally debt just like most other mezzanine products. On the other hand, they are also unsecured just like all the other mezzanine products. Where they deviate is that they do not directly enjoy the equity uptick that other products have built into their mechanics. It could be argued, however, that the higher spread that is built into the compensation scheme intrinsically includes that equity component. The counterargument is that an increased spread cannot reflect equity performance, it can only reflect higher risk patterns absorbed by the instruments, and in no way can it reflect the potential up- or downside that equity exposure can bring. So you could either argue that they belong to the debt product group (if you overweight the legal debt qualification) or that they are positioned in the outer space of the mezzanine cosmos (if you overweight the unsecured position and the higher overall risk profile they have relative to their peers in the debt group). One could say that there is a difference when defining mezzanine products sensu lato and sensu stricto. Some products are finite and others are infinite in nature. Besides the perpetual loans and non-redeemable preferred shares, all products are finite in nature. Most of the products (except for preferred equity) are debt instruments (in their legal qualification), which raises the question about the semantics of the term mezzanine capital versus the term mezzanine debt. Nevertheless, most of the products have a risk profile much closer to equity than their legal qualification initially suggests.

So, you can see for yourself that the jury is still out on some of these products in terms of their qualification, or at least that there is a mixed bag of characteristics within the mezzanine product group. An alternative way of looking at the product group is through its risk profile, which we will do in Section 1.4. The historical distinction between debt and equity doesn’t make our life a lot easier. In fact, you might wonder if there is a justification for treating debt and equity in such different ways. In particular, the different tax treatment has raised many questions among scholars, none providing a compelling argument for why the difference emerged, nor for why we should keep the distinction intact, especially since the differences trigger specific behaviors among market participants. Given the (lower) net cost of debt there is an inclination among market agents to use (too) much debt to fund their activities. That in itself is not evil, but raises the fixed cost levels in the firm (as they are fixed commitments). In days of poor economic performance or market volatility, or just lower levels of liquidity in the banking sector, that situation can trigger issues for firms operating high levels of debt, as the 2008 financial crisis demonstrated. Furthermore, as a country you can wonder if it is so attractive to have a lot of thinly capitalized firms in your economy, as they pose an intrinsic risk to other market participants through enhanced counterparty risk when dealing with them. Many countries have therefore introduced ‘thin capitalization rules’ in their tax code, which essentially are there to cap the amount of deductible interests a firm can deduct for tax purposes in any given period. The technical way that is determined differs slightly for each country, but the rules either put a nominal cap on the amounts of interests that can be deducted and/or put in place maximum debt/equity relations for any given period. For example, if your debt to equity ratio is higher than 3:1, the interest due on any debt amount above the 3:1 ratio is no longer deductible for tax purposes, making the instrument more expensive on a net basis.

36


Introduction

7

However, only one country in the world went as far as abolishing the distinction between debt and equity for tax purposes. That country is Belgium. In 2007 (yes, before the financial crisis) the Belgian government introduced what is known as the ‘notional interest deduction.’ The mechanism allows for the tax deductibility of an artificial dividend from the equity side of the financing mix. They don’t look at the effective dividends (which are not tax deductible) but at an artificially constructed dividend based on the T-bond rates in that period increased by a certain spread. The level of the spread is then based on certain conditions. This way an equity investment holds the same benefits as a debt investment. Besides the significant impact the introduction of this rule had on the budget, the government intended to ensure a better capitalized economic environment in the country. That is pretty understandable as the country enjoys major inbound investments every year, and is often the prime location for overseas investors to locate their European holding (and consequently Belgian holdings capitalize many subsidiaries in other European countries). Consequently, the capitalization of that holding determines the economic strength of its subsidiaries in Europe, especially when the economic tide shifts. Since 2007, the rule has been adapted a few times to remove possible abuse situations and non-intended usages within international tax planning schemes. Going even beyond that, questions can be raised about the true nature of an equity or debt instrument. All too often we look at the legal characteristics of the product to judge its nature. In most cases that is fine, but there are some exceptions that might make you wonder. If one provides a loan (in legal terms) to a firm which is in such a desperate economic state that it almost certainly will not be able to pay back the loan and interests due, one can wonder if the legal qualification is still adequate. The jurisprudence in many countries has responded to these situations by denying the deduction of the interest, re-qualifying the loan to equity and/or re-qualifying the interest to a ‘deemed dividend.’ In order to do that, the legal system needs to allow the tax authorities to ignore the legal reality of a business transaction in favor of the economic reality underlying the business transaction.1 Whether a legal system allows the economic theory doctrine to be applied is often a matter of legal principle in that jurisdiction and the answer often needs to be derived from other parts of the law beyond the tax code. In countries which do not have an economic theory in place, the tax authorities will have to turn to the ‘abuse of law’ provisions in their tax codes and argue that the participants in the deal were intending a different outcome to the one the legal qualification would normally imply. That is an uphill battle for tax authorities and disputes are therefore mostly settled out of court. I think it is fair to temporarily conclude that the debt to equity spectrum is a diamond with many angles, which are colored differently depending on your perspective.

1.3 POSITIONING AND USE OF MEZZANINE FINANCE Maybe we will get some further answers when looking at the reason why mezzanine finance exists to begin with and for what purposes it is used. When looking at the transactions for which mezzanine finance is used there is a long list of transactions that keep coming up. 1 In The Netherlands this line of thinking originated from the ‘bodemloze put’ theory based on a number of historical court cases. It refers to the idea that if you throw money into a bottomless pit you will never see your money again despite the legal claim you might have according to the instrument.

37


8

Mezzanine Financing

On that list are:

• • • • • • • • • • • •

Funding M&A activity (industry related or not) or funding organic growth and spin-offs. Restructuring or reorganization of the business. Funding the acquisition of portfolio companies by private equity firms (LBOs or otherwise). Management buy-ins/outs. Internationalization. Succession planning. Project finance. Change of strategic direction. Providing ‘bridge’ financing to portfolio companies on their way towards an IPO (when owned by a private equity firm). Recapitalizations. Funding the introduction of new products or service groups, plant expansion or the development of new distribution channels. Overall refinancing of activities or financing overall growth ambitions.

It is fair to say that mezzanine financing often comes on the radar for management or business owners if there is no sufficient collateral that would justify bringing in additional senior secured debt, or where the visibility of future cash flows is blurred or prone to many externalities. Added to that list are limited profitability or a deviant corporate risk profile. It is also fair to say that, given its deviant evolution, mezzanine is looked at differently in the US versus Europe. The US, with its more mature and developed capital markets, has developed a mezzanine group that is seen as a variation on publicly traded bonds (convertibles etc.) and therefore can be called public mezzanine. On the other hand, in Europe, where bank lending has played a more critical role in corporate funding, a private mezzanine market has been developing which tends to be closer to debt financing (subordinated and participating loans etc.). Other critical differences are discussed throughout the book. First, however, let’s consider the life stages of a company and the primary ways of financing in each of the individual stages (Table 1.1). Firms always have to decide whether they will finance their operations going forward using internal or external sources. Internal financing is often preferred, given the cost of, or access to, external funding, but it is not always realistic given the cash flow generation of the firm or the level of funding needed. It is fair to say that reality is not as clinical and sharply distinct as reflected in the chart below. Transitions are smoother or less defined and firms may have many ways to reinvent themselves in order to fight off the decline of their product group(s). That can range from introducing new product groups and/or services, to making acquisitions into (un)related industries and offloading certain asset groups that have a higher stand-alone value or are no longer core to the business strategy. The availability and cost of debt and equity also have an impact on how funding activities will arise. The recent financial crisis of 2008 and the emerging equity gap2 could push

2

McKinsey Global Institute, ‘The emerging equity gap,’ October 2011.

38


Introduction Table 1.1

9

Financing the individual life stages of a company

External funding needs Internal financing External financing

High, unconstrained Low or negative Owner’s equity Bank debt

Growth stage

Start-up Venture Capital/ Private Equity

High v-a-v firm value Low or negative VC/ Common stock Expansion Initial Public Offering

Moderate v-a-v firm value Low relative to financing needs Common stock, Warrants, Convertibles High growth Ad. Equity

Declining v-a-v firm value High relative to financing needs Debt

Low as opportunities are rare Higher than funding needs Retire debt, stock buy backs

Mature growth Bonds/C. Bonds

Decline or re-up

the cost of financing up, although some of that will be offset by historically low interest rates applied to the market both in the US and in Europe; interest rates have been hovering around 0–1% for a number of years now and are expected to stay there for at least a few more years, although in early 2013 central banks were starting to prepare the market for the fact that quantitative easing will end at some point. This might happen more unexpectedly than the average market participant would envisage. Pricing in the secondary government bond market already seems to hint that increased interest rates are expected. In emerging markets interest rates are higher, mainly as they are fighting (somewhat) higher levels of inflation, whereas throughout 2011–2012 the main theme was fighting deflation in the US and Europe. One thing is clear: in cases where senior debt is not an option (or is not sufficient to cover the whole funding need), mezzanine is a plug variable (it plugs the gap between debt and equity). It allows a firm’s debt financing to grow, without the owner losing control over company assets. That, however, carries an intrinsic risk, whereby the owner tries to avoid a (further) dilution of their equity stake at any cost, but burdens their company with so many priority debt claims that he or she literally erodes the residual cash flow generating ability of the underlying assets for the equity owners. It is often emotional reasons which make smaller companies turn to mezzanine financing as a less costly (relative to bringing outside equity into the firm) but (partly) fixed cost option, often with no – or only temporary – dilution of their equity stake. The consequence is that, from a risk perspective, mezzanine products all sit between the layers of senior debt and pure equity. They should therefore, in a risk-return world, trigger higher compensation than senior debt and a lower return than common equity. These often difficult questions about pricing deserve a full chapter later on in the book (Chapter 4). When mezzanine debt is used in conjunction with senior debt it reduces the amount of equity needed in the business. As equity is the most expensive form of capital and dilutive to existing shareholders, it is common sense for owners or majority stakeholders to aim to create a situation that comes at the lowest cost possible and is least dilutive when the business comes to be expanded.

39


10

Mezzanine Financing

The following example in Table 1.2 illustrates the latter point:3 Table 1.2

Reducing the cost of capital Financing structure before mezzanine

(Senior) bank loan Mezzanine loan Debt Capital Equity Capital Total Capital

After mezzanine

US$

Cost of capital (%)Assumptions

US$

Cost of capital (%)

3 0 3 3 6

5 0 5 20 12.5

6 2 8 3 11

5 12 6.8 20 10.4

The advantages and disadvantages of mezzanine finance can be summarized as shown in Table 1.3:4 Table 1.3

Advantages and disadvantages of using mezzanine finance

Advantages

Disadvantages

• Remedies financial shortfalls and provides capital backing for implementing corporate projects; • Improves balance sheet structure and thus creditworthiness, which can have a positive effect on the company’s rating and can widen the room for maneuver as regards financing; • Strengthens economic equity capital without the need to dilute equity holdings or surrender ownership rights; • Tax-deductible interest payments and flexible remuneration structure; • Greater entrepreneurial freedom for the company and limited consultation right for mezzanine investor.

• More expensive than conventional loan financing; • Capital provided for a limited term only, in contrast to pure equity capital; • More stringent transparency requirements.

1.4 THE RISK–RETURN CONUNDRUM From a balance sheet point of view, mezzanine finance is positioned between senior secured debt and common equity. It is therefore subordinated to senior debt claims but junior to common equity claims, although the latter isn’t a claim in the full sense, but only an entitlement to the residual cash flows produced by the firm. Figure 1.2 is a visual representation of the risk–return continuum of the mezzanine space. It is best to ignore the vast variety of instruments listed, but to realize for now that the mezzanine continuum spans the risk–return matrix between senior secured debt and common equity, the two instruments listed at either end of 3 4

‘Mezzanine finance – A hybrid instrument with a future,’ Credit Suisse, Economic briefing, 2006, p.10. Ibid. p. 9.

40


Mathematics and Statistics for Financial Risk Management, 2nd Edition Michael B. Miller 978-1-118-75029-2 • Hardback • 336 pages • January 2014

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Chapter

1

L

some Basic math

I

TE R

IA

n this chapter we review three math topics—logarithms, combinatorics, and geometric series—and one financial topic, discount factors. Emphasis is given to the specific aspects of these topics that are most relevant to risk management.

MA

LogarIthms

In mathematics, logarithms, or logs, are related to exponents, as follows: (1.1)

D

logb a = x ⇔ a = b x

TE

We say, “The log of a, base b, equals x, which implies that a equals b to the x and vice versa.” If we take the log of the right-hand side of Equation 1.1 and use the identity from the left-hand side of the equation, we can show that:

GH

logb(bx) = logb a = x logb(bx) = x

(1.2)

CO

PY

RI

Taking the log of bx effectively cancels out the exponentiation, leaving us with x. An important property of logarithms is that the logarithm of the product of two variables is equal to the sum of the logarithms of those two variables. For two variables, X and Y: logb (XY ) = logb X + logb Y

(1.3)

Similarly, the logarithm of the ratio of two variables is equal to the difference of their logarithms: logb

X = logb X − logb Y Y

(1.4)

If we replace Y with X in Equation 1.3, we get: logb (X 2 ) = 2logb X

(1.5)

We can generalize this result to get the following power rule: logb (X n ) = n logb X

(1.6)

1 42


2

MatheMatics and statistics for financial risk ManageMent

5 4 3 2

ln (X )

1 0 0

1

2

3

4

5

6

7

8

9

10

11

12

–1 –2 –3 –4 –5

exhIBIt 1.1

X

Natural Logarithm

In general, the base of the logarithm, b, can have any value. Base 10 and base 2 are popular bases in certain fields, but in many fields, and especially in finance, e, Euler’s number, is by far the most popular. Base e is so popular that mathematicians have given it its own name and notation. When the base of a logarithm is e, we refer to it as a natural logarithm. In formulas, we write: ln(a) = x ⇔ a = e x

(1.7)

From this point on, unless noted otherwise, assume that any mention of logarithms refers to natural logarithms. Logarithms are defined for all real numbers greater than or equal to zero. Exhibit 1.1 shows a plot of the logarithm function. The logarithm of zero is negative infinity, and the logarithm of one is zero. The function grows without bound; that is, as X approaches infinity, the ln(X) approaches infinity as well.

Log returns One of the most common applications of logarithms in finance is computing log returns. Log returns are defined as follows: rt ≡ ln(1 + Rt)

43

where Rt =

Pt − Pt −1 Pt −1

(1.8)


3

Some Basic Math

exhIBIt 1.2

Log Returns and Simple Returns ln(1 + R)

R 1.00%

1.00%

5.00%

4.88%

10.00%

9.53%

20.00%

18.23%

Here rt is the log return at time t, Rt is the standard or simple return, and Pt is the price of the security at time t. We use this convention of capital R for simple returns and lowercase r for log returns throughout the rest of the book. This convention is popular, but by no means universal. Also, be careful: Despite the name, the log return is not the log of Rt, but the log of (1 + Rt). For small values, log returns and simple returns will be very close in size. A simple return of 0% translates exactly to a log return of 0%. A simple return of 10% translates to a log return of 9.53%. That the values are so close is convenient for checking data and preventing operational errors. Exhibit 1.2 shows some additional simple returns along with their corresponding log returns. To get a more precise estimate of the relationship between standard returns and log returns, we can use the following approximation:1 r ≈ R−

1 2 R 2

(1.9)

As long as R is small, the second term on the right-hand side of Equation 1.9 will be negligible, and the log return and the simple return will have very similar values.

CompoundIng Log returns might seem more complex than simple returns, but they have a number of advantages over simple returns in financial applications. One of the most useful features of log returns has to do with compounding returns. To get the return of a security for two periods using simple returns, we have to do something that is not very intuitive, namely adding one to each of the returns, multiplying, and then subtracting one: R2,t =

Pt − Pt − 2 = (1 + R1,t )(1 + R1,t −1) − 1 Pt − 2

(1.10)

Here the first subscript on R denotes the length of the return, and the second subscript is the traditional time subscript. With log returns, calculating multiperiod returns is much simpler; we simply add: r2,t = r1,t + r1,t −1

(1.11)

1 This approximation can be derived by taking the Taylor expansion of Equation 1.8 around zero. Though we have not yet covered the topic, for the interested reader a brief review of Taylor expansions can be found in Appendix B.

44


4

MatheMatics and statistics for financial risk ManageMent

By substituting Equation 1.8 into Equation 1.10 and Equation 1.11, you can see that these definitions are equivalent. It is also fairly straightforward to generalize this notation to any return length.

sampLe proBLem Question: Using Equation 1.8 and Equation 1.10, generalize Equation 1.11 to returns of any length. Answer: Rn,t =

Pt − Pt − n P P P P = t − 1 = t t −1 . . . t − n +1 − 1 Pt − n Pt − n Pt −1 Pt − 2 Pt − n

Rn,t = (1 + R1,t )(1 + R1,t −1) . . . (1 + R1,t − n +1) − 1 (1 + Rn,t ) = (1 + R1,t )(1 + R1,t −1) . . . (1 + R1,t − n +1) rn,t = r1,t + r1,t −1 + . . . + r1,t − n +1 To get to the last line, we took the logs of both sides of the previous equation, using the fact that the log of the product of any two variables is equal to the sum of their logs, as given in Equation 1.3.

LImIted LIaBILIty Another useful feature of log returns relates to limited liability. For many financial assets, including equities and bonds, the most that you can lose is the amount that you’ve put into them. For example, if you purchase a share of XYZ Corporation for $100, the most you can lose is that $100. This is known as limited liability. Today, limited liability is such a common feature of financial instruments that it is easy to take it for granted, but this was not always the case. Indeed, the widespread adoption of limited liability in the nineteenth century made possible the large publicly traded companies that are so important to our modern economy, and the vast financial markets that accompany them. That you can lose only your initial investment is equivalent to saying that the minimum possible return on your investment is −100%. At the other end of the spectrum, there is no upper limit to the amount you can make in an investment. The maximum possible return is, in theory, infinite. This range for simple returns, −100% to infinity, translates to a range of negative infinity to positive infinity for log returns. Rmin = −100% ⇒ rmin = −∞ Rmax = +∞ ⇒ rmax = +∞

(1.12)

As we will see in the following chapters, when it comes to mathematical and computer models in finance it is often much easier to work with variables that are

45


5

Some Basic Math

unbounded—that is, variables that can range from negative infinity to positive infinity. This makes log returns a natural choice for many financial models.

graphIng Log returns Another useful feature of log returns is how they relate to log prices. By rearranging Equation 1.10 and taking logs, it is easy to see that: rt = pt − pt −1

(1.13)

where pt is the log of Pt, the price at time t. To calculate log returns, rather than taking the log of one plus the simple return, we can simply calculate the logs of the prices and subtract. Logarithms are also useful for charting time series that grow exponentially. Many computer applications allow you to chart data on a logarithmic scale. For an asset whose price grows exponentially, a logarithmic scale prevents the compression of data at low levels. Also, by rearranging Equation 1.13, we can easily see that the change in the log price over time is equal to the log return: ∆pt = pt − pt −1 = rt

(1.14)

It follows that, for an asset whose return is constant, the change in the log price will also be constant over time. On a chart, this constant rate of change over time will translate into a constant slope. Exhibits 1.3 and 1.4 both show an asset whose

650

550

Price

450

350

250

150

50 0

1

2

3

4

5 Time

exhIBIt 1.3

Normal Prices

46

6

7

8

9

10


6

MatheMatics and statistics for financial risk ManageMent

7.0

6.5

Log(Price)

6.0

5.5

5.0

4.5

4.0 0

1

2

3

4

5

6

7

8

9

10

Time

exhIBIt 1.4

Log Prices

price is increasing by 20% each year. The y-axis for the first chart shows the price; the y-axis for the second chart displays the log price. For the chart in Exhibit 1.3, it is hard to tell if the rate of return is increasing or decreasing over time. For the chart in Exhibit 1.4, the fact that the line is straight is equivalent to saying that the line has a constant slope. From Equation 1.14 we know that this constant slope is equivalent to a constant rate of return. In Exhibit 1.4, we could have shown actual prices on the y-axis, but having the log prices allows us to do something else. Using Equation 1.14, we can easily estimate the average return for the asset. In the graph, the log price increases from approximately 4.6 to 6.4 over 10 periods. Subtracting and dividing gives us (6.4 − 4.6)/10 = 18%. So the log return is 18% per period, which—because log returns and simple returns are very close for small values—is very close to the actual simple return of 20%.

ContInuousLy Compounded returns Another topic related to the idea of log returns is continuously compounded returns. For many financial products, including bonds, mortgages, and credit cards, interest rates are often quoted on an annualized periodic or nominal basis. At each payment date, the amount to be paid is equal to this nominal rate, divided by the number of periods, multiplied by some notional amount. For example, a bond with monthly coupon payments, a nominal rate of 6%, and a notional value of $1,000 would pay a coupon of $5 each month: (6% × $1,000)/12 = $5.

47


7

Some Basic Math

How do we compare two instruments with different payment frequencies? Are you better off paying 5% on an annual basis or 4.5% on a monthly basis? One solution is to turn the nominal rate into an annualized rate: RAnnual = 1 +

RNominal n

n

−1

(1.15)

where n is the number of periods per year for the instrument. If we hold RAnnual constant as n increases, RNominal gets smaller, but at a decreasing rate. Though the proof is omitted here, using L’Hôpital’s rule, we can prove that, at the limit, as n approaches infinity, RNominal converges to the log rate. As n approaches infinity, it is as if the instrument is making infinitesimal payments on a continuous basis. Because of this, when used to define interest rates the log rate is often referred to as the continuously compounded rate, or simply the continuous rate. We can also compare two financial products with different payment periods by comparing their continuous rates.

sampLe proBLem Question: You are presented with two bonds. The first has a nominal rate of 20% paid on a semiannual basis. The second has a nominal rate of 19% paid on a monthly basis. Calculate the equivalent continuously compounded rate for each bond. Assuming both bonds can be purchased at the same price, have the same credit quality, and are the same in all other respects, which is the better investment? Answer: First, we compute the annual yield for both bonds: R1, Annual = 1 + R2, Annual = 1 +

20% 2

2

19% 12

12

− 1 = 21.00% − 1 = 20.75%

Next, we convert these annualized returns into continuously compounded returns: r1 = ln(1 + R1, Annual ) = 19.06% r2 = ln(1 + R2, Annual ) = 18.85% All other things being equal, the first bond is a better investment. We could base this on a comparison of either the annual rates or the continuously compounded rates.

48


8

MatheMatics and statistics for financial risk ManageMent

ComBInatorICs In elementary combinatorics, one typically learns about combinations and permutations. Combinations tell us how many ways we can arrange a number of objects, regardless of the order, whereas permutations tell us how many ways we can arrange a number of objects, taking into account the order. As an example, assume we have three hedge funds, denoted X, Y, and Z. We want to invest in two of the funds. How many different ways can we invest? We can invest in X and Y, X and Z, or Y and Z. That’s it. In general, if we have n objects and we want to choose k of those objects, the number of combinations, C(n, k), can be expressed as: C(n, k) =

n n! = k k!(n − k)!

(1.16)

where n! is n factorial, such that: n! =

1 n=0     n(n − 1)(n − 2). . .1 n>0

(1.17)

In our example with the three hedge funds, we would substitute n = 3 and k = 2 to get three possible combinations. What if the order mattered? What if instead of just choosing two funds, we needed to choose a first-place fund and a second-place fund? How many ways could we do that? The answer is the number of permutations, which we express as: P(n, k) =

n! (n − k)!

(1.18)

For each combination, there are k! ways in which the elements of that combination can be arranged. In our example, each time we choose two funds, there are two ways that we can order them, so we would expect twice as many permutations. This is indeed the case. Substituting n = 3 and k = 2 into Equation 1.18, we get six permutations, which is twice the number of combinations computed previously. Combinations arise in a number of risk management applications. The binomial distribution, which we will introduce in Chapter 4, is defined using combinations. The binomial distribution, in turn, can be used to model defaults in simple bond portfolios or to backtest value at risk (VaR) models, as we will see in Chapter 7. Combinations are also central to the binomial theorem. Given two variables, x and y, and a positive integer, n, the binomial theorem states: (x + y)n =

n

k=0

n n−k k x y k

(1.19)

For example: (x + y)3 = x3 + 3x2 y + 3xy2 + y3

(1.20)

The binomial theorem can be useful when computing statistics such as variance, skewness, and kurtosis, which will be discussed in Chapter 3.

49


9

Some Basic Math

dIsCount FaCtors Most people have a preference for present income over future income. They would rather have a dollar today than a dollar one year from now. This is why banks charge interest on loans, and why investors expect positive returns on their investments. Even in the absence of inflation, a rational person should prefer a dollar today to a dollar tomorrow. Looked at another way, we should require more than one dollar in the future to replace one dollar today. In finance we often talk of discounting cash flows or future values. If we are discounting at a fixed rate, R, then the present value and future value are related as follows: Vt =

Vt + n (1 + R)n

(1.21)

where Vt is the value of the asset at time t and Vt + n is the value of the asset at time t + n. Because R is positive, Vt will necessarily be less than Vt + n. All else being equal, a higher discount rate will lead to a lower present value. Similarly, if the cash flow is further in the future—that is, n is greater—then the present value will also be lower. Rather than work with the discount rate, R, it is sometimes easier to work with a discount factor. In order to obtain the present value, we simply multiply the future value by the discount factor: Vt =

1 1+ R

n

Vt + n = δ nVt + n

(1.22)

Because the discount factor δ is less than one, Vt will necessarily be less than Vt + n. Different authors refer to δ or δ n as the discount factor. The concept is the same, and which convention to use should be clear from the context.

geometrIC serIes In the following two subsections we introduce geometric series. We start with series of infinite length. It may seem counterintuitive, but it is often easier to work with series of infinite length. With results in hand, we then move on to series of finite length in the second subsection.

Infinite series The ancient Greek philosopher Zeno, in one of his famous paradoxes, tried to prove that motion was an illusion. He reasoned that in order to get anywhere, you first had to travel half the distance to your ultimate destination. Once you made it to the halfway point, though, you would still have to travel half the remaining distance. No matter how many of these half journeys you completed, there would always be another half journey left. You could never possibly reach your destination.

50


10

MatheMatics and statistics for financial risk ManageMent

While Zeno’s reasoning turned out to be wrong, he was wrong in a very profound way. The infinitely decreasing distances that Zeno struggled with foreshadowed calculus, with its concept of change on an infinitesimal scale. Also, infinite series of a variety of types turn up in any number of fields. In finance, we are often faced with series that can be treated as infinite. Even when the series is long but clearly finite, the same basic tools that we develop to handle infinite series can be deployed. In the case of the original paradox, we are basically trying to calculate the following summation: S=

1 1 1 ... + + + 2 4 8

(1.23)

What is S equal to? If we tried the brute force approach, adding up all the terms, we would literally be working on the problem forever. Luckily, there is an easier way. The trick is to notice that multiplying both sides of the equation by ½ has the exact same effect as subtracting ½ from both sides: Multiply both sides by ½:

Subtract ½ from both sides:

1 1 1 ... + + + 2 4 8 1 1 1 1 ... + S= + + 2 4 8 16

1 1 1 ... + + + 2 4 8 1 1 1 1 ... S− = + + + 2 4 8 16

S=

S=

The right-hand sides of the final line of both equations are the same, so the lefthand sides of both equations must also be equal. Taking the left-hand sides of both equations, and solving: 1 1 = S 2 2 1 1 S− S = 2 2 1 1 S= 2 2 S =1 S−

(1.24)

The fact that the infinite series adds up to one tells us that Zeno was wrong. If we keep covering half the distance but do it an infinite number of times, eventually we will cover the entire distance. The sum of all the half trips equals one full trip. To generalize Zeno’s paradox, assume we have the following series: ∞

S = ∑δ i

(1.25)

i =1

In Zeno’s case, δ was ½. Because the members of the series are all powers of the same constant, we refer to these types of series as geometric series. As long as |δ | is

51


11

Some Basic Math

less than one, the sum will be finite and we can employ the same basic strategy as before, this time multiplying both sides by δ . ∞

δ S = ∑ δ i +1 i =1

δS = S − δ δ = S(1 − δ ) δ S= 1− δ

(1.26)

Substituting ½ for δ , we see that the general equation agrees with our previously obtained result for Zeno’s paradox. Before deriving Equation 1.26, we stipulated that |δ | had to be less than one. The reason that |δ | has to be less than one may not be obvious. If δ is equal to one, we are simply adding together an infinite number of ones, and the sum is infinite. In this case, even though it requires us to divide by zero, Equation 1.26 will produce the correct answer. If δ is greater than one, the sum is also infinite, but Equation 1.26 will give you the wrong answer. The reason is subtle. If δ is less than one, then δ ∞ converges to zero. When we multiplied both sides of the original equation by δ , in effect we added a δ ∞ + 1 term to the end of the original equation. If |δ | is less than one, this term is zero, and the sum is unaltered. If |δ | is greater than one, however, this final term is itself infinitely large, and we can no longer assume that the sum is unaltered. If this is at all unclear, wait until the end of the following section on finite series, where we will revisit the issue. If δ is less than −1, the series will oscillate between increasingly large negative and positive values and will not converge. Finally, if δ equals −1, the series will flip back and forth between −1 and +1, and the sum will oscillate between −1 and 0. One note of caution: In certain financial problems, you will come across geometric series that are very similar to Equation 1.25 except the first term is one, not δ . This is equivalent to setting the starting index of the summation to zero (δ 0 = 1). Adding one to our previous result, we obtain the following equation: ∞

S = ∑δ i = i =0

1 1− δ

(1.27)

As you can see, the change from i = 0 to i = 1 is very subtle, but has a very real impact on the sum.

sampLe proBLem Question: A perpetuity is a security that pays a fixed coupon for eternity. Determine the present value of a perpetuity that pays a $5 coupon annually. Assume a constant 4% discount rate.

52


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MatheMatics and statistics for financial risk ManageMent

Answer: ∞

$5

V =∑

i =1 (1.04) ∞

V = $5∑

i =1

i

1 1.04

i

1 1 = $5 1.04 = $5 = $5 ⋅ 25 1 1.04 − 1 1− 1.04

V = $125

Finite series In many financial scenarios—including perpetuities and discount models for stocks and real estate—it is often convenient to treat an extremely long series of payments as if it were infinite. In other circumstances we are faced with very long but clearly finite series. In these circumstances the infinite series solution might provide us with a good approximation, but ultimately we will want a more precise answer. The basic technique for summing a long but finite geometric series is the same as for an infinite geometric series. The only difference is that the terminal terms no longer converge to zero. S=

n −1

∑δi i =0

δS =

n −1

∑ δ i +1 = S − δ 0 + δ n

(1.28)

i =0

S=

1− δn 1− δ

We can see that for |δ | less than one, as n approaches infinity δ n goes to zero, and Equation 1.28 converges to Equation 1.27. In finance, we will mostly be interested in situations where |δ | is less than one, but Equation 1.28, unlike Equation 1.27, is still valid for values of |δ | greater than one (check this for yourself). We did not need to rely on the final term converging to zero this time. If δ is greater than one, and we substitute infinity for n, we get: S=

−∞ 1− δ∞ 1− ∞ = = =∞ 1− δ 1− δ 1− δ

(1.29)

For the last step, we rely on the fact that (1 − δ ) is negative for δ greater than one. As promised in the preceding subsection, for δ greater than one, the sum of the infinite geometric series is indeed infinite.

53


13

Some Basic Math

sampLe proBLem Question: What is the present value of a newly issued 20-year bond with a notional value of $100 and a 5% annual coupon? Assume a constant 4% discount rate and no risk of default. Answer: This question utilizes discount factors and finite geometric series. The bond will pay 20 coupons of $5, starting in a year’s time. In addition, the notional value of the bond will be returned with the final coupon payment in 20 years. The present value, V, is then: 20

20 $5 $100 1 $100 + = $5∑ + i 20 i 20 (1.04) (1.04) (1.04) (1.04) i =1 i =1

V =∑

We start by evaluating the summation, using a discount factor of δ = 1/1.04 ≈ 0.96: 20

S=∑

20

1

i =1 (1.04 )

i

=∑

i =1

1 1.04

i

20

= ∑ δ i = δ + δ 2 + . . . + δ 19 + δ 20 i −1

δ S = δ 2 + δ 3 + . . . + δ 20 + δ 21 δ S = S − δ + δ 21 δ − δ 21 = S(1 − δ ) δ − δ 21 1− δ S = 13.59 S=

Inserting this result into the initial equation, we obtain our final result: V = $5 × 13.59 +

$100 = $113.59 (1.04)20

Note that the present value of the bond, $113.59, is greater than the notional value of the bond, $100. In general, if there is no risk of default and the coupon rate on the bond is higher than the discount rate, then the present value of the bond will be greater than the notional value of the bond. When the price of a bond is less than the notional value of the bond, we say that the bond is selling at a discount. When the price of the bond is greater than the notional value, as in this example, we say that it is selling at a premium. When the price is exactly the same as the notional value we say that it is selling at par.

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MatheMatics and statistics for financial risk ManageMent

proBLems 1. Solve for y, where: a. y = ln(e5) b. y = ln(1/e) c. y = ln(10e) 2. The nominal monthly rate for a loan is quoted at 5%. What is the equivalent annual rate? Semiannual rate? Continuous rate? 3. Over the course of a year, the log return on a stock market index is 11.2%. The starting value of the index is 100. What is the value at the end of the year? 4. You have a portfolio of 10 bonds. In how many different ways can exactly two bonds default? Assume the order in which the bonds default is unimportant. 5. What is the present value of a perpetuity that pays $100 per year? Use an annual discount rate of 4%, and assume the first payment will be made in exactly one year. 6. ABC stock will pay a $1 dividend in one year. Assume the dividend will continue to be paid annually forever and the dividend payments will increase in size at a rate of 5%. Value this stream of dividends using a 6% annual discount rate. 7. What is the present value of a 10-year bond with a $100 face value, which pays a 6% coupon annually? Use an 8% annual discount rate. 8. Solve for x, where ee = 10 . x

9. Calculate the value of the following summation:

9

∑(−0.5)i i =0

10. The risk department of your firm has 10 analysts. You need to select four analysts to serve on a special audit committee. How many possible groupings of four analysts can be put together? 11. What is the present value of a newly issued 10-year bond with a notional value of $100 and a 2% annual coupon? Assume a constant 5% annual discount rate and no risk of default.

55


Mathematical Methods for Finance Tools for Asset and Risk Management Sergio M. Focardi, Frank J. Fabozzi & Turan G. Bali 978-1-118-31263-6 • Hardback • 320 pages • November 2013

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CHAPTER

1

Basic Concepts

MA T

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Sets, Functions, and Variables

I

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n mathematics, sets, functions, and variables are three fundamental concepts. First, a set is a well-defined collection of objects. A set is a gathering together into a whole of definite, distinct objects of our perception, which are called elements of the set. Sets are one of the most fundamental concepts in mathematics. Set theory is seen as the foundation from which virtually all of mathematics can be derived. For example, structures in abstract algebra, such as groups, fields, and rings, are sets closed under one or more operations. One of the main applications of set theory is constructing relations. Second, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Functions are the central objects of investigation in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. Others are given by a picture, called the graph of the function. A function can be described through its relationship with other functions, for example, as an inverse function or as a solution of a differential equation. Finally, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. Variables are further distinguished as being either a dependent variable or an independent variable. Independent variables are regarded as inputs to a system and may take on different values freely. Dependent variables are

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MATHEMATICAL METHODS FOR FINANCE

those values that change as a consequence of changes in other values in the system. The concepts of sets, functions, and variables are fundamental to many areas of finance and its applications. Starting with the meanvariance portfolio theory of Harry Markowitz in 1952, then the capital asset pricing model of William Sharpe in 1964, the option pricing model of Fischer Black and Myron Scholes in 1973, and the more recent developments in financial econometrics, financial risk management and asset pricing, financial economists constantly use the concepts of sets, functions, and variables. In this chapter we discuss these concepts.

What you will learn after reading this chapter:      

The notion of sets and set operations How to define empty sets, union of sets, and intersection of sets. The elementary properties of sets. How to describe the dynamics of quantitative phenomena. The concepts of distance and density of points. How to define and use functions and variables.

INTRODUCTION In this chapter we discuss three basic concepts used throughout this book: sets, functions, and variables. These concepts are used in financial economics, financial modeling, and financial econometrics.

SETS AND SET OPERATIONS The basic concept in calculus and in probability theory is that of a set. A set is a collection of objects called elements. The notions of both elements and set should be considered primitive. Following a common convention, let’s denote sets with capital Latin or Greek letters: A,B,C, � . . . and elements with small Latin or Greek letters: a,b, ω. Let’s then consider collections

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of sets. In this context, a set is regarded as an element at a higher level of aggregation. In some instances, it might be useful to use different alphabets to distinguish between sets and collections of sets.1

Proper Subsets An element a of a set A is said to belong to the set A written as a ∈ A. If every element that belongs to a set A also belongs to a set B, we say that A is contained in B and write: A⊂B. We will distinguish whether A is a proper subset of B (i.e., whether there is at least one element that belongs to B but not to A) or if the two sets might eventually coincide. In the latter case we write A ⊆ B. In the United States there are indexes that are constructed based on the price of a subset of common stocks from the universe of all common stock in the country. There are three types of common stock (equity) indexes: 1. Produced by stock exchanges based on all stocks traded on the particular exchanges (the most well known being the New York Stock Exchange Composite Index). 2. Produced by organizations that subjectively select the stocks included in the index (the most popular being the Standard & Poor’s 500). 3. Produced by organizations where the selection process is based on an objective measure such as market capitalization. The Russell equity indexes, produced by Frank Russell Company, are examples of the third type of index. The Russell 3000 Index includes the 3,000 largest U.S. companies based on total market capitalization. It represents approximately 98% of the investable U.S. equity market. The Russell 1000 Index includes 1,000 of the largest companies in the Russell 3000 Index while the Russell 2000 Index includes the 2,000 smallest companies in the Russell 3000 Index. The Russell Top 200 Index includes the 200 largest companies in the Russell 1000 Index and the Russell Midcap Index includes the 800 smallest companies in the Russell 1000 Index. None of the indexes include non-U.S. common stocks. 1 In this book we consider only the elementary parts of set theory which is generally referred to as naive set theory. This is what is needed to understand the mathematics of calculus. However, set theory has evolved into a separate mathematical discipline which deals with the logical foundations of mathematics.

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Let us introduce the notation: A = all companies in the United States that have issued common stock I3000 = companies included in the Russell 3000 Index I1000 = companies included in the Russell 1000 Index I2000 = companies included in the Russell 2000 Index ITop200 = companies included in the Russell Top 200 Index IMidcap = companies included in the Russell Midcap 200 Index We can then write the following: I3000 ⊂A

I1000 ⊂I3000 IMidcap ⊂ I1000

(every company that is contained in the Russell 3000 Index is contained in the set of all companies in the United States that have issued common stock) (the largest 1,000 companies contained in the Russell 1000 Index are contained in the Russell 3000 Index) (the 800 smallest companies in the Russell Midcap Index are contained in the Russell 1000 Index)

ITop200 ⊂ I1000 ⊂ I3000 ⊂ A IMidcap ⊂ I1000 ⊂ I3000 ⊂ A Throughout this book we will make use of the convenient logic symbols ∀ and ∃ that mean respectively, “for any element” and “an element exists such that.” We will also use the symbol ⇒ that means “implies.” For instance, if A is a set of real numbers and a ∈ A, the notation ∀a: a < x means “for any number a smaller than x” and ∃a: a < x means “there exists a number a smaller than x.”

Empty Sets Given a subset B of a set A, the complement of B with respect to A written as BC is formed by all elements of A that do not belong to B. It is useful to consider sets that do not contain any elements called empty sets. The empty set is usually denoted by ∅. For example, stocks with negative prices form an empty set.

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Basic Concepts

Union of Sets Given two sets A and B, their union is formed by all elements that belong to either A or B. This is written as C = A ∪ B. For example,

(the union of the companies contained in the Russell 1000 Index and the Russell 2000 Index is the set of all companies contained in the Russell 3000 Index) IMidcap ∪ ITop200 = I1000 (the union of the companies contained in the Russell Midcap Index and the Russell Top 200 Index is the set of all companies contained in the Russell 1000 Index) Let ILong lived be those stocks that existed in the last 30 years. I1000 ∪ I2000 = I3000

Intersection of Sets Given two sets A and B, their intersection is formed by all elements that belong to both A and B. This is written as C = A ∩ B. For example, let IS&P = companies included in the S&P 500 Index The S&P 500 is a stock market index that includes 500 widely held common stocks representing about 77% of the New York Stock Exchange market capitalization. (Market capitalization for a company is the product of the market value of a share and the number of shares outstanding.) Call ILong lived those stocks that existed in the last 30 years. Then IS&P ∩ ILong lived = C We can also write: I1000 ∩ I2000 = ∅

(the stocks contained in the S&P 500 Index that existed for the last 30 years) (companies included in both the Russell 2000 and the Russell 1000 Index is the empty set since there are no companies that are in both indexes)

Elementary Properties of Sets Suppose that the set � includes all elements that we are presently considering (i.e., that it is the total set). Three elementary properties of sets are given below: Property 1. The complement of the total set is the empty set and the complement of the empty set is the total set: �C = ∅, ∅C = �

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Property 2. If A,B,C are subsets of �, then the distribution properties of union and intersection hold: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) Property 3. The complement of the union is the intersection of the complements and the complement of the intersection is the union of the complements: (B ∪ C)C = BC ∩ CC

(B ∩ C)C = BC ∪ CC

DISTANCES AND QUANTITIES Calculus describes the dynamics of quantitative phenomena. This calls for equipping sets with a metric that defines distances between elements. Though many results of calculus can be derived in abstract metric spaces, standard calculus deals with sets of n-tuples of real numbers. In a quantitative framework, real numbers represent the result of observations (or measurements) in a simple and natural way.

n -tuples An n-tuple, also called an n-dimensional vector, includes n components: (a1 , a2 , . . . , an ). The set of all n-tuples of real numbers is denoted by Rn . The R stands for real numbers. For example, suppose the monthly rates of return on a hedge fund portfolio in 2011 are as shown in Table 1.1 with the actual return for the S&P 500 (the benchmark index for the hedge fund portfolio manager).2 Then the monthly returns, rport , for the hedge fund portfolio can be written as a 12-tuple and has the following 12 components: rport = 2



0.41%, 1.23%, 0.06%, 1.48%, −1.20%, −1.18% 0.23%, −3.21%, −3.89%, 2.67%, −1.29%, −0.43%

The monthly rate of return on the S&P 500 is computed as follows: Dividends paid on all the Change in the index value + stock in the index for the month −1 Value of the index at the beginning of the period

62




7

Basic Concepts

TABLE 1.1

Monthly Returns for the Hedge Fund Composite and S&P 500 Indexes

Month January February March April May June July August September October November December

Hedge Fund Portfolio 0.41% 1.23% 0.06% 1.48% −1.20% −1.18% 0.23% −3.21% −3.89% 2.67% −1.29% −0.43%

S&P 500 2.26% 3.20% −0.10% 2.85% −1.35% −1.83% −2.15% −5.68% −7.18% 10.77% −0.51% 0.85%

Similarly, the return rS&P on the S&P 500 can be expressed as a 12-tuple as follows: rS&P =



2.26%, 3.20%, −0.10%, 2.85%, −1.35%, −1.83% −2.15%, −5.68%, −7.18%, 10.77%, −0.51%, 0.85%



One can perform standard operations on n-tuples. For example, consider the hedge fund portfolio returns in the two 12-tuples. The 12-tuple that expresses the deviation of the hedge fund portfolio’s performance from the benchmark S&P 500 index is computed by subtracting from each component of the return 12-tuple from the corresponding return on the S&P 500. That is, rport − rS&P   0.41%, 1.23%, 0.06%, 1.48%, −1.20%, −1.18% = 0.23%, −3.21%, −3.89%, 2.67%, −1.29%, −0.43%   2.26%, 3.20%, −0.10%, 2.85%, −1.35%, −1.83% − −2.15%, −5.68%, −7.18%, 10.77%, −0.51%, 0.85%   −1.86%, −1.96%, 0.17%, −1.37%, 0.15%, 0.65% = 2.37%, 2.46%, 3.29%, −8.10%, −0.78%, −1.29% It is the resulting 12-tuple that is used to compute the tracking error of a portfolio—the standard deviation of the variation of the portfolio’s return from its benchmark index’s return.

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Coming back to the portfolio return, one can compute a logarithmic return for each month by adding 1 to each component of the 12-tuple and then taking the natural logarithm of each component. One can then obtain a geometric average, called the geometric return, by multiplying each component of the resulting vector and taking the 12th root.

Distance Consider the real line R1 (i.e., the set of real numbers). Real numbers include rational numbers and irrational numbers. A rational number is one that can be expressed as a fraction, c /d, where c and d are integers and d �= 0. An irrational number is one that cannot be expressed as a fraction. Three examples of irrational numbers are √ 2∼ = 1.4142136 Ratio between diameter and circumference =π ∼ = 3.1415926535897932384626 Natural logarithm = e ∼ = 2.7182818284590452353602874713526 On the real line, distance is simply the absolute value of the difference between two numbers |a − b| which also can be written as  (a − b)2

Rn is equipped with a natural metric provided by the Euclidean distance between any two points d[(a1 , a2 , . . . , an ), (b1 , b2 , . . . , bn )] =

 

(ai − bi )2

Given a set of numbers A, we can define the least upper bound of the set. This is the smallest number s such that no number contained in the set exceeds s. The quantity s is called the supremum and written as s = supA. More formally, the supremum is that number, if it exists, that satisfies the following properties: ∀a : a ∈ A, s ≥ a ∀ε > 0, ∃a : s − a ≤ ε where ε is any real positive number. The supremum need not belong to the set A. If it does, it is called the maximum.

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Similarly, infimum is the greatest lower bound of a set A, defined as the greatest number s such that no number contained in the set is less than s. If infimum belongs to the set it is called the minimum.

Density of Points A key concept of set theory with a fundamental bearing on calculus is that of density of points. In fact, in financial economics we distinguish between discrete and continuous quantities. Discrete quantities have the property that admissible values are separated by finite distances. Continuous quantities are such that one might go from one to any of two possible values passing through every possible intermediate value. For instance, the passing of time between two dates is considered to occupy every possible instant without any gap. The fundamental continuum is the set of real numbers. A continuum can be defined as any set that can be placed in a one-to-one relationship with the set of real numbers. Any continuum is an infinite non-countable set; a proper subset of a continuum can be a continuum. It can be demonstrated that a finite interval is a continuum as it can be placed in a one-to-one relationship with the set of all real numbers. The intuition of a continuum can be misleading. To appreciate this, consider that the set of all rational numbers (i.e., the set of all fractions with integer numerator and denominator) has a dense ordering, that is, has the property that given any two different rational numbers a,b with a < b, there are infinite other rational numbers in between. However, rational numbers have the cardinality of natural numbers. That is to say rational numbers can be put into a one-to-one relationship with natural numbers. This can be seen using a clever construction that we owe to the seventeenth-century Swiss mathematician Jacob Bernoulli. Using Bernoulliâ&#x20AC;&#x2122;s construction, we can represent rational numbers as fractions of natural numbers arranged in an infinite two-dimensional table in which columns grow with the denominators and rows grow with the numerators. A one-to-one relationship with the natural numbers can be established following the path: (1,1) (1,2) (2,1) (3,1) (2,2) (1,3) (1,4) (2,3) (3,2) (4,1) and so on (see Table 1.2). TABLE 1.2 Bernoulliâ&#x20AC;&#x2122;s Construction to Enumerate Rational Numbers 1/1 2/1 3/1 4/1

1/2 2/2 3/2 4/2

1/3 2/3 3/3 4/3

65

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MATHEMATICAL METHODS FOR FINANCE

Bernoulli thus demonstrated that there are as many rational numbers as there are natural numbers. Though the set of rational numbers has a dense ordering, rational numbers do not form a continuum as they cannot be put in a one-to-one correspondence with real numbers. Given a subset A of Rn , a point a ∈ A is said to be an accumulation point if any sphere centered in a contains an infinite number of points that belong to A. A set is said to be “closed” if it contains all of its own accumulation points and “open” if it does not.

FUNCTIONS The mathematical notion of a function translates the intuitive notion of a relationship between two quantities. For example, the price of a security is a function of time: to each instant of time corresponds a price of that security. Formally, a function f is a mapping of the elements of a set A into the elements of a set B. The set A is called the domain of the function. The subset R = f(A) ⊆ B of all elements of B that are the mapping of some element in A is called the range R of the function f. R might be a proper subset of B or coincide with B. The concept of function is general: the sets A and B might be any two sets, not necessarily sets of numbers. When the range of a function is a set of real numbers, the function is said to be a real function or a real-valued function. Two or more elements of A might be mapped into the same element of B. Should this situation never occur, that is, if distinct elements of A are mapped into distinct elements of B, the function is called an injection. If a function is an injection and R = f(A) = B, then f represents a one-to-one relationship between A and B. In this case the function f is invertible and we can define the inverse function g = f –1 such that f(g(a)) = a. Suppose that a function f assigns to each element x of set A some element y of set B. Suppose further that a function g assigns an element z of set C to each element y of set B. Combining functions f and g, an element z in set C corresponds to an element x in set A. This process results in a new function, function h, and that function takes an element in set A and assigns it to set C. The function h is called the composite of functions g and f, or simply a composite function, and is denoted by h(x) = g[f(x)].

VARIABLES In applications in finance, one usually deals with functions of numerical variables. Some distinctions are in order. A variable is a symbol that represents

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any element in a given set. For example, if we denote time with a variable t, the letter t represents any possible moment of time. Numerical variables are symbols that represent numbers. These numbers might, in turn, represent the elements of another set. They might be thought of as numerical indexes which are in a one-to-one relationship with the elements of a set. For example, if we represent time over a given interval with a variable t, the letter t represents any of the numbers in the given interval. Each of these numbers in turn represents an instant of time. These distinctions might look pedantic but they are important for the following two reasons. First, we need to consider numeraire or units of measure. Suppose, for instance, that we represent the price P of a security as a function of time t: P = f(t). The function f links two sets of numbers that represent the physical quantities price and time. If we change the time scale or the currency, the numerical function f will change accordingly though the abstract function that links time and price will remain unchanged. Variables can be classified as qualitative or quantitative. Qualitative (or categorical) variables take on values that are names or labels. Examples of qualitative variables would include the color of a ball (e.g., red, green, blue) or a dummy variable (also known as an indicator variable) taking the values 0 or 1. Quantitative variables are numerical. They represent a measurable quantity. For example, when we speak of the population of a city, we are talking about the number of people in the city, which is a measurable attribute of the city. Therefore, population would be a quantitative variable. Variables can also be classified as deterministic or random. In probability and statistics, a random variable, or stochastic variable, is a variable that can take on a set of possible different values, each with an associated probability. For example, when a coin is tossed 10 times, the random variable is the number of tails (or heads) that are noted. X can only take the values 0, 1, . . . , 10, so in this example X is a discrete random variable. Variables might represent phenomena that evolve over time. A deterministic variable evolves according to fixed rules, for example an investment that earns a fixed compound interest rate that grows as an exponential function of time. A random variable might evolve according to chance. One important type of function is a sequence. A sequence is a mapping of the set of natural numbers into real numbers.

KEY POINTS   

A set is a collection of objects called elements. Empty sets are sets that do not contain any elements. The union of two sets is formed by all elements that belong to either of the two sets.

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MATHEMATICAL METHODS FOR FINANCE

The intersection of two sets is formed by all elements that belong to both of the sets. Calculus describes the dynamics of quantitative phenomena. Real numbers represent the result of observations (or measurements) in a simple and natural way. Discrete quantities have the property that admissible values are separated by finite distances. Continuous quantities are such that one might go from one to any of two possible values passing through every possible intermediate value. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. A variable is a value that may change within the scope of a given problem or set of operations. Numerical variables are symbols that represent numbers. A deterministic variable is a variable whose value is not subject to variations due to chance. A random variable or stochastic variable is a variable whose value is subject to variations due to chance or randomness.

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Risk Management and Financial Institutions, 3rd Edition John Hull 978-1-118-26903-9 • Hardback • 672 pages • May 2012

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CHAPTER

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Introduction

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magine you are the Chief Risk Officer (CRO) of a major corporation. The CEO wants your views on a major new venture. You have been inundated with reports showing that the new venture has a positive net present value and will enhance shareholder value. What sort of analysis and ideas is the CEO looking for from you? As CRO it is your job to consider how the new venture fits into the company’s portfolio. What is the correlation of the performance of the new venture with the rest of the company’s business? When the rest of the business is experiencing difficulties, will the new venture also provide poor returns, or will it have the effect of dampening the ups and downs in the rest of the business? Companies must take risks if they are to survive and prosper. The risk management function’s primary responsibility is to understand the portfolio of risks that the company is currently taking and the risks it plans to take in the future. It must decide whether the risks are acceptable and, if they are not acceptable, what action should be taken. Most of this book is concerned with the ways risks are managed by banks and other financial institutions, but many of the ideas and approaches we will discuss are equally applicable to nonfinancial corporations. Risk management has become progressively more important for all corporations in the last few decades. Financial institutions in particular are finding they have to increase the resources they devote to risk management. Large “rogue trader” losses such as those at Barings Bank in 1995, Allied Irish Bank in 2002, Soci´et´e G´en´erale in 2007, and UBS in 2011 would have been avoided if procedures used by the banks for collecting data on trading positions had been more carefully developed. Huge “subprime” losses at banks such as Citigroup, UBS, and Merrill Lynch would have been less severe if risk management groups had been able to convince senior management that unacceptable risks were being taken. This opening chapter sets the scene. It starts by reviewing the classical arguments concerning the risk-return trade-offs faced by an investor who is choosing a portfolio of stocks and bonds. It then considers whether the same arguments can be used by a company in choosing new projects and managing its risk exposure. The chapter concludes that there are reasons why companies—particularly financial institutions—should be concerned with the total risk they face, not just with the risk from the viewpoint of a well-diversified shareholder.

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RISK MANAGEMENT AND FINANCIAL INSTITUTIONS

1.1 RISK VS. RETURN FOR INVESTORS As all fund managers know, there is a trade-off between risk and return when money is invested. The greater the risks taken, the higher the return that can be realized. The trade-off is actually between risk and expected return, not between risk and actual return. The term “expected return” sometimes causes confusion. In everyday language an outcome that is “expected” is considered highly likely to occur. However, statisticians define the expected value of a variable as its average (or mean) value. Expected return is therefore a weighted average of the possible returns, where the weight applied to a particular return equals the probability of that return occurring. The possible returns and their probabilities can be either estimated from historical data or assessed subjectively. Suppose, for example, that you have $100,000 to invest for one year. One alternative is to buy Treasury bills yielding 5% per annum. There is then no risk and the expected return is 5%. Another alternative is to invest the $100,000 in a stock. To simplify things, we suppose that the possible outcomes from this investment are as shown in Table 1.1. There is a 0.05 probability that the return will be +50%; there is a 0.25 probability that the return will be +30%; and so on. Expressing the returns in decimal form, the expected return per year is: 0.05 × 0.50 + 0.25 × 0.30 + 0.40 × 0.10 + 0.25 × (−0.10) + 0.05 × (−0.30) = 0.10

This shows that in return for taking some risk you are able to increase your expected return per annum from the 5% offered by Treasury bills to 10%. If things work out well, your return per annum could be as high as 50%. But the worst-case outcome is a −30% return or a loss of $30,000. One of the first attempts to understand the trade-off between risk and expected return was by Markowitz (1952). Later Sharpe (1964) and others carried the Markowitz analysis a stage further by developing what is known as the capital asset pricing model. This is a relationship between expected return and what is termed “systematic risk.” In 1976, Ross developed arbitrage pricing theory which can be viewed as an extension of the capital asset pricing model to the situation where there are several sources of systematic risk. The key insights of these researchers have had a profound effect on the way portfolio managers think about and analyze the risk-return trade-offs that they face. In this section we review these insights.

TABLE 1.1 Return in One Year from Investing $100,000 in Equities Probability

Return

0.05 0.25 0.40 0.25 0.05

+50% +30% +10% −10% −30%


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3

Introduction

Quantifying Risk How do you quantify the risk you are taking when you choose an investment? A convenient measure that is often used is the standard deviation of return over one year. This is 

E(R2 ) − [E(R)]2

where R is the return per annum. The symbol E denotes expected value so that E(R) is expected return per annum. In Table 1.1, as we have shown, E(R) = 0.10. To calculate E(R2 ) we must weight the alternative squared returns by their probabilities: E(R2 ) = 0.05 × 0.502 + 0.25 × 0.302 + 0.40 × 0.102 + 0.25 × (−0.10)2 + 0.05 × (−0.30)2 = 0.046

The standard deviation of returns is therefore

0.046 − 0.12 = 0.1897 or 18.97%.

Investment Opportunities Suppose we choose to characterize every investment opportunity by its expected return and standard deviation of return. We can plot available risky investments on a chart such as Figure 1.1 where the horizontal axis is the standard deviation of return and the vertical axis is the expected return. Once we have identified the expected return and the standard deviation of the return for individual investments, it is natural to think about what happens when we combine investments to form a portfolio. Consider two investments with returns R1

Expected return

. .. . . . .

... . ..

Standard deviation of return

FIGURE 1.1 Alternative Risky Investments


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RISK MANAGEMENT AND FINANCIAL INSTITUTIONS

and R2 . The return from putting a proportion w1 of our money in the first investment and a proportion w2 = 1 − w1 in the second investment is w1 R1 + w2 R2 The portfolio expected return is (1.1)

 P = w1  1 + w2  2

where 1 is the expected return from the first investment and 2 is the expected return from the second investment. The standard deviation of the portfolio return is given by P =



w12 12 + w22 22 + 2 w1 w2 1 2

(1.2)

where 1 and 2 are the standard deviations of R1 and R2 and  is the coefficient of correlation between the two. Suppose that 1 is 10% per annum and 1 is 16% per annum while 2 is 15% per annum and 2 is 24% per annum. Suppose also that the coefficient of correlation,  , between the returns is 0.2 or 20%. Table 1.2 shows the values of  P and P for a number of different values of w1 and w2 . The calculations show that by putting part of your money in the first investment and part in the second investment a wide range of risk-return combinations can be achieved. These are plotted in Figure 1.2. Most investors are risk-averse. They want to increase expected return while reducing the standard deviation of return. This means that they want to move as far as they can in a “northwest” direction in Figures 1.1 and 1.2. Figure 1.2 shows that forming a portfolio of the two investments we have been considering helps them do this. For example, by putting 60% in the first investment and 40% in the second, a portfolio with an expected return of 12% and a standard deviation of return equal to 14.87% is obtained. This is an improvement over the risk-return trade-off for the

TABLE 1.2 Expected Return,  P , and Standard Deviation of Return, P , from a Portfolio Consisting of Two Investments w1

w2

P

P

0.0 0.2 0.4 0.6 0.8 1.0

1.0 0.8 0.6 0.4 0.2 0.0

15% 14% 13% 12% 11% 10%

24.00% 20.09% 16.89% 14.87% 14.54% 16.00%

The expected returns from the investments are 10% and 15%; the standard deviation of the returns are 16% and 24%; and the correlation between returns is 0.2.


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16

Expected return (%)

14 12 10 8 6 4 2 Standard deviation of return (%) 0 0

5

10

15

20

25

30

FIGURE 1.2 Alternative Risk-Return Combinations from Two Investments (as Calculated in Table 1.2)

first investment. (The expected return is 2% higher and the standard deviation of the return is 1.13% lower.)

1.2 THE EFFICIENT FRONTIER Let us now bring a third investment into our analysis. The third investment can be combined with any combination of the first two investments to produce new riskreturn combinations. This enables us to move further in the northwest direction. We can then add a fourth investment. This can be combined with any combination of the first three investments to produce yet more investment opportunities. As we continue this process, considering every possible portfolio of the available risky investments, we obtain what is known as an efficient frontier. This represents the limit of how far we can move in a northwest direction and is illustrated in Figure 1.3. There is no investment that dominates a point on the efficient frontier in the sense that it has both a higher expected return and a lower standard deviation of return. The area southeast of the efficient frontier represents the set of all investments that are possible. For any point in this area that is not on the efficient frontier, there is a point on the efficient frontier that has a higher expected return and lower standard deviation of return. In Figure 1.3 we have considered only risky investments. What does the efficient frontier of all possible investments look like? Specifically, what happens when we include the risk-free investment? Suppose that the risk-free investment yields a return of RF . In Figure 1.4 we have denoted the risk-free investment by point F and drawn a


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Expected return

Efficient frontier

Individual risky investments

Standard deviation of return

FIGURE 1.3 Efficient Frontier Obtainable from Risky Investments

Expected return

. J

New efficient frontier

E(RJ)

Previous efficient frontier

.

M E(RM)

. I

E(RI) RF

.

F

Standard deviation of return βI σM

σM

βJ σM

FIGURE 1.4 The Efficient Frontier of All Investments Point I is achieved by investing a percentage I of available funds in portfolio M and the rest in a risk-free investment. Point J is achieved by borrowing J − 1 of available funds at the risk-free rate and investing everything in portfolio M.


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Introduction

tangent from point F to the efficient frontier of risky investments that was developed in Figure 1.3. M is the point of tangency. As we will now show, the line F J is our new efficient frontier. Consider what happens when we form an investment I by putting I of the funds we have available for investment in the risky portfolio, M, and 1 − I in the risk-free investment F (0  I  1). From equation (1.1) the expected return from the investment, E(RI ), is given by E(RI ) = (1 − I )RF + I E(RM ) and from equation (1.2), because the risk-free investment has zero standard deviation, the return RI has standard deviation I M where M is the standard deviation of return for portfolio M. This risk-return combination corresponds to the point labeled I in Figure 1.4. From the perspective of both expected return and standard deviation of return, point I is I of the way from F to M. All points on the line F M can be obtained by choosing a suitable combination of the investment represented by point F and the investment represented by point M. The points on this line dominate all the points on the previous efficient frontier because they give a better risk-return combination. The straight line F M is therefore part of the new efficient frontier. If we make the simplifying assumption that we can borrow at the risk-free rate of RF as well as invest at that rate, we can create investments that are on the continuation of FM beyond M. Suppose, for example, that we want to create the investment represented by the point J in Figure 1.4 where the distance of J from F is J times the distance of M from F (J  1). We borrow J − 1 of the amount that we have available for investment at rate RF and then invest everything (the original funds and the borrowed funds) in the investment represented by point M. After allowing for the interest paid, the new investment has an expected return, E(RJ ) given by E(RJ ) = J E(RM ) − (J − 1)RF and the standard deviation of the return is J M This shows that the risk and expected return combination corresponds to point J . The argument that we have presented shows that, when the risk-free investment is considered, the efficient frontier must be a straight line. To put this another way there should be linear trade-off between the expected return and the standard deviation of returns, as indicated in Figure 1.4. All investors should choose the same portfolio of risky assets. This is the portfolio represented by M. They should then reflect their appetite for risk by combining this risky investment with borrowing or lending at the risk-free rate.


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It is a short step from here to argue that the portfolio of risky investments represented by M must be the portfolio of all risky investments. Suppose a particular investment is not in the portfolio. No investors would hold it and its price would have to go down so that its expected return increased and it became part of portfolio M. In fact, we can go further than this. To ensure a balance between the supply and demand for each investment, the price of each risky investment must adjust so that the amount of that investment in portfolio M is proportional to the amount of that investment available in the economy. The investment represented by point M is therefore usually referred to as the market portfolio.

1.3 THE CAPITAL ASSET PRICING MODEL How do investors decide on the expected returns they require for individual investments? Based on the analysis we have presented, the market portfolio should play a key role. The expected return required on an investment should reflect the extent to which the investment contributes to the risks of the market portfolio. A common procedure is to use historical data to determine a best-fit linear relationship between returns from an investment and returns from the market portfolio. This relationship has the form: R = a +  RM + 

(1.3)

where R is the return from the investment, RM is the return from the market portfolio, a and  are constants, and  is a random variable equal to the regression error. Equation (1.3) shows that there are two uncertain components to the risk in the investmentâ&#x20AC;&#x2122;s return: 1. A component  RM , which is a multiple of the return from the market portfolio. 2. A component , which is unrelated to the return from the market portfolio. The first component is referred to as systematic risk. The second component is referred to as nonsystematic risk. Consider first the nonsystematic risk. If we assume that the s for different investments are independent of each other, the nonsystematic risk is almost completely diversified away in a large portfolio. An investor should not therefore be concerned about nonsystematic risk and should not require an extra return above the risk-free rate for bearing nonsystematic risk. The systematic risk component is what should matter to an investor. When a large well-diversified portfolio is held, the systematic risk represented by  RM does not disappear. An investor should require an expected return to compensate for this systematic risk. We know how investors trade off systematic risk and expected return from Figure 1.4. When  = 0 there is no systematic risk and the expected return is RF . When  = 1, we have the same systematic risk as the market portfolio, which is represented by point M, and the expected return should be E(RM ). In general E(R) = RF + [E(RM ) â&#x2C6;&#x2019; RF ]

(1.4)


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Expected return, E(R)

E(R) = RF + β[E(RM) − RF]

E(RM)

RF

Beta, β 1.0

FIGURE 1.5 The Capital Asset Pricing Model

This is the capital asset pricing model. The excess expected return over the risk-free rate required on the investment is  times the excess expected return on the market portfolio. This relationship is plotted in Figure 1.5. The parameter  is the beta of the investment. EXAMPLE 1.1 Suppose that the risk-free rate is 5% and the return on the market portfolio is 10%. An investment with a beta of 0 should have an expected return of 5%. This is because all of the risk in the investment can be diversified away. An investment with a beta of 0.5 should have an expected return of 0.05 + 0.5 × (0.1 − 0.05) = 0.075 or 7.5%. An investment with a beta of 1.2 should have an expected return of 0.05 + 1.2 × (0.1 − 0.05) = 0.11 or 11%. The parameter, , is equal to  /M where  is the correlation between the return from the investment and the return from the market portfolio,  is the standard deviation of the return from the investment, and M is the standard deviation of the return from the market portfolio. Beta measures the sensitivity of the return from the investment to the return from the market portfolio. We can define the beta of any investment portfolio as in equation (1.3) by regressing its returns against the returns


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from the market portfolio. The capital asset pricing model in equation (1.4) should then apply with the return R defined as the return from the portfolio. In Figure 1.4 the market portfolio represented by M has a beta of 1.0 and the riskless portfolio represented by F has a beta of zero. The portfolios represented by the points I and J have betas equal to I and J , respectively.

Assumptions The analysis we have presented leads to the surprising conclusion that all investors want to hold the same portfolios of assets (the portfolio represented by M in Figure 1.4.) This is clearly not true. Indeed, if it were true, markets would not function well at all because investors would not want to trade with each other! In practice, different investors have different views on the attractiveness of stocks and other risky investment opportunities. This is what causes them to trade with each other and it is this trading that leads to the formation of prices in markets. The reason why the analysis leads to conclusions that do not correspond with the realities of markets is that, in presenting the arguments, we implicitly made a number of assumptions. In particular: 1. We assumed that investors care only about the expected return and the standard deviation of return of their portfolio. Another way of saying this is that investors look only at the first two moments of the return distribution. If returns are normally distributed, it is reasonable for investors to do this. However, the returns from many portfolios are non-normal. They have skewness and excess kurtosis. Skewness is related to the third moment of the distribution and excess kurtosis is related to the fourth moment. In the case of positive skewness, very high returns are more likely and very low returns are less likely than the normal distribution would predict; in the case of negative skewness, very low returns are more likely and very high returns are less likely than the normal distribution would predict. Excess kurtosis leads to a distribution where both very high and very low returns are more likely than the normal distribution would predict. Most investors are concerned about the possibility of extreme negative outcomes. They are likely to want a higher expected return from investments with negative skewness or excess kurtosis. 2. We assumed that the s for different investments in equation (1.3) are independent. Equivalently we assumed the returns from investments are correlated with each other only because of their correlation with the market portfolio. This is clearly not true. Ford and General Motors are both in the automotive sector. There is likely to be some correlation between their returns that does not arise from their correlation with the overall stock market. This means that their s are not likely to be independent of each other. 3. We assumed that investors focus on returns over just one period and the length of this period is the same for all investors. This is also clearly not true. Some investors such as pension funds have very long time horizons. Others such as day traders have very short time horizons. 4. We assumed that investors can borrow and lend at the same risk-free rate. This is approximately true for a large financial institution in normal market conditions with a good credit rating. But it is not true for small investors.


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5. We did not consider tax. In some jurisdictions, capital gains are taxed differently from dividends and other sources of income. Some investments get special tax treatment and not all investors are subject to the same tax rate. In practice, tax considerations have a part to play in the decisions of an investor. An investment that is appropriate for a pension fund that pays no tax might be quite inappropriate for a high-marginal-rate taxpayer living in New York, and vice versa. 6. Finally, we assumed that all investors make the same estimates of expected returns, standard deviations of returns, and correlations between returns for available investments. To put this another way, we assumed that investors have homogeneous expectations. This is clearly not true. Indeed, as indicated earlier, if we lived in a world of homogeneous expectations there would be no trading. In spite of all this, the capital asset pricing model has proved to be a useful tool for portfolio managers. Estimates of the betas of stocks are readily available and the expected return on a portfolio estimated by the capital asset pricing model is a commonly used benchmark for assessing the performance of the portfolio manager, as we will now explain.

Alpha When we observe a return of RM on the market, what do we expect the return on a portfolio with a beta of  to be? The capital asset pricing model relates the expected return on a portfolio to the expected return on the market. But it can also be used to relate the expected return on a portfolio to the actual return on the market: E(RP ) = RF + (RM − RF ) where RF is the risk-free rate and RP is the return on the portfolio. EXAMPLE 1.2 Consider a portfolio with a beta of 0.6 when the risk-free interest rate is 4%. When the return from the market is 20%, the expected return on the portfolio is 0.04 + 0.6 × (0.2 − 0.04) = 0.136 or 13.6%. When the return from the market is 10%, the expected return from the portfolio is 0.04 + 0.6 × (0.1 − 0.04) = 0.076 or 7.6%. When the return from the market is −10%, the expected return from the portfolio is 0.04 + 0.6 × (−0.1 − 0.04) = −0.044


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20

Expected return on portfolio (%)

15 10 5 –30

–20

–10

0 –5

Return on market (%) 0

10

20

30

–10 –15 –20

FIGURE 1.6 Relation between Expected Return on Portfolio and the Actual Return on the Market When Portfolio Beta is 0.6 and Risk-Free Rate is 4% or −4.4%. The relationship between the expected return on the portfolio and the return on the market is shown in Figure 1.6. Suppose that the actual return on the portfolio is greater than the expected return: RP  RF + (RM − RF ) The portfolio manager has produced a superior return for the amount of systematic risk being taken. The extra return is  = RP − RF − (RM − RF ) This is commonly referred to as the alpha created by the portfolio manager. EXAMPLE 1.3 A portfolio manager has a portfolio with a beta of 0.8. The one-year risk-free rate of interest is 5%, the return on the market during the year is 7%, and the portfolio manager’s return is 9%. The manager’s alpha is  = 0.09 − 0.05 − 0.8 × (0.07 − 0.05) = 0.024 or 2.4%. Portfolio managers are continually searching for ways of producing a positive alpha. One way is by trying to pick stocks that outperform the market. Another is by market timing. This involves trying to anticipate movements in the market as a


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whole and moving funds from safe investments such as Treasury bills to the stock market when an upturn is anticipated and in the other direction when a downturn is anticipated. Chapter 4 explains other strategies used by hedge funds to try to create positive alpha. Although the capital asset pricing model makes simplifying assumptions, the alpha and beta parameters that come out of the model are widely used to characterize investments. Beta describes the return obtained from taking systematic risk. The higher the value of beta, the greater the systematic risk being taken and the greater the extent to which returns are dependent on the performance of the market. Alpha represents the extra return made from superior portfolio management (or perhaps just good luck). An investor can make a positive alpha only at the expense of other investors who are making a negative alpha. The weighted average alpha of all investors is zero.

1.4 ARBITRAGE PRICING THEORY Arbitrage pricing theory can be viewed as an extension of the capital asset pricing model. The return from an investment is assumed to depend on several factors. (These factors might involve variables such as the gross national product, the domestic interest rate, and the inflation rate.) By exploring ways in which investors can form portfolios that eliminate their exposure to the factors, arbitrage pricing theory shows that the expected return from an investment is linearly dependent on the factors. The assumption that the s for different investments are independent in the equation (1.3) ensures that there is just one factor driving expected returns (and therefore one source of systematic risk) in the capital asset pricing model. This is the return from the market portfolio. In arbitrage pricing theory there are several factors affecting investment returns. Each factor is a separate source of systematic risk. Unsystematic (i.e., diversifiable) risk in arbitrage pricing theory is the risk that is unrelated to all the factors.

1.5 RISK VS. RETURN FOR COMPANIES We now move on to consider the trade-offs between risk and return made by a company. How should a company decide whether the expected return on a new investment project is sufficient compensation for its risks? The ultimate owners of a company are its shareholders and a company should be managed in the best interests of its shareholders. It is therefore natural to argue that a new project undertaken by the company should be viewed as an addition to its shareholderâ&#x20AC;&#x2122;s portfolio. The company should calculate the beta of the investment project and its expected return. If the expected return is greater than that given by the capital asset pricing model, it is a good deal for shareholders and the investment should be accepted. Otherwise it should be rejected. The argument just given suggests that nonsystematic risks should not be considered when accept/reject decisions on new projects are taken. In practice of course, companies are concerned about nonsystematic as well as systematic risks. For example, most companies insure themselves against the risk of their buildings being


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burned down—even though this risk is entirely nonsystematic and can be diversified away by their shareholders. They try to avoid taking high risks and often hedge their exposures to exchange rates, interest rates, commodity prices, and other market variables. Earnings stability and the survival of the company are important managerial objectives. Companies do try and ensure that their expected returns on new ventures are consistent with the risk-return trade-offs of their shareholders. But there is an overriding constraint that the total risks taken should not be allowed to get too large. Most investors are also concerned about the overall risk of the companies they invest in. They do not like surprises and prefer to invest in companies that show solid growth and meet earnings forecasts. They like companies to manage risks carefully and limit the overall amount of risk—both systematic and nonsystematic—they are taking. The theoretical arguments we presented in Sections 1.1 to 1.4 suggest that investors should not behave in this way. They should hold a well-diversified portfolio and encourage the companies they invest in to make high risk investments when the combination of expected return and systematic risk is favorable. Some of the companies in a shareholder’s portfolio will go bankrupt, but others will do very well. The result should be an overall return to the shareholder that is satisfactory. Are investors behaving suboptimally? Would their interests be better served if companies took more nonsystematic risks? There is an important argument to suggest that this is not necessarily the case. This argument is usually referred to as the “bankruptcy costs” argument. It is often used to explain why a company should restrict the amount of debt it takes on, but it can be extended to apply to a wider range of risk management decisions than this.

Bankruptcy Costs In a perfect world, bankruptcy would be a fast affair where the company’s assets (tangible and intangible) are sold at their fair market value and the proceeds are distributed to bondholders, shareholders, and other stake holders using well-defined rules. If we lived in such a perfect world, the bankruptcy process itself would not destroy value for shareholders. Unfortunately, the real world is far from perfect. By the time a company reaches the point of bankruptcy, it is likely that its assets have lost some value. The bankruptcy process itself invariably reduces the value of its assets further. This further reduction in value is referred to as bankruptcy costs. What is the nature of bankruptcy costs? Once a bankruptcy has been announced customers and suppliers become less inclined to do business with the company; assets sometimes have to be sold quickly at prices well below those that would be realized in an orderly sale; the value of important intangible assets such as the company’s brand name and its reputation in the market are often destroyed; the company is no longer run in the best interests of shareholders; large fees are often paid to accountants and lawyers; and so on. The story in Business Snapshot 1.1 is representative of what often happens in practice. It illustrates how, when a high risk decision works out badly, there can be disastrous bankruptcy costs.


Counterparty Credit Risk and Credit Value Adjustment, 2nd Edition A Continuing Challenge for Global Financial Markets Jon Gregory 978-1-118-31667-2 • Hardback • 480 pages • August 2012

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1 Introduction

MA TE RI

AL

If history repeats itself, and the unexpected always happens, how incapable must Man be of learning from experience. George Bernard Shaw (1856–1950)

CO P

YR

IG H

TE

D

Between 2004 and 2006, US interest rates rose from 1% to over 5%, triggering a slowdown in the US housing market. Many homeowners, who had been barely able to afford their payments when interest rates were low, began to default on their mortgages. Default rates on subprime loans (made to those with a poor or no credit history) hit record levels. US households had also become increasingly in debt, with the ratio of debt to disposable personal income rising. Many other countries (although not all) had ended up in a similar situation. Years of poor underwriting standards and cheap debt were about to catalyse a global financial crisis. Many of the now toxic US subprime loans were held by US retail banks and mortgage providers such as Fannie Mae and Freddie Mac. However, the market had been allowed to spread due to the fact that the underlying mortgages had been packaged up into complex structures (using financial engineering techniques), such as mortgage-backed securities (MBSs), which had been given good credit ratings from the rating agencies. As a result, the underlying mortgages ended up being held by institutions that did not originate them, such as investment banks and institutional investors outside the US. Financial engineering had created a global exposure to US mortgages. In mid-2007, a credit crisis began, caused primarily by the systematic mispricing of US mortgages and MBSs. Whilst this caused excessive volatility in the credit markets (which had been quiet for a number of years), it was not believed to be a severe financial crisis (for example, the stock market did not react particular badly). The crisis, however, did not go away. In July 2007, Bear Stearns informed investors they would get very little of their money back from two hedge funds due to losses in subprime mortgages. In August 2007, BNP Paribas told investors that they would be unable to take money out of two funds because the underlying assets could not be valued due to “a complete evaporation of liquidity in the market”. Basically, this meant that the assets could not be sold at any reasonable price. In September 2007, Northern Rock, a British Bank, sought emergency funding from the Bank of England as a “lender of last resort”. This prompted the first run on a bank1 for over a

1 This occurs when a large number of customers withdraw their deposits because they believe the bank is, or might become, insolvent.

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century. Northern Rock, in 2008, would be taken into state ownership to save depositors and borrowers. By the end of 2007, some insurance companies, known as “monolines”, were in serious trouble. Monolines provided insurance to banks on mortgage and other related debt. The Triple-A ratings of monolines had meant that banks were not concerned with a potential monoline default, despite the obvious misnomer that a monoline insurance company appeared to represent. Banks’ willingness to ignore the counterparty risk had led them to build up large monoline exposures without the requirement for monolines to post collateral, at least as long as they maintained their excellent Triple-A credit ratings. However, monolines were now reporting large losses and making it clear that any downgrading of their credit ratings may trigger collateral calls that they would not be able to make. Such downgrades began in December 2007 and banks were forced to take losses totalling billions of dollars due to the massive counterparty risk they now faced. This was a particularly bad form of counterparty risk, known as wrong-way risk, where the exposure to a counterparty and their default probability were inextricably linked. By the end of 2007, although not yet known, the US economy was in recession and many other economies would follow. The crisis was now affecting the general public and yet this was only the tip of the iceberg. In March 2008, Bear Stearns was purchased by JP Morgan Chase for just $2 a share, assisted by a loan of tens of billions of dollars from the Federal Reserve, who were essentially taking $30 billion of losses from the worst Bear Stearns assets to catalyse the sale. This clearly represented a form of bailout, with the US taxpayer essentially funding some of the purchase of Bear Stearns. The sale price of Bear Stearns was shocking, considering that it had been trading at $93 a share only a month previously. Something was clearly going very wrong. In early September 2008, mortgage lenders Fannie Mae and Freddie Mac, who combined accounted for over half the outstanding US mortgages, were placed into conservatorship (a sort of short-term nationalisation) by the US Treasury. Treasury secretary Henry Paulson stated that the combined debt levels posed a “systemic risk” to financial stability. In September 2008 the unthinkable happened when Lehman Brothers, a global investment bank and the fourth largest investment bank in the US with a century-long tradition, filed for Chapter 11 bankruptcy protection (the largest in history). This occurred after teams of bankers failed during the weekend spent in the Federal Reserve Building to agree any better solution, in particular with Barclays and Bank of America pulling out of buying Lehman. The US government was reluctant to rescue Lehman due to the moral hazard that such bailouts encourage. The bankruptcy of Lehman had not been anticipated, with all major rating agencies (Moody’s, Standard & Poor’s and Fitch) all giving at least a Single-A rating right up to the point of Lehman’s failure and the credit derivative market not pricing an actual default. Saving Lehman’s would have cost the US taxpayer again and exasperated moral hazard problems since a bailout of Lehman’s would not punish their excessive risk taking (their exposure to the mortgage market and risky behaviour in understating the need for new funding). However, a Lehman default was not an especially pleasant prospect either. Firstly, there was estimated to be around $400 billion of credit default swap (CDS) insurance written on Lehman Brothers debt. Since the debt was now close to worthless, this would trigger massive payouts on the underlying CDS contracts and yet the opacity of the OTC derivatives market meant that it was not clear who actually owned most of the CDS referencing Lehman.

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5

Another counterparty might now have financial problems due to suffering large losses because of providing CDS protection on Lehman. Secondly, Lehman had around one and a half million derivatives trades with around 8,000 different counterparties that all needed to be unwound, a process that would take years and lead to many legal proceedings. Most counterparties probably never considered that their counterparty risk to Lehman’s was a particular issue nor did they realise that the failure of counterparty risk mitigation methods such as collateral and special purpose vehicles (SPVs) would lead to legal problems. On the same day as Lehman’s failed, Bank of America agreed a $50 billion rescue of Merrill Lynch. Soon after the remaining two investment banks, Morgan Stanley and Goldman Sachs, opted to become commercial banks. Whilst this would subject them to more strict regulation, it allowed full access to the Federal Reserve’s lending facilities and prevented them suffering the same fate as the bankrupt Lehman Brothers or the sold Bear Stearns or Merrill Lynch. In case September 2008 was not exciting enough, the US government provided American International Group (AIG) with loans of up to $85 billion in exchange for a four-fifths stake in AIG.2 Had AIG been allowed to fail through bankruptcy, not only would bondholders have suffered but also their derivative counterparties (the major banks) would have experienced significant losses. Prior to the crisis, the counterparty risk of AIG was typically considered minimal due to their size, excellent credit rating and the fact that (unlike monoline insurers) they did post collateral. The reason for the rescue of AIG and non-rescue of monolines was partly timing – the AIG situation occurred at the same time as the Lehman bankruptcy and immediately after the Fannie Mae and Freddie Mac rescues. However, another important fact was that AIG had an exposure that was not dissimilar to the total exposure of the monoline insurers but concentrated within a single financial entity. AIG was “too big to fail”. Three of the largest US investment banks had now either gone bankrupt (Lehman Brothers) or been sold at fire sale prices to other banks (Bear Stearns and Merrill Lynch). The remaining two had given up their prized investment bank status to allow them to be bailed out. Later in September 2008 Washington Mutual, America’s biggest savings and loan company, was sold to JP Morgan for $1.9 billion and their parent company, Washington Mutual Inc., filed for Chapter 11 bankruptcy protection. A CDS contract purchased from any of the aforementioned US banks on any of the other US banks was now clearly seen to have enormous, almost comical amounts of wrong-way counterparty risk. By now, trillions of dollars had simply vanished from the financial markets and therefore the global economy. Whilst this was related to the mispricing of mortgage risk, it was also significantly driven by the recognition of counterparty risk. On October 6, the Dow Jones Industrial Average dropped more than 700 points and fell below 10,000 for the first time in four years. The systemic shockwaves arising from the failure of the US banking giants led to the Troubled Asset Relief Program (TARP) of not too much short of $1 trillion to purchase distressed assets and support failing banks. In November 2008, Citigroup, prior to the crisis the largest bank in the world but now reeling following a dramatic plunge in its share price, needed TARP assistance, via a $20 billion cash injection and government backing for around $300 billion of loans. The contagion had spread far beyond the US. In early 2009, the Royal Bank of Scotland (RBS) reported a loss of £24.1 billion, the biggest in British corporate history. The majority of this loss was borne by the British government, now the majority owner of RBS, having 2

AIG would receive further bailouts.

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paid ÂŁ45 billion3 to rescue RBS in October 2008. In November 2008 the International Monetary Fund (IMF), together with other European countries, approved a $4.6 billion loan for Iceland after the countryâ&#x20AC;&#x2122;s banking system collapsed in October. This was the first IMF loan to a Western European nation since 1976. From late 2009, fears of a sovereign debt crisis developed in Europe driven by high debt levels and a downgrading of government debt in some European states. In May 2010, Greece received a D 110 billion bailout from Eurozone countries and the IMF. Greece was to be bailed out again and support was also given to other Eurozone sovereign entities, notably Portugal, Ireland and Spain. Banks again were heavily exposed to potential failures of European sovereign countries. Again, the counterparty risk of such entities had been considered low but was now extremely high and made worse by the fact that sovereign entities generally did not post collateral. By now, it was clear that no counterparty (Triple-A entities, global investment banks, retail banks, sovereigns) could ever be regarded as risk-free. Counterparty risk, previously hidden via spurious credit ratings, collateral or legal assumptions, was now present throughout the global financial markets. CVA (credit value adjustment), which defined the price of counterparty risk, had gone from a rarely used technical term to a buzzword constantly associated with financial markets. The pricing of counterparty risk into trades (via a CVA charge) was now becoming the rule and not the exception. Whilst the largest investment banks had built trading desks and complex systems and models around managing CVA, all banks (and some other financial institutions and large derivatives users) were now focused on expanding their capabilities in this respect. By 2009, new fast-tracked financial regulation was beginning to take shape around the practices of banks. The Basel III global regulatory standard (developed in direct response to the crisis) was introduced to strengthen bank capital bases and introduce new requirements on liquidity and leverage. The US Doddâ&#x20AC;&#x201C;Frank Wall Street Reform and Consumer Protection Act 2009 and European Market Infrastructure Regulation (EMIR) were aimed at increasing the stability of the over-the-counter (OTC) derivative markets. Regulatory response to the global financial crisis (as it was now known) revolved very much around counterparty credit risk, with the volatility of CVA, collateral management and wrongway risk all receiving attention. The regulatory focus on CVA seemed to encourage active hedging of counterparty risk so as to obtain capital relief. However, the market that would be most important for such hedging, credit derivatives, was having its own problems. Whilst credit derivatives, such as single-name and index credit default swaps, allowed counterparty risk transfer, being OTC instruments, they also introduced their own form of counterparty risk, which was the wrongway type highlighted by the monoline failures. Indeed, the CDS market was almost seizing up due to this severe wrong-way risk. Counterparty risk was the principle linkage among participants in the CDS market that could cause systemic failures. Regulatory proposals to deal with this problem involved pushing heavily towards the central clearing of certain standard OTC derivatives, notably CDSs. Whilst, prior to the crisis, much of the interest rate swap market was already moving towards central clearing, without regulatory intervention the CDS market was arguably years away. Whilst central counterparties (CCPs) provided advantages such as transparency that the OTC derivatives market clearly lacked, this also introduced the question of what would 3

Hundreds of billions of pounds were provided in the form of loans and guarantees.

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happen if a CCP ever failed. Since CCPs were likely to take over from the likes of Lehman, Citigroup and AIG as the hubs of the complex financial network, such a question was clearly key, and yet not particularly extensively discussed. Furthermore, other potential unintended consequences of increased regulation on counterparty risk could be seen as early as 2010 when, for example, the Bank of England commented that “CVA desks” hedging counterparty risk were causing European sovereign spreads to widen “away from levels solely reflecting the underlying probability of sovereign default”.4 Although the need to ensure investment banks were better capitalised for risk taking was not under debate, arguments developed over the correct level of capitalisation and the potential adverse and unintended consequences of new regulation. At the same time as a renewed focus on counterparty risk, other changes in derivatives markets were taking place. A fundamental assumption in the pricing of derivative securities had always been that the risk-free rate could be appropriately proxied by LIBOR. However, practitioners realised that the OIS (overnight indexed spread) was actually a better proxy for the risk-free rate. The LIBOR–OIS spread had historically hovered around 10 basis points, showing a close linkage. However, this close relationship had broken down, even spiking to around 350 basis points around the Lehman bankruptcy. This showed that even the simplest types of derivative, which had been priced in the same way for decades, needed to be valued differently, in a more sophisticated manner. Since CVA is an adjustment to the risk-free value of a transaction, this topic was clearly closely related to counterparty risk. Another, almost inevitable dynamic was that the spreads of banks (i.e., where they could borrow unsecured cash on a longer term than in a typical LIBOR transaction) had increased. Historically, this borrowing cost of a bank was in the region of a few basis points but had now entered the realms of hundreds of basis points in most cases. It was clear that these now substantial funding costs should be quantified alongside CVA. The cost of funding was named FVA (funding value adjustment). Funding costs were also clearly linked to counterparty risk in terms of the calculation and also their similarity to something now known as DVA (debt value adjustment). DVA for some banks was the only silver lining of the counterparty risk cloud. DVA allowed banks to account for their own default in the value of transactions and therefore acted to counteract counterparty risk-related losses due to an increase in CVA driven by the widening credit spread environment. However, many commentators believed this to be nothing more than an accounting trick as banks reported billions of dollars of profits from DVA simply due to the fact that their own credit spread implied they were more likely to default in the future. Basel III capital rules moved to remove DVA benefits to avoid effects such as “an increase in a bank’s capital when its own creditworthiness deteriorates”. The net result of the financial crisis and the impact of regulation led banks to consider the joint impact of risk-free valuation, counterparty risk and funding costs in the valuation of derivatives. Not surprisingly, the increase in funding costs and counterparty risk naturally led banks to tighten up collateral requirements. However, this created a knock-on effect for typical end-users of derivatives that historically had not been able or willing to enter into collateral agreement for liquidity and operational reasons. Some sovereign entities considered posting collateral, not only to avoid the otherwise large CVA and funding costs levied upon them, but also to avoid the issue that banks hedging their counterparty risk may buy CDS protection on them, driving their credit spread wider and potentially causing them 4

This would trigger the consideration of a sovereign exemption with respect to CVA capital charges.

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more problems. A sovereign posting their own bonds in collateral would ease the problems but this would not be the ideal answer due to another manifestation of wrong-way risk. Furthermore, corporates other than non-collateral posting entities had issues, for example an airline predicted more volatile earnings “not because of unpredictable passenger numbers, interest rates or jet fuel prices, but because it does not post collateral in its derivatives transactions”.5 End-users of derivatives, although not responsible, were now being hit as badly as the orchestrators of the financial crisis. Meanwhile, many taxpayers were experiencing poor economic conditions and counting the cost of bailouts via higher taxes and reduced government spending. Businesses and individuals were struggling to borrow money from the heavily capitalised banks. All of this was created by a crisis fuelled to a large extent by counterparty risk. Because of the above, counterparty risk has become a major subject for global financial markets. It is necessary to consider how to define and quantify counterparty risk. Counterparty risk mitigation methods need to be understood, and their side-effects and any residual risks need to be defined. The question of the role of central counterparties must be examined, alongside the consideration of the risks they will represent. It is important to define how CVA can be quantified and managed, together with other related components such as DVA and FVA. Wrong-way risk must be understood and mitigated or avoided completely. The role and positioning of a CVA desk within a bank or other institution must be defined. The regulation around counterparty risk must be understood, together with the likely impact this will have on banks and the financial markets in which they operate. Finally, the consideration of how all of the above changes are likely to define counterparty risk practices in the future is important. If any of the above are of interest, then please read on.

5

“Corporates fear CVA charge will make hedging too expensive”, Risk, October 2011.

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Emerging Markets in an Upside Down World Challenging Perceptions in Asset Allocation and Investment Jerome Booth 978-1-118-87967-2 • Hardback • 336 pages • March 2014

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1 Globalisation and the Current Global Economy ‘Globalisation should not be just about interconnecting the bell jars of the privileged few.’ De Soto (2000, p. 219) ‘The benefits of globalization of trade in goods and services are not controversial among economists. Polls of economists indicate that one of [the] few things on which they agree is that the globalization of international trade, in which markets are opened to flows of foreign goods and services, is desirable. But financial globalization, the opening up to flows of foreign capital, is highly controversial, even among economists …’ Mishkin (2006) In this chapter we discuss some of the background to attitudes towards money and debt. We explore the historical erosion of despotic power. We aim to understand globalisation, both ancient and modern, identifying the trends most important for current events and policy actions.

1.1

What is globalisation?

Globalisation has been through a number of cycles including in the nineteenth century period of free trade.1 The term requires careful use: its range and ambiguity in common parlance can cause misunderstanding. Globalisation is both a state and a process. It has an economic facet, perhaps best described as the greater interconnectedness of trade and investment as transactions costs and barriers reduce, but also the idea of lack of constraint on markets by government. It is this element that investors are ultimately most interested in. But globalisation also has a technological aspect (not distinct from the economic aspect), notably as represented recently by innovations and speed in modern communications. And it has a cultural facet, as exposed in the spread of common means of entertainment and ideas. It homogenises, and through standardisation commodifies, but also creates diversity of choice; complicates and simplifies; brings benefits and conflicts; produces winners and losers. For emerging markets today, globalisation accelerates convergence to the living standards of developed markets. For some, in a world in which the voices of those with something to lose are louder than those who gain, the term is laced with emotive content, often negative, and while it creates jobs and wealth, globalisation is, for many, associated with job losses and erosion of local values. 1 The term has many definitions and while Findlay and O’Rourke (2007, p. 108) argue that globalisation may have begun with the Mongol unification of the Eurasian land mass, that process is a distant shadow of what is called globalisation today.

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Ridley (2010) argues that, among other things, it was trade which propagated innovation, technology and civilisation, as do Findlay and O’Rourke (2007). Jane Jacobs in her book Systems of Survival (1992) uses a Platonic dialogue to describe the different logics of politics, which is a zero-sum game, and commerce, a positive-sum game. Nations have historically competed for scarce territory, which, if one gained, another must lose; whereas both parties gain from a trade freely entered into. If we want to avoid conflicts, commerce has a positive role to play. It is no mere historical coincidence that periods of protectionism and limited international trade often precede wars. The failed logic of isolationism and of fighting over land and other limited resources leads from mercantilism to gunboats, to strategic invasions of third countries, and to empire. Empires fall, however, or at best are managed into relative decline. The human tendency to barter and trade is certainly older than recorded history, and has long been geographically broad in extent. Though this is a generalisation, in the progress of greater economic interconnectedness there are waves, affected by human policy and history, as well as trends, driven by technology. Wars of the ‘hard’ and trade variety, restrictions on economic activity and trade, mass migration and natural disasters have all been disruptive but also sometimes stimulate innovation and new forms of economic activity. In contrast, political stability and incentive structures compatible with innovation have generally nurtured both existing patterns in trade and globalisation. Braudel (1998) in his history of the ancient Mediterranean world argues that early transhumance (seasonal migration between summer and winter pastures) established a pattern of seasonal trade in the region. The world has clearly seen ebbs and flows in the extent of trade links and civilisations. Toynbee (1946) and others have categorised the rise and fall of civilisations, and with them trade and international links. The story of lack of stability wreaking havoc on economies and trade has repeated itself many times. Globalisation can and does ebb as well as flow. Technology has reversed on occasion as inventions have been forgotten once civilisations collapse. Our European Renaissance is in name a rediscovery. Arguably, however, it takes the destruction of civilisation to reverse technology, and in the modern era, as during periods of stability within earlier civilisations, it has been tenacious and non-reversible. Technology profoundly impacts globalisation. It can aid economic growth, productivity and, by reducing transport costs, trade. Technology, by changing relative prices, also changes our institutions, as Douglass North (1990) has taught us. For example, technology effects disruptive upheavals in communication from time to time. Neil Postman (1985) has described how the written word, printing and then newspapers changed the pace and nature of interconnectedness. For example, in the 19th century, the telegram helped create the commercial success of newspapers and their news – the interest and novelty of new information from a long distance being of interest primarily, if not solely, because it was new. This ‘news’ content eroded and then eclipsed more considered thought, telescoping cultural knowledge and political debate to focus more heavily on the near present. Thus with the telegram came the modern newspapers, and with them came trivia, including the invention of the crossword puzzle – to test the reader’s knowledge of news trivia. Subsequently broadcasting has impacted our communication patterns: for example, in the 1850s US presidential candidates would deliver speeches several hours long in public debates, long enough to justify meal breaks. That voters would spend the time to listen to such debates, and that they could comprehend the complex structured paragraphs which were so characteristic, stands in stark contrast to the norm of exchange so typical today.

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Have we since ‘dumbed down’, and does the process of globalisation contain a series of dumbing-down episodes? Not entirely: the telegram, newspapers and then radio and television created a breadth of participation in culture not previously experienced. Political debates became less elitist and more inclusive, with more elite communication and interaction continuing, but less dominantly – less unchallenged. The perception of dumbing down, and indeed the collapse of our sense of history to a more myopic immediate past, is clearly a strong one but not just a 19th-century one. The impact of television is an issue studied by Postman and especially in the post-Second-World-War US context by Robert Putnam (2000). His book Bowling Alone created a vigorous debate about whether television has been the main factor behind the postwar decline of US civic culture (an example of which has been the decline of community bowling alleys). Cries of ‘Dumbing down!’ go all the way back in history. The move from the oral tradition to the written word was lamented in ancient Greece and seen as destructive of the memory skills developed in the time when Homer’s ‘Iliad’ and ‘Odyssey’ – arguably still the greatest epics of literature – were related by word of mouth.2 Broad access to books, particularly the Bible in 16th-century Europe, facilitated religious revolution and war. Dumbing down may look sacrilegious to an elite,3 but while it may represent a destruction of the means of valuable interchange of ideas, at the same time it can be revelatory and intellectually enriching for many more people not previously communicating with each other. Technological change in the media has been not only traumatic but also irresistible as old technologies have been replaced. It affects the way newer generations think and interact. There is a feeling of erosive unstoppable destruction of the old as globalisation, via new media, invades. New technologies and the young bring myopia and collective amnesia. Older generations and traditional societies alike feel the tension as their children and communities adopt new modes of speech and ways of thinking and abandon the past. And this is not new. We may fear (or embrace) such change but we can’t credibly blame (or give all the credit to) our children. Globalisation may be a more convenient and acceptable receptacle for our emotional discomfort. Modern communications have massively increased information flow, and the technologies of the Internet and mobile phone have leapfrogged older technologies in many developing countries.4 As with technological change before, much of this is inexorable and non-reversible. Knowledge of the wider world and aspirations for a better life combine in emerging countries to increase awareness. As populations become more vocal, this leads to pressure on elites for political and economic reform at home. Economic growth and international competitiveness is in part the result of greater entrepreneurial opportunities. Others leave and migrate to the developed world, competing in labour markets there. Either way, the result is greater economic competition with the developed world, which either has to adapt or face job losses from increased competition. Thus many in the developed world feel threatened by globalisation, while at the same time it opens vast new opportunities to many in developing economies. Part of globalisation is significant international trade, and also substantial cross-border flows of factors of production (capital, labour, technology). These flows take advantage of See also Gleick (2011) p. 48 for more recent examples of complaints about the loss of oral culture. 3 See for example Judt (2010, p. 172): “In the US today, town hall meetings and ‘tea parties’ parody and mimic the 18th century originals. Far from opening debate, they close it down. Demagogues tell the crowd what to think; when their phrases are echoed back to them, they boldly announce that they are merely relaying popular sentiment.” 4 See for example Jeffrey, R., and A. Doron’s The Great Indian Phone Book (2013). 2

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pricing differences, but in the process, also help reduce them – globalisation helps move the global economy towards an equalisation of returns to factors of production. It also involves multilateral production, and with it the spread of ideas and technology. There is greater openness to foreign inward investment. There is competition between governments for that investment, and for the jobs and knowledge which come attached. Different parts of the same production process may take place in several countries, exploiting comparative advantages. This is made possible by sufficiently low levels of protectionism and reliable low cost transport.

1.2

Economic history and globalisation

To concentrate on the economic facets of globalisation, it may be useful to consider its historical precedents. Large-scale globalisation is not new. Maddison5 argues that ‘[i]n proportionate terms, globalisation was much more important from 1500 to 1870 than it has been since. A great part … due to gains from increased specialisation and increases in the scale of production’. International trade and capital flows are much larger today, but so is the global economy. There was an interruption as the world went to war in the 20th century, and then protectionism was only reduced gradually, but globalisation is clearly not a novelty. There are also long economic waves of concern with inflation and deflation. Allen (2005) for example argues that the inflation of the 1970s was partly born from the concern over employment that had previously dominated since the Depression, and similar long waves have been picked by many others since Kondratiev (1925). Kaplinsky (2005) makes a comparison between the late 19th and early 20th century period of internationalisation on the one hand, and on the other hand the period of globalisation starting in the late 20th century. He comments on the different mix of goods traded, and on the different migration patterns – of the poor in the earlier phase and the skilled and a greater proportion of the monied in the latter.6 He also points out7 that there is a high correlation between effective financial intermediation and economic growth, but that excessive volatility can reduce growth. Hence policymakers often want the competition, ideas and capital which come with openness but are concerned about volatility. Although portfolio investors are not necessarily short term in their outlook, some policymakers – not liking potential volatility in their exchange rate driven by short-term changes in cross-border portfolio flows – are attracted to the idea of discouraging portfolio flows through taxing capital inflows rather than trying to attract more long-term stable investors. Yet trying to prevent inflows rarely has more than a temporary impact on the exchange rate; given inevitable efforts to bypass the restrictions, it can encourage speculative pools of capital and discourage longer-term flows. Hence the simple mantra that characterises

Maddison (2007) pp. 78/9. He also asserts that the recent period saw short-term as opposed to long-term capital flows. Yet, although the speed at which financial transactions can occur has quickened, there were in both periods crises involving short-term bank loans as well as longer-term bonds. Moreover, after the Brady plans and certainly since the Russian crisis of 1998, as we shall relate in more detail in Chapter 2, the dominant investors in emerging debt moved from those with more speculative motives to those with long-term liabilities making strategic allocations. Markets have remained liquid and on occasion volatile, but both the bonds and the timeframes of the investors are now longer term. 7 p. 78. 5 6

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portfolio flows as speculative and thus undesirable may be misplaced. Indeed, efforts to restrict such flows can result in more not less volatility.8 1.2.1

the desire to control and its impact on trade

Why do simple policy measures to reduce volatility so often backfire? Today’s environment is one of economic complexity, economic liberty and freedom of thought and action. There is a lot of uncontrolled international movement of goods and capital, whereas in the preindustrial past the movement that did exist was smaller and simpler. The state may have become less able to impose direct control on the mass of individuals and firms, but many have also become more sophisticated at indirect control and at exploiting the behaviour of firms. As Lucas (1976) pointed out in the so-called ‘Lucas critique’, the use of aggregate macroeconomic data to predict the effect of policy changes can be frustrated. This is due to the behaviour captured by such aggregate data not being independent from policy, but affected in complex ways. Political control in many spheres has changed. It has been decentralised in some cases as smaller groups have asserted themselves and the centre become less powerful, such as during the fall of Rome in the 4th century, but also due to deliberate delegation of responsibility downwards. In other spheres power has centralised, and many of the problems faced by policymakers today require action above the level of the nation-state to be effective, including some aspects of anti-terrorism and environmental policy. As people’s identities and loyalties have multiplied and become more complex and global, identification with the state has also changed, and the degree to which countries can co-opt their citizens in certain ways. But democracy and well-being are both probably strengthened by this greater complexity. The multiplication of special interests, competing with each other, reaches a point beyond which any central source of political power can command a majority of support whatever mix of policies is chosen. Democratic institutional forms constitute instead legitimising filter mechanisms, the function of which is not merely to create compromises between political groupings but also to allow all politically active groups and individuals to accept and abide by these compromises. Such decentralisation of power is incompatible with authoritarianism. Authoritarian governments fail when their populations no longer acquiesce to their policies. Today, the freedom of action which comes from the failure of totalitarianism and central power through filter mechanisms such as democracy, erodes national boundaries and creates more scope for globalisation. Competition of ideas and in markets aids creativeness and wealth production. Let us cast our minds back to medieval Europe, and in particular England. A useful working hypothesis for any government is that it strives to maximise revenue in order, in turn, to maximise power.9 Medieval monarchs needed revenues for wars, and could often justify taxes to finance them. How they managed this is instructive for how economies, international trade and capital markets developed. A characteristic of England’s history is that the king’s power, being weaker with regard to the aristocracy compared with that of the king of France, had greater need to legitimise taxation. The Magna Carta of 1215 limited King John’s and 8 Li and Rajan (2011) conclude from an empirical study that controls on equity inflows tend to raise the volatility of those inflows, and controls on FDI (foreign direct investment) and also on debt outflows may both increase the volatility of equity outflows – substitution effects. Controls on FDI inflows may also raise the volatility of FDI outflows. Controls on debt inflows tend to raise the volatility of those inflows. See also Frenkel et al. (2001). 9 See Levi (1988).

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subsequent monarchs’ powers (weakening under the Tudors and Stuarts in particular), establishing personal and property freedoms and elevating the rule of law above the will of the monarch. Subsequent efforts to raise taxes were notoriously difficult, but this led to an ironic reversal. ‘The relatively weaker bargaining position of English monarchs vis-à-vis their constituents led to concessions that French monarchs did not have to make. However, the Parliament that evolved ultimately enhanced the ability of English monarchs to tax. Parliament provided a forum for conditional cooperation. It engendered quasi-voluntary compliance and reduced transactions costs.’ Levi (1988) Compared to 18th-century France or Rome under the later Caesars, tax farming in England was not widely employed, but rather the taxes collected by Parliament and later the bonds issued involved lower transaction costs, were more legitimate and more reliable. The range of taxes to finance the monarchs (and their wars) was varied, but was also driven by and impacted the pattern of trade. Taxes needed to be collectible with minimum transaction costs and maximum legitimacy, and hence moved from general levies (amounts collected across the population) to consumer goods to trade to income. But strategic and mercantilist concerns over trade led to developments in policy too. In the mid-16th century the focus of English trade policy was to generate employment and food after the devastating costs of war on the continent (the English were at war for much of the previous 50 years, with a break in the 1530s). The discouragement of domestic production of luxuries including luxury clothing, seen as unnecessary and sapping of the national economy, led to surges of some of these items as imports, and so eventually the reversal of the original trade policy.10 Then mercantilist and strategic concerns regarding foreign trade started to give way in the later 17th century to the appreciation that ‘projects’ (schemes of domestic investment for home consumption) were important for the country’s overall income and economic health.11 Patents, starting from the Tudors (the first in 1552 for a technique for making glass, then in 1554 to search for and work metals in England), were established to promote production but often led to the aristocratic holders of such exclusive licences closing down domestic (and less aristocratic) competition. International trade was a small share of the total economy, but it was also clearly impacted by the dominant position of government policy in the national economy. We can say there were periods of great increase in foreign trade, but it was still very much monitored and to a large extent controlled or controllable by governments. Governments in turn acted for a combination of political, strategic and revenue-maximising ways, both directly and through taxes, distorting the incentives to trade. Today’s economic freedoms contrast with more restricted governance structures dominated by guilds and serfdom, tariffs and trade restrictions, economic dependency and personal immobility, and general government heavy-handedness. Whereas the norm in medieval Europe was that companies would seek a licence to engage in certain activities, now companies are prevented from not doing certain things – i.e. they can do anything else. Over time,

10 Sir Thomas Smith listed various imports in his Discourse of the Commonwealth, and then sat on a committee in 1559 which framed plans for legislation to promote import substitution for a similar list of goods. 11 As described by Joan Thirsk (1978).

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governments have become less able to ignore the wishes of their citizens. And this is true globally not just nationally. 1.2.2

the influence of money

While our focus is economics, other social forces have also constrained and shaped economic activity. If importation of luxuries was long seen in medieval England as a distraction from more legitimate economic activities, attitudes to money as the medium of exchange take centre stage in the battle between God and Mammon. The history of money is fascinating, as is its sociology and philosophy.12 The association of money with moral impurity is a common thread from Judas Iscariot to the laws against usury and right up to the present day. In Christian Europe at least, financial market development was restricted by religious mores. However, monarchs still needed to fight, and that cost money. The first banks began in the 15th century, and international loans commonly funded wars between monarchs. Potosí silver fuelled the wealth and power of 16th-century Spain, but the lack of development of a domestic capital market led to Spain under Philip II defaulting again and again to foreign bankers. Florence, Genoa and Amsterdam built their economies on international loans as well as international trade. Banks were originally a place to secure one’s money. Once they started lending out more than they had through issuing notes, there was a risk of bank runs… and the bigger the bank, the bigger the run. Though the Bank of England (1664) and Sveriges Bank (1668) were already established, the mass creation of credit proposed by John Law to the French government, in effect creating a central bank, was initially rejected in 1715, even though the French government was near default following the War of the Spanish Succession (1701–1714) and the Sun King’s defeats at the hands of the Duke of Malborough and Prince Eugene. However, Law was allowed to establish the Banque Général, a private bank allowed to issue bank notes in place of scarce gold and so stimulate the economy. The bank in effect became the central bank, and from there Law’s scope for credit creation grew and grew in an 18th-century version of our modern-day quantitative easing (QE). Initially providing assistance in financing government, by 1717, Law’s notes were legal tender for paying taxes. The attraction of printing money and credit extension became apparent as a giant means of financing government. Depositors and equity holders came to trust in paper returns. The bank also became an investor in the Mississippi, and shares in the bank were bid up in a financial bubble fuelled by promises of profits which were not forthcoming. It all ended in tears with one of the largest bubble-bursts in history in 1720; but for about 15 months this Scotsman, made Duke of Arkansas but wanted for murder in England,13 was the most powerful man in France. Love of ingenious financial alchemy (the successful stimulus to the French economy by the initial period of credit creation) was followed by hate (the bursting of the Mississippi speculative bubble); just as today international bank alchemy (a key element of modern globalisation) can create huge benefits but then excessive leverage and crises, followed by public opprobrium.

See for example Dodd (1994), Buchan (1998), Galbraith (1975), Shell (1982) and Simmel (1990). John Law initially fled to Scotland to escape justice, and lobbied against the Union with England, but then had to flee Scotland when the Act of Union (Scotland with England) was passed in 1707. 12 13

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The closeness of bankers to political power continues to the present day.14 The Rothschilds’ agent in 19th-century Berlin, Gerson Bleichröder, became Bismarck’s personal banker but also was central to the finances of the German state and even to foreign policy. Bleichröder provided Bismarck with backchannels via the Rothschilds to the government in Paris and to Disraeli in London. He also was heavily involved in foreign investment, particularly in railways (see Stern, 1977). Likewise in the 20th century, John Pierpont Morgan was famous for playing the role of domestic central bank, stopping the US financial panic of 1907. The associations between finance, international relations and globalisation have long been strong. 1.2.3

trade and commodification

International trade enables international specialisation. In Britain’s case it was the colonies and the ability to import food and raw materials which enabled the industrial revolution. One needs political stability and trust for international trade and globalisation, and trust is personal and built on reputation – hence the growth of family partnership merchant banks, with their own money on the line. These banks had detailed knowledge about others; but, as they lived or died on their reputation, which could be shattered by a single scandal, they kept secrets well. Globalisation also entails creating the demand for international trade. Trade has existed for centuries, but large-scale trade had to wait for the consumer society. Prior to this, trade was either in luxuries for the few, or in one or two goods for the many. Roman imports of grain from North Africa were clearly considerable in scale, and a staple for the urban population, but the more normal pattern has been of relative self-sufficiency in most staples until the past few centuries, when large-scale trade in grain and textiles resumed. Trade built over several centuries in Europe, but important steps on the way were recognition from the late 17th century of the importance of domestic demand; increasing rural industry and incomes; agricultural enclosure and labour specialisation; and urbanisation. Commodification – assigning economic value to things not previously so considered – was also a crucial step. London’s Great Exhibition of 1851 was a triumph for the establishment of the commodity at centre stage. The exhibits were not explicitly for sale, but rather there for the glorification of industry and the production of items – commodities from soap to tea to heavy machinery – of use to the consumer and society. This was a revolutionary change and to a large extent the attraction of the exhibition: the focus of the commodity from derivative to dominator of human relations (and not just economic relations). Modern advertising and branding were born, and in some of the pictorial advertisements of the time people were in clearly subservient (smaller and not as important) positions to the commodity.15 Complementary to this radical change was the British Empire, acquired as if by accident for an unknown purpose, but now perceived as having an important role in supplying the growing needs of the consumer (even if the Americas in practice were more important in this role). If the Great Exhibition drove the desire for domestic consumption, truly dominant mass consumption had to wait for Henry Ford in the US during the early 20th century.

14 In Atlantic Monthly May 2009, Simon Johnson, Former IMF Chief Economist, referred to this bankingpolitics nexus as a “financial oligarchy that is blocking essential reform” http://www.theatlantic.com/magazine/ archive/2009/05/the-quiet-coup/307364/ 15 See Richards (1990).

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Commodification continues to this day and is a distinctive part of globalisation, combined with its offspring, advertising and branding. 1.2.4

nationalism

Interaction between nations has also changed. Nationalism is a fairly new concept in its modern sense, with nation-states developing in the 1700s, as Hobsbawm (1990) has pointed out. It may yet, as a result of globalisation and the political consequences of societal complexity already mentioned, give way to more multinational political structures. It has already changed greatly. No longer (with a few exceptions) is it an extension of a monarch’s ego: ‘L’état, c’est moi’ as Louis XIV, the Sun King, is supposed to have described it. The peace of Westphalia in 1648 after the devastating Thirty Years’ War between Catholic and Protestant forces defined the sovereign state and established the principle of non-interference in the affairs of other sovereign states. But as Philip Bobbitt (2002) has described, the state has been through several stages of development since. Most recently, as the 1990s Balkan wars demonstrated, the concept of non-interference established in 1648 is now in conflict with that of self-determination. Having said that, global interference has always been with us: stronger states interfering in the affairs of smaller ones for a combination of reasons: their own (individual or collective) security, economic self-interest and humanitarian aid. In all but the short term, however, self-interest of some description invariably dominates.16 What global media and culture have aided is the move to a new reality in which the winning of hearts and minds is central to the modern strategic battleground, and in which traditional armed forces are largely redundant. As a population becomes more educated it will organise and will demand political rights: its voice17 will be heard and authority perceived to be unjust becomes more difficult to preserve. The days when the 1000-strong Indian Civil Service of British expatriate administrators could run a subcontinent of 300 million is long gone, as was predicted since the British enhanced education for Indians from the 1830s. The values the British chose to spread in India were incompatible with their longer-term presence. Today the spread of these and similar values makes similar long-term passive subjugation of nations quite impossible. In today’s world of the Internet and global media, guerrilla not industrial warfare, mass political participation not autocracy, control by physical force alone has become absurdly difficult – even if this is not yet sufficiently understood to have prevented some recent attempts. Winning minds is the clear preferred route to stable prosperity in today’s world, with a more limited support role reserved for physical force. This is in contrast to much of the structure of defence spending, as discussed by two modern generals with recent experience in the Balkans: Clark (2001) and Smith (2005). What has changed is not merely our education and communications technology, but the number of independent countries18 and also the principle of non-intervention in what were previously considered the internal affairs of nation-states. The principle of such non-interference is now in conflict with the desires, often supported by international opinion, of certain sub-national groups for self-determination. The nation-state 16 So-called humanitarian imperialism is not particularly credible as a justification for armed intervention in a foreign country for the simple reason that it tends not to work. 17 See Hirschman (1970). 18 The increase in the number of countries has made international policy co-ordination more difficult. This fragmentation has been the result of the end of empire, decolonisation and more self-determination. These processes in turn have been assisted by globalisation and with it the spread of economic liberty, education and liberal values.

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has changed its form several times before. As nationalism is a relatively modern phenomenon in many ways, one should expect it to change further.19 Jane Jacobs describes politics as a zero-sum game, but maybe it is even worse: due to fragmentation and more issues requiring international co-operation, states are experiencing shrinking power. Some international problems which would have been resolved by a few countries in the past are now not being resolved. In the wake of globalisation, national politics are becoming less and less autonomous. A number of immigration, environmental and economic issues require supranational governance. In the face of these issues, and in the absence of powerful international institutions, national governments are becoming more impotent; and electorates, realising this, are becoming more frustrated that issues are not being resolved – more apathetic (as shown by voter participation trends), more difficult to please. Winning minds is about having people agree with you, after letting them freely choose to do so. For the West this freedom or empowerment means allowing people to run their own lives, but also giving up some power – including sharing responsibility with emerging markets. Much more serious reform of the voting shares of the IMF, still heavily dominated by the US and Western Europe, would be a start. The problem is that some Western politicians have great difficulty with implementing this, or giving up their influence, especially when they have little central collective leadership, or are leaders with outdated world views. They often seem oblivious to the observable reality that their policies are getting in the way. Investors, the ultimate pragmatists, have the potential to offset the zero-sum (or all too often negative-sum) logic of politics. Commerce is an important component in bridging conflicts and avoiding them, of getting over ideological prejudices, of creating mutually aligned incentives: in short, of keeping down the testosterone levels in politics. History can teach us a lot about globalisation but we have to be cautious in interpretation. A reader may misinterpret the values and motives of past decision makers. How do we square Britain’s great historical achievements with urban squalor, Irish famine in the 1840s, and Orwell’s description of waning empire in Burmese Days? Much of the past has been horrific, and governments have gone to great efforts to rewrite and in some cases to deny history20, but we also need to recognise that moral values change over time and geography.21 And values remain different in different geographies today, even if people in distant lands consume some of the same brands and superficially may appear very similar in their values. Also, in the midst of global economic dynamism, there can still be a tendency to be surprised, antisympathetic and hostile to change. The combination of remaining partially myopic yet more interconnected leads to greater risk of sudden uncomfortable change, and indeed conflict.

1.3

rEcEnt globalisation

International trade often collapses during war, and economies have struggled with inflation and debts in peacetime. Hence the importance of local and global rules to facilitate trade and capital flows – to facilitate globalisation. Stability matters, as Maddison (2007, p. 111) writing about the period 1500–1800, points out:

See Bobbitt (2002) and Hobsbawm (1990). See for example Paris (2000). 21 See Harris (2010) for an interesting exposition of how science can determine morality. 19 20

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‘In the UK and the Netherlands, the legal system protected commercial property rights and ensured the enforceability of contracts. State levies were predictable and not arbitrary, and credit for long term ventures was available. As a result groups of capitalists in these countries were able to establish corporations like the Dutch Far East Company (VOC), and the British East India Company (EIC) which could organise risky ventures over huge distances.’ The Bank of England had established the model for central banks up to the 19th century, balancing liquidity needs in the economy with the avoidance of inflation;22 and the gold standard had emerged to create stability in foreign exchange transactions, with major currencies convertible to gold. This facilitated global trade. The gold standard, however, was vulnerable to supply shocks as new gold deposits were discovered and, in times of war and crisis, countries abandoned it. The Treaty of Versailles in 1919 imposed unrealistically high costs on Germany, which (as John Maynard Keynes warned in The Economic Consequences of the Peace, written in 1919) later forced an exit from the gold standard as their debts became unpayable (and unpaid for their creditors), and set the scene for hyperinflation. 1.3.1

bretton Woods

The roaring twenties and the stock market boom of 1929 were followed by deflation and depression and then World War II, during which trade patterns were radically curtailed and war economies operated in more planned fashion. Given the strong desire to avoid the inter-war protectionism, and the periods of both deflation and then inflation, in 1944 at Bretton Woods a new global monetary architecture was designed. The International Monetary Fund (IMF) was created to police exchange rates. The main arm of the World Bank, the International Bank for Reconstruction and Development, was tasked to help rebuild Europe. An international trade organisation failed to be agreed to, but belatedly in 1947 the General Agreement on Tariffs and Trade (GATT) was established instead to promote multilateral trade, replaced by the World Trade Organization (WTO) in 1995. An objective was to start to reverse protectionism and promote current account convertibility. The agenda at Bretton Woods after the inter-war deflation was thus to re-establish some form of managed gold standard. However, there was not enough gold in the world (without a major and geopolitically unacceptable price increase which would have benefitted Russia and South Africa) for full convertibility. Keynes conceived that all foreign exchange transactions would continue to go through central banks, as during the war, and suggested a new international currency called ‘Bancor’ which would be the unit of account for international transactions, expressed in units of gold. A new international clearing union would facilitate transactions and prevent the build-up of major imbalances. Keynes’ design was rejected by the US. This was because, as a major creditor, the US decided not to have penalties imposed on her Bancor surpluses: countries running excessive trade deficits are eventually penalised by being cut off from capital as their credit-worthiness deteriorates, but for every deficit there is necessarily an equivalent surplus somewhere,23 and so to avoid the build-up of deficits Keynes also proposed that interest be charged on excessive Bancor surpluses. See for example Galbraith (1975) for a history of the development of the banking system and central banking. Though it is to be noted that for a well-functioning gold standard the converse is not necessarily the case: while there is a surplus for every deficit, there is not always a deficit for every surplus. 22 23

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Instead of Keynes’s plan, a system with an inbuilt tendency towards imbalance was implemented, and still (in 2014) codified in the ‘Articles of Agreement Establishing the IMF’. Currencies had fixed exchange rates to the US dollar, which in turn was convertible to gold at $35 an ounce (the official US Treasury price since 1934). Though other countries could have also chosen to have their currencies convertible to gold, none did. Other major currencies were pegged to the dollar. This led to the so-called Triffin dilemma: a national currency, which is also the international currency, has conflicting pressures of attaining short-term monetary balance nationally and longer-term international balance. Currency and yielding government securities are issued to meet international demand. Otherwise international trade and growth would fall. This, however, creates a tendency towards trade deficits for the issuing country, as the money is printed there and then makes its way into the international economy through being used to purchase goods and assets (as opposed to a more international currency which might be distributed, on printing, more evenly across countries). This in turn builds US debts to the rest of the world. In order to prevent requests that these claims be converted to gold (this leading to an eventual breakdown of the system), the US would either have to raise interest rates on the government securities issued and which are held by foreigners; or to tighten fiscally in order to shrink the economy and its indebtedness, or otherwise reduce the trade deficit. There is an understandable reluctance to do either. They could (as Triffin observed) also allow the price of gold to rise, but this was outside the Bretton Woods agreement and could create destabilising speculative moves into gold by both central banks and private investors – in turn draining US gold stocks and undermining the ability to intervene, and so faith in the reserve system. The desire by foreigners to offer their goods in exchange for one’s currency (in the case of the dollar) can be an attractive alternative to greater domestic fiscal discipline. If, however, there is a tendency to fiscal indiscipline or substantial overseas expenditure, there will be more debt growth relative to the gold supply (eventually reducing the credibility of the promise of convertibility to gold). The problem is exacerbated if the international economy outside the US expands faster than that of the US: then international demand for dollars also expands faster than domestic demand for dollars. At the end of the war, this system, initially assisted by the Marshall Plan, helped create global stability and the rapid re-industrialisation of Europe and Japan – the (re-)emerging countries of the day.24 With the US dominating global tradable goods production, European countries bought US goods with the US dollars from the Marshall Plan. The recovery of these economies was successful. The pattern of strong growth in Europe and Japan then continued after the Marshall Plan and the initial period of US surpluses ended. By the early 1960s Europe and Japan had become highly competitive. The fixed exchange rate facing the US had become inappropriately high. The move to current account convertibility in 1958 had put additional pressure on the dollar, as had European concerns about the fiscal policies of the newly elected US president Kennedy. The dollar traded as low as $40 an ounce in 1960. The response was the London gold pool: an agreement whereby the US and seven European central banks co-ordinated sales of gold in the London gold market, buying dollars, which they then invested in US Treasuries. This was no more than a temporary fix, though. In this monetary system the US in the immediate postwar period was doing the rest of the world a

24

The term ‘re-emerging markets’ is from Wolf (2009).

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huge favour by creating demand for their goods, but at the cost of building up more and more debt.25 As Herb Stein, US President Nixon’s adviser at the time, said: ‘If something cannot go on forever, it will stop.’ Add the cost of the Vietnam War and the unpalatable choice of fiscal adjustment through higher taxes, and the pressure grew. The more aggressive stance by the incoming Nixon administration towards Europe over gold purchases, and specifically the rhetoric of his Treasury Secretary John Connally, backfired and led to market pressure on the gold price. The German mark was floated in May 1971 and then on August 13th the Bank of England asked the US to convert some of its dollars to gold before it was too late. Nixon decided instead to de-link from gold on August 15th, devaluing the dollar, which then rapidly fell from $35 an ounce to $44 an ounce. As the dis-equilibrium had grown to such a level, there was indeed little else he could have done.26 Sterling floated in June 1972 and some other currencies still pegged to the dollar until early 1973, but the credibility of their anchor had been damaged. Setting a precedent for the more recent build-up in global imbalances in the early 21st century, it was the action of surplus central banks which forced the 1970s crisis. US debts were far in excess of gold reserves. Foreign surplus central banks, wanting to preserve the purchasing power of their reserves, started buying back gold on the secondary market, and eventually asked for gold from the US Treasury in exchange for dollars. Nixon then had a choice: start giving out the gold, run out and then renege on the commitment to convertibility; or renege early and keep the gold. He quite sensibly chose the latter option, although technically another option would have been to raise just the gold price, but that had not been agreed with Europe. Without the monetary anchors of the Bretton Woods system, inflation became a larger problem from 1973. Oil prices rose as OPEC exerted newfound bargaining power, and food prices spiked due to supply disruption. But the main cause of the 1973 uptick in inflation was arguably the macroeconomic policies in the OECD at the time of loose money which accommodated fiscal deficits. By the end of 1974 gold had reached $195 an ounce, but was volatile, not least due to official gold sales. With inflation, more instability in global (now floating) exchange rates had returned. Countries with large domestic investor bases managed to borrow in their own currencies, which they could then debauch. Without the discipline of the gold standard or fixed parity with the dollar, deficit spending became the norm and inflation became a preferred form of taxation. Gold had been a part of the global monetary system from prehistory to 1971, but has not been since and may never be again. Indeed, in a world of floating exchange rates, inflation may again be used as the principal method of reneging on Western government debt obligations. 1.3.2

ideological shifts

After World War II, involving as it did enormous state economic planning and mobilisation by all of the major combatants, the consensus was for the state to continue taking a prominent

25 The creation of IMF Special Drawing Rights (SDRs) in 1968 was designed to create a new reserve currency and complement the limited stock of gold to meet growing reserve asset demand, but this need was averted by the growth of the Eurodollar market – private sector borrowing in dollars offshore (in Europe) – which reserve managers could purchase instead of US official debt assets. See Isard (2005), p. 33. 26 For a more detailed account see Eichengreen (2011).

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role in the economy. Added to that were the anthropological27 and political priorities of building societies with less inequality, leading to the start of the creation of the modern European welfare state. There were very few economists who thought let alone argued differently.28 With state dominance came government control in a wide range of areas, including (and consistent with the Bretton Woods agreement) European blanket controls on the free flow of cross-border capital.29 The modern period of globalisation is thus associated with the period when these controls came off, which they started to do in 1979 with the lifting of UK exchange controls. The experience of World War II and the need to rebuild afterwards were clearly behind the desire for a large economic role for the state, but ideology was also at play. When this fell to more pro-market ideology in the 1980s, policies shifted dramatically, in some cases with a slapdash disregard for consequences, in the opposite direction. Indeed, I experienced the force of an ideological argument myself. Late in George H.W. Bush’s presidency I was working in the Strategic Planning Office of the US Treasury-controlled Plans and Programs Department of the Inter-American Development Bank. Following a plebiscite in Uruguay against privatisations, a topic which had become highly politicised, there was concern that privatisations might be stopped in several countries. Hence I wrote a technical paper on when and how to privatise (and thus by extension also when not and how not to).30 It was explained to me officially in a bizarre meeting that, while there was nothing wrong with the content of the paper, it was inappropriate that it should be seen to be written from inside the Department. As in Umberto Eco’s Name of the Rose: knowledge is sin. In Eco’s book the medieval library in which the plot is set is eventually burned down to avoid the revelations of knowledge in an ancient Greek text. My paper was banned from distribution, which, perhaps predictably, had the opposite effect to that intended.31 The ‘Washington Consensus’ is shorthand for some of the new thinking. The term was originally coined by John Williamson at a conference in 1989 to describe 10 areas of policy reform being enacted by Latin American governments: prudent fiscal deficit management, public expenditure priorities, tax reform, interest rates, the exchange rate, trade policy, foreign direct investment, privatisation, deregulation and property rights.32 The term was controversial partly because of its name. Frances Stewart has argued, and Williamson did not deny, that by calling it the Washington Consensus as opposed to the more obvious Latin American Consensus, the intention was to create US support for what were highly pragmatic and largely orthodox policies Latin American governments wanted to continue to follow.33 What started as a rough pragmatic list of what was happening soon hardened into (right-wing) dogma. And part of the dogma became free trade and free capital movement across borders: another part of the story of globalisation’s progress. Globalisation was also pushed in the post-World War II era in the successive trade rounds of GATT and then (after 1995) the WTO, though, in consequence of (certainly perceived) 27 For example, the Beveridge report on social insurance and allied services can be seen as anthropological in nature. 28 See Skidelsky (1995). 29 US capital controls only began in the 1960s and had limited effect – though one was to stimulate the creation of the Eurodollar market in 1963. 30 The full paper can be found on Jerome Booth’s blog on newsparta.net. 31 Distribution of an earlier draft escalated. I have been told subsequently the paper was used several years later as a guide for privatising CVRD, now known as Vale, one of the largest companies in Brazil. 32 Williamson, Ed. (1990). 33 Stewart (1997).

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relative bargaining power at the time, with a clear favouritism to the developed world. The emphasis was on free movement of goods, but also capital and (much later) protection of intellectual property rights. Fligstein (2001) categorises three types of globalisation which followed: an increase in world trade, the rise of the Asian Tigers (Hong Kong, Singapore, South Korea and Taiwan) at the expense of the first world, and the growth in financial markets in debt, equity and foreign exchange. We do not live in a world of free trade though, but in a world of more-or-less free trade, except in agriculture and textiles, where protectionism is alive and well – and highly distorting and disadvantageous to emerging countries.34 Nevertheless, developing countries have benefited enormously from globalisation. They have taken advantage of greater trade opportunities, grown fast and learnt from their own mistakes and those of others. The sharing of policy experiences across countries should not be underestimated as a great stimulus to better policies. While the bottom billion35 in failed states in sub-Saharan Africa and Central Asia remain misgoverned,36 aid-dependent37 and poor, other economies have grown at the highest rates ever recorded in history. Low-skill jobs have moved to developing countries, but higher skilled ones are moving there too. India and China alone (accounting as they do for 36% of world population) have pulled hundreds of millions out of poverty. 1.3.3

Participating in globalisation: living with volatility

Protectionist sentiment and the import substitution industrialisation (ISI) ideas of Raúl Prebisch and others to support infant industries, popular in the 1960s and 1970s, went out of fashion with the rise of the Washington Consensus in the 1980s and 1990s. Capital accounts started to be liberalised in the Thatcher/Reagan period in a number of countries, both developed and developing.38 Countries risk incurring severe costs should they cut themselves off from the outside world. Policymakers are right to be concerned about capital flow volatility, but lack of international competition can reduce both productive and allocative efficiency. Nearly all choose to participate in global markets, but some want to retain an element of control. No country, once partially liberalised, is currently planning blanket capital controls, but a number of measures have been tried to reduce capital flow volatility. However, while so-called macroprudential policies (not a clearly defined set of policies, but ones focused on reducing financial sector systemic risks) may be advisable to reduce risks of financial contagion and other spill-over effects from other countries’ financial systems, capital control measures (as opposed to central bank intervention) designed to affect the exchange rate have no clear history of success except in the very short term. Investors seem always, in time, able to devise structures to get around them. Capital controls in the form of taxes on portfolio inflows can moreover be highly distortionary, and once imposed can create uncertainty over future policy and deter inward investment and damage investor sentiment – so raising borrowing costs for the government. In particular, they can discourage long-term institutional investors and encourage the more flighty speculative investors, and this in turn, ironically, can lead to great volatility. Volatility is often a function of fundamental factors inside or outside the country, See for example Booth (1992). Paul Collier (2008). Paul Collier (2010). 37 See Easterly (2006) and also Moyo (2009). 38 See for example Allen (2005), from p. 151. 34 35 36

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including rapidly changing perceptions of risk, and heightened by significant offshore pools of capital. We can see globalisation not as the primary cause of contagion or volatility, but rather as the medium. Central bank intervention can reduce volatility, but one needs reserves for that, and the willingness to use them. Beyond that, the way to reduce volatility is to address the fundamental problems, such as fiscal and other domestic imbalances, or factors such as global imbalances or bank deleveraging (a regulatory matter). However, the structure of the international monetary system is in dire need of overhaul and is cause for concern â&#x20AC;&#x201C; an issue we shall return to.

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Funds Private Equity, Hedge and All Core Structures Matthew Hudson 978-1-118-79040-3 • Hardback • 360 pages • February 2014

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1 Introduction to funds

1.1 Why this book? I have sought to write the manual I always wanted to find on the shelves. In my career as both an asset manager and a legal adviser to asset managers and investors, I have often been asked to recommend a guide that covers the broad ambit of fund and manager structures. In the world of asset management, knowledge is often assumed, jargon is sometimes opaque and there can be a tendency towards mystification. Frequently, for example, I am asked ‘What is market?’, and certainly one possible answer to that question is that ‘market’ means whatever is investment worthy at that particular moment in time and given the particular investment: following the money has, after all, always been a plausible strategy. However, in these fast changing times where the industry is being required to adapt to survive, it is more crucial than ever to understand the logic behind the structures that have come to dominate this sector. Broadly, these pages are intended to function as a guide to all things funds and fund managers. Although approached principally from a United Kingdom (UK), United States (US) and European Union (EU) perspective, this book also references other core fund establishment locations, as well as core economic or asset jurisdictions such as China and Japan. The book approaches its subject from a structural, legal, tax and regulatory perspective. It is, however, a guide and not an in-depth review. The latter would require a number of separate volumes. I hope it succeeds in pointing the reader in the right direction.

1.2 AlternAtive Assets I am going to focus principally on funds comprising what are known as alternative assets. ‘Alternative’ as opposed to the mainstream world that is largely composed of listed equities and bonds. The phrase derives from the pension fund term ‘alternative allocation’, which refers to the proportion of a fund’s portfolio that is invested in alternative assets. This type of fund comprises principally private equity, hedge, venture capital, real estate, energy, infrastructure, credit and related funds. The managers of these funds tend to fall into the category of ‘2 and 20’ managers, where the ‘2’ refers to the annual percentage fee received by management of the cost or value of assets under management and the ‘20’ refers to the percentage of profit to be made by the manager as a percentage of profit for investors as a whole. A fund is a fluid concept. It can refer to any pooling of capital or assets. Historically, the concept of alternative assets and funds perhaps finds its origins in the age of exploration. At the heart of Christopher Columbus’s expedition to the Americas was an agreement that is an example of financial pooling. Columbus was backed in part by a ‘fund’ from Italian financiers and was able to convince the King of Spain to provide the top-up funding required

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Funds

for the trip. Columbus and his ‘management team’ had their overheads covered and were promised a generous share of performance profits, as well as real management power within any newly discovered lands, the ‘portfolio assets’. Success would also mean prestigious titles and backing for the next ‘fund’. The agreement was in fact quite detailed. Together with any treasure looted, Columbus would receive 10% of revenues reaped from newly discovered lands as well as having a right of first refusal to invest at a discount in any commercial venture deriving from the newly discovered territories – the King of Spain apparently believed that success or indeed Columbus’s return were unlikely investment outcomes. Management and co-investment opportunities rarely come better!

1.3 WhAt is A fund? A fund is a broad term, but as we have seen is used to describe any pooling of assets. These assets may be cash, shares, loans or tangible or intangible assets. A fund can even be a vehicle that holds a single asset (such as Vallar (now Bumi plc) and Vallares (now Genel Energy plc) – both originally special purpose cash shells established by the financier Nathaniel Rothschild to acquire specific companies), although, typically a fund is established to hold more than one asset. The term fund can of course be applied to other industries and concepts, for example: or ‘stable’ of pop artists, managed by an expert pop promoter, manager or agent. • aThefundmore stars under management, the greater the diversification fund or ‘library’ of knowledge or • aa fund or ‘team’ of football stars (where the assets are footballers) that are bought and sold. • Almost any economic gathering or pooling may be regarded in terms of a fund. A fund could almost better be defined by describing what does not constitute a fund, such as a single purpose operating company with a small balance sheet, unlike Rothschild’s cash shells referred to above. Typically, a fund would not otherwise include a large single purpose operating company, unless of courses it uses off (or near-off) balance sheet side vehicles underpinned by external capital, a fairly common feature of large energy, real estate and infrastructure companies. A fund may have one owner, or many owners who subscribe, acquire and sell positions, shares or units. One of the defining features of a fund is that it often has a professional fund manager (usually regulated) that manages and advises the fund. Funds can be operated for a variety of different purposes:

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• • • • •

to make a profit or to be run on a not-for-profit basis (e.g. a charity) to spread risk to obtain leverage (by debt financing) on assets to take advantage of a specialist manager to operate the fund • to attract investors (a bank may create a fund to house certain assets and then seek other investors to generate management fees for the bank) • to build an asset management group (although mere ‘asset gathering’ is sometimes criticized by investors)

1.4 1.4.1

CAtegories of funds

Ways to categorize

It is clear the term ‘fund’ is a broad one. However, in this book we are considering funds that occur in the investment management or financial services industries. But even within these sectors the range of different types of fund is wide. Investors and managers refer to a ‘hedge fund’ or ‘private equity fund’ or ‘mutual fund’, which descriptions embrace many investment strategies, structures and management arrangements. I would categorize funds within the alternative asset sector using the categories below. Categorization by industry (by example):

Hedge Private equity Infrastructure Energy Fixed income Real estate

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112 What this often leads to is a tradable fund trading at a premium to embedded value at moments of investor exhilaration, but at a discount the rest of the time. Sentiment or recognition can bear little correlation to actual asset value.

• illiquidity • ‘trading at a discount’ to asset value • market, economy or investor sentiment.

Tradable model Many retail or tax-driven funds A tradable fund is one where the shares or units in the fund are traded, usually on a public market. The capital is not distributed to investors although regular and larger one-off dividends can be made. The funds may or may not have a fixed life and gains and profits made within the fund should cause the fund’s share price to increase. However, tradable funds are subject to the ups and downs of trading and:

Most private equity funds The fund ‘draws down’ money from investors when required for investment. Drawing down funds only when required as opposed to in their entirety in advance should have the effect of enhancing the fund’s internal rate of return (IRR) when measured against the date of exit or realization of a particular investment. On exits, the original cost and the capital gain or profits relating to each asset are then ‘distributed’ to investors and are seldom re-invested. The fund usually has a fixed life, and the intention is to invest and then ‘return’ the entire capital and profits, before winding up the fund. A share of the fund profits (or ‘carried interest’) is distributed to the management team. In a drawdown and distribution model fund, assets remaining after distribution at the end of the life of a fund can be sold on the ‘secondary market’, as can an investor’s position. Income generated from investments is usually distributed as it arises, for example, net yield from real estate, rental receipts or fixed income gilts. The fund is usually ‘closed’ and not ‘open’ (meaning that the number of investors and amount invested are fixed and have a fixed life).

Categorization by investor returns (or how they get their money back plus a profit)

Drawdown and distribution model

table 1.1 NAV or redemption model

Most hedge funds This fund redeems or prepays units held by investors in the fund and on (or within a defined time of) redemption also pays investors any profit ‘attaching’ to those units. A share of the profits is paid as a performance fee to the fund’s management team. Units are often redeemed at, or correlated to, the net asset value (NAV) of that unit. A unit’s NAV is the total of the fund’s gross assets, less leverage and liabilities, divided by the number of units in the fund. It is typically the manager or administrator and also third party valuers that calculate NAV. The fund is usually ‘open’ and not ‘closed’ (meaning the number of investors and amount invested fluctuates as investor commitments are made and redeemed) and can exist for an undetermined period of time, unless the fund is wound up.

4 Funds


Introduction to funds

5

Categorization by investment strategy (by example):

Buyout Long/short equity Venture capital Growth or development capital High yield Mezzanine Macro or directional Fine art

Categorization by vehicle:

Limited partnership Tax efficient corporate Listed

Offshore corporate or partnership

1.5

Choosing A vehiCle

Choosing the correct vehicle for a particular fund will depend on a number of factors. Some to consider are: vehicle that is most tax efficient for the target investor base and for the fund’s manage• the ment team (taking into account the fund’s likely assets and their location) regulatory regime that is least onerous while still providing an appropriate degree of • the credibility to the fund (taking into account the likely views of potential investors) limitation on the target investors (either internal or external) or their ability to invest • any in certain vehicles previous experience of the potential investors and the manager with different fund • the vehicles.

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1.6 1.6.1

open-ended And Closed-ended fund struCtures introduction

Alternative assets can also be divided into two other types of categories, those that are illiquid such as private equity, venture capital, real estate and infrastructure and those that are more liquid such as listed securities, commodities and derivatives. This has led to the development of, broadly, two types of fund structure: open-ended and closed-ended. table 1.2

Open-ended and closed-ended fund structures

Type

Liquidity/investment

Assets

Further reading

Open-ended

The vast majority of the fund’s assets are realized over a relatively short period of time. The fund has an indefinite life. Investors may redeem their interest (wholly or in part) or increase their interest during the course of the fund’s life.

Typically a large number of small assets (for example, listed shares) or assets whose size can be readily adjusted (for example, derivative positions). The fund can acquire new assets with additional proceeds invested. It funds withdrawals by investors through a partial realization of fund assets.

Common with hedge funds – Chapter 3.

Assets are held for a minimum period of time (for example, to restructure a portfolio company or refurbish a commercial property). Usually a smaller number of larger assets are held, e.g. private equity portfolio companies or specific real estate.

Closed-ended funds – Chapter 2. Growth of secondary trading of illiquid fund interests – Chapter 5, section 5.11.

Closed-ended An illiquid structure. The identity of investors usually fixed by final closing. Not generally possible for investors to withdraw during the life of the fund as the fund is unable to liquidate assets in order to finance withdrawals. Only possible to invest during the first half or so of the fund’s life to allow time to exit assets. The larger size of assets means that there are only, say, up to a dozen investments per fund. The fund operates for a finite period, terminating once all of the assets are disposed of.

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Introduction to funds

1.6.2

7

impact of the credit crisis

This book was written during a period often described as the ‘credit’ or ‘financial’ crisis. For our purposes, this period started in February 2007 with HSBC reporting record losses for US bad mortgage debt and was quickly followed by the collapse of the sub-prime industry in the US. The crisis spread in the US with the implosion of leveraged Bear Sterns hedge funds, the capitulation of structured investment vehicles (SIVs), the contagion of many US, UK and European banks (Northern Rock being a notable example) and arguably reached what in retrospect was its early peak with the collapse of Lehman Bros. The US, UK and European markets (which were considered more sophisticated than the rest of the world) were among the most seriously affected during the crisis. Some hedge funds were wiped out during the peak of the crisis due to over-leverage and also by ‘rehypothecation’. This is where the collateral pledged by funds with broker-dealers was called upon by those broker-dealers to satisfy their own liabilities. Lehman and Bear Sterns were market-dominant prime brokers at the time of their collapse. When the larger investment banks such as these two began defaulting, more hedge funds followed suit. This ‘Credit Crisis’ usually refers to the period mid 2007 to late 2009 but was then eased by floods of central bank liquidity. Mid-to-late 2009 to the end of 2013 was a continuation of this period, known overall as the ‘Financial Crisis’. The later period is marked by a certain stability returning in the US credit markets, but overall being marked by poor growth and the Eurozone crisis. The later period of the Financial Crisis was characterized by: and huge mark-downs (sometimes overdone in my view) • restructuring bank weakness • continued regulation – again in my view, often driven by headline-seeking politics and • increased naïveté and leading to the disinclination of banks to lend on a scale that might otherwise have restimulated economies.

All manner of funds were impacted by the financial crisis. Despite negative publicity on the sector, funds themselves (whether private equity, hedge, or otherwise) were not a root cause of the crisis. Instead, funds were caught in the pre-crisis enthusiasm, over-leveraging and over-pricing funds and assets. The adverse effects on funds have since been keenly felt. During the crisis, funds have found that the fund-raising has become more difficult as investment in general has slowed, which has been aggravated by the difficulty of borrowing. Private equity funds are, by their nature, long-term investments. To an extent they have been able to ride out the financial storms. Some managers have been criticized for not continuing to invest during what might come to be viewed as vintage years for investment. Hedge funds adapted relatively quickly owing to their shorter-term investment horizons with rights to redeem (despite manager rights to ‘gate’, that is to say restrict withdrawals, or lock up investments), scaling down, reducing in size, investing differently, usually with much less leverage, as well as adapting their structure to managed accounts (see Chapter 4, section 4.7 for a full definition) and other more transparent investment programmes. Alternative asset allocation is now starting to increase. The denominator effect has largely run its course (for the moment) as listed markets start to rebound. Funds are being sought out by investors:

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8

Funds

funds as adjuncts to broader investment strategy • hedge equity funds for growth • private funds for better than dismal bank interest and • credit • real estate, infrastructure and energy for the anticipated asset valuation rebound. It is too easy to be a doom-monger although some highly intelligent people believe we have entered a new low growth paradigm. However, I believe cycles will always exist, and that trends overshoot.

1.7

Contents of this book

To help you find your way through this book, the main contents are set out below. table 1.3

Main contents of the book

Chapters

Contents

2 and 3

4 5 6 7 8 9 10 11 12 13

Dedicated to two types of funds that are significant in this book: private equity funds and hedge funds, although the structures for each are also used for other alternative asset strategies such as real estate, infrastructure, credit and energy. These chapters also cover the two principal structures of alternative investment funds, being closed-ended funds (Chapter 2) and open-ended funds (Chapter 3). The chapters dedicated to these types of funds go into detail about the most common structures, jurisdictions and the market terms Analysis of other private fund structures Investment strategies employed by different funds with an analysis of each Key jurisdictions for funds to list on stock exchanges and the key types of listed funds and the regimes that apply to them Principal ‘offshore’ fund locations and a summary of their regulatory and tax regimes and stock markets Key global economies, the type of fund entities that exist there and the prospects for investors Large investor players: sovereign wealth funds, state funds, pension funds and charities Fund managers – the common investment manager structures and their commercial operations Taxation of funds, investors and managers Regulation of funds and managers Conclusion – reviews the ground covered and remarks on future trends

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