2022 FRM Exam Part 2 - Risk Management and Investment Management [5] 9780444535948, 0137686579, 9780137686575

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GARP FRM

Financial Risk Manager

Risk Management and Investment Management

Pearson

Copyright © 2022, 2021 by the Global Association of Risk Professionals All rights reserved. This copyright covers material written expressly for this volume by the editor/s as well as the compilation itself. It does not cover the individual selections herein that first appeared elsewhere. Permission to reprint these has been obtained by Pearson Education, Inc. for this edition only. Further reproduction by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, must be arranged with the individual copyright holders noted. Grateful acknowledgment is made to the following sources for permission to reprint material copyrighted or controlled by them: "Factor Theory," "Factors," "Alpha (and the Low-Risk Anomaly)" by Andrew Ang, reprinted from Asset Management: A Systematic Approach to Factor Investing (2014), by permission of Oxford University Press. "Portfolio Construction," by Richard Gringold and Ronald Kahn, reprinted from Active Porfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk, 2nd edition, (2000), by permission of McGraw-Hill Companies. "Empirical Tests of Biases in Equity Portfolio Optimization," by Peter Muller, in Financial Optimization, edited by Stavros A. Zenios (Cambridge: Cambridge University Press, 1993), Table 4-4. "Portfolio Risk: Analytical Methods" and "VaR and Risk Budgeting in Investment Management" by Philippe Jorion, reprinted from Value at Risk: The New Benchmark for Managing Financial Risk, 3rd edition, (2007), by permission of McGraw-Hill Companies. "Risk Monitoring and Performance Management," by Bob Litterman and the Quantitative Resources Group, reprinted from Modern Investment Management: An Equilibrium Approach (2003), by permission of John Wiley & Sons, Inc. All rights reserved. Used under license from John Wiley & Sons, Inc. "Portfolio Performance Evaluation," by Zvi Bodie and Alan J. Marcus, reprinted from Investments, 12th edition (2020), by permission of the McGraw-Hill Companies. "Hedge Funds" reproduced from William Fung and David A. Hsieh, l-landbook of the Economics of Finance, Volume 2B: Financial Markets and Asset Pricing, 9780444535948, 2013, Constantinides et al. Ch 16, Pg 1063-1125. "Performing Due Diligence on Specific Managers and Funds," by Kevin R. Mirabile, reprinted from Hedge Fund Investing: A Practical Approach to Understanding Investor Motivation, Manager Profits, and Fund Performance, Second Edition (2016), by permission of John Wiley & Sons, Inc. All rights reserved. Used under license from John Wiley & Sons, Inc. "Predicting fraud by investment managers" is reprinted from the Journal of Financial Economics, Vol 105, Stephen G. Dimmock, William C. Gerken, "Predicting fraud by investment managers," 153-173, 2012, with permission from Elsevier. Learning Objectives provided by the Global Association of Risk Professionals. All trademarks, service marks, registered trademarks, and registered service marks are the property of their respective owners and are used herein for identification purposes only. Pearson Education, Inc., 330 Hudson Street, New York, New York 10013 A Pearson Education Company www.pearsoned.com Printed in the United States of America ScoutAutomatedPrintCode

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Pearson

ISBN 10: 0137686579 ISBN 13: 9780137686575

1

1.7 The Fall of Efficient Market Theory

10

1.1 Chapter Summary

2

1.8 The 2008-2009 Financial Crisis Redux

11

1.2 The 2008-2009 Financial Crisis

2

1.3 Factor Theory

2

1.4 CAPM

4

Chapter 1

Factor Theory

CAPM Lesson 1: Don't Hold an Individual A sset, Hold the Factor

4

CAPM Lesson 2: Each Investor Has His Own Optim al Exposure of Factor Risk

5

CAPM Lesson 3: The A verage Investor Holds the M arket

5

CAPM Lesson 4: The Factor Risk Premium Has an Econom ic Story

5

CAPM Lesson 5: Risk Is Factor Exposure

6

CAPM Lesson 6: A ssets Paying O ff in Bad Tim es Have Low Risk Premiums

6

1.5 Multifactor Models

7

Pricing Kernels

7

Pricing Kernels versus Discount Rate M odels

7

M ultifactor Model Lessons

8

1.6 Failures of the CAPM

9

Chapter 2

Factors

13

2.1 Chapter Summary

14

2.2 Value Investing

14

2.3 Macro Factors

14

Econom ic Grow th

15

Inflation

15

Volatility

17

O ther Macro Factors

19

2.4 Dynamic Factors

21

Fam a-French (1993) Model

21

Size Factor

22

2.5 Value Factor

23

Rational Theories of the Value Premium

23

Behavioral Theories of the Value Premium

24

Value in O ther A sset Classes

25

Momentum

25

2.6 Value Investing Redux

27 ••• in

Chapter 3 Alpha (and the Low Risk Anomaly) 29

57

Risk-Factor-Neutral Alphas

57

4.4 Transactions Costs

57

4.5 Practical Details

58

3.1 Chapter Summary

30

4.6 Portfolio Revisions

59

3.2 GM Asset Management and Martingale

30

4.7 Techniques for Portfolio Construction

60

3.3 Active Management

30

Screens

61

Definition of Alpha

31

Stratification

61

Benchm arks M atter

31

Linear Programming

61

Creating Alpha

32

Q uadratic Programming

62

3.4 Factor Benchmarks

34

Factor Regressions

34

Doing without Risk-Free A ssets

37

Time-Varying Factor Exposures

39

Non-Linear Payoffs

43

Does Alpha Even Exist?

44

3.5 Low Risk Anomaly

44

History

44

Volatility Anom aly

45

Beta Anom aly

46

Risk Anom aly Factors

47

Explanations

49

3.6 GM Asset Management and Martingale Redux

Chapter 4 Portfolio Construction 4.1 Introduction

iv

Benchmark- and Cash-Neutral Alphas

51

53 54

4.2 Alphas and Portfolio Construction

54

4.3 Alpha Analysis

56

Scale the Alphas

4.8 Tests of Portfolio Construction Methods

62

4.9 Alternatives to Mean/Variance Optimization

63

4.10 Dispersion

64

Exam ple

65

Characterizing Dispersion

65

Managing Dispersion

65

Summary

Chapter 5 Portfolio Risk: Analytical Methods

67

69

5.1 Portfolio VaR

70

5.2 VaR Tools

73

Marginal VaR

73

Incremental VaR

73

Com ponent VaR

75

5.3 Summary

76

5.4 Examples

77

A Global Portfolio Equity Report

77

56

Barings: An Exam ple in Risks

77

Trim Alpha O utliers

56

Neutralization

56

5.5 VaR Tools for General Distributions

79

■ Contents

5.6 From VaR to Portfolio Management

80

From Risk M easurem ent to Risk M anagem ent

80

From Risk M anagem ent to Portfolio M anagem ent

80

Conclusions

Chapter 6 VaR and Risk Budgeting in Investment Management 6.1 VaR Applications to Investment Management

82

83

84

Sell Side versus Buy Side

84

Investm ent Process

85

Hedge Funds

85

Chapter 7 Risk Monitoring and Performance Measurement 95 7.1 Overview

96

7.2 The Three Legs of Financial Accounting Control: Planning, Budgeting, and Variance Monitoring

97

7.3 Building the Three-Legged Risk Management Stool: The Risk Plan, the Risk Budget, and the Risk Monitoring Process

98

The Risk Plan

98

The Risk Budget

99

Risk Monitoring

101

7.4 Risk Monitoring— Rationale and Activities

101

O bjectives of an Independent Risk M anagem ent Unit

102

86

Policy Mix and A ctive M anagem ent Risk

Exam ples of the Risk M anagem ent Unit in Action

103

86

Q uantifying Illiquidity Concerns

106

Funding Risk

87

C redit Risk Monitoring

107

Sponsor Risk

88

6.2 What Are theRisks?

86

Absolute and Relative Risks

6.3 Using VaR to Monitor and Control Risks

88

Using VaR to Check Com pliance

88

Using VaR to M onitor Risk

89

The Role of the Global Custodian

90

The Role of the M oney M anager

90

6.4 Using VaR to Manage Risks

90

Using VaR to Design G uidelines

90

Using VaR for the Investm ent Process

91

6.5 Risk Budgeting

92

Budgeting across A sset Classes

92

Budgeting across A ctive M anagers

93

Conclusions

94

7.5 Performance Measurement— Tools and Theory

107

Reasons That Support Using Multiple Perform ance M easurem ent Tools

107

How to Im prove the M eaningfulness of Perform ance M easurem ent Tools

107

Tool #1— The Green Zone

108

Tool #2— A ttribution of Returns

110

Tool #3— The Sharpe and Information Ratios

110

Tool #4— Alpha versus the Benchm ark

111

Tool #5— Alpha versus the Peer Group

111

Summary

112

Appendix A

113

Representative Q uestions to Help Define M anager Philosophies/Processes

Contents

113

■ v

Appendix B

114

Sector and Security Selection Decisions

134

Calculation of Account Perform ance

114

Summing Up Com ponent Contributions

136

Dollar-W eighted Return

114

Tim e-W eighted Return

115

Com puting Returns

116

Chapter 8 Portfolio Performance Evaluation 8.1 The Conventional Theory of Performance Evaluation

117

118

A verage Rates of Return

118

Tim e-W eighted Returns versus DollarW eighted Returns

118

Adjusting Returns for Risk

119

Risk-Adjusted Perform ance M easures

120

The Sharpe Ratio for O verall Portfolios

120

The M 2 M easure and the Sharpe Ratio

121

The Treynor Ratio

121

The Information Ratio

123

The Role of Alpha in Perform ance M easures

123

Implementing Perform ance M easurem ent: An Exam ple

124

Realized Returns versus Exp ected Returns 125 Selection Bias and Portfolio Evaluation

8.2 Style Analysis

126

126

8.3 Performance Measurement with Changing Portfolio Composition 128 Perform ance Manipulation and the M orningstar Risk-Adjusted Rating

8.4 Market Timing

130

The Potential Value of M arket Timing

131

Valuing M arket Timing as a Call Option

132

The Value of Im perfect Forecasting

133

8.5 Performance Attribution Procedures A sset Allocation Decisions

vi

129

■ Contents

133 134

Summary

137

Problem Sets

138

CFA® Problems

142

Solutions to Concept Checks

146

Chapter 9

Hedge Funds

147

9.1 The Hedge Fund Business Model—A Historical Perspective

148

9.2 Empirical Evidence of Hedge Fund Performance

150

W ere the Lofty Expectations of Early Hedge Fund Investors Fulfilled?

151

The Arrival of Institutional Investors

154

Hedge Fund Perform ance— The Post Dot-com Bubble Era

154

A bsolute Return and Alpha— A Rose by Any O ther N am e?

155

9.3 The Risk in Hedge Fund Strategies

161

From Passive Index Strategies to A ctive Hedge Fund Styles

161

Peer-Group Style Factors

162

Return-Based Style Factors

162

Top-Down versus Bottom-Up M odels of Hedge Fund Strategy Risk

163

Directional Hedge Fund Styles: Trend Follow ers and Global Macro

163

Event-Driven Hedge Fund Styles: Risk A rb itrag e and D istressed

165

Relative Value and Arbitrage-like Hedge Fund Styles: Fixed Income A rb itrag e, Convertible A rb itrag e, and Long/Short Equity

167

Niche Strategies: D edicated Short Bias, Em erging M arket and Equity M arket Neutral

170

9.4 Where Do Investors Go from Here? Portfolio Construction and Perform ance Trend

172 172

9.5 Risk Management and a Tale of Two Risks

177

9.6 Alpha-Beta Separation, Replication Products, and Fees

181

Concluding Remarks

183

Chapter 10 Performing Due Diligence on Specific 187 Managers and Funds 10.1 Be Prepared

188

10.2 Learn from the Past— From Both Successes and Failures

188

10.3 If It Looks Too Good to Be True, It Probably Is

189

10.4 Remember, It's Still about Returns!

189

10.5 Common Elements of the Due Diligence Process

189

10.6 Investment Management

190

W hat Is Your Strateqy, and How Does It W ork?

190

How Is Equity O w nership Allocated among the Portfolio M anagem ent, Trading, and Research Team s?

191

Is the Track Record Reliable?

191

W ho A re the Principals, and Are They Trustw orthy?

10.7 Risk Management Process

191

192

How Is Risk M easured and M anaged?

192

How A re Securities Valued?

192

W hat Is the Portfolio Leverage and Liquidity?

192

Does the Strategy Exp o se the Investor to Tail Risk?

193

How O ften Do Investors G et Risk Reports, and W hat Do They Include?

193

Do the Fund Terms Make Sense for the Strategy?

193

10.8 Fund Operating Environment, Documentation, Financials, and Service Providers 193 Internal Control A ssessm ent

193

Docum ents and Disclosures

194

Service Provider Evaluation

196

10.9 Business Model Risk

196

10.10 Fraud Risk

198

Summary

199

Chapter 11 Predicting Fraud by Investment Managers 201 11.1 Introduction

202

11.2 Related Research

203

11.3 Data

203

Investm ent Fraud

203

Form A D V Data

205

Fund-Level Data: Returns and Fees

208

11.4 Predicting Fraud

208

Prediction Models

209

The Econom ic Interpretation of the Prediction Models

212

Out-of-Sam ple Prediction of Fraud

215

Annual Cross-Sectional Regressions

216

Initiation versus Continuance of Fraud

216

Firm -W ide Fraud versus Fraud by Rogue Em ployees

218

11.5 Are Investors Compensated for Fraud Risk?

Contents

218

■ vii

221

11.7 Conclusion

226

Appendix A

226

Variable Definitions

viii

Appendix B

11.6 Data Access and Implementation

■ Contents

226

Supplementary Data

Index

227 227

229

On behalf of our Board of Trustees, GARP's staff, and particu­ larly its certification and educational programs teams, I would like to thank you for your interest in and support of our Financial Risk Manager (FRM®) program.

The FRM program addresses the financial risks faced by both non-financial firms and those in the highly interconnected and sophisticated financial services industry, because its coverage is not static, but vibrant and forward looking.

The past couple of years have been difficult due to COVID-19. And in that regard, our sincere sympathies go out to anyone who was ill or suffered a loss due to the pandemic.

The FRM curriculum is regularly reviewed by an oversight com­ mittee of highly qualified and experienced risk-management professionals from around the globe. These professionals con­ sist of senior bank and consulting practitioners, government regulators, asset managers, insurance risk professionals, and academics. Their mission is to ensure the FRM program remains current and its content addresses not only standard credit and market risk issues, but also emerging issues and trends, ensur­ ing FRM candidates are aware of what is or is expected to be important in the near future. We're committed to offering a pro­ gram that reflects the dynamic and sophisticated nature of the risk-management profession and those who are making it a career.

The FRM program also experienced many virus-related chal­ lenges. Because we always place candidate safety first, we cancelled the May 2020 FRM exam offering and deferred all can­ didates to October, while reserving an optional date in January 2021 for candidates not able to sit for the examination in October. A change like this has never happened before. Ultimately, we were able to offer the FRM exam to all 2020 registered candidates who wanted to sit for it during the year and were not constrained by COVID-related restrictions, which was most of our registrants. Since its inception in 1997, the FRM program has been the global industry benchmark for risk-management professionals wanting to demonstrate objectively their knowledge of financial risk-management concepts and approaches. Having FRM hold­ ers on staff also tells companies' that their risk-management professionals have achieved a demonstrated and globally adopted level of expertise. In a world where risks are becoming more complex daily due to any number of technological, capital, governmental, geopoliti­ cal, or other factors, companies know that FRM holders possess the skills to understand and adapt to a dynamic and rapidly changing financial environment.

We wish you the very best as you study for the FRM exams, and in your career as a risk-management professional. Yours truly,

Richard Apostolik President & CEO

Preface

■

ix

Chairperson Michelle McCarthy Beck

Former GARP Board Member

Members Richard Apostolik

Dr. Attilio Meucci, CFA

President and CEO, Global Association of Risk Professionals

Founder, ARPM

Richard Brandt

Dr. Victor Ng

MD Operational Risk Management, Citigroup

MD Head of Risk Architecture, Goldman Sachs

Julian Chen, FRM, SVP FRM Program Manager, Global Association of Risk Professionals

Dr. Matthew Pritsker Senior Financial Economist and Policy Advisor / Supervision, Regulation, and Credit, Federal Reserve Bank of Boston

Dr. Christopher Donohue, MD GARP Benchmarking Initiative, Global Association of Risk Professionals

Dr. Samantha Roberts, FRM

SVP Balance Sheet Analytics & Modeling, PNC Bank

Donald Edgar, FRM

Dr. Til Schuermann

MD Risk & Quantitative Analysis, BlackRock

Partner, Oliver Wyman

Herve Geny

Nick Strange Senior Technical Advisor, Operational Risk & Resilience, Supervisory Risk Specialists, Prudential Regulation Authority, Bank of England

Former Group Head of Internal Audit, London Stock Exchange Group and former CRO, ICAP Keith Isaac, FRM

VP Capital Markets Risk Management, TD Bank Group William May, SVP

Global Head of Certifications and Educational Programs, Global Association of Risk Professionals

x

■

FRM® Com m ittee

Dr. Sverrir Porvaldsson, FRM Senior Quant, SEB

Facto r Theo ry Learning Objectives A fter com pleting this reading you should be able to: Provide exam ples of factors that im pact asset prices and

D escribe m ultifactor m odels and com pare and contrast

explain the theory of factor risk premiums.

m ultifactor m odels to the C A PM .

Discuss the capital asset pricing model (CAPM ) including

Explain how stochastic discount factors are created and

its assum ptions and explain how factor risk is addressed in

apply them in the valuation of assets.

the C A PM . Explain the im plications of using the CAPM to value

D escribe efficient m arket theory and explain how m arkets can be inefficient.

assets, including equilibrium and optimal holdings, exposure to factor risk, its treatm ent of diversification benefits, and shortcom ings of the CA PM .

E x c e rp t is C h a p ter 6 o f A sset M anagem ent: A System atic Approach to Factor Investing, by A n d re w A n g . S e e bibliography on p p . 195-200.

1

1.1 CHAPTER SUMMARY

W hy did so many asset classes crash all at once? And given that they did, was the concept of diversification dead?

A ssets earn risk premiums because they are exposed to under­

In this chapter, we develop a theory of factor risk prem iums.

lying factor risks. The capital asset pricing model (C A PM ), the

The factor risks constitute different flavors of b a d tim es and the

first theory of factor risk, states that assets that crash when the

investors who bear these factor risks need to be com pensated

m arket loses money are risky and therefore must reward their

in equilibrium by earning factor risk premiums. A ssets have risk

holders with high risk prem iums. W hile the CAPM defines bad

premiums not because the assets them selves earn risk prem i­

tim es as tim es of low m arket returns, m ultifactor m odels capture

ums; assets are bundles of factor risks, and it is the exposures to

multiple definitions of bad tim es across many factors and states

the underlying factor risks that earn risk prem iums. These factor

of nature.

risks m anifest during bad tim es such as the financial crisis in late 2008 and early 2009.

1.2 THE 2008-2009 FINANCIAL CRISIS During the financial crisis of 2008 and 2009, the price of most

1.3 FACTOR THEORY

risky assets plunged. Table 1.1 shows that U.S. large cap equities

Factors are to assets w hat nutrients are to food. Table 1.2 is

returned —37% ; international and em erging m arkets equities

from the Food and Nutrition Board, which is part of the Institute

had even larger losses. The riskier fixed income securities,

of M edicine of the National A cadem ies, and lists recom m ended

like corporate bonds, em erging m arket bonds, and high yield

intakes of the five m acronutrients— water, carbohydrates, pro­

bonds, also fell, tum bling along with real estate. "A lternative"

tein, fiber, and fat— for an "averag e" male, fem ale, and child.

investm ents like hedge funds, which trum peted their immunity

Carbohydrates can be obtained from food made from cereals

to m arket disruptions, w ere no safe refuge: equity hedge funds

and grains. Protein is obtained from m eat and dairy products.

and their fixed income counterparts fell approxim ately 20%.

Fiber is available from w heat and rice. Fat we can consume

Com m odities had losses exceeding 30% . The only assets to go

from animals but also certain plant foods such as peanuts. Each

up during 2008 were cash (U.S. Treasury bills) and safe-haven

type of food is a bundle of nutrients. Many foods contain more

sovereign bonds, especially long-term U.S. Treasuries.

than just one m acronutrient: for exam ple, rice contains both

Table 1.1

2

Returns of Asset Classes in 2008

Cash

Three-m onth T-bill

1.3%

Core Bonds

Barcap A ggregate Index

5.2%

Global Bonds

Citigroup World G overnm ent

10.9%

TIPS

Citigroup US Inflation Linked

- 1.2%

Em erging M arket Bonds

JP M Em erging M arkets Bond Index

- 9 .7 %

US High Yield

Merrill Lynch High Yield M aster

- 2 6 .3 %

Large C ap Equity

S&P 500

- 3 7 .0 %

Small Cap Equity

Russell 2000

- 3 3 .8 %

International Equity

M SCI World ex US

- 4 3 .2 %

Em erging M arkets Equity

IFC Em erging M arkets

- 5 3 .2 %

Public Real Estate

N A R EIT Equity REITS

- 3 7 .7 %

Private Real Estate

N C R EIF Property Index

- 1 6 .9 %

Private Capital

Venture Econom ics (Venture and Buyouts)

- 20.0%

Equity Hedge Funds

HFRI Equity Hedge Index

- 20.6%

Fixed Income Hedge Funds

HFRI Fixed Income Index

- 1 7 .8 %

Com m odities

Dow Jo n es A IG Com m odity Index

- 3 5 .7 %

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Table 1.2

Nutrients and Food Macronutrients Male

Female

Child

Examples of Food

W ater

3.7 L/day

2.7 L/day

1.7 L/day

Carbohydrates

130 g/day

130 g/day

130 g/day

Bread, Beans, Potato, Rice

Protein

56 g/day

46 g/day

19 g/day

C heese, Milk, Fish, Soya bean

Fiber

38 g/day

25 g/day

25 g/day

Peas, W heat, Rice

Fat

20-35% of calories

25-35% of calories

Oily fish, Peanuts, Anim al fat

Source: Food and Nutrition Board, National Academies, 2004. carbohydrates and fiber. Different individuals, w hether sick or

nutrients. Sim ilarly, some asset classes can be considered

healthy, male or fem ale, or young or old, have different m acro­

factors them selves— like equities and governm ent fixed

nutrient requirem ents. W e eat food for the underlying nutrients;

income securities— while other assets contain many differ­

it is the nutrients that give sustenance.

ent factors. Corporate bonds, hedge funds, and private

Factor risks are the driving force behind assets' risk prem i­ ums. An im portant theory of factor risk is the C A P M , which we explore in the next section. The CA PM states that there is only one factor driving all asset returns, which is the m arket return in excess of T-bills. All assets have different exposures to the m arket factor and the greater the exposure, the higher the risk prem ium. The m arket is an exam ple of a tradeable, investm ent factor. O ther exam ples include interest rates, value-growth investing, low volatility investing, and momentum portfolios. Factors can also be fundam ental macro factors, like inflation and econom ic growth. A ssets have different payoffs during high or low inflation periods or during econom ic recessions and expan­ sions. We leave a com plete exposition of the various types of factors to the next chapter. In this chapter, we describe the underlying theory of factor risk. There are three sim ilarities betw een food and assets: 1. Factors matter, not assets.

equity contain different amounts of equity risk, volatility risk, interest rate risk, and default risk. Factor theory predicts these assets have risk premiums that reflect their underlying factor risks.

3. Different investors need different risk factors. Ju st as different people have different nutrient needs, different investors have different optimal exposures to different sets of risk factors. Volatility, as we shall see, is an im portant factor. Many assets and strategies lose money during tim es of high volatility, such as observed during the 2007-2008 financial crisis. Most investors dislike these tim es and would prefer to be protected against large increases in volatility. A few brave investors can afford to take the opposite position; these investors can w eather losses during bad tim es to col­ lect a volatility premium during normal tim es. They are paid risk premiums as com pensation for taking losses— som e­

If an individual could obtain boring, tasteless nutrients

tim es big losses, as in 2008-2009— during volatile tim es.

made in a laboratory, she would com fortably m eet her

A nother exam ple is that investors have different desired

nutrient requirem ents and lead a healthy life. (She would,

exposure to econom ic growth. O ne investor may not

however, deprive herself of gastronom ic enjoym ent.) The

like tim es of shrinking G D P growth because he is likely

factors behind the assets matter, not the assets them selves.

to becom e unem ployed in such circum stances. Another

Investing right requires looking through asset class labels to

investor— a bankruptcy lawyer, perhaps— can tolerate low

understand the factor content, just as eating right requires

G D P growth because his labor income increases during

looking through food labels to understand the nutrient

recessions. The point is that each investor has different

content.

preferences, or risk aversion coefficients, for each different

2. A ssets are bundles of factors.

source of factor risk.

Foods contain various com binations of nutrients. Certain

There is one difference, however, betw een factors and nutrients.

foods are nutrients them selves— like w ater— or are close

Nutrients are inherently good for you. Factor risks are bad. It

to containing only one type of nutrient, as in the case of

is by enduring these bad experiences that we are rewarded

rice for carbohydrates. But generally foods contain many

with risk premiums. Each different factor defines a different set

Chapter 1 Factor Theory

■ 3

of bad tim es. They can be bad econom ic tim es— like periods

of finance: 75% of finance professors advocate using it, and 75%

of high inflation and low econom ic growth. They can be bad

of C FO s em ploy it in actual capital budgeting decisions despite

tim es for investm ents— periods when the aggregate m arket or

the fact that the CA PM does not hold.*1 It works approxim ately,

certain investm ent strategies perform badly. Investors exposed

and well enough for most applications, but it fails m iserably in

to losses during bad tim es are com pensated by risk premiums

certain situations (as the next chapter will detail). Part of the

in good tim es. The factor theory of investing specifies different

tenacious hold of the CAPM is the way that it conveys intuition

types of underlying factor risk, where each different factor rep­

of how risk is rewarded.

resents a different set of bad tim es or experiences. We describe the theory of factor risk by starting with the most basic factor risk premium theory— the CAPIVI, which specifies just one factor: the m arket portfolio.

W hat does the CA PM get right?

CAPM Lesson 1: Don't Hold an Individual Asset, Hold the Factor

1.4 CAPM

The CA PM states that one factor exists and that factor is the

The CAPM was revolutionary because it was the first cogent

m arket capitalization. This corresponds to a m arket index fund.

theory to recognize that the risk of an asset was not how that asset behaved in isolation but how that asset moved in relation to other assets and to the m arket as a whole. Before the C A P M , risk was often thought to be an asset's own volatility. The CA PM said this was irrelevant and that the relevant measure of risk was how the asset covaried with the m arket portfolio— the beta of the asset. It turns out that asset volatility itself m atters, as we shall see in Chapter 2, but for the purpose of describing the CA PM and its incredible im plications, we can ignore this for the tim e being. The CAPM was form ulated in the 1960s by Ja c k Treynor (1961), W illiam Sharpe (1964), John Lintner (1965), and Jan Mossin (1966), building on the principle of diversification and meanvariance utility introduced by Harry M arkowitz in 1952. For their work on CAPM and portfolio choice, Sharpe and M arkowitz received the 1990 Nobel Prize in econom ics. (Merton Miller was awarded the Nobel Prize the same year for contributions to corporate finance.) Lintner and Mossin, unfortunately, had both died by then. Treynor, whose original m anuscript was never pub­ lished, has never received the recognition that he deserved. I state upfront that the CA PM is well known to be a spectacular failure. It predicts that asset risk prem iums depend only on the asset's beta and there is only one factor that m atters, the market portfolio. Both of these predictions have been dem olished in thousands of em pirical studies. But, the failure has been glori­ ous, opening new vistas of understanding for asset owners who must hunt for risk premiums and manage risk. The basic intuition of the CAPM still holds true: that the factors underlying the assets determ ine asset risk premiums and that these risk premiums are com pensation for investors' losses dur­

m arket portfolio, where each stock is held in proportion to its The factor can be optim ally constructed by holding many assets so that nonfactor, or idiosyncratic risk, is diversified away. A sset owners are better off holding the factor— the m arket portfolio— than individual stocks. Individual stocks are exposed to the m arket factor, which carries the risk premium (it is the nutrient), but also have idiosyncratic risk, which is not rewarded by a risk premium (this is the part that carries no nutritional value). Investors can diversify away the idiosyncratic part and increase their returns by holding the m arket factor portfolio, rather than any other com bination of individual stocks. The m arket portfolio represents system atic risk, and it is pervasive: all risky assets have risk premiums determ ined only by their exposure to the m arket portfolio. M arket risk also affects all investors, excep t those who are infinitely risk averse and hold only risk-free assets. The key to this result is diversification. The CAPM is based on investors having mean-variance utility and the most im portant concept in mean-variance investing is diversification. Diversification ensures that, absent perfect correlation, when one asset performs badly, some other assets will perform well, and so gains can partly offset losses. Investors never want to hold assets in isolation; they improve their risk-return trade­ off by diversifying and holding portfolios of many assets. This balance across many assets that are not perfectly correlated im proves Sharpe ratios. Investors will diversify more and more until they hold the most diversified portfolio possible— the market portfolio. The market factor is the best, most-well diversified portfolio investors can hold under the CA PM . The CA PM states that the m arket portfolio is held by every investor— a strong implication that is outright rejected in data.

ing bad tim es. Risk is a property not of an asset in isolation but how the assets move in relation to each other. Even though the CA PM is firmly rejected by data, it remains the workhorse model

4

■

1 See Welch (2008) and Graham and Harvey (2001), respectively.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

N evertheless, it is useful to understand how we can leap from a

disappear. The m arket factor is system atic and affects all assets.

diversified portfolio to the m arket being the only relevant factor.

The m arket risk premium is a function of the underlying inves­

The mean-variance frontier with the capital allocation line (CA L), is shown in Figure 1.1. This is the solution to the mean-variance investing problem . Investors hold different amounts of the risk-free asset and the mean-variance efficient (MVE) portfolio depending on their risk aversion. Now here come the strong assum ptions of the C A P M . Assum e that the set of m eans, vola­ tilities, and correlations are the sam e for all investors. Then all investors hold the same M VE portfolio—just in different quanti­ ties depending on their own risk aversion. Since everyone holds the sam e M VE and this is the best portfolio that can be held by all investors, the M VE portfolio becom es the m arket factor in equilibrium .

Equilibrium The equilibrium concept is extrem ely im portant. Equilibrium occurs when investor dem and for assets is exactly equal to sup­ ply. The m arket is the factor in equilibrium because in CAPM land, everyone holds the M VE portfolio (except for those who are infinitely risk averse). If everyone's optimal risky portfolio (which is the MVE) assigns zero w eight to a certain asset, say A A stock, then this cannot be an equilibrium . Som eone must hold A A so that supply equals dem and. If no one wants to hold A A , then A A must be overpriced and the expected return of A A is too low. The price of A A falls. The expected payoff of A A stays constant under CA PM assum ptions, so that as the price of A A falls, the expected return of A A increases. AA 's price falls until investors want to hold exactly the number of A A shares

tors' risk aversions and utilities. That is, the risk premium of the m arket factor reflects the full setup of all people in the econ­ omy. The factors that we introduce later— tradeable factors like value-growth investing and volatility investing or macro factors like inflation and econom ic growth— will also carry risk premiums based on investor characteristics, the asset universe, and the production capabilities of the econom y. They will disappear only if the econom y totally changes. Equilibrium factor risk premiums will not disappear because clever hedge funds go and trade them — these types of investm ent strategies are not factors. Investors cannot arbitrage away the m arket factor and all other system atic factors.

CAPM Lesson 2: Each Investor Has His Own Optimal Exposure of Factor Risk In Figure 1.1, all investors will hold the m arket portfolio, just in different proportions. Pictorially, they have different proportions of the risk-free asset and the m arket portfolio and lie on differ­ ent positions on the C A L line. Thus, each individual investor has a different am ount of factor exposure just as different individuals have different nutrient requirem ents.

CAPM Lesson 3: The Average Investor Holds the Market The m arket portfolio represents the average holdings across

outstanding. Then, the expected return is such that supply is

investors. The intersection of the C A L with the mean-variance

equal to dem and in equilibrium . Since all investors hold the

frontier represents an investor who holds 100% in the MVE port­

M VE portfolio, the M VE portfolio becom es the m arket port­

folio. This tangency point represents the average investor. The

folio, and the m arket consists of each asset in term s of m arket

risk aversion corresponding to this 100% portfolio position is the

capitalization w eights.

risk aversion of the m arket.2

Equilibrium ensures that the factor— the m arket portfolio—

Note that as investors differ from the average investor, they will

will have a risk premium and that this risk premium will not

be exposed to more or less m arket factor risk depending on their own risk preferences.

CAPM Lesson 4: The Factor Risk Premium Has an Economic Story The C A L in Figure 1.1 for a single investor is called the capital m arket line (CM L) in equilibrium , since under the strong assum p­ tions of the CA PM every investor has the same CM L. (The MVE

2 Technically speaking, the market is the wealth-weighted average across all investors.

Chapter 1 Factor Theory

■ 5

portfolio is the m arket factor portfolio.) The equation for the

the higher the co-m ovem ent (the higher cov(r,-, rm)), the higher

C M L pins down the risk premium of the m arket:

the asset's beta.

E ( r J ~ rf = ycr2 mi

(1. 1)

I will not form ally derive Equation (1.2).3 But it contains som e nice intuition: m ean-variance investing is all about d iversifica­

where E(rm) — ry is the m arket risk prem ium, or the expected return on the m arket in excess of the risk-free rate; 7 is the risk aversion of the "averag e" investor; and crm is the volatility of the m arket portfolio. The CA PM derives the risk premium in term s of underlying agent preferences (7 is the average risk aversion across all investors, where the average is taken weighting each individual's degree of risk aversion in proportion to the wealth of that agent).

tion benefits. B eta— the C A P M 's m easure of risk— is a m easure of the lack o f diversification potential. Beta can be w ritten as A = Pi,m(TJ (Trr» w here p ( m is the correlation betw een asset i's

return and the m arket return, rr, is the volatility of the return of asset /, and crm is the volatility of the m arket factor. The lower the correlation with a portfolio, the greater the diversification benefit with resp ect to that portfolio because the asset w as more likely to have high returns when the portfo­

According to the CA PM in Equation (1.1), as the market

lio did badly. Thus, high betas mean low diversification

becom es more volatile, the expected return of the market

benefits.

increases and equity prices contem poraneously fall, all else equal. We experienced this in 2008 and 2009 when volatility sky­ rocketed and equity prices nosedived. Expected returns in this period on were very high (and realized returns were indeed high in 2009 and 2010). It is intuitive that the m arket risk premium in Equation (1.1) is proportional to m arket variance because under the CA PM investors have mean-variance preferences: they dis­ like variances and like expected returns. The m arket portfolio is the portfolio that has the lowest volatility among all portfolios that share the same mean as the m arket, or the m arket has

If we start from a diversified portfolio, investors find assets with high betas— those assets that tend to go up when the m arket goes up, and vice versa— to be unattractive. These high beta assets act like the diversified portfolio the investor already holds, and so they require high exp ected returns to be held by investors. In contrast, assets that pay off when the mar­ ket tanks are valuable. These assets have low betas. Low beta assets have trem endous diversification benefits and are very attractive to hold. Investors, therefo re, do not need to be com ­ pensated very much for holding them . In fact, if the payoffs of

the highest reward-to-risk ratio (or Sharpe ratio). The m arket

these low beta assets are high enough when the m arket return

removes all idiosyncratic risk. This remaining risk has to be rew arded, and Equation (1.1) states a precise equation for the risk premium of the m arket. As the average investor becom es more risk averse to variance (so 7 increases), the risk premium of the m arket also increases.

is low, investors are willing to pay to hold these assets rather than be paid. That is, assets with low enough betas actually have n eg a tive exp ected returns. Th ese assets are so attractive because they have large payoffs when the m arket is crashing. G o ld , or som etim es governm ent bonds, are often presented as exam ples of low (or negative) beta assets which tend to pay

CAPM Lesson 5: Risk Is Factor Exposure

off when the stock m arket crashes. (G overnm ent bonds w ere

The risk of an individual asset is measured in term s of the factor

in 2008.)

exposure of that asset. If a factor has a positive risk prem ium, then the higher the exposure to that factor, the higher the expected return of that asset. The second pricing relationship from the CA PM is the traditional

one of the few asset classes to do well in the financial crisis

CAPM Lesson 6: Assets Paying Off in Bad Times Have Low Risk Premiums

beta pricing relationship, which is form ally called the security

A nother way to view the SM L relationship in Equation (1.2) is

m arket line (SML). Denoting stock i's return as r(- and the risk-free

that the risk premium in the CAPM is a reward for how an asset

return as rf, the SM L states that any stock's risk premium is pro­

pays off in bad tim es. Bad tim es are defined in term s of the fac­

portional to the m arket risk premium:

tor, which is the m arket portfolio, so bad tim es correspond to

m

cov(n, rm) - rf = ----- ( E ( r J - rf) v a r(rj

(1.2)

- b,(E(rm) - rf).

low (or negative) m arket returns. If the asset has losses when the m arket has losses, the asset has a high beta. W hen the m arket has gains, the high beta asset also gains in value. Investors are, on average, risk averse so that the gains during good tim es

The risk premium on an individual stock, E(r,) — rf, is a function of that stock's beta, fy — cov(r/r rm)/var(rm). The beta is a m ea­ sure of how that stock co-moves with the m arket portfolio, and

6

■

3 A textbook MBA treatment is Bodie, Kane, and Marcus (2011). A more rigorous treatment is Cvitani'c and Zapatero (2004).

Financial Risk Manager Exam Part II: Risk Management and Investment Management

do not cancel out the losses during bad tim es. Thus, high beta

bad tim es with multiple variables. The CA PM is actually a special

assets are risky and require high expected returns to be held in

case where m is linear in the m arket return:4

equilibrium by investors. Conversely, if the asset pays off when the m arket has losses, the asset has a low beta. This asset is attractive and the expected return on the asset can be low— investors do not need much com pensation to hold these attractive assets in equilibrium . More generally, if the payoff of an asset tends to be high in bad tim es, this is a valuable asset to hold and its risk premium is low.

m — a + b X rm,

(1.3)

for som e constants a and b. (A pricing kernel that is linear in the m arket gives rise to a SM L that with asset betas with respect to the m arket in Equation (1.2).) W ith our "m " notation, we can specify multiple factors very easily by having the SDP depend on a vector of factors, F — (f1r f2, • • • • f/0bt T fi/t/

(3.12)

v---------------------- V ------------------------------- '

$1

where rjt is the return of C a lP ER S , rst is the S&P 500 equity m arket return, and r^t is a bond portfolio return— in this case, the Ibbotson A ssociates long-term corporate bond total return index. To obtain a benchm ark portfolio, we require the restric­ tion that

French regression, implying that adding the momentum factor has not improved the fit of the factor regression. Buffett's alpha

ck

$1

P s + Pb = 1 •

That is, the portfolio w eights must sum to one. Then, $1 placed into C alP ER S on the left-hand side of Equation (3.12) can be replicated by a portfolio of stocks and bonds (with portfolio w eights, which also must sum to one) on the right-hand side, plus any alpha generated by the C alP ER S ' funds manager. Estim ating Equation (3.12) on C alP ER S ' annual returns from 1990 to 2011, we get the following:

+ $0.66 in the m arket portfolio — $0.50 in small caps + $0.50 in large caps

Coefficient

T-stat

- 1. 11%

- 1 .1 6

+ $0.36 in value stocks — $0.36 in growth stocks

Alpha

— $0.04 in past winning stocks + $0.04 in past losing stocks

Bond Loading

0.32

13.97

Stock Loading

0.68

13.97

Adj R2

0.90

Buffett is also adding: + 0 .68% (alpha) per month. Figure 3.2 shows cum ulative excess returns relative to the FamaFrench benchm ark in the dashed line and the Fam a-French plus momentum benchm ark in the solid line. Both lie below the

The high adjusted R2 of 90% is am azing: C alP ER S' returns are extrem ely well explained by this mimicking portfolio of 32%

CAPM benchm ark, which is mainly a consequence of lowering

bonds and 68% stocks!

Buffett's alpha by including the H M L value-growth factor.

The point estim ate of C alP ER S alpha is negative, at 21.11 % per

Doing without Risk-Free Assets

year. Should w e im m ediately fire the C alP ER S funds m anager and put everything into low-cost index funds? Form ally, w e can only make the statem ent that "w e fail to reject the hypothesis

Benchm ark portfolios need not include risk-free assets.

that C alPER S adds value relative to the 32% bonds/68% stocks

CalPERS

benchm ark portfolio at the 95% level" because the t-statistic is

C alP ER S is the largest public pension fund in the United States and had $246 billion of assets at Ju n e 30, 2 0 11.10 A benchm ark

10 Data and additional information for this section is from "California Dreamin': The Mess at CalPERS," Columbia CaseWorks, #120306 and "Factor Investing: The Reference Portfolio and Canada Pension Plan Investment Board," Columbia CaseWorks #120302.

less than two in absolute value. C a lP E R S , how ever, is an exp en sive fund. In 2011 its internal estim ate of its exp en se ratio was upward of 0 .5 0 % , while exp en se ratios inferred from its annual reports exceed 0 .80 % . (W hat a travesty that it does not exp licitly report its exp ense ratio in its annual report!) Th ese exp en se ratios are much higher than those of industry p eers. The m edian exp en se ratio

Chapter 3 Alpha (and the Low-Risk Anomaly)

■ 37

of the largest pension plans studied by Bauer, C rem ers, and

portfolio of stocks, bonds, and, potentially, listed REITs, which

Frehen (2009) w as 0 .2 9 % ; at the largest 30% of defined ben­

offer indirect real estate exposure?

efit plans, the exp en se ratios are just 0 .1 5 % . Thus, C a lP E R S

Real estate returns are com plicated because they are not trade-

is three to four tim es more exp en sive than the m edian fund

able. Leaving aside this problem , I take quarterly real estate

in Bauer, C rem ers, and Frehen's sam ple, and nearly nine

returns from the National Council of Real Estate Investm ent

tim es more exp en sive than the largest 30% of pension plans! Exp e n se ratios for m anaging typical index stock or bond funds at C a lP E R S ' scale are w ay below 0 .1 0 % . (The N orw egian so v­ ereign w ealth fund had an exp en se ratio of 0.06% in 2012.) So yes, given that C a lP E R S could run a benchm ark stock-bond portfolio for close to zero, perhaps it should consider firing its funds m anager and going co m p letely index.

Fiduciaries from Ju n e 1978 to D ecem ber 2011 (my left-hand side variable). I consider factor benchm ark regressions using S&P 500 stock returns, Ibbotson long-term corporate bond returns, and the FT S E N A R EIT index returns (my right-hand side variables). I run the following factor regressions:

Figure 3.3 plots cum ulative excess returns for C alP ER S. The

rit =

a + PREiTR E IT t + A /b t

estim ated 32% stocks/68% bonds benchm ark portfolio is shown

rit

a

in the solid line and a standard 40% stocks/60% bonds portfolio

Ot

oc

is overlaid for com parison. Note the sim ilarity. C alP ER S per­

T Pr

e ij R

+ e it>

(3.13)

AbLbt T (3srst+ s lt,

E I T i + Abrbt "P /3srst + s )t,

where REIT, is the return to the N A R EIT portfolio consisting of

form ance im proves during 2000-2007. But during the financial crisis in 2008, things com pletely fall apart, and the fund's perfor­ mance continued to deteriorate in 2010 and 2011. A large part

traded REITs, rbt is the bond return, and rst is the stock return, which have factor loadings of /3RE/T, (3b, and /3S, respectively. We require that, in all cases, the factor loadings add up to one so

of this dismal showing was due to C alP ER S ' failure to rebalance in 2008 and 2009: it sold equities rather than buying them when

that they can be interpreted as a factor portfolio benchm ark.

prices w ere low.

Real Estate Canada Pension Plan considers real

Coefficient

T-stat

Coefficient

T-stat

Coefficient

T-stat

- 0 .5 1 %

- 1.02

- 0 .4 3 %

- 0 .9 0

- 1 .5 0 %

- 1 .0 5

estate to have many characteristics

Alpha

in common with fixed income and

REIT Loading

0.30

Bond Loading

0.70

equities— so much in common that the plan doesn't consider real estate a sep ­ arate asset class. But can real estate

5.92 14.0

Stock Loading

0.65 0.35

12.7 6.95

0.12

1.81

0.26

3.75

0.61

11.6

exposure be replicated by a factor The estim ated coefficients are shown in the table above. For all of th ese facto r b enchm arks, d irect real estate does not offer sig n ifican t returns in e xcess of a facto r b enchm ark. In fa ct, the point estim ates are negative and around 0 .5 0 % per quarter. In terestin g ly, the facto r benchm ark consisting of ju st bonds and stocks ind icates that the optim al com bination of stocks and bonds to m im ic real estate is 35% stocks and 65% bonds. Figure 3.4 graphs cum ulative excess returns of direct real estate relative to these factor benchm arks. W hile there was some value added in the early 1980s relative to these REIT, bond, and stock factors, the factor benchm arks did much better than direct real estate from the mid-1980s to the early 2000s. Direct real estate picked up relative to the factor benchm arks in the mid-2000s, ------ 40% Bond/60% Equity

Fiaure 3.3

38

■

32% Bond/ 68% Equity

CalPERS cumulated excess returns.

coinciding with the period's property boom . Figure 3.4 clearly shows the crash in real estate m arkets in 2008 and 2009 toward the end of the sam ple.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

0.6 -i

Here are the Fam a-French and momentum factor regressions using constant factor w eights:

0.4 0.2

0

LSVEX

FMAGX

Alpha

0 .00%

- 0 .2 7 %

- 0 .1 4 %

0 .22%

t-stat

0.01

- 2 .2 3

- 1 .3 3

0.57

M K T Loading

0.94

1.12

1.04

0.36

t-stat

0.8

-1

Figure 3.4

1985

1990

1995

2000

2005

2010

Cum ulative N C R EIF excess returns.

38.6

42.2

BRK

3.77

S M B Loading

0.01

- 0 .0 7

- 0.12

- 0 .1 5

t-stat

0.21

- 1 .4 4

- 3 .0 5

- 0 .9 7

H M L Loading

0.51

- 0 .0 5

- 0 .1 7

0.34

14.6

- 1 .3 6

- 4 .9 5

2.57

UM D Loading

0.2

0.02

0.00

- 0 .0 6

t-stat

1.07

1.00

- 0 .1 7

- 0 .7 7

t-stat

1980

36.9

GSCGX

The only alpha that is statistically significant is Fidelity M agel­ lan, which is —0.27% per month or —3.24% per year. Poor

Time-Varying Factor Exposures William Sharpe, one of the inventors of the C A PM , introduced a powerful fram ework to handle time-varying benchmarks in 1992. He called it "style analysis." In our context, style analysis is a fac­ tor benchmark where the factor exposures evolve through tim e.11 To illustrate time-varying factor exposures in the spirit of Sharpe's style analysis, consider four funds: LSVEX: LSV Value Equity. LSV is a "quantitative value equity

investors in Fidelity lose money, and their losses are statistically significant. Berkshire Hathaway's alpha estim ate is positive but insignificant. O ur analysis in section 3.1 had a significantly posi­ tive alpha but we started in 1990. Now, starting ten years later in 2001, we don't even obtain statistical significance for Buffett. Detecting statistical significance of outperform ance is hard, even in sam ples of more than ten years. Looking at the factor loadings, LSV seem s to be a big value shop— with a large H M L loading of 0.51 (with a massive t-statistic of 14.6). Berkshire Hathaway is still value, too, with an H M L load­

m anager providing active m anagem ent for institutional inves­

ing of 0.34. Fidelity is a levered play on the m arket, with a beta

to rs" and was named after its founding academ ics: Jo se f

of 1.12. Since none of the UM D loadings are large or significant,

Lakonishok, Andrei Shleifer, and Robert Vishny. 12

none of these funds are momentum players.

FM A G X : Fidelity M agellan. O ne of the most fam ous retail

Style analysis seeks to rectify two potential shortcom ings of our

mutual funds, it grew to prom inence under superstar man­

analysis so far:

ager Peter Lynch in the 1980s and 1990s. G S C G X : Goldm an Sachs Capital G row th. How can we not include a Goldm an Sachs name? BRK: Berkshire Hathaway. Since w e've been using Buffett's exam ple, let's stay with it. I use monthly data from January 2001 to D ecem ber 2011.

1. The Fam a-French portfolios are not trad e ab le . 13 2. The factor loadings may vary over tim e.

Style Analysis with No Shorting Style analysis tries to replicate the fund by investing passively in low-cost index funds. The collection of index funds that replicate the fund is called the "style w e ig h t."

11 Computing standard errors for alphas when factor loadings vary over time, and even when the alphas themselves vary over time, is tricky, as Ang and Kristensen (2012) show. For a summary of style analysis, see Horst, Nijman, and de Roon (2004). 12 See http://www.lsvasset.com/about/about.html.

13 GM Asset Management has implemented tradeable versions of the Fama-French portfolios. See Scott (2012) for further details. Cremers, Perajisto, and Zitzewitz (2012) argue that the nontradeability of the Fama-French indices leads to distortions in inferring alpha.

Chapter 3 Alpha (and the Low-Risk Anomaly)

■ 39

To illustrate, let's take the following index ETFs:

beginning of the sam ple and at the end of the sam ple is just growth (SPYG ). Buffett's factor exposure is the most interesting.

SPY: SPD R S&P 500 ETF, which is designed to mimic

He starts off in 2006 being strongly value (SPYV). During the

the S&P 500;

financial crisis, he switches styles to becom e growth. Then as the

SPYV: SPD R S&P 500 Value ETF, which tracks the S&P

crisis subsides, he goes back to being a strong value manager.

500 value index; and

The excess return for t + 1 is the return of the fund at the end

S P Y G : SPDR S&P 500 Growth ETF, which replicates

of the period, t t o t + 1, minus the benchm ark portfolio form ed

the S&P 500 growth index.

using the w eights at tim e t:

Th ese low -cost ind ex E T F s are tra d e a b le , unlike the

ff+1 — rt+1 — [/^spy,t 5 P Y t+1 + /3SPyvt S P W t+1 + (3$pYG,t S P Y G t+ 1].

Fam a-French portfolios. Th ey belong to the SPD R (pro­

V

___________________________________________________________________________________________________________________________________ ______________________ ______________ ______________ ______________ ______________ ______________ ______________ ______________

V

nounced "sp id e r") fam ily of E T F s sponsored by State Street G lobal A d viso rs.

„

rt+ 1

I graph the excess returns in Panel B of Figure 3.5. The cum u­

O ur benchm ark factor regression for fund / (but I avoid the / sub­

lated excess returns are zero for LSV. Fidelity M agellan's returns

scripts to make the notation clearer) is

trend downward (recall that Magellan significantly subtracts

rt+1 ~ a t + fe y ,t5 P Y t+1 + /3SPyv,tSPYV t+1

(3.14)

+ P sP Y G ,tSp Y G t +'\ + et+1/

where we im pose the restriction PsPY.t + PsPYV.t + PsPYG.t ~ 1/ so that the factor loadings, or factor w eights, sum to one. The factor w eights on the right-hand side of Equation (3.14) consti­ tute a replicating portfolio for fund i. The main idea with style analysis is that we use actual trade-

value in the full-sam ple regressions). Goldm an's growth fund also has zero cum ulative excess returns. The only fund with an upward trend is Berkshire Hathaway.

Style Analysis with Shorting W hat if we allow shorting? In Figure 3.6, I allow the investor to take short positions in the ETFs. I use the following factor regression: rt+i — rf,t+1 = a i,t T ^spy,t(5PYt+1 — rf t+1)

(3.15)

+ ht(SPYV t+1 - S P Y G t+1) + et+1.

able funds in the facto r benchm ark. I used SPD R E T F s in Eq u a­

This is the " E T F version" of the Fam a-French (1993) regression

tion (3.14), but I could have used other E T Fs or index mutual

that we estim ated in Equation (3.10), without the S M B factor,

funds for the benchm ark portfolio. Note the timing in Equation (3.14). The w eights are estim ated using information up to tim e t. The return of the fund over the next period, t + 1, is equal to the replicating portfolio form ed at

excep t that we allow the factor loadings to change over tim e. The SPYV-SPYG is an investm ent that goes long the value SPYV E T F and sim ultaneously shorts the growth SPYG ETF. Thus, it is analogous to the H M L factor.

the beginning of the period at tim e t plus a fundspecific resid­

The factor loadings plotted in Panel A of Figure 3.6 show

ual, et+i and the fund alpha, a t for that period. The w eights can

the strong value bias of LSV; with a positive h loading

change over tim e. Equation (3.14) asks, "Can we find a robot

on the SPYV-SPYG factor. Magellan becom es more of a

that makes tim e-varying investm ents in SPY, SPYV, and SPYG

growth fund over tim e, with increasingly negative h loadings, as

that, together, match the returns of Buffett?" Figure 3.5 graphs the factor w eights (or style weights) of the four funds. I estim ate the factors using data over the previ­

does Goldm an's growth fund. Berkshire Hathaway's changing factor loadings from value to growth to value can be seen in its negative h loadings during 2008 and 2009.

ous sixty months, t — 60 to t, to form the benchm ark weights

Allowing shorting does not much change the cum ulated excess

at tim e t. In addition to imposing that the factor w eights sum

returns in Panel B of Figure 3.6. But allowing shorting, not sur­

to one, I also constrain the factor w eights to be all positive

prisingly, reduces the alphas. M agellan's trend line for cum u­

(so there is no shorting). The first factor w eight is estim ated at

lated excess returns becom es more negative when shorting is

January 2006.

allow ed. Although Buffett's excess returns are positive, they are

Panel A of Figure 3.5 shows that LSV is merely a combination of the m arket (SPY) and value (SPYV). Fidelity Magellan starts

shifted downward in Figure 3.6, Panel B, com pared to the cor­ responding long-only picture in Figure 3.5, Panel B.

off in 2006 as a com bination of all three ETFs but, at the end

My final com m ent is that the problem s of statistical inference

of 2012, ends up being all growth (SPYG ). Goldm an's growth

with tim e-varying portfolio benchm arks are serious. It is hard

fund is mostly m arket exposure (SPY) and growth (SPYG ) at the

enough to detect statistical significance with constant portfolio

40

■

v

bm k

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Panel A Factor Weights

SPY

LSVEX

FMAGX

GSCGX

BRK

-------- SPYV

................. SPYG Panel B Cumulated Excess Returns

LSVEX

FMAGX

GSCGX

BRK

Fiau re 3.5

Chapter 3 Alpha (and the Low-Risk Anomaly)

■ 41

Panel A Factor Weights, with Shorting LSVEX

FMAGX

GSCGX

BRK

Cumulated Excess Returns, with Shorting LSVEX

FMAGX

GSCGX

BRK

Fiaure 3.6

42

Financial Risk Manager Exam Part II: Risk Management and Investment Management

CAPM Regression Alpha = 0.0741

benchm arks, and estim ated tim e-varying styles will have even larger standard errors. 14

Non-Linear Payoffs W ith alphas and information ratios, any m anager can appear to have talent when he actually doesn't. Alphas are computed in a linear fram ework. There are many non­ linear strategies, especially those involving dynamic option strate­ gies, that can masquerade as alpha. 15 To give an extrem e (and adm ittedly stylized) exam ple, consider Figure 3.7. It is produced by selling put options on the market portfolio in a small sample, just using Black-Scholes (1973) prices. The returns on these put options are recorded with crosses. I then run a CAPM regression with these simulated returns. The "alpha" appears to be positive— ta da!— but we know that in the Black-Scholes world there is no extra value created in puts or calls. The alpha is purely illusory. This is not a result of a small sample, even though small samples exacerbate the problem. No nonlinear strategy can be adequately captured in a linear fram ew ork

. 1 6

This is a serious

problem because many common hedge fund strategies, including merger arbitrage, pairs trading, and convertible bond arbitrage, have payoffs that resemble nonlinear option volatility strategies.17 W hy do dynam ic, nonlinear strategies yield false measures of alpha? Because buying and selling options— or any dynamic strategy— changes the distribution of returns.18 Static m easures, like the alpha, inform ation, and Sharpe ratios, capture only cer­ tain com ponents of the whole return distribution. O ften, short volatility strategies can inflate alphas and information ratios because they increase negative skew ness. These strategies increase losses in the left-hand tails and make the middle of the distribution "thicker" and appear to be more attractive to linear perform ance m easures. Skewness and other higher moments are not taken into account by alphas and information ratios. There are two ways to account for nonlinear payoffs.

Include Tradeable Nonlinear Factors Aggregate market volatility risk is an important factor, dis­ cussed in Chapter 7, and an easy way to include the effects of short volatility strategies is to include volatility risk factors. O ther nonlinear factors can also be included in factor benchmarks. By doing so, the asset owner is assuming that she can trade these nonlinear factors by herself. Som etim es, however, the only way to access these factors is through certain fund managers. Control­ ling for nonlinear factors crucially changes the alphas of hedge funds. Fung and Hsieh (2001), among many others, show that hedge fund returns often load significantly on option strategies.

Examine Nontradeable Nonlinearities It is easy to test w hether fund returns exhibit nonlinear patterns by including nonlinear term s on the right-hand side of factor

14 See comments by DiBartolomeo and Witkowski (1997). 15 This was first shown in a seminal paper by Dybvig and Ingersoll (1982). Technically, this is because any factor model used (Dybvig and Ingersoll used the CAPM) implicitly allows the pricing kernel to be nega­ tive and permits arbitrage (see Chapter 1). The linear pricing kernel correctly prices all benchmark assets (stocks) but incorrectly prices non­ linear payoffs like derivatives. 16 For a more formal treatment see Lhabitant (2000), to (2001), and Guasoni, Huberman, and Wang (2011). You can always beat a market Sharpe ratio (or information ratio) by selling volatility. See Mitchell and Pulvino (2001), Gatev, Goetzmann, and Rouwenhorst (2006), and Agarwal et. al. (2011), respectively.

regressions. Com m on specifications include quadratic term s, like rf, or option-like term s like m ax(rt, 0).19 The disadvantage is that, after including these term s, you do not have alpha— we always need tradeable factors on the right-hand side to com ­ pute alphas. But w e must move beyond alpha if we want evaluation measures that are robust to dynam ic m anipulation. These will not be alphas, but they can still be used to rank m anagers and evaluate

17

18 This is true even of simple rebalancing.

19 These can be traced to Treynor and Mazuy (1966) and Henriksson and Merton (1981), respectively.

Chapter 3 Alpha (and the Low-Risk Anomaly)

■ 43

skill. O ne state-of-the-art measure has been introduced by

that alpha. For that asset owner, Fidelity may be providing

Goetzm ann et. al. (20 07).20 W ith long enough sam ples, this

alpha. For another asset owner, Fidelity may well be adding

measure cannot be m anipulated in the sense that selling options

negative alpha because she can do all the appropriate fac­

will not yield a false measure of perform ance.

tor exposure (and im plem ent the underlying replicating factor benchm ark portfolios) on her own.

The Goetzm ann et. al. evaluation measure is

Choosing the right set of factors, then, is the most relevant issue (3.16)

for asset owners. Alpha is primarily a statem ent about the fac­ tor benchm ark (or lack of a factor benchm ark). W e now have

where y is set to three. Funds can be ranked on this measure

enough knowledge of risk adjustm ents to judge different alpha

from high to low, with the best funds having the highest val­

opportunities, and so we turn to one source of alpha that has

ues. Equation (3.16) is indeed a C R R A or pow er utility function.

recently stirred up debate.

(More precisely, it's the certainty equivalent of a C R R A utility function.) Goetzm ann et. al. report that M orningstar uses a vari­ ant of this m easure:

3.5 LOW RISK ANOMALY The low-risk anomaly is a com bination of three effects, with the

---------------------- -------------------------

U = 1 (1 +

rt ~

/"ft)2

which is also a C R R A utility function with risk aversion y = 2.

third a consequence of the first tw o :22

1. Volatility is negatively related to future returns; 2. Realized beta is negatively related to future returns; and

Does Alpha Even Exist?

3. Minimum variance portfolios do better than the m arket.

Since alpha is based on a benchm ark and estim ates of alpha

Th e risk anom aly is that risk— m easured by m arket beta or

are very sensitive to that benchm ark, is there even such a

vo latility— is neg atively related to returns. Robin G re e n ­

thing as true alpha? It could ju st be a wrong benchm ark. The

w o o d , a pro fesso r at H arvard Business School and my fello w

acad em ic literature calls this a jo in t h y p o th e sis p ro b le m , and

ad vise r to M artingale A sse t M anag em ent, said in 2010, "W e

the search for alpha is the sam e as the testing for m arket effi­

keep regurgitating the data to find yet one more variation

cie n cy.21 In a m ajor co ntribution, Hansen and Jag ann ath an

of the size, valu e, or m om entum anom aly, when the M other

(1997) show that it is alw ays possible to find an ex-post b ench­

of all in efficien cies may be standing right in front of us— the

m ark portfolio that produces no alpha. This is less useful ex

risk an o m aly."

ante, but it shows that a benchm ark portfolio can alw ays be constructed w here no alpha exists after the fact. Since Grossman and Stig litz (1980), the profession recognizes that per­

History

fectly efficient m arkets cannot exist (see C h a p te r 1)— so there

The negative relation between risk (at least measured by market

is alpha— but as the analysis of this section has show n, even

beta and volatility) and returns has a long history. The first stud­

for a recognized m aster of investing like Buffett, alpha can be

ies showing a negative relation appeared in the late 1960s and

very hard to d e te ct statistically.

early 1970s.23 Friend and Blume (1970) exam ined stock portfolio

The joint hypothesis problem — that alpha and the benchm ark are sim ultaneously determ ined— is the key problem for asset

returns in the period 1960-1968 with CA PM beta and volatility risk m easures. They concluded (my italics):

owners. It is of little use for an academ ic to say that Fidelity has

The results are striking. In all cases risk-adjusted perfor­

no alpha, when the asset owner cannot access the com plicated

mance is dependent on risk. The relationship is inverse

size, value-growth, and momentum factors used to com pute

and highly significant.

20 For some other notable manipulation-free performance measures, see Glosten and Jagannathan (1994) and Wang and Zhang (2011).

22 Some references for the third are Haugen and Baker (1991), Jagan­ nathan and Ma (2003), and Clarke, de Silva, and Thorley (2006). I cover references for the others later.

21 For a summary of this large literature, see Ang, Goetzmann, and Schaefer (2011).

23 In addition to the papers in the main text, also see Pratt (1971), Sodolfsky and Miller (1969), and Black (1972).

44

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Haugen and Heins (1975) use data from 1926 to 1971 and also

unrelated to fundam ental valuation, higher vo latilities are

investigate the relation betw een beta and volatility risk m ea­

asso ciated with higher risk p rem ium s.25

sures and returns. They report (my italics): Th e results of our em p irical effo rt do not sup p o rt the conventional hypothesis that risk— system atic or o th erw ise— g en e rate s a special rew ard. Ind eed , our results indicate th at, over the long run, s to c k p o r t­ fo lio s with le sse r variance in m on th ly retu rn s have e x p e rie n c e d g re a te r a vera g e retu rn s than "risk ie r" co u n te rp a rts.

The Ang et. al. (2006) results show exactly the opposite. Particularly notable is the robustness of the negative relation betw een both idiosyncratic and total vo latility with returns. W e em ployed a large num ber of controls fo r size, value, leverag e, liquidity risk, volum e, turnover, bid-ask spreads, co-skew ness risk, dispersion in analysts' fo recasts, and m om entum . W e also did not find that ag g reg ate vo latility risk exp lained our result— even though vo latility risk is a pervasive

Must of these results w ere forgotten. But these old results

risk facto r (see C h a p te r 2). In sub seq u en t w ork, A ng et. al.

recently have come roaring back.

(2009), w e show ed that the vo latility effect existed in each G 7 country and across all d evelo p ed stock m arkets. W e also

Volatility Anomaly

controlled for private inform ation, transactio ns costs, analyst co ve rag e , institutional ow nership, and delay m easures, which

I was fortunate to write one paper that helped launch the new

recorded how fast inform ation is im pounded into stock prices.

"risk anom aly" literature in 2006 with Robert Hodrick, one of my

Skew ness did not explain the puzzle.

colleagues at Colum bia Business School, and two of our form er students, Yuhang Xing and Xiaoyan Zhang, who are now profes­

Lagged Volatility and Future Returns

sors at Rice University and Purdue University, respectively. We

To see the volatility anom aly, I take U.S. stocks, rebalance quar­

found that the returns of high-volatility stocks were "abysm ally low." So low that they had zero average returns. This paper now generates the most cites per year of all my papers and has spawned a follow-up literature attem pting to replicate, explain, and refute the results.24 First, should there even be a relation betw een vo latility and returns? The w hole point of the C A PM and the many m ultifac­ tor extensio ns (see C h a p te r 2) w as that stock return vo latility itself should not m atter. E xp e cte d returns, according to these m odels, are determ ined by how assets covary with facto r risks. Idiosyncratic vo latility, or tracking error (see Equation (3.3)), should d efinitely n o t have any relation to exp ected returns under the C A P M . But in m arkets that are segm ented due to clientele effects— w here som e agents cannot diversify or w here som e agents p refer to hold som e assets over others for exogenous reasons— idio syncratic vo latility should be p osi­ tively related to returns. Intuitively, agents have to be paid for bearing id io syncratic, risk, resulting in a positive relation betw een idio syncratic risk and vo latility in equilibrium . In later m odels with "no ise tra d e rs," who trad e for random reasons

terly from Septem ber 1963 to D ecem ber 2011, and form quin­ tile portfolios. I construct monthly frequency returns. I sort on idiosyncratic volatility using the Fam a-French (1993) factors with daily data over the past quarter. (Ranking on total volatility pro­ duces very similar results.) I m arket w eight within each quintile sim ilar to Ang et. al. (2006, 2009). In Figure 3 .8 , I repo rt the mean and standard d eviatio ns of the quintile p o rtfo lio s on the left-hand axis in the tw o bars. Th e vo latilities increase going from the low- to high-volatility q u in tiles, by co nstructio n. The averag e returns are above 10% fo r the first three q u in tiles, fall to 6 .8% fo r quintile 4, and then plum m et to 0 .1 % fo r the highest vo latility sto cks. High vo latility stocks certain ly do have "ab ysm ally low " returns. Th e right-hand axis reports raw Sharpe ratios, which are the ratios of the m eans to the standard d eviatio n s. Th ese monoto n ically d ecline from 0.8 to 0 .0 going from the low- to highvo latility quintiles.

Contemporaneous Volatility and Returns Do stocks with high volatilities also have high returns over the sam e period used to measure those volatilities?

24 Volatility makes many appearances, of course, in tests of cross-sec­ tional asset pricing models before Ang et. al. (2006), but most of them are negative results or show a slight positive relation. For example, in Fama and MacBeth's (1973) seminal test of the CAPM, volatility is included and carries an insignificant coefficient. Eric Falkenstein (2012) recounts that he uncovered a negative relation between volatil­ ity and stock returns in his PhD dissertation in 1994, which was never published.

I exam ine this question in Figure 3.9 by form ing portfolios at the end of the period based on realized idiosyncratic volatilities.

0^

For clientele models, see Merton (1981). For noise trader models, see Delong et. al. (1990).

Chapter 3 Alpha (and the Low-Risk Anomaly)

■ 45

40%

Raw Mean

Stdev

Raw Sharpe Ratio (RH axis)

35% -

r 1.00

Beta Anomaly

- 0.90

The first tests of the CA PM done in the 1970s did find positive relations between beta and

- 0.80

expected returns, but they did not find that pure

30% -

form s of the CAPM w orked. Black, Je n se n , and

- 0.70 25% -

> 2, pn = p „_i + 0.5 • (he,n- i + h B,n)We have 0 < p-| < p2 < • • • < P n - i < P n < 1- Find the normal variate zn that satisfies pn — 4>{zn}, where O is the cumulative normal distribution. We can use the z variables as alphas, after adjustments for location and scale.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

the neutralization process recenters the alphas to rem ove the benchm ark alpha. From the portfolio perspective, benchm ark

Table 4.2 Modified

neutralization means that the optimal portfolio will have a beta of 1, i.e ., the portfolio will not make any bet on the benchm ark.

Modified

Benchmark-Neutral

Alpha

Alpha

Stock

Beta

Am erican Express

1.21

- 1 .1 4 %

- 1 .1 6 %

A T& T

0.96

0.30%

0.29%

Chevron

0.46

0 . 11%

0 . 10%

Coca Cola

0.96

- 0 .7 8 %

- 0 .7 9 %

Disney

1.23

0.60%

0.58%

industry, and factor neutralization. Do our alphas contain any

Dow Chem ical

1.13

0 .22%

0 .20%

information distinguishing one industry from another? If not,

DuPont

1.09

- 0 .6 5 %

- 0 .6 7 %

Eastm an Kodak

0.60

0.14%

0.13%

Exxon

0.46

- 0 .1 9 %

- 0 .20%

G eneral Electric

1.30

- 1. 10%

- 1. 12%

G eneral Motors

0.90

- 0 .5 2 %

- 0 .5 3 %

IBM

0.64

- 0 .5 1 %

- 0 .5 2 %

0 alpha, although the benchm ark may experience exceptional

International Paper

1.18

0 .01%

- 0 .01%

return. Setting the benchm ark alpha to 0 ensures that the alphas

Johnson & Johnson

1.13

0 .66%

0.64%

are benchm ark-neutral and avoids benchm ark tim ing.

M cDonalds

1.06

0.14%

0 . 12%

In the same spirit, we may also want to make the alphas

Merck

1.06

0 .20%

0.18%

3M

0.74

0.91%

0.90%

Philip Morris

0.94

0 . 12%

0 . 10%

Procter & G am ble

1.00

0.44%

0.42%

Sears

1.05

0.35%

0.33%

Neutralization is a sophisticated procedure, but it isn't uniquely defined. We can achieve even benchm ark neutrality in more than one way. This is easy to see from the portfolio perspec­ tive: We can choose many different portfolios to hedge out any active beta. As a general principle, w e should consider a priori how to neu­ tralize our alphas. The choices will include benchm ark, cash,

then industry-neutralize. The a priori approach works better than simply trying all possibilities and choosing the best performer.

Benchmark- and Cash-Neutral Alphas The first and sim plest neutralization is to make the alphas benchm ark-neutral. By definition, the benchm ark portfolio has

cash-neutral; i.e ., the alphas will not lead to any active cash position. It is possible to make the alphas both cash- and benchm ark-neutral. Table 4.2 displays the modified alphas from Table 4.1 and shows how they change when we make them benchm ark-neutral. In this exam ple, the benchm ark alpha is only 1.6 basis points, so subtracting /3n * a B from each modified alpha does not change the alpha very much. We have shifted the alpha of the bench­

For exam ple, a m anager can ensure that her portfolios contain

mark Major M arket Index from 1.6 basis points to 0. This small

no active bets on industries or on a size factor. Here is one sim ­

change in alpha is consistent with the observation that the opti­

ple approach to making alphas industry-neutral: Calculate the

mal portfolio before benchm ark neutralizing had a beta very

(capitalization-weighted) alpha for each industry, then subtract

close to 1.

the industry average alpha from each alpha in that industry. W e can modify the alphas to achieve desired active common-

Risk-Factor-Neutral Alphas

factor positions and to isolate the part of the alpha that does not influence the com m on-factor positions.

The m ultiple-factor approach to portfolio analysis separates return along several dim ensions. A m anager can identify each of those dim ensions as either a source of risk or a source of value added. By this definition, the m anager does not have any ability

4.4 TRANSACTIONS COSTS

to forecast the risk factors. Therefore, he or she should neutral­

Up to this point, the struggle has been between alpha and

ize the alphas against the risk factors. The neutralized alphas will

active risk. Any klutz can juggle two rubber chickens. The ju g ­

include only information on the factors the m anager can fore­

gling becom es com plicated when the third chicken enters the

cast, along with specific asset inform ation. O nce neutralized, the

perform ance. In portfolio construction, that third rubber chicken

alphas of the risk factors will be 0 .

is transactions costs, the cost of moving from one portfolio to

Chapter 4 Portfolio Construction

■ 57

another. It has been said that accurate estim ation of transactions

will be transactions costs (recall that we start and end with cash)

costs is just as im portant as accurate forecasts of exceptional

of $0.75, $1.50, $1.50, $1.50, and $0.75 at 0, 6 , 12, 18, and

return. That is an overstatem ent, 5 but it does point out the

24 months, respectively. The total trading cost is $6, the gain

crucial role transactions costs play.

on the shares is $8, the profit over 2 years is $2, and the annual

In addition to com plicating the portfolio construction prob­

percentage return is 1 percent.

lem, transactions costs have their own inherent difficulties. We

With stock 2, over the 2-year period we will incur costs of $0.75

will see that transactions costs force greater precision on our

at 0 and 24 months. The total cost is $1.50, the gain is $8, the

estim ates of alpha. We will also confront the com plication of

profit is $6.50, and the annual percentage return is 3.25 percent.

com paring transactions costs at a point in tim e with returns and risk which occur over an investm ent horizon.

With the series of stock 1 trades, we realize an annual alpha of 4 percent and an annualized transactions cost of 3 percent. With

W hen w e consider only alphas and active risk in the portfolio

the single deal in stock 2, we realize an annual alpha of 4 percent

construction process, we can offset any problem in setting the

and an annualized transactions cost of 0.75 percent. For a

scale of the alphas by increasing or decreasing the active risk

6-month holding period, we double the round-trip transactions

aversion. Finding the correct trade-off betw een alpha and active

cost to get the annual transactions cost, and for a 24-month

risk is a one-dimensional problem . By turning a single knob, we

holding period, we halve the round-trip transactions cost to get

can find the right balance. Transactions costs make this a two-

the annual transactions cost. There's a general rule here:

dimensional problem . The trade-off between alpha and active risk remains, but now there is a new trade-off between the alpha and the transactions costs. We therefore must be precise in our choice of scale, to correctly trade off betw een the hypothetical alphas and the inevitable transactions costs.

The annualized transactions cost is the round-trip cost divided by the holding period in years. For the rem ainder of this chapter, w e will assume that w e know the cost for each anticipated trade.

The objective in portfolio construction is to m axim ize riskadjusted annual active return. Rebalancing incurs transac­ tions costs at that point in tim e. To contrast transactions costs incurred at that tim e with alphas and active risk expected over the next year requires a rule to allocate the transactions costs over the one-year period. We must am ortize the transactions costs to com pare them to the annual rate of gain from the alpha and the annual rate of loss from the active risk. The rate of amortization will depend on the anticipated holding period. An exam ple will illustrate this point. We will assume perfect

4.5 PRACTICAL DETAILS Before proceeding further in our analysis of portfolio construc­ tion, we should review som e practical details concerning this process. First, how do we choose a risk aversion param eter? We can find an optim ality relationship betw een the information ratio, the risk aversion, and the optimal active risk. That result is displayed here, translated from residual to active return and risk,

certainty and a risk-free rate of zero; and we will start and end

(4.3)

invested in cash. Stock 1's current price is $100. The price of stock 1 will increase to $102 in the next 6 months and then

The point is that we have more intuition about our information

remain at $102. Stock 2's current price is also $100. The price

ratio and our desired amount of active risk. Hence, we can use

of stock 2 will increase to $108 over the next 24 months and

Equation (4.3) to back out an appropriate risk aversion. If our

then remain at $108. The cost of buying and selling each

information ratio is 0.5, and we desire 5 percent active risk, we

stock is $0.75. The annual alpha for both stock 1 and stock

should choose an active risk aversion of 0.05. Note that we must

2 is 4 percent. To contrast the two situations more clearly,

be careful to verify that our optim izer is using percents and

let's assume that in 6 months, and again in 12 months and in

not decim als.

18 months, we can find another stock like stock 1.

A second practical m atter concerns aversion to specific as

The sequence of 6-month purchases of stock 1 and its succes­

opposed to com m on-factor risk. Several com m ercial optim izers

sors will each net a $2.00 profit before transactions costs. There

utilize this decom position of risk to allow differing aversions to these different sources of risk:

5 Perfect information regarding returns is much more valuable than per­ fect information regarding transactions costs. The returns are much less certain than the transactions costs. Accurate estimation of returns reduces uncertainty much more than accurate estimation of transactions costs.

58

■

U = ap —(Aa c f • ^ ,C F + AAS f • ^ , s p) (4.4) An obvious reaction here is, "Risk is risk, why would I want to avoid one source of risk more than another?" This is a useful

Financial Risk Manager Exam Part II: Risk Management and Investment Management

sentim ent to keep in mind, but there are at least two reasons to

churn the portfolio and suffer higher than expected transactions

consider im plem enting a higher aversion to specific risk. First,

costs and lower than expected alpha. A crude but effective cure

since specific risk arises from bets on specific assets, a high aver­

is to revise the portfolio less frequently.

sion to specific risk reduces bets on any one stock. In particular, this will reduce the size of your bets on the (to be determ ined) biggest losers. Second, for m anagers of multiple portfolios,

More generally, even with accurate transactions costs estim ates, as the horizon of the forecast alphas decreases, we exp ect them to contain larger amounts of noise. The returns them selves

aversion to specific risk can help reduce dispersion. This will

becom e noisier with shorter horizons. Rebalancing for very short

push all those portfolios toward holding the same names.

horizons would involve frequent reactions to noise, not signal.

The final practical details we will cover here concern alpha

But the transactions costs stay the sam e, w hether we are react­

coverage. First, what happens if we forecast returns on stocks

ing to signal or noise.

that are not in the benchm ark? W e can always handle that by expanding the benchm ark to include those stocks, albeit with zero w eight. This keeps stock n in the benchm ark, but with

This trade-off between alpha, risk, and costs is difficult to ana­ lyze because of the inherent im portance of the horizon. We exp ect to realize the alpha over some horizon. We must th ere­

no w eight in determ ining the benchm ark return or risk. Any

fore am ortize the transactions costs over that horizon.

position in stock n will be an active position, with active risk

W e can capture the im pact of new inform ation, and decide

correctly handled. W hat about the related problem , a lack of forecast returns for stocks in the benchm ark? For stock-specific alphas, we can use the following approach.

w hether to trade, by com paring the marginal contribution to value added for stock n, M C V A n, to the transactions costs. The marginal contribution to value added shows how value added, as m easured by risk-adjusted alpha, changes as the

Let N-1 represent the collection of stocks with forecasts, and N0

holding of the stock is increased, with an offsetting decrease in

the stocks without forecasts. The value-weighted fraction of

the cash position. A s our holding in stock n increases, a n m ea­

stocks with forecasts is

sures the effect on portfolio alpha. The change in value added H {N ,} =

2 hB,n nE/V,

(4.5)

of adding more of stock n. The stock's marginal contribution to active risk, M C A R n, m easures the rate at which active risk

The average alpha for group N-} is

changes as w e add more of stock n. The loss in value added ^B,n ’ a

a {N ' ] = ^

also depends upon the im pact (at the margin) on active risk

T

due to changes in the level of active risk will be proportional

rt

“

(4 6 )

To round out the set of forecasts, set a*n — a n — a f/V J for stocks in N-1 and a* — 0 for stocks in N0. These alphas are benchmarkneutral. Moreover, the stocks we did not cover will have a zero, and therefore neutral, forecast.

to M C A R n. Stock n's marginal contribution to value added depends on its alpha and marginal contribution to active risk, in particular: M C V A n = a n - 2 • Aa • , and ip is the track­

(relative to the com posite) and dispersion, with the sm allest

ing error of each portfolio relative to the com posite. Figure 4.3

dispersion exhibited when we assum ed the lowest transac­

displays this function. For a given tracking error, more portfolios

tions costs. Figure 4.4 displays the results. So even though

Fiaure 4.4

66

■

C o nverg ence. (S o u rce : BARRA.)

Financial Risk Manager Exam Part II: Risk Management and Investment Management

our starting portfolios differed, they steadily converged over a

such as portfolio insurance), alternatives to m ean/variance analy­

roughly 5-year period. In real-life situations, client-initiated con­

sis greatly com plicate portfolio construction without improving

straints and client-specific cash flows will act to keep separate

results. A t the stock selection level, results may be much w orse.

accounts from converging.

Finally, we analyzed the very practical issue of dispersion among

O ne final question is w hether we can increase convergence by

separately m anaged accounts. W e saw that m anagers can

changing our portfolio construction technology. In particular,

control dispersion— especially that driven by differing factor

what if we used dual-benchm ark optim ization? Instead of penal­

exposures— but should not reduce it to zero.

izing only active risk relative to the benchm ark, we would also penalize active risk relative to either the com posite portfolio or

References

the optimum calculated ignoring transactions costs. Dual-benchm ark optim ization can clearly reduce dispersion, but only at an undesirable price. Dual-benchm ark optimization sim ply introduces the trade-off w e analyzed earlier: dispersion

Chopra, Vijay K., and William T. Ziem ba. "The Effects of Errors in Means, Variances, and Covariances on Optim al Portfolio C ho ice." Journal o f Portfolio M anagem ent, vol. 19, no. 2, 1993, pp. 6-11.

versus return. Unless you are willing to give up return in order to

Connor, Gregory, and Hayne Leland. "Cash Management for Index

lower dispersion, do not im plem ent the dual-benchm ark optim i­

Tracking." Financial Analysts Journal, vol. 51, no. 6, 1995, pp. 75-80.

zation approach to managing dispersion.

G rinold, Richard C . "The Information H orizon." Jou rn a l o f Port­ folio M anagem ent, vol. 24, no. 1, 1997, pp. 57-67.

SUMMARY The them e of this chapter has been portfolio construction in a less than perfect w orld. W e have taken the goals of the portfo­

-------- . "M ean-Variance and Scenario-Based Approaches to Portfolio Selectio n." Jou rn a l o f Portfolio M anagem ent, vol. 25, no. 2, W inter 1999, pp. 10-22. Jo rio n , Philippe. "Portfolio O ptim ization in Practice." Financial

lio m anager as given. The m anager wants the highest possible

A nalysts Jou rnal, vol. 48, no. 1, 1992, pp. 68-74.

after-cost value added. The before-cost value added is the port­

Kahn, Ronald N. "M anaging D ispersion." BA R R A Equity

folio's alpha less a penalty for active variance. The costs are for

Research Seminar, Pebble Beach, C alif., June 1997.

the transactions needed to maintain the portfolio's alpha.

Kahn, Ronald N ., and Daniel Stefek. "H eat, Light, and Downside

Understanding and achieving this goal requires data on alphas,

Risk." B A R R A Preprint, D ecem ber 1996.

covariances betw een stock returns, and estim ates of trans­

Leland, Hayne. O ptim al A s s e t Rebalancing in the P resen ce o f

actions costs. Alpha inputs are often unrealistic and biased. Covariances and transactions costs are measured im perfectly. In this less than perfect environm ent, the standard reaction is to com pensate for flawed inputs by regulating the outputs of the portfolio construction process: placing limits on active stock positions, limiting turnover, and constraining holdings in certain categories of stocks to match the benchm ark holdings. These are valid approaches, as long as we recognize that their purpose is to com pensate for faulty inputs. W e prefer a direct attack on the causes. Treat flaws in the alpha inputs with alpha analysis: Remove biases, trim outlandish values, and scale alphas in line with expectations for value added. This strengthens the link between research and portfolio construction. Then seek out the best possible estim ates of risk and transactions costs. As

Transactions C osts. University of California Research Program in Finance, Publication 261, O cto b er 1996. M ichaud, Richard. "The M arkowitz O ptim ization Enigm a: Is 'O ptim ized' O p tim al?" Financial A nalysts Journal, vol. 45, no. 1, 1989, pp. 31-42. Muller, Peter. "Em pirical Tests of Biases in Equity Portfolio O p ti­ m ization." In Financial O ptim ization, edited by Stavros A . Zenios (Cam bridge: Cam bridge University Press, 1993), pp. 80-98. Rohweder, Herold C . "Im plem enting Stock Selection Ideas: Does Tracking Error O ptim ization Do Any G o o d ?" Jou rn al o f Portfolio M anagem ent, vol. 24, no. 3, 1998, pp. 49-59. Rudd, Andrew . "O ptim al Selection of Passive Portfolios." Finan­ cial M anagem ent, vol. 9, no. 1, 1980, pp. 57-66.

appropriate, use a powerful portfolio construction tool with as

Rudd, Andrew , and Barr Rosenberg. "Realistic Portfolio O ptim i­

few added constraints as possible.

zation." TIM S Stu d y in the M anagem ent S cie n ces, vol. 11, 1979,

Near the end of the chapter, we returned to the topic of alterna­ tive risk m easures and alternatives to m ean/variance optim iza­

pp. 21-46. Stevens, Guy V. G . "O n the Inverse of the Covariance M atrix in

tion. For most active institutional m anagers (especially those

Portfolio A nalysis." Jou rn a l o f Finance, vol. 53, no. 5, 1998,

who do not invest in options and optionlike dynam ic strategies

p p . 1821-1827.

Chapter 4 Portfolio Construction

■ 67

Portfolio Risk: A nalytical M ethods Learning Objectives A fter com pleting this reading you should be able to: Define, calculate, and distinguish between the following

Explain the risk-minimizing position and the risk and

portfolio VaR m easures: diversified and undiversified

return-optimizing position of a portfolio.

portfolio VaR, individual VaR, incremental VaR, marginal VaR, and com ponent VaR. Explain the im pact of correlation on portfolio risk.

Explain the difference betw een risk m anagem ent and portfolio m anagem ent and describe how to use marginal VaR in portfolio m anagem ent.

A pply the concept of marginal VaR to guide decisions about portfolio VaR.

E x c e rp t is C h a p ter 7 o f Value at Risk: The New Benchm ark for Managing Financial Risk, Third Edition , by Philippe Jo rio n .

69

m anagem ent of risk, in particular, risk minimization. W e then Trust not all your goods to one ship.

integrate risk with expected returns and show how VaR tools can — Erasm us

A bsent any insight into the future, prudent investors should diversify across sources of financial risk. This was the m essage of portfolio analysis laid out by Harry M arkowitz in 1952. Thus the concept of value-at-risk (VaR), or portfolio risk, is not new. W hat is new is the system atic application of VaR to many sources of financial risk, or portfolio risk. VaR explicitly accounts for lever­ age and portfolio diversification and provides a sim ple, single measure of risk based on current positions. There are many approaches to measuring VaR. The shortest road assum es that asset payoffs are linear (or delta) functions of normally distributed risk factors. Indeed, the delta-norm al

be use to move the portfolio toward the best com bination of risk and return.

5.1 PO RTFO LIO V a R A portfolio can be characterized by positions on a certain num­ ber of constituent assets, expressed in the base currency, say, dollars. If the positions are fixed over the selected horizon, the portfolio rate of return is a linear com bination of the returns on underlying assets, where the w eights are given by the relative amounts invested at the beginning of the period. Therefore, the VaR of a portfolio can be constructed from a com bination of the risks of underlying securities. Define the portfolio rate of return from t t o t + 1 as N

m eth o d is a direct application of traditional portfolio analysis

R p ,t+ 1 =

based on variances and covariances, which is why it is som e­ tim es called the covariance m atrix approach.

1=1

1

(5-1)

where N is the num ber of assets, R/t+1 is the rate of return on

This approach is analytical because VaR is derived from closed-

asset i, and w( is the w eight. The rate o f return is defined as the

form solutions. The analytical method developed in this chapter

change in the dollar value, or dollar return, scaled by the initial

is very useful because it creates a more intuitive understanding

investm ent. This is a unitless m easure.

of the drivers of risk within a portfolio. It also lends itself to a sim ple decom position of the portfolio VaR.

W eights are constructed to sum to unity by scaling the dollar positions in each asset VV( by the portfolio total m arket value W.

This chap ter shows how to m easure and m anage portfolio

This im m ediately rules out portfolios that have zero net invest­

VaR. The first section details the construction of VaR using

ment W — 0, such as som e derivatives positions. But we could

inform ation on positions and the covariance m atrix of its

have positive and negative w eights w,-, including values much

constituent com ponents.

larger than 1, as with a highly leveraged hedge fund. If the net

The fact that portfolio risk is not cum ulative provides great diversification benefits. To manage risk, however, we also need to understand what will reduce it. The section that follows pro­ vides a detailed analysis of VaR tools that are essential to control portfolio risk. These include marginal VaR, increm ental VaR, and com ponent VaR. These VaR tools allow users to identify the asset that contributes most to their total risk, to pick the best hedge, to rank trades, or in general, to select the asset that

portfolio value is zero, we could use another m easure, such as the sum of the gross positions or absolute value of all dollar positions W *. All w eights then would be defined in relation to this benchm ark. Alternatively, we could express returns in dollar term s, defining a dollar am ount invested in asset / as W, = w(W. We will be using x as representing the vector of dollar amount invested in each asset so as to avoid confusion with the total dollar amount W.

provides the best risk-return trade-off. Then, a fully worked out

It is im portant to note that in traditional mean-variance analysis,

exam ple of VaR com putations for a global equity portfolio and

each constituent asset is a security. In contrast, VaR defines the

for Barings' fatal positions will be presented.

com ponent as a risk factor and w, as the linear exposure to this

The advantage of analytical m odels is that they provide closedform solutions that help our intuition. The m ethods presented

risk factor. W hether dealing with assets or risk factors, the m ath­ em atics of portfolio VaR are equivalent, however.

here, however, are quite general. We will show how to build

To shorten notation, the portfolio return can be written using

these VaR tools in a nonparam etric environm ent. This applies to

m atrix notation, replacing a string of numbers by a single vector:

sim ulations, for exam ple. Finally, we will be taken toward portfolio optim ization, which should be the ultimate purpose of VaR. W e first show how the passive m easurem ent of risk can be extended to the

70

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Financial Risk Manager Exam Part II: Risk Management and Investment Management

w 'R (5.2)

where w' represents the transposed vector (i.e., horizontal)

A t this point, we also can define the individual risk of each com ­

of w eights, and R is the vertical vector containing individual

ponent as

asset returns.

VaR,- — acr/| W/| — acr,| w,j W

The portfolio expected return is

(5.8)

Note that we took the absolute value of the w eight w( because N

E(Rp) = i i p =

(5.3)

1=1

and the variance is

it can be negative, whereas the risk measure must be positive.

Individual VaR n

N

The VaR of one com ponent taken in

isolation.

N W jW jO -jj

/=1 N

-

;= iy = ij# 1 N

2

Equation (5.4) shows that the portfolio VaR depends on vari­

N

+2;=21/ Rf t

(6 -2 )

where R b represents the return on the benchm ark for fund /, and w b is its policy w eight. If the pension plan deviates from its policy mix (w,-

w b), the active-m anagem ent portion can be

decom posed further into a term that represents policy decisions and m anager perform ance.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

The funds' total VaR can be obtained from the policy-mix VaR, the

is A S = A A — A L Normalizing by the initial value of assets,

active-m anagem ent VaR, and a cross-product term . As an exam ­

we have

ple, the Ontario Teachers' Pension Plan Board (O TPPB) estimates that its annual VaR at the 99 percent level of confidence can be decom posed as follows (in percent of the initial fund value):

Source of Risk

VaR

Policy-mix VaR

19.6%

Active-m gt. VaR A sset VaR

AA A

k k^k =R^ asse t

L liabilities

(6.3)

A

where labilitiesis the rate of return on liabilities. While the value of assets can be measured by marking to market, liabilities are more difficult to evaluate. For pension funds, this represents accum ulated-benefit obligations, which measure the

1.6%

present value of pension benefits owed to employees discounted at

19.3%

an appropriate interest rate. When liabilities consist mainly of nomi­

This table points to a number of interesting observations. First, most of the risk is due to the policy mix. This is a general result owing to Brinson et al. (1986), who dem onstrated that most of the variation in portfolio perform ance can be attributed to the choice of asset classes. In other words, the choice of mix of stocks and bonds will have more effect on the portfolio perfor­ mance than the choice of a particular equity or bond manager. The second interesting result is that the active-m anagem ent VaR is rather small. A pparently, the fund diversifies away much of the risk of m anagers deviating from their benchm arks through a careful choice of various styles or many m anagers. Another explanation is that most of the assets are invested in indexed or closely indexed funds. Finally, the table shows that the policy-mix VaR and activem anagem ent VaR do not add up to the total-asset VaR. In fact, there is a slightly negative correlation betw een the tw o, lead­ ing to a lower overall asset VaR. If this occurs, active m anagers could take greater deviations from their benchm ark without affecting the plan's total VaR. This analysis is a good exam ple of insights created by a VaR analysis. Such decom position can help sponsors to make more informed decisions.

nal payments, their value in general will behave like a short position in a long-term bond. Thus decreases in interest rates, while benefi­ cial for equities on the asset side, can increase even more the value of liabilities, thereby negatively affecting the surplus. If liabilities are indexed to inflation, they behave like inflation-protected bonds. The minimum-risk position then corresponds to an im m unized portfolio, where the duration of the assets m atches that of the liabilities. In practice, it may not be possible to immunize the liabilities com pletely if the existing pool of long-term bonds is insufficient. More generally, immunization carries an opportunity cost if other asset classes generate greater returns over tim e. This funding risk represents the true long-term risk to the owner of the fund. If the surplus turns negative, it will have to provide additional contributions to the fund. Som etim es this is called surplus at risk (SAR). An exam ple is given in Box 6.2. As an exam ple, consider a hypothetical pension plan. Call it Public Em ployee Retirem ent Fund (PER F). P ER F has $1000 in assets and $900 in liabilities, for a surplus S of $100 million. The duration of liabilities is 15 years; this high number is typical for pension funds. Assum e that the expected return on the surplus, scaled by assets, is 5 percent. This translates into an expected growth of $50 million over 1 year, creating an expected surplus of $150 million. For Canadian pension funds, the typical volatility of the surplus is 9.4 percent, leading to an annual VaR of 22 per­

Funding Risk

cent, or $220 million at the 99 percent confidence level.3 Taking

Focusing on the volatility of assets alone, however, may not be appropriate if the assets are supposed to cover fixed liabilities. Notably, a pension fund with d e fin e d b en efits prom ises a stream of fixed paym ents to retirees. If the assets are not sufficient to cover these liabilities, the shortfall will have to be made up by the fund's owner. On the other hand, defined-contribution plans put the risk on the em ployees. In other w ords, risk should be view ed in an asset/liability m anagem ent (ALM) fram ew ork. We can define funding risk as the risk that the value of assets will not be sufficient to cover the liabilities of the fund. The relevant variable is the surplus S, defined as the difference between the value of assets A and liabilities L. The change then

the deviation between the expected surplus and VaR, we find that there is a 1 percent probability that over the next year the surplus will turn into a deficit of $70 million or more. The trad e­ off between this number and an expected surplus growth of $50 million defines the risk profile of the fund. If acceptable, risk budgeting then allocates the SAR of $220 million to different aspects of the investm ent process. 3 This assumes a normal distribution, with a = 2.33. Ambachtsheer (2002) provides an interesting analysis of the risk profile of a sample of Canadian and U.S. pension funds. The average surplus volatility is 8.1 and 18.1 percent for these funds, respectively. Over the 1997-2001 period, however, the growth in the surplus has been very small, which reflects poorly performing stock markets.

Chapter 6 VaR and Risk Budgeting in Investment Management

■

87

BOX 6.2 SURPLUS AT RISK AT OTPPB The O ntario Teachers' Pension Plan Board (O TPPB) has been at the forefront of applying VaR techniques among institutional investors. O TP P B is the biggest pension fund in Canada, with about C$90 billion (US$78 billion) in assets in 2005.

annum. This translates into a surplus VaR of 22 percent, which is also C$20 billion when applied to assets.

The plan is required to deliver d e fin e d b en efits to Ontario's teachers during their retirem ent years. Its stated objective is to earn a high rate of return, at least as great as the rate of inflation plus 5 percent per annum, while minimizing the risk of a contribution increase. Until 1990, O TP P B could invest in O ntario bonds only. Starting in 1990, the plan em barked on an am bitious drive to expand into broader asset classes, with the guidance of a risk m anagem ent system .

In 1996, O TP P B purchased a firm wide risk m anagem ent system sold by Sailfish that cost about $500,000. M anage­ ment has access to daily risk reports, and the board receives monthly risk reports. VaR is measured as the worst loss at the 99 percent confidence level over 1 year. Thus we would expect on average a loss worse than C$20 billion in 1 year out of a hundred. O f course, this invites quips about risk man­ agers not likely to be around for a century. The risk m anagers then patiently explain that these param eters are equivalent to a confidence level of 90 percent over 4 years.* Thus this loss would be expected in one of ten periods of 4 years.

The O TP P B has decided on a policy mix of 45 percent equi­ ties, 23 percent fixed-incom e and absolute strategies, and 32 percent inflation-sensitive investm ents (i.e., com m odi­ ties, real estate, and real-return bonds). The goal of this mix is to achieve a long-term surplus growth of 1.3 percent per

* See De Bever et al. (2000). This transformation assumes normal and i.i.d. returns, in which case the ratio of 90 and 99 percent normal deviates is 1.28/2.33, which multiplied by V 4 indeed gives a number close to 1.

Sponsor Risk This notion of surplus risk can be extended to the risk to the owner of the fund, the plan sponsor, who ultim ately bears responsibility for the pension fund. O ne can distinguish between the following risk m easures: •

Cash-flow risk, which is the risk of year-to-year fluctuations in contributions to the pension fund. Plan sponsors that can absorb greater variations in funding costs, for instance, can

•

6.3 USING Va R TO MONITOR AND CONTROL RISKS VaR system s can be used to measure and control m arket risks. This also applies to the investm ent m anagem ent industry. VaR system s allow investors to check that their m anagers com ply with guidelines and to monitor their m arket risks. C red it risk usually is controlled through limits on exposures on a name-by-name basis. VaR system s provide som e protection

adopt a more volatile risk profile.

against operational risk, which is also controlled by policies

Eco n o m ic risk, which is the risk of variation in total econom ic

and procedures. Such applications are still passive or d efen sive

earnings of the plan sponsor. The surplus risk may be less of a

in nature.

concern, for instance, if falls in the surplus occur in an envi­ ronm ent where the firm enjoys greater operating profits.4 From the view point of the plan sponsor, risk is measured not only by m ovem ents in the assets, or even the surplus, but also

Using VaR to Check Compliance The im petus for centralized risk m anagem ent in the invest­

by the ultimate effect on the econom ic value of the firm . Thus

ment m anagem ent industry cam e from the realization that the

pension-plan m anagem ent should be integrated with the overall

industry is not immune to the "rogue trad er" syndrom e that has

financial goals of the plan sponsor. This is in line with the trend

plagued the banking industry. Indeed Box 6.3 explains how the

toward enterprisew ide risk m anagem ent.

Com mon Fund lost $138 million from unauthorized trading. This has led to a reorganization of the fund with a centralized risk m anagem ent function.

4 When the pension fund is heavily invested in stocks, the opposite effect will occur. Downturns in the economy will push down the value of the fund's assets, precisely when the company is less able to make contributions. Black (1980) also pointed out that because returns in pension funds are not taxed, corporate bonds should be the preferred investment.

88

■

The lessons from this loss are applicable to any "m anager of m anagers," that is, a m anager who delegates the actual invest­ ment decisions to a stable of m anagers. W hile rogue traders, fortunately, are rare, minor violations of investm ent guidelines occur routinely. Some securities may be prohibited because of

Financial Risk Manager Exam Part II: Risk Management and Investment Management

BOX 6.3 NONCOMPLIANCE AT THE COMMON FUND In 1995, the Common Fund, a nonprofit organization that man­ ages about $20 billion on behalf of U.S. schools and universi­ ties, announced that it had lost $138 million from unauthorized trading by one of its managers. Apparently, Kent Ahrens, a trader at First Capital Strategies, had deviated from what should have been a safe index-arbitrage strategy between stock index futures and underlying stocks. One day he failed to com plete the hedge and lost $250,000. He then tried to trade his way out of this loss but with little success. The growing loss was concealed for 3 years until Ahrens confessed in June 1995. This loss was all the more disturbing because after the Bar­ ings affair, the Com m on Fund had specifically asked First Capital to dem onstrate that a rogue trader could not do the sam e thing at First C apital. The firm answered that market neutrality was being verified daily. In this case, it seem s that proper checks and balances were not in place.

their risks or for other reasons (e.g ., political or religious). Bank

Although the dollar loss was not large com pared with the size of the asset pool, it severely dam aged the reputation of the Com m on Fund. Several fund investors left, taking $1 billion with them . The fallout also forced the president of the C o m ­ mon Fund the resign. In retrospect, the Com mon Fund realized that running an operation with a large num ber of fund m anagers requires strong centralized controls. To prevent such mishaps, the fund created the new position of "independent risk over­ sight officer." The fund also set up new risk m anagem ent com m ittees, one of which is at the board level. Its custo­ dian, Mellon Trust, developed online software that checks for violations of investm ent policies. To reduce operational risk, the fund also cut the number of active m anagers and custodial agreem ents.

•

A m anager taking m ore risk. VaR allows dynam ic risk monitor­

custodians, however, indicate that fund m anagers som etim es

ing of m anagers, who are given a VaR limit or risk budget.

trade in and out of unauthorized investm ents before the client

Any exceedence of the VaR limit will be flagged and should

realizes what happened. With monthly reporting, it is hard to

be exam ined closely. For instance, if this is an unauthorized

catch such m ovem ents. Centralized risk m anagem ent system s,

trade, the infraction should be corrected at once. O therw ise,

in contrast, can monitor investm ents in real tim e.

the exceedence requires a discussion with the manager. There may be good reasons to increase the risk profile. Per­

Such occurrences have moved the pension-fund industry toward

haps the risk increase is tem porary or justified by current con­

centralized risk m anagem ent. VaR system s provide a central

ditions. In any event, it is im portant to understand the reason

repository for all positions. Independent reconciliation against

behind the change.

m anager positions makes fraud a lot more difficult. VaR system s also allow users to catch deviations from stated policies quickly.

•

D ifferent m anagers taking similar b e ts. This can happen, for instance, when m anagers increase their allocation to a par­

Using VaR to Monitor Risk

ticular sector, which is perhaps becom ing more attractive or

W ith a VaR system in place, investors can monitor their m arket

ers operate in isolation, such a problem can be caught only at

risk better. This applies to both passive and active allocations.

the portfolio level. To decrease the portfolio risk, m anagers

Passive allocation, or benchm arking, does not keep risk constant

can be given appropriate instructions.

has perform ed well in the recent past. Because active m anag­

because the com position of the indices can change substan­

•

M ore volatile m arkets. VaR can increase if the current envi­

tially. The late 1990s, for exam ple, w itnessed a high-tech bubble

ronment becom es more volatile, assuming that tim e variation

that increased the m arket capitalization of firm s in high-tech

in risk is explicitly m odeled, such as with G A R C H m odels.

industries. As a result, m arket-capitalization benchm arks such as

The plan sponsor then will have to decide w hether it is worth

the Standard & Poor's (S&P) 500 becam e increasingly exposed

accepting greater volatility. If the risks are deem ed to be

to the high-tech industry, which sharply increased the volatility

too large, positions can be cut. Increased volatility, however,

of the indices. Such trends would be picked up by a forward-

often is associated with falls in asset prices leading to cor­

looking risk m easurem ent system .

respondingly higher expected returns. Thus the rebalancing

A ctive portfolio m anagem ent can change the risk profile of the fund. Suppose, for instance, that the investor notices a sudden jum p increase in the reported VaR of the fund. The key is to

decision involves a delicate trade-off between risk and return. As seen in Box 6.4, however, some investors prefer to set up their system so as to smooth out spikes in risk.

identify the reason for the jum p. Several explanations are pos­

More generally, VaR can be reverse engineered to understand

sible, each requiring different actions.

where risk is coming from using VaR tools. M easures of marginal

Chapter 6 VaR and Risk Budgeting in Investment Management

■

89

BOX 6.4 SMOOTHING OUT RISK AT OTPPB The O TP P B risk m easurem ent system is based on histori­ cal simulation because of its ability to represent non­ normal m arket m ovem ents. The system loads more than 10,000 positions on a daily basis, which are com bined with historical data going to January 1987. As of 2005, this rep­ resents an expanding w indow spanning 19 years. This long history was selected for two reasons. First, the risk m anagers wanted to include the crash of O ctober 1987 in the sam ple period so as to model the possibility of a future crash. Second, this long w indow decreases the w eight on recent observations, which sm oothes out the volatility process. Shorter windows lead to greater fluctua­ tions in risk m easures, which create problem s when invest­ ment m anagers are subject to strict risk limits. O TP PB 's risk m anagers indicated that "using a lot of history avoids a potential conflict betw een risk control and investm ent strateg y."

can better incorporate VaR system s into operations. Larger plans also benefit from econom ies of scale, spreading the cost of risk m anagem ent system s over a large asset base, and also require tighter control when their assets are partly m anaged internally. These clients are the exception, however. Most investors may be content with risk m anagem ent reports developed by custodians. Such system s, however, are not cheap to develop. As a result, the trend will be toward few er custodians that can provide more services. Already, large custodian banks such as Deutsche Bank, JP M Chase, Citibank, and State Street are providing risk man­ agem ent products. State Street, for instance, is already provid­ ing a W eb-based system , called VaR Calculator, that allows users to perform VaR calculations on dem and.

The Role of the Money Manager On the money m anagem ent side, m anagers are now under pres­ sure from clients to dem onstrate that they have in place a sound risk m anagem ent system . More and more clients are explicitly asking for risk analysis because they are no longer satisfied with

and com ponent VaR can be used to identify where position

quarterly perform ance reports only.

changes will have the greatest effect on the total portfolio risk.

Increasingly, clients are asking their m anagers, "W hat is your

This assum es, however, that all the relevant risks are captured

risk m anagem ent system ?" Leading-edge investm ent m anagers

by the risk m anagem ent system . As explained earlier, risk can­ not be measured easily for som e im portant asset classes such as real estate, venture capital, and som e categories of hedge funds owing to illiquidity. O ther series may have very short histories, such as em erging m arkets, or none at all, such as initial public offerings. In som e cases, the missing series can be replaced by a proxy, using a mapping approach. The risk m anager should be

already have adapted VaR system s into their investm ent man­ agem ent process. M anagers who do not have com prehensive risk m anagem ent system s put them selves at a serious com peti­ tive disadvantage. Indeed, the "Risk Standards" developed in 1996 for institutional investors recomm end measuring the risk of the overall portfolio, as well at that of each instrum ent. The report also notes that m anager differentiation increasingly is cre­

aware of the limitations of the system .

ated by providing risk m anagem ent services to clients.

The Role of the Global Custodian

6.4 USING Va R TO MANAGE RISKS

The philosophy behind VaR is centralized risk m anagem ent. The easiest path to centralization is to use one global custodian only.

VaR system s can be used to manage risk, which is an active application. VaR can be used to improve investm ent guidelines

This explains why many investors now are aggregating their

for active m anagers and to help with the investm ent process. In

portfolio holdings with a single custodian. With one global cus­

theory, VaR also could be used to com pute the risk-adjusted per­

todian, position reports directly give a consolidated picture of

form ance of investm ent m anagers, as is done for bank traders.

the total exposure of the fund. Custodians becom e the natural focal point for this analysis because they already maintain posi­ tion information and have m arket data. The next level of service is to com bine the current position with forward-looking risk m easures.

Using VaR to Design Guidelines VaR system s can be used to design better investm ent guide­ lines. M anagers' guidelines generally are set up in an ad hoc

Not all agree, however, that the risk m easurem ent function can

fashion to restrict the universe of assets in which the m anagers

be delegated to the custodian. Some larger plans have decided

can invest and, to som e extent, to control risk. Typically, guide­

to develop their own internal risk m anagem ent system . Their

lines include limits on notionals, for exam ple, maximum sector

rationale is that they have tighter control over risk m easures and

w eight deviations for equities and maximum currency positions,

90

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

or limits on sensitivities, such as duration gaps betw een fixed-

fails to recognize the effects of marginal adjustm ents from the

income portfolios and their benchm arks.

selected portfolio.

Banking institutions, however, have learned the hard way that

Since VaR is, after all, perfectly consistent with a mean-variance

limits on notionals and sensitivities are insufficient. Limits on

fram ew ork, VaR tools can be used to allocate funds across asset

notionals work best with sim ple portfolios with no derivatives

classes. Box 6.5 shows how increm ental VaR can yield useful

and leverage. They do not account for variations in risk nor cor­

insights into the risk drivers of a fund.

relations. Limits on sensitivities are an im provem ent but still have blind spots, such as for hedged portfolios. In contrast, VaR limits are com parable across assets and account for risk, diversification, leverage, and derivatives (provided the system is well designed).

Risk m anagem ent system s are also useful at the trading level. Portfolio m anagers are paid to take bets. Presum ably, they've developed skills in one dimension of the risk-return space. They are expected to identify expected returns on various investm ents. W hile expected returns can be estim ated on an

Says Leo de Bever, risk m anager at Ontario Teachers, "Typically,

individual basis, assessing the contribution of a particular stock

you control positions by saying, T h o u shalt not have more than

to the total portfolio risk is much less intuitive. Even if analysts

X million of this.' W hen you do that, you end up with a whole bunch of rules on what you can and cannot do, but not a handle on how much you might lose on any given day." Another problem is that the spirit of these limits can be skirted with new financial instrum ents. For exam ple, a m anager may not be allowed to trade in futures that may be viewed as too "risky," such as futures contracts. Instead, investm ents may be allowed in high-grade medium-term notes, often view ed as safe because they have no credit risk. The problem is that these notes can be designed as stru ctu red notes with as much m arket risk as futures contracts. Hence detailed guidelines, like governm ent regulations, are one step behind continuously changing financial m arkets. Traditional guidelines cannot cope well with new instru­ ments or leverage. They also totally ignore correlations. This is precisely what VaR attem pts to m easure. Instead of detailed guidelines, plan sponsors could specify that the anticipated volatility of tracking error cannot be more than 3 percent, for instance. Position limits can be set consistently across m arkets.

Using VaR for the Investment Process A good risk m anagem ent system can be used to improve the investm ent process, starting with the top-level assetallocation process all the way down to trading decisions for individual stocks. As explained earlier, the strategic asset-allocation decision is the first and most im portant step in the investm ent process for pension funds. It is usually based on a mean-variance optim iza­ tion that attem pts to identify the portfolio with the best riskreturn trade-off using a set of long-term forecasts for various asset classes. In practice, the optimization usually is constrained in an effort to obtain solutions that look "reaso nab le." This adjustm ent, how­

BOX 6.5 V a R AND CURRENCY HEDGING Bankers Trust (now Deutsche Bank) recently provided its R A R O C 2020 risk m anagem ent system to the Chrysler pension fund. The system provides m easures of total and incremental VaR for the various asset classes in which the fund is invested. It can be used, among other things, to evaluate the effectiveness of hedging strategies. In par­ ticular, the fund was considering adding a currency hedge to protect the currency position of its foreign stock and bond investm ents. The R A R O C system showed that the "individual" risk of a $250 million currency position was $44 million at the 99 percent level over 1 year, which appears substantial. However, the pension fund realized that the "increm en­ tal" contribution to total risk of a passive currency hedge program was only $3 million.* This means that currency risk already was largely diversified in the existing portfolio. The fund decided not to hedge its currency exposure, thereby saving hefty m anagem ent fees. These savings more than offset the m odest cost of the R A R O C system , which was priced at around $50,000 per year. This result parallels the discussion in the academ ic lit­ erature, where currency hedging initially was advocated as a "free lunch," that is, lower risk at no cost.^ Indeed, currency hedging reduces the volatility of individual asset returns, but this is not the relevant issue. A bsent currency view s, what m atters is total portfolio risk. Em pirically, total risk generally is not much affected by currency hedging if the proportion of assets invested abroad is small. Thus there is not much benefit from currency hedging. * Incremental risk is the change in risk when the position is dropped. * As in Perold and Schulman (1988). Jorion (1989), however, argues that the benefit of hedging must be viewed in the context of total portfolio risk.

ever, partly defeats the purpose of portfolio optim ization and

Chapter 6 VaR and Risk Budgeting in Investment Management

■ 91

Budgeting across Asset Classes

could measure the individual risk of the particular stock they are considering, they cannot possibly be aware of the relationships

Consider again our pension fund, PERF, that needs to allocate

between all existing positions of the fund. This is where VaR sys­

$1000 million to four asset classes, U .S. and foreign stocks and

tem s help.

bonds. Table 6.2 displays the average returns, volatilities, and

For each asset to be added to the portfolio, analysts should be

correlations estim ated from 1978-2005 data. These are taken as

given a measure of its marginal VaR. If two assets have similar

inputs into the portfolio-allocation process.

projected returns, the analyst should pick the one with the low­

Assum e now that PERF's board of trustees has decided

est marginal VaR, which will lead to the lowest portfolio risk.

on a total volatility profile for the fund of 10 percent. This

Assum e, for instance, that the analyst estim ates that two stocks,

translates into an annual VaR of 23.3 percent, or $233

a utility and an Internet stock, will generate an expected return

million, at the 99 percent confidence level. In what fo l­

of 20 percent over the next year. If the current portfolio is

lows, we assume normal distributions and com pute VaR as

already heavily invested in high-tech stocks, the two stocks will have a very different marginal contribution to the portfolio risk.

acrw — 2.33 X 0.10 X $1,000 = $233 million.

Say that the utility stock has a portfolio beta of 0.5 against 2.0

Given this risk appetite, the optimal asset allocation is listed

for the other stock, leading to a lower marginal VaR for the first

in Table 6.3. These optimal weights can be converted into risk

stock. W ith equal return forecasts, the utility stock is clearly the

budgets, or individual VaRs. For instance, for U.S. stocks, this is

preferred choice. Such analysis is only feasible within the context

2.33 X 0.151 X $525 = $184 million. Note that the risk budgets

of a portfoliowide VaR system .

sum to $308 million, which is the undiversified VaR. The actual fund VaR is lower, at $233 million, owing to diversification effects.

6.5 RISK BUDGETING

The same process can be continued at the next level. Assum e that PER F allocates the $525 million principal in U.S. stocks

Advances in VaR have led to risk b u d g etin g , which is spreading

to two active m anagers. The two m anagers are equally

rapidly in investm ent m anagem ent. This concept is equivalent

good and receive the same amount, $262.5 million each.

to a top-down allocation of econom ic risk capital starting from

They run portfolios with volatility of 16 percent and cor­

the asset classes down to the choice of the active m anager and

relation of 0.78 with each other. This gives a risk budget of

even to the level of individual securities.

acrW — 2.33 X 0.16 X $262.5 = $98 million each. Again, the

Table 6.2

A sset C lasses: Risk and Exp ected Returns Correlations

Asset

Expected Return

Volatility

2

1

4

3

U.S. stocks

1

13.4%

15.1%

1.00

Non-U.S. stocks

2

12.8%

16.7%

0.54

1.00

U.S. bonds

3

8 .0%

7.3%

0.19

0.11

1.00

Non-U.S. bonds

4

9.0%

10.9%

0.05

0.52

0.40

Table 6.3

1.00

Risk Budgeting A cross A sset C lasses (Millions)

Asset

Weight

Volatility

Principal

Risk Budget

U.S. stocks

52.5%

15.1%

$525

$184

Non-U.S. stocks

10.4%

16.7%

$104

$41

U.S. bonds

12.2%

7.3%

$122

$21

Non-U.S. bonds

24.9%

10.9%

$249

$63

100.0%

10.0%

$1000

$233

Portfolio

92

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Table 6.4

Risk Budgeting Across Active Managers (Millions) Inputs

Outputs

TEV to,

Information Ratio IR;

Weight x t

Allocated Principal x,W

Excess Return Xjfi,

Relative Risk Budget

M anager 1

6 .0%

0.60

55%

$291

2 .0%

$40.6

M anager 2

6 .0%

0.40

37%

$194

0.9%

$27.1

Index

0 .0%

0.00

8%

$40

0 .0%

$0.0

Portfolio

4.0%

0.72

100%

$525

2.9%

$48.9

risk budgets sum to an amount that is greater than the risk bud­

Now assume that the deviations for each m anager are indepen­

get for this asset class owing to diversification effects. The total

dent of each other.6 The portfolio T E V is fixed at

risk budget is V $ 9 8 2 + $982 + 2 X 0.78 X $98 X $98 = $184

2 2 x fo jf

million. Each m anager then is charged to earn the highest return on these risk units. A nother advantage of this approach is that it avoids micromanaging the investm ent process. A s long as man­

( 6 . 6)

M aximizing the portfolio information ratio subject to a fixed T E V gives the following solution:

agers stay within their risk guidelines, they can execute new

X j(O j

transactions without requiring approval of senior m anagem ent.

—

I

R

(6.7)

;

Thus the relative risk budgets should be proportional to the information ratios.

Budgeting across Active Managers This approach can be refined further if we are willing to make assum ptions about the expected perform ance of active m anag­ ers. For better or for w orse, active m anagers usually are evalu­ ated in term s of their tracking error (TE), defined as the active return minus that of the benchm ark.5 Define /i as the expected T E and co as its volatility (TEV). The inform ation ratio then is

Table 6.4 gives an exam ple. P E R F w ants to allocate $525 million to a pool of active m anagers so as to m axim ize the inform ation ratio of the fund subject to an overall T E V of 4 percent. This is equivalent to a risk budget of $48.9 million. Each m anager has a T E V of 6 percent. To achieve an exact T E V of 4 percent, w e also need som e residual investm ent in the benchm ark, which has a T E V of zero. The fund m anagers have

defined as

different cap ab ilities; their IRs are 0.60 and 0 .4 0 , respectively. IR = f±/u

(6.4)

Equation (6.7) gives a solution of 55 percent w eight for m an­ ager 1 , 3 7 percent for m anager 2, and the residual of 8 percent

M anagers are com m only evaluated on the basis of their IR. Grinold and Kahn (1995), for exam ple, assert that an IR of 0.50

in the index.

is "g o o d ," meaning in the top quartile of the active m anagers.

This portfolio is expected to return 2.9 percent. With 4 percent

Logically, a greater risk budget should be allocated to m anagers

TEV, this translates into an information ratio of 2 .9 /4 .0 = 0.72.

with better perform ance, as measured by the IR criterion.

This is higher than the IR of both m anagers and is due to the fact that we assum ed that the active returns w ere independent

The optim ization problem for active m anager allocation attem pts to maximize the IR for the total portfolio subject to a

of each other, leading to substantial diversification benefits.7

T E V constraint. Define x, as the fraction invested in m anager /, who has a tracking error of

o j,

and excess return of j u The value

added for the total portfolio p is /ip = 2 x i/x/ = 2 x '(iR < x "/) •

I

•

(6.5)

I

5 Note that this approach is a second-best because it fails to control total risk. As shown in Roll (1992) and Jorion (2003), active managers who only pay attention to relative risk often end up increasing total risk.

6 This is a major simplification for what follows. The analysis, however, can be extended to the more realistic case of nonzero correlations using a correlation matrix. 7 If the IR were the same for each manager, the total IR would be IR/V2 = 0.707 or, more generally, for N managers, IR,a / n . This is also known as the law of active management. In theory, the fund's informa­ tion ratio would tend to infinity as N grows large. In practice, however, it is difficult to find a very large number of totally unrelated trading strategies.

Chapter 6 VaR and Risk Budgeting in Investment Management

■ 93

Such structured, top-down risk allocation adds trem endous rigor

through the maze of diversification rules, benchm ark portfolios,

to the investment m anagem ent process. It has been of great

and investm ent guidelines. VaR system s allow analysts to make

value to early adopters, such as the O TP P B . The VaR system has

better risk-return trade-offs. VaR, of course, will not tell you

reduced the number of investment rules and has facilitated the

where to invest. The goal is not to elim inate risk but rather to

closer supervision of risks. O TPPB's focus on risk and diversifica­

get the just reward for risk that m anagers elect to take.

tion has led to greater investment in alternative asset classes. Since 1990, the plan has beaten its benchmark by an average of 4 percent per annum and has provided $16 billion in value added.

CO N CLUSIO N S Centralized risk m anagem ent system s, by now w idely adopted on Wall Street, are also taking hold in the investm ent m anage­ ment industry. Even though institutional investors have a longerterm horizon than bank trading departm ents, they also greatly benefit from the discipline provided by VaR system s.

Such risk m anagem ent system s are spreading quickly among institutional investors, changing the face of the industry. They are affecting the custody business, forcing custodians to offer risk m anagem ent reporting capabilities. M anagers are affected, too. Those who do not have a risk m anagem ent system put them selves at a serious com petitive disadvantage. It is som ew hat ironic that the investm ent m anagem ent industry, which has long relied on modern portfolio theory, is only now turning to fund-wide risk m easurem ent system s. These system s have been developed by "quants" on Wall Street who were originally trying to get a grip on their short-term derivatives

Traditionally, risk has been measured using historical returns or

risk. W hat we are learning now is that these m ethods can be

as the occurrence of a big loss. W hile useful for som e purposes,

extended usefully from the short-term trading environm ent to

these risk m easures have severe shortcom ings because they are

the longer-term fram ew ork of patient investors.

backward-looking. In contrast, VaR provides forward-looking measures of risk, using a com bination of current positions with risk forecasts.

This turn of events w as inevitable. Since advances in tech n o l­ ogy and com m unications create alm ost instantaneous flow s of inform ation across the globe, plan sponsors cannot con­

W hen im plem ented at the level of the total plan, VaR allows

tinue to rely on m onthly or quarterly hard-copy reports on

improved control of portfolio risk and of m anagers. It cuts

their investm ents.

94

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Risk M onitoring and Perform ance M easurem ent Learning Objectives A fter com pleting this reading you should be able to: Describe the three fundam ental dim ensions behind risk

D escribe how risk monitoring can confirm that investm ent

m anagem ent and their relation to VaR and tracking error.

activities are consistent with expectations.

Describe risk planning, including its objectives, effects,

D escribe the Liquidity Duration Statistic and how it can be

and the participants in its developm ent.

used to measure liquidity.

Describe risk budgeting and the role of quantitative

D escribe the objectives of perform ance m easurem ent

m ethods in risk budgeting.

tools.

Describe risk monitoring and its role in an internal control

D escribe the use of alpha, benchm arks, and peer groups

environm ent.

as inputs in perform ance m easurem ent tools.

Identify sources of risk consciousness within an organization. Describe the objectives and actions of a risk m anagem ent unit in an investm ent m anagem ent firm .

E x c e rp t is C h a p ter 77 o f Modern Investm ent M anagem ent: An Equilibrium A pproach, b y Ja c o b R osen garten and P e te r Zangari.

7.1 O V ERV IEW The O xfo rd English D ictionary describes risk as:

(a) the chance or hazard of com m ercial loss; also . . . (b) . . . the chance that is accepted in econom ic enterprise and considered the source of (an entrepreneur's) profit. This definition asserts that risk reveals itself in the form of uncer­ tainty. This uncertainty of loss, which risk professionals quantify using the laws of probability, represents the cost that businesses accept to produce profit. Loss potential (i.e., "risk") represents the "shadow price" behind profit expectations. A willingness to accept loss in order to generate profit suggests that a cost ben­ efit process is present. For a return to be deem ed desirable, it should attain levels that com pensate for the risks incurred. There are typically policy limits that constrain an organization's willingness to assume risk in order to generate profit. To man­ age this constraint, many organizations form ally budget risk usage through asset allocation policies and m ethods (e.g ., mean-variance optimization techniques). The result yields a blend of assets that will produce a level of expected returns and risk consistent with policy guidelines.

has its own VaR). An owner of capital who wishes to incur only the risks and returns of a particular asset class might invest in an index fund type product that is designed to replicate a particular index with precision. To the extent that the owner wishes to enjoy som e discretion around the com position of the index, he or she allows the investm ent m anagers to hold views and posi­ tions that are som ew hat different than the index. The ability to take risks away from the index is often referred to as active man­ agem ent. Tracking error is used to describe the extent to which the investm ent m anager is allowed latitude to differ from the index. For the owner of capital, the VaR associated with any given asset class is based on the com bination of the risks associ­ ated with the asset class and the risks associated with active m anagem ent.1 The same prem ise holds for the VaR associated with any com bination of asset classes and active m anagem ent related to such asset classes. By now it is apparent that risk— w hether expressed as VaR or tracking error— is a scarce resource in the sense that individuals and organizations place limits on their willingness to accept loss. For any given level of risk assum ed, the objective is to engage into as many intelligent profit-making opportunities as possible. If risk is squandered or used unwisely, the ability of the organi­ zation to achieve its profit objectives is put at risk. If excessive

Risk, in financial institutions, is frequently defined as value-at-risk

levels of risk are taken vis a vis budget, the organization is risk­

(VaR). VaR refers to the maximum dollar earnings/loss potential

ing unacceptably large losses in order to produce returns that it

associated with a given level of statistical confidence over a

neither expects nor desires. If too little risk is taken vis a vis bud­

given period of tim e. VaR is alternatively expressed as the num­

geted levels, return expectations will likely fall short of budget.

ber of standard deviations associated with a particular dollar

The point here is that the ability of an organization to achieve its

earnings/loss potential over a given period of tim e. If an asset's

risk and return targets may be put at risk anytime that risk capi­

returns (or those of an asset class) are normally distributed,

tal is used w astefully or in amounts inconsistent with the policies

67 percent of all outcom es lie within the asset's average returns

established by such organization.

plus or minus one standard deviation.

With the above as context, we now delve into the concepts and

A sset m anagers use a concept analogous to VaR— called track­

m ethods behind risk monitoring and perform ance m easurem ent

ing error— to gauge their risk profile relative to a benchm ark. In

in greater depth. The chapter is organized along five them es:

the case of asset m anagers, clients typically assign a benchm ark and a projected risk and return target vis a vis that benchm ark for all monies assigned to the asset manager's stew ardship. The risk budget is often referred to as tracking error, which is

1. We em phasize that risk monitoring is a fundam ental part of the internal control environm ent. It helps ensure that the organization is entering into transactions that are

defined as the standard deviation of excess returns (the dif­ ference between the portfolio's returns and the benchmark's returns). If excess returns are normally distributed, 67 percent of all outcom es lie within the benchm ark's returns plus or minus one standard deviation. VaR is som etim es expressed as dollar value-at-risk by multiplying the VaR by assets under m anagem ent. In this manner, the owner of the capital is able to estim ate the dollar im pact of losses that could be incurred over a given period of tim e and with a given confidence level. To achieve targeted levels of dollar VaR, own­ ers of capital allocate capital among asset classes (each of which

96

■

1 More formally, the return of the portfolio (Rp) invested in a particular asset class can be described as follows: (Rp) = (Rp ~ Ra) + Ra

where Ra refers to the return of the index or benchmark. The term in parentheses is often referred to as active or excess return. From this expression, one can see that the variance of the portfolio's return (Vp) can be reduced to: Vp = Variance(Excess return) + Variance(Benchmark) + 2 (Covariance between excess return and benchmark return) The standard deviation of the portfolio is of course the square root of the variance.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

authorized and properly scaled; it helps distinguish

factors make these other risks more apparent and costly. For

betw een events that are unusual and those that should

this reason, all of these sources of risk are w orthy of separate

have been anticipated.

study and investigation.

2 . W e show that there are three fundam ental dim ensions behind risk m anagem ent— planning, budgeting, and monitoring. W e observe that these three dim ensions are intim ately related and that they can be more com pletely understood by looking at their com m only used counterparts in the world of financial accounting controls. W e posit that there is a direct correspondence betw een financial plan­ ning, financial budgeting, and financial variance monitoring and their risk m anagem ent counterparts— namely, risk plan­ ning, risk budgeting, and risk monitoring. 3 . W e introduce the concept of a risk m anagem ent unit (RMU) and describe its role and placem ent within the organization. W e discuss its objectives as well as the need for it to remain independent of portfolio m anagem ent activities. As we will see, the existence of an independent RMU is a "b est prac­ tice" for all types of investors, including asset m anagers, pension funds, and corporations.

4. W e describe techniques the RMU uses to monitor exp o ­ sures in portfolios and provide sam ples of reports that might be used to deliver such inform ation.

7.2 THE TH REE LEG S O F FINANCIAL ACCO UN TIN G CON TROL: PLANNING, BUDGETING, AND VARIANCE MONITORING In the world of financial accounting controls, the concepts of planning, budgeting, and variance monitoring are intim ately related. Each is one of the legs of a three-legged stool that defines organizational structure and control. Each leg is funda­ mental to the success of the organization's raison d'etre. As w e will see, the risk m anagem ent process also can be described as a three-legged stool. Effective risk m anagem ent processes also have planning, budgeting, and variance monitor­ ing dim ensions. It is intuitive that there should exist such a close correspondence between the m odels that support risk man­ agem ent and those that support financial accounting controls. Rem em ber that risk is the cost of returns— the shadow price of returns. Hence, behind every number in a financial plan or bud­

5 . Last, we introduce tools that are com m only used in the

get there must exist a corresponding risk dim ension. This duality

world of perform ance m easurem ent. We observe that

suggests that risk m anagem ent can be described, organized,

there is a duality betw een risk monitoring and perfor­

and im plem ented using an approach that is already commonly

mance m easurem ent. Risk monitoring reports on risk

used in the world of financial controls— namely, planning, bud­

that is possible, w hereas perform ance m easurem ent

geting, and monitoring.

reports on perform ance (and so risk) that has m aterial­ ized. We posit that perform ance m easurem ent is a form of model validation.

For a m om ent, let's focus on the world of financial accounting to explore this point further. Consider how the "financial con­ trols stool" is constructed. The first leg of this stool is a strate­

W e would be remiss if we did not briefly observe that because

gic plan or vision that describes earnings targets (e .g ., return on

the sources of risk are many, the modern organization must have

equity, earnings per share, etc.) and other goals for the organi­

a m ultidisciplinary approach to risk m anagem ent. In their book,

zation (e .g ., revenue diversification objectives, geographic loca­

The Practice o f Risk M anagem ent, Robert Litterman and Robert

tion, new product developm ent, m arket penetration standards,

G um erlock identify at least six distinct sources of risk.2 These

etc.). The strategic plan is a policy statem ent that broadly artic­

include m arket, credit, liquidity, settlem ent, operational, and

ulates bright lines that define points of organizational success

legal risk. Professional standards, quantitative tools, preem ptive

or failure.

actions, internal control system s, and dedicated m anagem ent team s exist in the modern organization to address each of these. Frequently, these risks overlap and various professional disciplines are required to work together to creatively craft solu­ tions. W hile in this paper, our primary focus will be m anagem ent and m easurem ent of m arket risk and perform ance, these other risks are ever present and m aterial. O ften, stresses in m arket

O nce a plan exists, the second leg of the financial controls stool— a financial budget— is created to give form to the plan. The financial budget articulates how assets are to be expended to achieve earnings and other objectives of the plan. The bud­ get represents a financial asset allocation plan that, in the opin­ ion of m anagem ent, should be follow ed to best position the organization to achieve the goals laid out in the strategic plan. The budget— a statem ent of expected revenues and expenses

2 The Practice o f Risk Management, by Robert Litterman and Robert Gumerlock, Euromoney Publications PLC, 1998, p. 32.

by activity— is a numeric blueprint that quantifies how the strate­ gic plan's broad vision is to be im plem ented.

Chapter 7 Risk Monitoring and Performance Measurement

■ 97

The strategic plan and financial budget both presuppose scar­

use scenario analysis to explore those kinds of factors that

city. In a world of unlimited resources, there is clearly no need

could cause the business plan to fail (e.g ., identify unafford­

for either a budget or a plan. Any mistake could easily be

able loss scenarios) and strategic responses in the event

rectified. In a world of scarcity, however, it is apparent that a

these factors actually occur. The risk plan helps ensure that

variance monitoring process— the third leg of the stool— helps

responses to events— be they probable or im probable— are

ensure that scarce resources are spent w isely in accordance with

planned and not driven by em otion. Difficult business cli­

the guidance offered by the plan and the budget. Monitoring

mates have happened before and they will happen again.

exists because material variances from financial budget put the

The planning process should explore the many "paths to

long-term strategic plan at risk.

the long term " and prepare the organization, and its own­

In the world of risk m anagem ent, these same three elem ents of control— planning, budgeting, and monitoring— apply as well. Although this paper focuses primarily on risk m onitoring, it is useful to step back and provide a more com plete context for risk monitoring.

ers and m anagers, for the bum ps3 along the way. If any of these bumps are m aterial, concrete contingency plans should be developed and approved by the organization's owners and m anagers.4

2. The risk plan should define points of success or failure. Exam ples are acceptable levels of return on equity (RO E) or returns on risk capital (RO RC). For the purposes of the plan­

7.3 BUILDING THE TH REE-LEG G ED RISK M AN AGEM EN T STOOL: THE RISK PLAN, THE RISK BUDGET, AND THE RISK MONITORING PROCESS The Risk Plan The follow ing discussion of w hat constitutes a risk plan may at first blush seem highly th eo retical. But upon closer review, the reader will see that sound financial planning standards already incorporate many of the elem ents that are discussed . W e e xp e ct many of the ideas referred to here already exist within the body of a com prehensive strateg ic planning docum ent. For exam p le, m ost strateg ic plans include a strengths, w e a k ­ nesses, opp ortunities, and threats (SW O T) section in which m ajor risks to the organization are discussed . By introducing the co ncep t of a separate risk plan, however, w e are propos­ ing an even g reater deg ree of form ality for discussion of risk them es and issues. W e believe that the risk plan should be incorporated as a separate section of the organization's strategic planning docum ent. As such, it should receive all of the vetting and discussion that any other part of the planning docum ent would receive. W hen in final form , its main them es should be capable of being articulated to analysts, auditors, boards, actuaries, m anagem ent team s, suppliers of capital, and other interested constituencies.

ning docum ent, risk capital might be defined using value-atrisk (VaR) m ethods. Since organizations typically report and budget results over various tim e horizons (monthly, quar­ terly, annually), separate VaR measures for each tim e inter­ val should be explored. The VaR (or risk capital) allocated to any activity should be sized in such a way that the exp o ­ sures and upside associated with the activity are at levels that are deem ed appropriate by the organization's owners and m anagers. A second benefit of attem pting to measure the risk capital associated with each activity is that the pro­ cess helps m anagem ent understand the uncertainty levels associated with each activity in the plan. The greater the amount of uncertainty and the greater the cost associated with the downside of the VaR estim ate actually m aterial­ izing, the more intensive must be the quality of contingency and remedial planning.

3. The risk plan should paint a vision of how risk capital will be deployed to m eet the organization's objectives. For exam ­ ple, the plan should define minimum acceptable RO RCs for each allocation of risk capital. In so doing, it helps ensure that the return per unit of risk m eets minimum standards for any activity pursued by the organization. The plan should also explore the correlations among each of these RO RCs as well to ensure that the consolidated RO RC yields an expected R O E, and variability around such expectation, that is at acceptable levels. Finally, the plan should also have a diversification or risk decom position policy. This policy

The risk plan should include five guideposts: 1. The risk plan should set expected return and volatility (e.g ., VaR and tracking error) goals for the relevant tim e period and establish m ileposts which would let oversight bodies recognize points of success or failure. The risk plan should

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3 In statistical terms, a "bump" might be defined as a three or greater standard deviation event in a relatively short period of time. 4 Note that scenario analysis can be explored qualitatively as well as quantitatively. In fact, many extreme events lend themselves more to qualitative analysis than quantitative methods.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

should address how much of the organization's risk capital

consider a possible challenge faced by a pension plan. It is

should be spent on any one th e m e .5

conceivable that periods of econom ic downturn could coin­

4. A risk plan helps organizations define the bright line betw een those events that are merely disappointing and those that inflict serious dam age. Strategic responses should exist for any franchise-threatening event— even if such events are low-probability situations. The risk plan should identify those types of losses that are so severe that insurance coverage (e.g ., asset class puts) should be sought

cide with lower investm ent perform ance, acceleration of lia­ bilities, and a decreased capacity of the contributing organization to fund the plan. For this reason, scenario planning for the pension plan should explore what other factors affect the pension plan's business model in both good and bad environm ents and develop appropriate steps to help the plan succeed.

to cover the dow nside. For exam ple, every organization

An effe ctive risk plan requires the active invo lvem ent of

pays fire insurance premiums to insure against the unafford­

the o rg an izatio n 's m ost sen io r lead e rsh ip . This invo lvem ent

able costs of a fire. Fire is one of those events that is so

cre ate s a m echanism by w hich risk and return issues are

potentially devastating that there is universal agreem ent on

a d d re sse d , u n d ersto o d , and articu lated to su p p liers of ca p i­

the need to carry insurance protection. Now, consider a

tal (ow ners or b e n e ficiarie s), m anagem ent, and o versig h t

more com plex exam ple from the world of investm ent port­

boards. It helps d e scrib e the philosophical co n te xt fo r allo ­

folio policy. From an investm ent standpoint, there may be

cations of risk and financial capital and helps organizations

losses of such m agnitude— even if they are infrequent and

ensure th at such allo catio n s reflect organizational strengths

im probable— that they endanger the long-term viability of

and und erp inn ing s. It helps o rg anizatio ns discuss and under­

the investm ent plan. For exam ple, firm s or plans with large

stand the shadow price th at m ust be acce p te d in o rd er to

equity holdings6 could face material loss and earnings vari­

g e n e rate returns.

ability in the event of protracted and substantial stock mar­ ket losses. In this case, the risk plan should explore the potential merits of financial insurance (e.g ., options on broad m arket indexes). A t a minimum, if such insurance is not purchased, the decision to self-insure should be for­ mally discussed and agreed upon by the organization's owners and m anagem ent.

The existence of a risk plan makes an im portant statem ent about how business activities are to be m anaged. It indicates that owners and m anagers understand that risk is the fuel that drives returns. It suggests that a higher standard of business maturity is present. Indeed, its very existence dem onstrates an understanding that the downside consequences of risk— loss and disappointm ent— are not unusual. These consequences

5. The risk plan should identify critical dependencies that

are directly related to the chance that m anagem ent and own­

exist inside and outside the organization. The plan should

ers accept in seeking profit. This indicates that m anagem ent

describe the nature of the responses to be follow ed if there

aspires to understand the source of profit. The risk plan also

are breakdowns in such dependencies. Exam ples of criti­

prom otes an organizational risk awareness and the devel­

cal dependencies include reliance on key em ployees and

opm ent of a common language of risk. It dem onstrates an

im portant sources of financing capacity.

intolerance for m istakes/losses that are m aterial, predictable,

The risk plan should explore how key dependencies behave

and avoidable.

in good and bad environm ents.7 Frequently, very good and or very bad events don't occur in a vacuum ; they occur sim ultaneously with other material events. For exam ple,

The Risk Budget Th e risk b u d g et— often called asset allo catio n— should quantify the vision of the plan. O nce a plan is put into p lace, a

5 Diversification policies are routinely included in strategic planning. Such policies take the form of geographic diversification, product diver­ sification, customer base diversification, and so on. Just as organizations produce standards on how much revenue should come from any one source, so too should they examine how much risk originates from any one theme (asset class, portfolio manager, individual security, etc.). 6 In this context, a "large" holding refers to one that can generate earn­ ings exposures that are deemed material vis a vis the business plan. 7 Once again, examining correlations among critical business depen­ dencies in periods of stress may be done in a qualitative or quantitative manner.

form al budgeting process should exist to exp ress exactly how risk capital will be allo cated such that the organization's stra­ te g ic vision is likely to be realized. Th e b ud g et helps the o rg a­ nization stay on course with resp ect to its risk plan. For each allocation of risk b ud g et, there should be a corresponding (and accep tab le) return e xp e ctatio n . For each return e x p e c ta ­ tio n, som e sense of e xp e cte d variab ility around that e x p e c ta ­ tion should be e xp lo red . W hen all of the e xp e cte d returns, risks, and co variatio ns am ong risk budgets are co nsid ered , the e xp e cte d return stream s, and the variab ility of such, should be

Chapter 7 Risk Monitoring and Performance Measurement

■ 99

co nsistent with the organization's strateg ic o b jectives and risk to le ran ce s. As noted earlier, there are many sim ilarities betw een financial budgets and risk budgets. Financial budgets calculate net

of this portfolio on reported earnings and, therefore, share price. In constructing a risk budget for this portfolio, the organization might: •

is then estim ated as net income divided by capital invested. In the case of risk budgets, a risk "ch arg e"— defined as VaR or som e other proxy for "risk e xp e n se "— can be associated with each line item of projected revenue and expense. Hence,

• •

these w eights over various tim e horizons, and test the sen­ sitivity of this perform ance to changes in return and covari­

In the case of both financial and risk budgets, presum ably RO E

ance assum ptions. •

revenues. Ju st as the financial budget allocates revenue and

appropriate levels vis a vis the business and risk plan. •

a vis a com petitor's R O E and R O R C , the earnings profile

ity, so too should a risk budget exist for each activity in order to

might be deem ed to be low quality by the m arketplace.

estim ate the risk-adjusted profitability of the activity. Ju st as

A ccordingly the risk budgeting process must concern itself

financial budgets show a contribution to RO E by activity, so too

with not only the absolute m agnitude of the R O R C at the

can risk budgets show a contribution to overall risk capital usage

strategy and overall portfolio levels, but also the variability

by activity. For exam ple, standard mean-variance optimization asset class, in addition to overall estim ates of portfolio stan­

in such m agnitude. •

owners and m anagers identify such dow nside as m erely dis­

each allocation.

appointing and not unacceptably large (i.e ., lethal) given the

Note that both R O R C and R O E can and should be estim ated investm ent boards m eet monthly and are likely to react to short-term perform ance, monthly RO RC is relevant. Hence, m anagem ent must define the tim e horizons over which risk budget allocations are to be spent and over which RO RC should be m easured.9 An exam ple at this point might be helpful. Assum e that an organization has a material investm ent portfolio. The organiza­ tion is concerned about the im pact of the earnings volatility

Explore the dow nside scenarios associated with each allo­ cation over various tim e horizons. Ensure that the plan's

dard deviation and the marginal contribution to risk8 from

over all tim e intervals that are deem ed relevant. For exam ple, if

Ensure that the exp ected variability around exp ected RO RC is at accep tab le levels. If there is too much variability vis

expense amounts across activities to determ ine their profitabil­

m ethods produce estim ates of w eights to be assigned to each

Ensure that the levels of risk assum ed at the individual asset class level as well as for the portfolio taken as a whole are at

the organization is sufficiently com pensated— in cost/benefit term s— for the expenses and/or risks associated with generating

Sim ulate the perform ance of a portfolio (including the behavior of related liabilities, if relevant) constructed with

aggregation of all activities.

deem ed acceptable. Both statistics are concerned with w hether

Using mean variance optimization or other techniques, deter­ mine appropriate w eights for each investm ent class.

a RO RC can be associated with each activity as well as for the

and RO RC must exceed som e minimum levels for them to be

From the risk and business plan, identify acceptable levels of R O R C and R O E over various tim e horizons.

income as the difference betw een revenue and expenses. RO E

plan's objectives. •

In each significant downside scenario, loop back to the planning process and ensure that contingency steps exist to bring about a logical and measured response. Ensure that owners, m anagers, and other outside constituen­ cies (e.g ., suppliers of capital) are aware and supportive of these responses.

C learly, risk budgeting incorporates elem ents of m athem atical m odeling. A t this point, som e readers may assert that quantita­ tive m odels are prone to failure at the w orst possible m om ents and, as such, are not sufficiently reliable to be used as a control

8 The marginal contribution to risk from any asset is defined as the change in risk associated with a small change in the underlying weight of that asset in the portfolio.

tool. We do not agree. The reality is that budget variances are

9 We know that risk across different time dimensions does not simply scale by the square root of time. The path to the long term may be much bumpier than a simple scaling might imply. In fact, the long-term result may be entirely consistent with a fair number of short-term anom­ alies. If so, management must ensure that risk allocations are sized in such a manner that losses associated with short-term market difficulties can be negotiated effectively. Hence, in a manner analogous to finan­ cial budgeting, the risk budget helps managers size the bets in each revenue-producing area.

factors (e .g ., inefficiency) or com pletely unforeseen anom alies

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a fact of life in both financial budgeting and risk budgeting. Variances from budget can result from organization-specific (e .g ., m acroeconom ic events, w ars, w eather, etc.). Even though such unforeseen events cause R O E variances, som e of which may even be large, most m anagers still find value in the pro­ cess of financial budgeting. The existence of a variance from budget, per se, is not a reason to condem n the financial bud­ geting exercise.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

So, too, we believe that the existence of variances from risk

•

Investors them selves are expected to have more firsthand

budget by unforeseen factors does not mean that the risk

knowledge about their investm ent choices. Perhaps this

budgeting process is irrelevant. To the contrary. Frequently

has been driven, in part, by the notoriety of losses incurred

the greatest value of the risk budget derives from the budget­

by Procter & G am ble, Unilever, Gibson G reeting Cards,

ing p ro ce ss itself— from the discussions, vetting, argum ents,

O range County (California), the Com m on Fund, and others.

and harmonies that are a natural part of w hatever budget is

A fter these events, organizations have becom e interested in

ultim ately agreed to. M anagers who perform risk budgeting

stresses and the portfolio's behavior in more unusual environ­

understand that variances from budget are a fact of life and are

ments. Further, in the asset m anagem ent w orld, asset m anag­

unavoidable, but are not a reason to avoid a formal risk bud­

ers increasingly must be able to explain, ex ante, how their

geting process. To the contrary, understanding the causes and

products will fare in stressful environm ents. This enhanced

extent of such variances and ensuring that appropriate remedial

client dialogue disclosure is beneficial from two perspectives:

responses exist make the budgeting and planning process even

First, it raises the level of client confidence in the manager.

more valuable.

Second, it reduces the risk of return litigation arising from types of events that were predictable on an ex ante basis.

Risk Monitoring

In response to this heightened level of risk consciousness, many

Variance monitoring is a basic financial control tool. Since rev­ enue and expense dollars are scarce, monitoring team s are established to identify material deviations from target. Unusual deviations from target are routinely investigated and explained as part of this process. If w e accep t the prem ise that risk capital is a scarce com m od­ ity, it follow s that m onitoring controls should exist to ensure that risk capital is used in a m anner consistent with the risk budget. M aterial variances from risk budget are threats to the investm ent vehicle's ability to m eet its R O E and R O R C targets. If excessive risk is used, unacceptable levels of loss may result. If too little risk is spent, unacceptable shortfalls in earnings may result. Risk m onitoring is required to ensure that m aterial deviations from risk budget are d etected and addressed in a tim ely fashion.

organizations and asset managers have formed independent risk m anagem ent units (RMUs) that oversee the risk exposures of portfolios and ensure that such exposures are authorized and in line with risk budgets. This trend was definitely spurred on by a highly influential paper authored by the Working G roup10 in 1996. The W orking Group suggested that the RMU's reporting line should incorporate a segregation of duties— a fundam ental elem ent of an effective internal controls environm ent. To be effective, the RMU should be independent in both fact and appearance. This assertion is ratified by industry and profes­ sional guidance. For exam ple, the Third Standard produced by the Working Group reads in part: W here p o ssib le , an in d e p e n d e n t internal g ro u p . . . sh ou ld perform oversight. . . . Functions ch e ck e d in d e­ p en d e n tly sh o u ld include: •

7.4 RISK M ONITORING— RATIONALE AND ACTIVITIES

•

There is an increasing sense of risk consciousness among and

•

within organizations. This risk consciousness derives from several sources: •

Banks that lend to investors increasingly care about where assets are placed.

•

Boards of investm ent clients, senior m anagem ent, investors, and plan sponsors are more know ledgeable of risk m atters and have a greater awareness of their oversight responsibili­ ties. Especially as investm ents becom e more com plicated, there is an increasing focus to ensure that there is effective oversight over asset m anagem ent activities— w hether such activities are m anaged directly by an organization or del­ egated to an outside asset manager.

O versig h t o f investm ent activity Lim its, m onitoring, exce p tio n rep o rts and action plans relating to excep tio n rep o rts

•

Stress tests and back tests . . . Fiduciaries sh o u ld verify that M anagers co n ­ d u ct in d e p e n d e n t risk oversig h t o f their em p lo yees and activities.

10 The Working Group was established in April 1996 by 11 individuals from the institutional investment community. Its mission was: "To create a set of risk standards for institutional investment managers and institu­ tional investors." In drafting the final standards, opinions were solicited from a wide range of participants in the financial community including asset managers, academics, plan sponsors, custodians, and regula­ tors. More recently, Paul Myners, in his report (dated March 6, 2001) addressed to the Chancellor of the Exchequer of the United Kingdom entitled Institutional Investment in the United Kingdom—A Review, argued persuasively for the increased need for professional develop­ ment and product understanding of those individuals charged with overseeing pension plans.

Chapter 7 Risk Monitoring and Performance Measurement

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101

In their book, The Practice o f Risk M anagem ent, Robert Gumer-

should be actively involved in the identification of and organi­

lock and Robert Litterman ratify this Standard by stating:

zational response to low-probability yet high-dam age events. It should prom ote discussion throughout the organization

It is essential that the risk m anagem ent function itse lf

and encourage developm ent of a context by which risk data

m ust b e esta b lish ed in d ep en d en tly from the business

and issues are discussed and internalized.

areas and o p era te as a controlling or m onitoring func­ tion. The role o f the risk m anagem ent function is to

•

The RMU is an elem ent of the risk culture. It should represent one of the nodes of managerial convergence— a locus where

p ro vid e assurance to sen io r m anagem ent and the Board that the firm is assessing its risk effectively, and is com ­

risk topics are identified, discussed, and dissem inated across

plying with its own risk m anagem ent standards. This

the organization and clients. In so doing, it helps promote

m eans that the risk m anagem ent function has to have an

enhanced risk awareness together with a common risk culture

in d e p e n d e n t reportin g line to sen io r m anagem ent.

and vocabulary.

The risk monitoring unit is a necessary part of the process that

•

ensure that transactions are authorized in accordance with

ensures best practices and consistency of approach across the

m anagem ent direction and client expectations. For exam ple,

firm . It helps ensure that a process exists by which risks are

the RMU should measure a portfolio's poten tial (i.e., ex ante)

identified, m easured, and reported to senior m anagem ent in a

tracking error and ensure that the risk profile is in consonance

tim ely fashion. The function is part of an internal control fram e­

with exp ectatio ns. 11

work designed to safeguard assets and ensure that such assets are managed in accordance with each organization's exp ecta­

As a part of the internal control environm ent, the RMU helps

•

Together with portfolio m anagers and senior m anage­ m ent, the RMU identifies and develops risk m easurem ent

tions and m anagem ent direction.

and perform ance attribution analytical tools. The RMU also assesses the quality of m odels used to m easure risk. This

Objectives of an Independent Risk Management Unit The objectives of the RMU are: •

task involves back testing of m odels and proactive research into "m odel risk." •

ating portfolio m anagers and m arket environm ents. This

The RMU gathers, m onitors, analyzes, and distributes risk

data, and the m ethodologies used to create it, must be of a

data to m anagers, clients, and senior m anagem ent in order

quality and credibility that it is both useful to and accepted

to better understand and control risk. This mission requires

by the portfolio m anagers. This risk data should be synthe­

that the RMU deliver the right information to the right con­

sized, and routinely circulated to the appropriate decision

stituency at the right tim e. •

The RMU helps the organization develop a disciplined pro­ cess and fram ew ork by which risk topics are identified and

makers and m em bers of senior m anagem ent. •

individual portfolios and the source of perform ance. It estab­

adoption and im plem entation of best risk practices and con-

lishes risk reporting and perform ance attribution system s to

sistency/com parability of approach and risk consciousness

portfolio m anagers and senior m anagem ent. In the process,

across the firm . As such it is a key prom oter of an organiza­

the RMU prom otes transparency of risk information.

tion's risk culture and internal control environm ent. To be vibrant, the RMU must be more than a publisher of periodic VaR inform ation. It must also proactively pursue topics and have a topical vein. The RMU should be actively involved in setting and im plem enting the risk agenda and

The RMU provides tools for both senior m anagem ent and individual portfolio m anagem ent to better understand risk in

addressed. The RMU is part of the process that ensures the

•

The RMU develops an inventory of risk data for use in evalu­

•

The RMU should not manage risk, which is the responsibility of the individual portfolio m anagers, but rather m easure risk for use by those with a vested interest in the process. The RMU cannot reduce or replace the decision m ethods and

related initiatives. •

The RMU w atches trends in risk as they occur and identifies unusual events to m anagem ent in a tim ely fashion. W hile it is helpful to identify a risk once it is present, it is more m eaning­ ful to identify a trend before it becom es a large problem .

•

The RMU is a catalyst for a com prehen sive discussion of riskrelated m atters, including those m atters that do not easily lend them selves to m easurem ent. For exam ple, the RMU

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11 For asset management firms, this oversight spans a different dimen­ sion of risk than the function currently performed by compliance depart­ ments. In fact, the RMU forms a natural complement to the efforts of the compliance department within asset management firms. By definition, the matching of actual positions with guidelines by the compliance department involves examining events that have already happened. In contrast, by stressing data and exploring both common and uncommon scenarios, the RMU explores the implications of what might happen in the future.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

responsibilities of portfolio m anagers. It also cannot replace

•

It is the result of a well-articulated and well-defined process

the activities of quantitative and risk support professionals

and risk culture whose major elem ents are understood and

currently working for the portfolio m anagers. Trading deci­

em bodied by the organization.

sions and the related software and research that support these decisions should remain the responsibility of the port­

•

folio m anagers and their support staffs. The RMU measures the extent to which portfolio m anagers trade in consonance with product objectives, m anagem ent expectations, and cli­ ent m andates. If the RMU finds what it deem s to be unusual activities or risk profiles, it should be charged with bringing these to the attention of the portfolio m anagers and senior m anagem ent so that an appropriate response can be devel­

degree of confidence. The RMU helps create system s to report risk information to interested constituencies (senior m anagem ent, control nodes, portfolio m anagers, etc.). This information should reveal several broad them es. In particular, it should allow the user to be con­ clusive concerning: •

oped and im plem ented.

Examples of the Risk Management Unit in Action

ment and the rest of the organization. Information flows allow m anagem ent to ask questions. Q uestions and the ability to probe into the process by which the business operates are fun­ dam ental to loss avoidance and profit m axim ization. Risk monitoring is principally concerned with w hether invest­ ment activities are behaving as exp ected . This suggests that there should be clear direction as to what results and risk pro­ files should be deem ed normal versus abnorm al. It is our exp eri­ ence that the very best m anagers in the world achieve success in no small part because they have a tim e-tested conviction and a philosophy that has a stable footprint. For exam ple, the best growth m anagers do not invest in value them es; the best U.S. fixed income m anagers do not take most of their risk in non-U.S. instrum ents; and so on. In fact, the prem ier m anagers remain true to their tim e-tested convictions, styles, and philosophies. Further, the best m anagers apply well-defined limits— expressed both in absolute term s as well as in marginal contribution to risk term s— on how they spend any given amount of risk budget.

W hether the m anager is generating a forecasted level of tracking error that is consistent with the target established by the m andate.

•

W hether, for each portfolio taken, individually and for the sum of all portfolios taken as a w hole, risk capital is spent in

An effective internal control environm ent requires tim ely, m ean­ ingful, and accurate information flows betw een senior m anage­

It is stable, consistent, and controlled. It produces results that can be explained and repeated across tim e with a high

the expected them es. •

W hether the risk forecasting model is behaving as predicted.

Is the Forecasted Tracking Error Consistent with the Target? The forecasted tracking error is an estim ate of the potential risk that can be inferred from the positions held by the portfolio derived from statistical or other forward-looking estimation techniques. An effective risk process requires that portfolio man­ agers take an appropriate level of risk (i.e., neither too high nor too low) vis a vis client expectations. This forecast should be run for each individual portfolio as well as for the sum of all portfo­ lios owned by the client. Tracking error forecasts should be com ­ pared to tracking error budgets12 for reasonableness. Policy standards should determ ine what m agnitude of variance from target should be deem ed so unusual as to prom pt a question and what m agnitude is so material as to prom pt im m ediate cor­ rective action. In this manner, unusual deviations across accounts will be easier to identify.

The result of this discipline is a portfolio that produces a return

Figure 7.1 is an exam ple of a tracking error forecast report for

distribution that m eets the following world-class standards:

a sam ple U.S. equity fund produced by Goldm an Sachs A sset

•

It is consistent with client expectations. The risk capital con­ sumed by the m anager approxim ates the amount of risk bud­ get the client authorized the m anager to spend.

•

It is derived from organizational or individual strengths (e.g ., stock selection, sectors, of the m arket growth or value, port­ folio construction techniques, etc.).

•

M anagem ent (GSAM ) on its proprietary portfolio analysis and construction environm ent (PACE) platform . PA C E is a risk and return attribution system that we use to forecast risk across the spectrum of equities m anaged by G SA M . O bserve from the header of this report that the forecasted tracking error for this account, as estim ated by the PA C E m odel, is 3.68 percent per annum. A second equity factor risk m odel, Barra, projects

It is high-quality in the sense that it is not the result of luck,

a tracking error forecast of 2.57 percent. Since each model

but rather of sound organizational plans and decisions that have been executed in accordance with philosophy and conviction.

12 Tracking error budgets should exist for each portfolio and be deter­ mined as part of the organization's asset allocation process.

Chapter 7 Risk Monitoring and Performance Measurement

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103

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This type of situation is often referred to as "style

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drift." An exam ple of this might be a growth

PACE Predicted Tracking Error: The tracking error predicted over the next year if today’s positions are held constant.

Account Report Date Portfolio Value Tracking Error Prev montfalsTE Num of A ssets R isk Horizon

m anager who is investing in consonance with the

Risk Monitor Summary

PA C E

correct overall tracking error target, but who is

Portfolio Mar SA P 500 Benchmark C ash (as % of total pv) 1.97 % 3 .2 5 % (ann) Tarqet T E 2 .5 7 % (ann) Barra U S E 3 T E 0 Exceptions PACE-1 Model

May 10, 2000 $ 3,252,453,362 3 .6 8 % (ann) 3.64 % (ann) 128 1 Month

placing most of the risk in value them es. In this case, the investor is acquiring the correct level of overall risk, but the wrong style decom position.

Risk Decomposition

Exam ples of risk decom position that a m anager

Risk measured as standard deviation (in %) Managed Total: Factor: Industry Style Specific: Stocks (128)

Active (TE)

25.65 24.87

3.68 2.01

26.36 5.12

1.96 1.93

6.25

3.08

should be able to articulate and which the RMU should monitor might include: •

The 10 biggest stock contributors to tracking error are: Stock

Contribution to Tracking Error: Of the portfolio’s total TE, roughly 6% is used, at the margin, by being overweight in STT.

Figure 7.1

Company

Contribution to TE

Active Weight

5.96 %

1.95%

LMGA AT&T CORP

5.91 %

WLA BMY

4.41 % 4.39 %

1.13% 1.32% 1.21 %

3.75 %

0.46 %

STT

STATE STR CORP WARNER LAMBERT CO BRISTOL M YERS SQUIBB

NSQL NETWORK SOLUTIONS INC

Risk report for a U.S. equity fund.

The range of acceptable active w eights (port­ folio holdings less benchm ark holdings) at the stock, industry, sector, and country levels.

•

The range of acceptable marginal contribu­ tions to risk at the stock, industry, sector, and country levels.

Refer again to Figure 7.1. For this particular portfolio, we observe that State Street Corp. represents an active w eight of

uses different assum ptions to forecast risk, it is not surpris­

1.95 percent of the total portfolio and that its marginal contribu

ing that two different m odels would produce different results.

tion to tracking error is 5.96 percent. The risk monitoring func­

W hat is com forting in this case is that both m easures of risk

tion should conclude as to w hether this active w eight and risk

are com parable to the targeted risk level of 3.25 percent

decom position— which may alternatively be described as the portfolio's diversification footprint— is in line with expectations.

per annum. This same report should be produced for each account that is supposed to be managed in a parallel manner to ensure consis­ tency of overall risk levels.

Is Risk Capital Spent in the Expected Themes for Each Portfolio?

W hat is being measured here is the extent to which the man­ ager is investing capital in accordance with stated policies. This report should be run at the m anager level as well as at the con­ solidated portfolio level to ensure that no undue (i.e ., unaccept­ ably large vis a vis budget) concentrations of risk are present. Figure 7.2 shows the largest active exposures and marginal contributions at the industry level. The risk monitor should

In financial variance m onitoring, it is insufficient to know only

be able to opine on w hether the levels of risk concentration

that the overall expense levels are in line with expectations.

observed are in accordance with m anager philosophy. O nce

Each line item that makes up the total must also correspond to

again, this report should be run at the m anager level as well

expectations. If there are material variances among line items

as at the consolidated portfolio level to ensure that no undue

that tend to offset each other, the person monitoring variances

(i.e., unacceptably large vis a vis budget) concentrations of risk

should be on notice that unusual activity may be present. A s an

are present that might put either a strategy or the overall plan

exam ple, if a departm ent m eets its overall expense budget but

at risk.

is m aterially over budget in legal fees (with favorable offsets in other areas), the review er might conclude that an event is pres­ ent that might put future returns at risk. The same principle holds for risk m onitoring. M anagers should be able not only to articulate overall tracking error expectations, but also to identify how such tracking error is decom posed into its constituent parts. This will let the risk m anager opine on w hether risk is being incurred in accordance with exp ecta­ tions both in total as well as at the constituent level. If the risk

Is the Risk Forecasting Model Behaving as Predicted? As indicated earlier, the risk forecasting model uses statistical m ethods to produce a forward-looking estim ate of tracking error. A ccordingly, the risk monitor is charged with knowing w hether the model is producing meaningful estim ates of risk. For exam ple, G SA M 's PA C E tabulates the num ber of tim es that

decom position is not in keeping with expectations, the m anager

a portfolio's actual return is m aterially different from its risk

may not be investing in accordance with the stated philosophy.

forecasts. As an exam ple of this test, please refer to Figure 7.3.

104

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Financial Risk Manager Exam Part II: Risk Management and Investment Management

PA C E

R isk Monitor Sum m ary

In d u stries (52)

Media

________+

4.87%

Home Products

1.99%

Financial Services

1.25%

T | h i 1 mil11 in i| iliu active exposures by Industry are: Telephones

-1.61%

Computer Hardware

-1.51%

Medical Products

-1.39%

The 5 biggest Industry contributors to tracking error are Industry Media Home Products Hotels Internet Publishing

implied paths, Monte Carlo m ethods are com m only applied.

The 3 most positive active exposures by Industry are:

The largest active exposure (overweight vs. benchmark) is a 4.87 percent exposure to media

that actually occurred. To exam ine these

Contribution to T E / / / /

Active Exposure 4.87 % 1.99% 0.96 % 0.67 % 0.71 %

8.55 % 2.80 % 1.87% 1.12% 1.00%

Figure 7.4 graphs the results of a Monte Carlo simulation for a sam ple equity port­ folio that was prepared to study how tracking error forecasts fluctuate depend­ ing on the environm ent used to estim ate the risk fo recast. 14 Note that as of April 26, 2002, for this portfolio, the PA C E risk

That 4.87 percent overweight in media consumes, at the margin, 8.55 percent of the portfolio's predicted tracking error.

Fiqure 7.2

Industry-level exposures and marginal contributions

model projected a tracking error of 5.08 percent per annum. The tracking error tar­ get for this portfolio was 5 percent. So, at first blush, it seem s as though the portfo­ lio has an overall risk profile that is closely aligned with the risk target. Com mon

Note that if the model is behaving as exp ected , the portfolio's

sense tells us, however, that the particular com bination of assets

actual returns should exceed the tracking error forecast by

held in the portfolio might exhibit quite different tracking error

approxim ately one day per month. O ver the four months ended

characteristics in different environm ents.

April 30, one therefore expects that there should be four occur­ rences w here actual returns exceed forecast. In fact, there are three. The risk m onitor can conclude that the model is behav­ ing appropriately over the period. Had this result not been reached, som e of the model's assum ptions might have needed to be revisited.

The PA C E forecast is derived by assuming that the underlying data have a halflife of about half a year. W hen estim ating the covariance m atrix15*that is at the heart of the risk forecast, data that are six months old are w eighted half as much as current data, and data that are one year old are w eighted about onequarter of current data, and so on. So, more im port is given to

Note from Figure 7.3 that this technique gives no guidance as to

recent data than to aged data in forecasting risk. This key

how much the model might underestim ate risk in the event that

assumption means that the co-variance m atrix itself fluctuates

the actual result exceeds forecast. It only explores the frequency

over tim e not only because different data are used to estim ate

with which this result occurs. The risk monitoring professional

its com ponents but also because the passage of tim e causes the

should also explore how tracking error might behave in more

im port of any particular elem ent in the m atrix to have an ever

unusual circum stances. 13

sm aller w eight.

There are many ways to exam ine how a portfolio might behave

To exam ine how a tracking error forecast might fluctuate over

during periods of stress. O ne technique is historical simulation.

tim e, Figure 7.4 sim ulates the frequency distribution of the

To apply this approach, one takes today's positions and applies

tracking error of the positions held at April 26, 2002, over the

historical price changes to them to see what the earnings im pact

period from Ju n e 1998 until April 26, 2002. These positions,

would have been had such positions been held fixed over a

when introduced into the Monte Carlo engine, would have

period of tim e. A shortfall of this method is that observed his­

yielded an average tracking error forecast that would have

tory produces only one set of realized outcom es. A more robust

peaked at 6.5 percent in late 1998 and mid-2000. A t these

approach would allow us to exam ine the myriad outcom es

tim es, the 98th percentile risk forecast reached levels of

that are probabilistically implied by the one set of outcom es

7 percent.

13 It is often true that a three standard deviation scenario is more draco­ nian than that value that is implied by multiplying a one standard devia­ tion loss by three. This result occurs for two reasons: (1) Many products have nonlinear payoff structures (i.e., embedded options); and (2) the global stresses that are present in a three standard deviation scenario are qualitatively different than those which are present in a one standard deviation scenario. As an example, counterparty credit risk increases in more unusual environments.

14 It is beyond the scope of this chapter to delve in depth into the cal­ culation methodology behind Monte Carlo methods. Rather we present an output of a Monte Carlo analysis to give the reader a sense as to the types of insights it might provide. 15 Recall that the standard deviation (or tracking error) is calculated by the formula: Tracking error = [WrS\A/]1 2 where W is an N X 1 matrix of weights applied to particular factors (e.g., risk factors, or market value of stock holdings, etc.) and £ represents the N X N covariance matrix associated with the returns of these factors.

Chapter 7 Risk Monitoring and Performance Measurement

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105

Forecasted Value at Risk vs. Active Returns

liquidity are an essential elem ent of the stress analysis. For exam ple, investors must be aware if a partial redem ption could cause an illiquid asset to exceed som e guideline.17 Since redem ption risk can correlate with difficult m arkets, some illiquid situations (e .g ., 144A securities, position concentrations, etc.) can coin­ cide with unanticipated redem ptions of capital. 18 The risks associated with many of these situations are often apparent only if large stresses are assum ed. A tool w e use at G SA M to assess the potential

c\j

o

Fiau re 7.3

CM

O

CO

o

CO

CO

o o Date

o

Model validation.

o

O

LD

O

im plications of illiquidity is the "liquidity duration" statistic. To calculate this statistic, begin by estim ating the average num ber of days required to liquidate a portfolio assum ing that the firm does not wish to exceed a specified percent of the daily volum e in any given security. The point here is that we wish to estim ate how long it would take to liquidate a portfolio's holdings in an orderly fashion— that is, w ithout m aterial m arket im pact. For exam ­ ple, suppose that we do not wish to exceed more than 15 percent of the daily volum e in any given secu­ rity holding. The num ber of days

stresses.

required to liquidate any given secu­

The risk monitoring professional should consider w hether these ranges of tracking error that might occur during periods of stress fall within acceptable levels vis a vis the long-term target of 5 percent. If these levels of tracking error are deem ed unac­

rity we term the liquidity duration for that security. More pre­ cisely, the liquidity duration for security / can be defined as: LD, = Q ,/(.1 5 • V,) where LD, — Liquidity duration statistic for security /, assum ­

ceptably large, an appropriate response might be to run the

ing that we do not wish to exceed 15% of the

portfolio at a lower risk profile (say, 4 percent) such that there is

daily volum e in that security

reason to believe that the tracking error is less likely to reach unacceptably large levels during periods of stress. 16

Quantifying Illiquidity Concerns Since a portfolio's liquidity profile can change dram atically dur­

Q, — Num ber of shares held in security / V, — Daily volum e of security / An estim ate of liquidity duration for the portfolio taken as a whole can be derived by weighting each security's liquidity dura­ tion by that security's w eight in the portfolio.

ing difficult m arket environm ents, tools that measure portfolio

16 Recall that tracking error is shorthand for the magnitude of earnings variability associated with a certain degree of statistical confidence. If this variability is unacceptably large, it may place the organization's over­ all strategic plan and goals at risk.

106

■

17 As an example, a U.S. mutual fund cannot hold more than 15 percent of its assets in illiquid securities. 18 An example of this statement is the acceleration of liabilities in a pen­ sion plan due to increases in early retirements in periods of recession.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Liquidity duration is readily calculated for equity holdings, as

•

volum e data are easily available. In the case of fixed income securities, where volum e information is not available, the esti­ mate of the num ber of days required to liquidate a position— and an overall portfolio— in an orderly fashion (i.e., without a material adverse earnings impact) will likely result from discus­ sions with portfolio m anagers.

To determ ine w hether a m anager generates superior riskadjusted perform ance vis a vis the peer group.

•

To determ ine w hether the returns achieved are sufficient to com pensate for the risk assum ed in cost/benefit term s.

•

To provide a basis for identifying those m anagers whose processes generate high-quality excess risk-adjusted returns. W e believe that consistently superior risk-adjusted per­ form ance results suggest that a manager's processes, and

Credit Risk Monitoring

the resulting perform ance, can be replicated in the future,

For the purposes of this discussion, we assume that the credit risk of each instrum ent is researched and understood by the portfolio manager. W e further assum e that through factor m od­ els or other techniques, the RMU professional can estim ate the VaR or tracking error consequences of credit exposures im bed­ ded in the securities held by the portfolio. In addition to quantifying security-specific and overall portfolio

making the returns high-quality.

Reasons That Support Using Multiple Performance Measurement Tools To calculate a risk-adjusted perform ance m easure, two items must be known:

credit exposure, it is im portant that the RMU understand the

1. Returns over the relevant tim e period. 19

credit consequences of dealing with brokers, custodians, execu­

2. Risk incurred to achieve such returns.

tion counterparties, and the like. It is a truism that credit risk is frequently the other side of the coin of m arket risk. Discussions on m arket risk are often, at their heart, driven by credit m atters. In certain asset classes (e.g ., em erging markets) credit risk and m arket risk may be virtually inseparable. Further, since credit risk is an attribute of perform ance, it should also be an elem ent of the risk process. As an exam ple, many global indexes (e.g ., IFC) now include em erging m arket countries. To the extent that financial system s in such countries (e.g ., Egypt and Russia) are evolving and im m ature, institutions face credit risk when settling trades. The expected return on such transactions is a function not only of issuer-specific risk, but of credit/settlem ent risk as w ell. For this reason, the RMU should ensure that all counterparties used to execute and settle trades m eet credit policy criteria.

7.5 PERFO RM AN CE M E A S U R E M E N T TO O LS AND THEORY

Risk is ultim ately a very human concept com prised of many human dim ensions (e .g ., em otion, psychological response to uncertainty, fear of underperform ance, etc.). Since no two human beings are identical, no tw o risk assessm ents are iden­ tical. To m easure risk and return most com prehensively, we have seen that a panoply of tools (e .g ., historical sim ulations, liquidity aw areness, Monte Carlo m ethods, etc.) can be help­ ful in order to gain the most com plete understanding of the risk present in a portfolio. If the tools yield m aterially different forecasts, the onus is on the risk professional, working to gether with senior m anagem ent and portfolio m anagers, to apply judgm ent to determ ine the most appropriate forecast under the circum stances.

How to Improve the Meaningfulness of Performance Measurement Tools Perform ance tools are especially robust when they confirm a priori expectations regarding the quality of returns. If we

Until now, we have largely focused our attention on measuring

can identify a disciplined and effective process, we should

potential risk— an estim ate of the risk and return that is possible.

exp ect that the process will generate superior risk-adjusted

The other side of this coin is m easurem ent of realized outcom es.

returns. The tools provide a means of measuring the extent

In theory, if the ex ante forecasts are m eaningful, they should

of the process's effectiveness. The tools should confirm our

be validated by the actual outcom es experienced . In this sense, perform ance m easurem ent might be thought of as a form of risk model validation. In general, the objectives of perform ance m easurement tools are: •

To determ ine w hether a m anager generates consistent excess risk-adjusted perform ance vis a vis a benchm ark.

19 In cases where a portfolio holds illiquid assets, returns are the product of human judgment to some degree. It is conceivable that two individu­ als looking at the same positions could arrive at materially different valuations—this phenomenon occurs because there can be a material divergence between value and price in illiquid markets. In contrast, for liquid securities, the low bid/ask spread is an indication that price is a good approximation of value.

Chapter 7 Risk Monitoring and Performance Measurement

■

107

belief that the process is indeed functioning the way it was

tools. In such cases, the organization will be even more dep en­

designed to. For exam ple, risk decom position analysis should

dent on measuring com pliance with m anager philosophy.20

show that small cap m anagers are in fact taking most of their risk in small cap them es. Sim ilarly, a m anager with a particular industry specialization should be able to dem onstrate that most of that risk budget is spent in securities in that industry. And so on. For a process to be present, one must be able to define "norm al behavior." If normalcy is not identified, the process is likely to be too am orphous to be quantified. Sim ply put, a pro­ cess cannot exist without well-defined expectations and d eci­ sion rules. Normal behavior suggests that behavior should be predictable. If a process is effective, continued normal behavior (i.e., trading in a manner consistent with the established process) should give us reason to conclude that high-quality returns observed in the past are likely to replicate them selves in the future. Later on in this chapter, we will introduce some commonly used perform ance tools. Before discussing these, however, it is worth noting that perform ance tools, while necessary, are not a substitute for tim ely m anagem ent intervention when there

A t this point, we turn our focus to identifying some commonly used perform ance tools and techniques. (A ppendix B, for the reader's reference, is a more m athem atical treatm ent of perfor­ mance calculation m ethodologies.)

Tool #1—The Green Zone Each portfolio m anager should be evaluated not only on the basis of ability to produce a portfolio with potential (i.e ., forecasted) risk characteristics com parable to targ et, but also on the basis of being able to achieve actual risk levels that approxim ate target. A m anager who can accom plish this task, and earn excess returns in the process, has dem onstrated the ability to anticip ate, react to, and profit from changing eco­ nomic circum stances. A t G SA M , we have pioneered a concept called the green zone21 to identify instances of perform ance or achieved tracking error that are outside of normal expectations. The green zone con­ cept em bodies the following elem ents:

1. For the prior w eek, month, and rolling 12 months, we calcu­

is an indication of abnormal behavior. By the tim e that abnor­

late the portfolio's norm alized returns, which are defined as

mal behavior manifests itself in the form of poor perform ance

excess returns over the period minus budgeted excess

statistics, the dam age might already be irreversible. For this

returns over such period, all divided by target tracking error

reason, we believe that perform ance tools must be supple­

scaled for tim e .22 This statistic might be view ed as a test of

mented with: •

A clear articulation of m anagem ent philosophy from each portfolio manager. This philosophy statem ent should identify how the m anager expects to extract returns from the m arket. It should identify ways of knowing when the m anager's pro­ cess is successful and when it is unsuccessful.

•

the null hypothesis that the achieved levels of excess

20 Even though an organization lacks sufficient data to measure the effectiveness of many managers based on their historical results, it still has sufficient information to conclude whether: •

A manager's philosophy and practices meet commonsense criteria and are likely to extract risk-adjusted performance from the market.

•

Each manager's portfolio is consistent with stated philosophy. For example, the RMU should be able to determine that the current portfolio has overall risk levels and risk decomposition characteristics that conform to the manager's philosophy.

A routine position and style monitoring process designed to identify deviations from philosophy or process. This is a type of early warning system .

A p p end ix A at the end of this chapter gives exam ples of the kinds of information that might be obtained from each m anager to help the RMU define and understand each manager's invest­ ment philosophy more com pletely. This list is not meant to be exhaustive, nor is it appropriate for every organization and man­ ager. W e provide it here as an exam ple of techniques used in identifying and monitoring "norm alcy." For quantitative portfolio m easurem ent tools to be effective, we must have a sufficient num ber of data points to form a conclu­ sion with a certain level of statistical confidence. For the pur­ poses of the rem ainder of this chapter, we will assum e away this issue. In practice, however, the dearth of perform ance data often hinders the effectiveness of perform ance m easurem ent

108

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An administrative process that measures congruence between man­ ager philosophy and actual trades, money management behavior, loss control, position sizing, and so on is also a form of performance mea­ surement, although not one that we intend to deal with in this paper. If the manager cannot articulate his portfolio management techniques effectively, and if adherence to stated techniques cannot be measured, it is difficult to conclude that a process exists which can be replicated successfully in the future. 21 Refer to an article entitled: "The Green Zone . . . Assessing the Quality of Returns," by Robert Litterman, Jacques Longerstaey, Jacob Rosengarten, and Kurt Winkelmann of Goldman Sachs & Co. (March 2000). 22 For example, in calculating the monthly normalized return, the denominator consists of the annual tracking error target divided by the square root of 12.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

3.

Time Series of Tracking Errors (Predicted vs. Actual)

For each of the calculation (2) above, we form policy decisions about what type of deviation from expectation is large enough, from a statistical standpoint, to say that it

CO v_

does not fall in the zone of reason­

O

able expectations that w e call the

LLl

U) C

•

green zone. If an event is unusual, but

■

u

still is expected to occur with some

CD

regularity, we term it a yellow zone event. Finally, red zone events are defined as truly unusual and requiring O

im m ediate follow-up. The definition

O

of when one zone ends and a second

Date

Fiau re 7.5

Example of rolling 20- and 60-day tracking errors (annualized).

begins is a policy consideration that is a function of how certain we would like to be that all truly unusual events

returns are statistically different from the targeted/

are detected in a tim ely fashion. For exam ple, if the cost of

budgeted excess returns.

an unusual event is very high, one would expect a very nar­

2. For the prior 20- and 60-day periods, we calculate the ratio of annualized tracking error to targeted tracking error. In this test, we exam ine w hether the variability in excess returns is statistically com parable to what was e xp e cte d .23

row green zone and quite wide yellow and red zones. In this case, one would exp ect to find more false positives, which are by-products of the policy's conservatism .

4. The results of the green zone analysis are sum m arized in a

Note that there is no one correct period of tim e over which

docum ent of the form shown in Figure 7.6. W hat follows

to measure tracking error. W hile for the purposes of this

is a brief description of this docum ent excerpted from the

chapter we have selected a shorter-term horizon, strong

article entitled The G reen Z one . . . A sse ssin g the Quality

argum ents can be made for including longer-term horizons

o f Returns.

as well. The point here is that unusual blips in volatility may serve as filters for identifying anom alous environm ents in which underlying risk dim ensions may be undergoing pro­ found change. This tool is designed to help m anagem ent and portfolio m anagers ask better and tim elier questions.

[In Figure 7.6] we sh ow an exam ple o f a portion o f one o f our w eekly perform an ce rep o rts (using hypothetical pro d u cts). This rep ort, known internally as the "green s h e e t," has colum ns that are co lo r-co d ed for easy re c o g ­ nition o f signals o f tracking error concerns. Fo r exam ple,

As an exam ple of this point, consider Figure 7.5, which

we have d e fin e d the g reen zone for a hypothetical s e t

shows the tim e series of predicted tracking errors ju xta ­

o f U .S. equity p o rtfo lio s, including all ratios o f realized

posed against rolling 20- and 60-day tracking errors. Not

20-day tracking error to ta rget b etw een .7 and 1.4, and

surprisingly, the 20-day measure is more volatile than

have d e fin e d the red zone as ratios b e lo w .6 or above 2.

the 60-day measure and is therefore more responsive to

F o r the 60-day tracking error we d efin e the g reen zone

changes in m arket behavior. The challenge for the risk

as the range b etw een .8 and 1.3. The red zon e is d e fin e d

monitoring professional is to ascertain w hether the signal

as ratios b elo w .7 or above 1.8.

is anom alous or w hether it carries information content that should be acted upon. A t G SA M , we use this signal as a basis for initiating dialogue between the RMU and portfolio m anagers to better understand the causes behind these two signals and their consequences.

. . . the p re d e fin e d green , yellow , and re d zon es p ro vid e clear exp ecta tio n s for the a sset m anagem ent division p o rtfo lio m anagers. W hen p o rtfo lio s m ove into the y e l­ low or red zone, which will happen every so often , it may be tim e for a discussion o f what is g o in g on. We n ever e x p e c t p o rtfo lio m anagem ent, or risk m onitoring, to be

23 This test is analogous to ANOVA techniques (e.g., the "F" test) in which one looks at the ratio of variances to determine whether they are statistically comparable. In this case, we are examining the ratio of stan­ dard deviations.

re d u ce d to a form ula, b u t th ese typ es o f quantitative tools have p ro v e d to be useful in settin g exp ecta tio n s and in providin g useful fe e d b a ck which can fo ste r b e tte r quality control o f the investm ent m anagem ent p ro ce ss.

Chapter 7 Risk Monitoring and Performance Measurement

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109

Net Performance

Normalized Return vs. Target

Portfolio

The point here is that port­

A nnualized T racking E rro r L ast

L ast

Last20D

Last60D

Target

Prior Week

Month To Date

Week

MTD

YTD

3 Mo

l2M o

20D

60D

/T arget

/T arget

TE

P

B

D

P

-1.21

-0.22

-0.16

-0.19

0.45

263

260

1.05

1.04

250

0.76

1.18

-0.42

-1.02

B

find most meaningful those

Benchmark

techniques that measure

U.S. E quity Portfolios Portfolio l

S&P 500

Portfolio 2

R 1000 Growth

0.37

0 .9 1

1.70

3.14

0 .9 1

526

390

1.75

1.30

300

2.13

1.98

0.15

0.62

0.06

(

Portfolio 3

R 1000 Value

0.26

0.85

1.44

1.22

1.36

226

240

0.90

0.96

250

1.32

1.23

0.09

-0.39

-0.83

(

Portfolio 4

R 2000

0.28

-0.12

0.37

-0.07

-0.68

300

288

0.86

0.82

350

4.39

4.25

0.14

1.68

Figure 7.6

folio managers will likely

- 0 .9 1 -(

1.76 -(

Note: This chart is to be used for illustrative purposes only. These are not, and should not be viewed as, predictions or projections of future returns of those classes of assets or any investments, including any fund or separate account managed by GSAM, Goldman Sachs & Co., or any other brokerage account.

A com m only used tool to measure the quality of returns is per­

internalize these issues. Once again, this argues

Representative green sheet.

Tool #2—Attribution of Returns

and describe risk in the same manner that they

for having a range of risk and attribution models in order to achieve the most robust understanding.

Tool #3—The Sharpe and Information Ratios

form ance attribution. This technique attributes the source of

The Sharpe ratio divides a portfolio's return in excess of the risk­

returns to individual securities and/or common factors. Recall

free rate by the portfolio's standard deviation. The information

that when analyzing the risk profile of a portfolio, we discussed

ratio divides a portfolio's excess returns (vis a vis the bench­

techniques (e.g ., risk decom position) to measure the extent to

mark) by the portfolio's tracking error. Both of these tools are

which the implied risks in a portfolio are consistent with e xp e c­

designed to produce estim ates of risk-adjusted returns, where

tations and m anager philosophy. So, too, when exam ining the

risk is defined in standard deviation or tracking error space.

actual returns of a portfolio, we are concerned that the returns were sourced from those them es where the m anager intended to take risk and that such returns are consistent with the risks implied by the ex ante risk analysis.

In theory, two different estim ates of standard deviation (or track­ ing error) could be used for these ratios— actual levels of stan­ dard deviation as well as forecasted levels. In our judgm ent, both are relevant. There are occasions where the realized risk—

O ne form of attribution, com m only called variance analysis,

the risk actually observed by the investor— is m aterially different

shows the contribution to overall perform ance for each security

from the potential risk forecasted by a risk m odel.24 In the

in the portfolio. Figure 7.7 is an excerpt of this kind of analysis

Monte Carlo analysis in Figure 7.4 we saw how stress tests can

for a stock portfolio. This same kind of analysis can be per­

be used to provide a picture of how identical holdings can have

form ed at the industry, sector, and country levels, essentially

quite different return and risk characteristics depending on the

by combining the perform ance of individual securities into the

environm ent. If the estim ates of potential risk capture these

correct groupings. The RMU professional can use this analysis

stressed scenarios, potential risk might well exceed realized risk.

to ascertain w hether the portfolio tended to earn returns in

A favorable Sharpe or information ratio calculated using realized

those securities, industries, sectors, and countries where the risk

risk might be much less attractive when expressed in potential

model indicated that the risk budget was being spent.

risk space. O ver tim e, if the risk model is accurate, the realized

To the extent that the m anager thinks of risk in factor space as

risk will center on the potential risk.

opposed to security-specific space, the attribution process can

The Sharpe and information ratios incorporate the following

be perform ed on this basis. Nam ely, the attribution process cap­

strengths:

tures the w eightings in various risk factors on a periodic basis and also accum ulates the returns to such factors in order to pro­ duce a variance analysis expressed in factor term s. As a general rule, it is most meaningful to attribute returns on

•

They can be used to measure relative perform ance vis a vis the com petition by identifying m anagers who generate superior risk-adjusted excess returns vis a vis a relevant peer group. RMUs and investors might specify some minimum rate

the same basis that ex ante risk for such returns is measured. For managers who think in factor terms, factor risk analysis and factor attribution will likely be more meaningful. For managers who think about risk in terms of individual securities, risk forecasting and attri­ bution at the security level will likely be more relevant. This is not to say that risk should not be measured using a range of models.

110

■

24 Risk models attempt to measure potential risk. Ultimately, the true potential risk is not knowable. We only see its footprints over time in the form of realized risk. Still, even this realized risk is only one outcome of an infinite number of outcomes that were in theory possible.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

PACE

Multi Period Attribution (All entries in %)

Contributors to Active Return by Asset

Top 30

(R anked from highest to low est A ctive C ontrib.)

Stock

Company

INTC INTU JNJ HD GE CSCO ABT IBM ENR MO TXN AMAT

INTEL CORP INTUIT INC JOHNSON & JOHNSON HOME DEPOT INC GENERAL ELECTRIC CO CISCO SYSTEMS INC ABBOTT LABS INTERNATIONAL BUSINESS ENERGIZER HOLDINGS INC PHILIP MORRIS COS INC TEXAS INSTRUMENTS INC APPLIED MATERIALS INC OMNICOM GROUP INC MERCK & CO INC WYETH

OMC MRK WYE

Fiau re 7.7

Contribution 1.45 0.88 0.46 0.41 0.34 0.27 0.25 0.25 0.23 0.23 0.23 0.21 0.17 0.16 0.16

•

Stock

-3.70 4.97 -3.05 -2.11 -6.73 -2.50 -0.89 -2.06 2.20 -1.08 -1.06

CVC

ecu UVN RMG VIA.B DISH HET EVC MGM WON FRE FNM PCS CD TSG

-0.81 -0.30 -1.69 -1.60

CABLEVISION SYSTEMS CORP CLEAR CHANNEL UNIVISION COMMUNICATIONS RAINBOW MEDIA GROUP VIACOM INC ECHOSTAR COMMUNICATIONS HARRAHS ENTERTAINMENT ENTRAVISION METRO GOLDWYN MAYER INC WESTWOOD ONE INC FEDERAL HOME LOAN

-0.86 -0.81 -0.78 -0.66 -0.61 -0.60 -0.56 -0.47 -0.45 -0.41 -0.41

FEDERAL NATIONAL SPRINT CORP CENDANT CORP SABRE GROUP HOLDINGS INC

-0.40 -0.35 -0.34 -0.33

Avg. Active Wgt. 1.30 2.45 3.78 0.88 8.59 2.52 7.65 2.03 1.68 3.88 5.32 5.78 0.51 3.03 3.37

Standard confidence tests can be applied to the regression's outputs. The alpha term can be tested for statistical significance

They test w hether the m anager has generated sufficient

to see if it is both positive and statistically different from zero.

excess returns to com pensate for the risk assum ed.

This perform ance tool incorporates the following strengths:

The statistics can be applied both at the portfolio level

•

have excess risk-adjusted perform ance at the sector or country level.

It allows m anagem ent to opine w hether skill is truly present or excess returns are happenstance. It tests w hether the man­

For exam ple, they can help determ ine which m anagers

ager has generated excess returns vis a vis the benchm ark. •

It allows m anagem ent to distinguish between excess returns due to leverage and excess returns due to skill.

The Sharpe and information ratios incorporate the following w eaknesses:

•

The alpha and beta statistics, and tests of significance, are easy to calculate.

They may require data that may not be available for either the m anager or many of his com petitors. O ften an insufficient

•

tiveness of the risk-adjusted returns. W hen one calculates the statistic based on achieved risk instead of potential risk, the statistic's relevance depends, to som e degree, on w hether the environm ent is friendly to the manager.

Tool #4—Alpha versus the Benchmark This tool regresses the excess returns of the fund against the excess returns of the benchm ark.

The beta statistic shows if an elem ent of the manager's returns are derived from being overweight or underweight the market

history is present for one to be conclusive about the attrac­ •

Contribution

m anager perform ance.

as well as for individual industrial sectors and countries.

•

(Ranked from low est to highest A ctive C ontrib.)

Company

Sample variance analysis.

of acceptable risk-adjusted return when evaluating •

Bottom 30

Avg. Active Wgt.

(occurs if the beta is statistically different from 1.0). This perform ance tool incorporates the following w eakness: •

There may not be a sufficient number of data points to per­ mit a satisfactory conclusion about the statistical significance of alpha.

Tool #5—Alpha versus the Peer Group This tool regresses the manager's excess returns against the excess returns of the manager's peer group. It is used to deter­ mine w hether the m anager dem onstrates skill over and above

The outputs of this regression are:

what is found in the peer group.

•

An intercept, often referred to as "alp h a," or skill.

The peer group's return is the capital-weighted average return

•

A slope coefficient against the excess returns of the

of all m anagers who trade com parable strategies. The peer

benchm ark, often referred to as "b e ta ."

group is basically the manager's com petitors in his strategy.

Chapter 7 Risk Monitoring and Performance Measurement

■ 111

The outputs of this regression are: •

An intercept, often referred to as "alp h a," or skill.

•

A slope coefficient against the excess returns of peer group, often referred to as "b e ta ."

The alpha term represents the m anager's excess return against the peer group. The beta term m easures the extent to which the m anager em ploys greater or lesser amounts of leverage than do com petitors.

in order to produce returns that it neither expects nor desires. If too little risk is taken vis a vis budgeted levels, return exp ecta­ tions will likely fall short of budget. The ability of an organization to achieve its risk and return targets is put at risk anytime that risk capital is used w astefully or in amounts inconsistent with the policies established by such organization. There are three fundam ental dim ensions behind risk m anagem ent— planning, budgeting, and m onitoring. We observe that these three dim ensions are intim ately related

Standard confidence tests can be applied to the regression's

and that they can be more com pletely understood by looking

outputs. The alpha term can be tested for statistical significance

at their com m only used counterparts in the world of finan­

to see if it is both positive and statistically different from zero.

cial accounting controls. W e posit that there is a direct cor­

This perform ance tool incorporates the following strengths: •

It allows m anagem ent to opine w hether skill is truly present or excess returns are happenstance. It tests w hether the man­ ager has generated excess returns vis a vis the peer group.

• •

the shadow cost behind returns. Hence behind every line item in a financial plan or budget must lie a corresponding risk dim en­ sion. Financial plans and budgets can therefore be alternatively

The alpha and beta statistics, and tests of significance, are

expressed using risk m anagem ent vocabulary.

easy to calculate.

The risk plan should set points of success or failure for the

There may not be a sufficient number of data points to per­ of alpha or beta.

•

m onitoring. This conclusion follows from the assertion that risk is

due to leverage and excess returns due to skill.

mit a satisfactory conclusion about the statistical significance •

counterparts— namely, risk planning, risk budgeting, and risk

It allows m anagem ent to distinguish betw een excess returns

This perform ance tool incorporates the following w eaknesses: •

respondence betw een financial planning, financial budgeting, and financial variance monitoring and their risk m anagem ent

organization (e.g ., return and volatility expectations, VaR poli­ cies, risk diversification standards, minimum acceptable levels of return on risk capital, etc.). The risk plan should be well vetted and discussed among the organization's senior leader­ ship and oversight bodies. Its main them es should be capable

Returns of the peer group are biased due to the existence of

of being articulated to analysts, boards, actuaries, m anage­

survivorship biases.

ment team s, and so on. For exam ple, strategic plans have

There is often a wide divergence in the amount of money

RO E targets and business diversification policies that are well

under m anagem ent among the peers. It is often easier to

known. The risk plan should describe how risk capital is to be

make larger risk-adjusted excess returns with sm aller sums

allocated such that the expected returns on such risk capi­

under m anagem ent than with larger sums.

tal yield the financial outcom es sought with a high degree of certainty.

SUMMARY Risk represents a shadow cost that businesses accept in order to produce profit. For a return to be deem ed acceptable, expected returns must be adequate to com pensate for the risk assum ed. Risk m anagem ent therefore im plies that cost benefit process is at work.

The risk budget— often called asset allocation— quantifies the vision of the risk plan. The risk budget is a num eric blueprint that gives shape and form to the risk plan. There are many sim ilarities betw een financial budgets and risk budgets. Finan­ cial budgets calculate net incom e as the difference betw een revenue and exp en ses. R O E is then estim ated as net incom e divided by capital invested. In the case of risk budgets, a risk "c h a rg e "— defined as VaR or som e other proxy for "risk

Risk is a scarce resource in the sense that organizations place

e x p e n se "— can be associated with each line item of projected

limits on their willingness to accept loss. For any given level of

revenue and exp en se. H ence, a R O R C (return on risk capital)

risk assum ed, the objective is to engage into as many intelligent

can be associated with each activity as well as for the ag g reg a­

profit-making opportunities as possible. If risk is squandered or

tion of all activities. In the case of both financial and risk bud­

used unwisely, the ability of the organization to achieve its profit

gets, R O E and R O R C must exceed som e minimum levels for

objectives is put at risk. If excessive levels of risk are taken vis a

them to be deem ed accep tab le. Both statistics are concerned

vis budget, the organization is risking unacceptably large losses

with w hether the organization is sufficiently com pensated— in

112

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

cost/benefit term s— for the exp enses and/or risks asso ci­ ated with generating revenues. Finally, both RO RC and R O E can and should be estim ated over all tim e intervals that are deem ed relevant. If we accept the prem ise that risk capital is a scarce com m od­

A P P EN D IX A Representative Questions to Help Define Manager Philosophies/Processes

ity, it follows that monitoring controls should exist to ensure

1. W hat sectors do you trade?

that risk capital is used in a manner consistent with the risk

2. W hat countries and regions do you trade?

budget. Material variances from risk budget are threats to the investm ent vehicle's ability to m eet its RO E and RO RC targets. If excessive risk is used, unacceptable levels of loss may result. If too little risk is spent, unacceptable shortfalls in earnings may result. Risk monitoring is required to ensure that material devia­ tions from risk budget are detected and addressed in a tim ely fashion. The chapter introduces the concept of an independent

3. W hat products do you trade (equities, over-the-counter (O TC) foreign exchange (FX), fixed incom e, etc.)?

4. If you trade O T C , do ISD A, FX Netting agreem ents, and so on exist?

5. How many accounts do you trade?

risk m anagem ent unit (RMU) as a best practice in risk monitoring

6 . Define your assets under m anagem ent.

space. It discusses its objectives and provides exam ples of how

7. Are you able to produce a historical track record?

it might operate in practice.

8. Does your strategy require a minimum amount of

The final part of the chapter deals with perform ance

money under m anagem ent in order for you to trade your

m easurem ent tools and related theory. Perform ance tools

entire portfolio?

are especially robust when they confirm a priori expectations regarding the quality of returns. Am ong the objectives of these tools are: •

To determ ine w hether a m anager generates consistent excess risk-adjusted perform ance vis a vis a benchm ark.

•

To determ ine w hether a m anager generates superior riskadjusted perform ance vis a vis the peer group.

•

To determ ine w hether the returns achieved are sufficient to com pensate for the risk assum ed in cost/benefit term s.

•

To provide a basis for identifying those m anagers whose pro­ cesses generate high-quality excess risk-adjusted returns. We believe that consistently superior risk-adjusted perform ance results suggest that a manager's processes, and the result­ ing perform ance, can be replicated in the future, making the returns high-quality.

9. Is your process capacity constrained? Can you estim ate at what point it might be? 10 . Describe the process by which you know that you are trading in accordance with client guidelines. 11 . Do you believe that your process is volum e sensitive in term s of the number of accounts under m anagem ent? If so, discuss. 12 . Describe how your process generates profits. That is, what is the source of your excess returns (e .g ., superior stock selection, superior quantitative m odeling, superior funda­ mental research, etc.)?

13. Define the list of your benchm arks. Are all of them easily calculated or are som e nonstandard? For nonstandard benchm arks, describe how you manage risk in your portfolio. Would you prefer standard benchm arks if that

The chapter then describes tools to measure the nature of per­ form ance. Unusual volatility and perform ance results can be identified by categorizing each outcom e as statistically expected (a green zone outcom e), som ew hat unusual (a yellow zone out­ com e), and statistically im probable (a red zone outcom e). O ther

option was available to you?

14. W hat risk system do you use to measure risk and build portfolios?

15. Have you found w eaknesses or problem s with

perform ance tools that are explored include return attribution,

these system s from tim e to tim e? To the extent

the Sharpe and information ratios, and portfolio m anager alpha

that these system s can be inadequate, how do

versus the benchm ark and versus a peer group. In each case,

you com pensate?

strengths and w eaknesses of the perform ance m easurem ent tool are briefly discussed.

16. Define the following on a daily, monthly, quarterly, and annual basis both in term s of active w eights vis a vis a

A p p end ix B provides a more m athem atical treatm ent of account

benchm ark as well as in term s of marginal contribution to

perform ance m easurem ent.

risk: maximum exposure by security; maximum exposure by

Chapter 7 Risk Monitoring and Performance Measurement

■

113

sector; maximum exposure by country; maximum exposure at the portfolio level.

A. For each of the above, define exposure at the one and three standard deviation levels.

B. W hen will you liquidate a position? Does this answer correlate to the answers given at (A) above?

C. A t what point are losses vis a vis the benchm ark so

APPEN D IX B Calculation of Account Performance Perform ance m easurem ent provides an o b jective, quantitative assessm ent of the change in value of a portfolio or portfolio segm ent over an evaluation p erio d, including the im pact of any cash flow s during that period. The calculation of total

large that you would conclude that your process is no

return in the absence of cash flow s for a period is based on

longer w orking?

the form ula

17. D escribe those environm ents that are harmful for you.

(B.1)

18 . D escribe those environm ents that are favorable for you. where rp(t) = Portfolio return

19. Is any part of your book vulnerable to m arket illiquid­

MVE = M arket value of portfolio at end of period,

ity? That is, does the genre of products you trade have

including all accrued income

evidence of becom ing much less illiquid (based on historical observation)?

MVB = Portfolio's m arket value at beginning of period,

20. Do you have risk limits in term s of: •

Maximum percentage of the security outstanding

•

Maximum percentage of daily volum e (alternatively, how

including all income accrued up to end of previous period This definition of a portfolio's return is valid only if there are

many days to liquidate if you never want to be more

no intraperiod cash flows. In practice, this condition is often

than, say, 15 percent of the daily volum e).

violated as cash flows frequently occur due to capital allocated

Describe how these limits are applied. Are they applied on an account-by-account basis as well as on an over­

to or removed from the portfolio (client's account) or through transactions from buying and selling securities.

all basis (i.e., the sum total of all accounts under

If cash flows do occur over the period in which returns are

your direction)?

calculated, we need to do the following:

21. Define the risk factors that drive your returns. Does your

•

risk software follow all of these factors? If not, how do you com pensate?

•

22. D escribe the process by which you review your daily results. W hat reports do you look at?

23. W hat process exists to ensure that accounts are traded in a parallel fashion?

24. O f the various fundam ental factors followed by your risk system , define a normal band around each one.

25. Does redem ption risk enter into your portfolio m anage­ ment? If so, how?

26. Have you had any material trading errors over the past year? If so, what w ere the circum stances?

27. A t year-end, how would you define successful portfolio m anagem ent? W hat statistics should we look to as guidance for measuring the quality of riskadjusted perform ance?

28. D escribe controls over valuation of your portfolio. 29. D escribe the nature of the credit review you perform for custodians and executing brokers.

114

■

Com pute the m arket value of the cash flows at the date/tim e at which they occur. Calculate the interim rate of return for the subperiod accord­ ing to Equation (B.1).

•

Link the sub-period returns to get the return for the entire period.

In equity m arkets, the primary drivers of perform ance include the shares held of each asset and its m arket price as well as accrued income from dividends. Dividends ex-not-paid affect a stock's price whereas cash dividends on the pay date do not. W hen cash flows occur, there are two proposed m ethods for measuring a portfolio's return. The first is a dollar-w eighted return and the second is a tim e-w eigh ted return.

Dollar-Weighted Return There are two m ethods for com puting a dollar-weighted return. The first is the internal rate of return and the second is the m odi­ fied Dietz m ethod. To com pute the internal rate of return of a portfolio we assume that the portfolio has 1(1 — 1, . . . , /) cash flows over som e period (e.g ., one day, one month, one quarter)

Financial Risk Manager Exam Part II: Risk Management and Investment Management

and solve for the internal rate of return, IR R A TE, such that the

where M V Ep is the m arket value of the portfolio at the end of

following relationship holds

the pth subperiod, before any cash flows in period p but includ­ ing accrued incom e for the period, and M VBp is the m arket

/ M V E = 2 FLO W , X (1 + IR R A T E p 1=1 where

(B.2)

this subperiod), including any cash flows at the end of the previ­

FLO W ) — /thcash flow over the return period, in the form of either a deposit (cash or security) or a withdrawal

explained here. Note that the main difference between the dollar-weighted

period that FLO W ) has been in (or out of)

return and the tim e-w eighted return is that the form er assumes

portfolio. The formula for w-, assuming cash

the same rate of return over the whole period. The time-

flows occur at end of day, is

w eighted return, on the other hand, uses the geom etric average

_

W: —

'

of returns from each individual period.

(CD - D,)

A good way to understand the methods described is to look

-----——------

CD

at a numerical exam ple. Suppose that on January 1, 2002, we

C D = Total number of days in return period

invested $100 in the Nasdaq Com posite index. On March 1,

Dj — Num ber of days since beginning of period

2002, we invest another $100. The total return on the Nasdaq from January 1, 2002, through February 28, 2002, was —11.22

when the flow, FLO W ,, occurred Equation (B.2) is also known as the modified Bank Adm inistra­ tion Institute method (modified BAI). It is an acceptable approxi­ mation to the tim e-weighted return (discussed in the next section) when the results are calculated at least quarterly and geom etrically linked o ve rtim e .

percent. Hence our initial investm ent of $100 is now worth $88.78. However, since we invested another $100, the total value of our investm ent is $188.78. By March 28, 2002, the total value of our investm ent has grown to $201.20 and we sell $100. The Nasdaq then declines until finally, on May 10, 2002, we are left with $87.79.

A portfolio's return based on the M odified Dietz method is

W e com pute our return on this investm ent as of May 10, 2002,

given by

under the different m ethods presented above. M V E - M VB - F ^ D ietz

where

ous subperiod and including accrued income up to the end of the previous period. This method is the most exact of the three

Wj — Proportion of the total number of days in

where

value at the end of the previous subperiod (i.e., beginning of

(B.3)

M VB + F W

•

The ideal tim e-w eighted return is [(88.78/100) X (201.20/188.78)

F — Sum of cash flows within period

X (87.79/101.20)] - 1 = -1 7 .9 2 %

F W — Sum of cash flows each multiplied by its w eight

•

The dollar-weighted annualized return based on the BAI method is

/ 2 FLO W j X

87.79 = 100(1 + IRRA TE)90/252

1=1

+ 100(1 + IR R A TE)50/252

Time-Weighted Return

- 100(1 + IRRA TE)30/252

Ideally, we would want to com pute a portfolio's return in such a way as to incorporate the precise tim e when the cash flows occur. To this end, the tim e-weighted rate of return (also known as the daily valuation method) for a portfolio is given by R r w r — (Si X S2 X . . .

x Sp)

1

(B.4)

IR R A T E = -2 5 .5 0 % •

According to the modified Dietz m ethod, the annualized return is 87.79 - 100 - (100 - 100) 100 + 7.94

-1 1 .3 1 %

where P(p = 1, . . . , P) is the number of subperiods that are Clearly, the dollar-weighted return calculation takes into account

defined within the period's return and

the timing of the decisions to sell or buy as reflected by the (B.5)

—25.50 percent return.

Chapter 7 Risk Monitoring and Performance Measurement

■ 115

Computing Returns

Siem ens equity (expressed in euros) to U .S. dollars. In g en­

Let R (n{t) represent the local return on the nth asset as measured in percent: Pflti + d n(t - h,t) - P (njt P (n(t ~ 1)

eral, the exchange rate is expressed in reporting over local currency. It follows from these definitions that the price of the nth asset

(B .6)

Pn(t) = Tim e t local price of security or asset d n(t — h,t) — Dividend (per share) paid out at tim e tfo r period t — h through t

expressed in reporting currency is Pn(t) = Pn€(t) X Xjj(t)

(B.7)

We use (B.7) as a basis for defining total return, local return, and exchange rate return. The total return of an asset or portfolio is simply the return that incorporates both the local return and

In a global fram ew ork we need to incorporate exchange rates

exchange rate return. Depending on how returns are defined—

into the return calculations. W e define exchange rates as the

continuous or discrete (percent)— we get different equations

reporting currency over the local currency (reporting/local).

for how returns are calculated. Following directly from (B.7), an

The local currency is som etim es referred to as the risk currency.

asset's total return, using percent returns, is defined as

For exam ple, U SD /G BP would be the exchange rate where the

Rn(t) = [1 + Pn€(t)][1 + E,y(t)] - 1

reporting currency is the U.S. dollar and the risk currency is the

= R fc) + Ejjit) + Pnf(t) X E/jit)

British pound. A USD-based investor with holdings in U .K. equi­ ties would use the U SD /G BP rate to convert the value of the stock to U.S. dollars. Suppose a portfolio with U.S. dollars as its reporting currency

where Rn(t) — One-period total return on the nth asset R„ — O ne-period percent return on the equity positions expressed in local currency (i.e.,

has holdings in G erm an, Australian, and Jap an ese equities. The local and/or risk currencies are EU R, A U D , and JPY, respectively. The total return of each equity position consists of the local

(B .8)

the local return) E;j(t) — O ne-period percent return on the rth cur­ rency per unit of currency j

return on equity and the return on the currency expressed in reporting/local.

E f t ) = Xjj(t)/Xjj[t - 1) - 1

W e assum e that a generic portfolio contains N assets

For exam ple, suppose that the nth position is a position in the

(n = 1 ,. . . , N). Let P (n(t) represent the price, in euros, of one

D A X equity index. In this case, Pp(t) is the local return on D A X

share of Siem ens stock. X^t) is the exchange rate expressed

and Ejj{i) is the return in the USD /EUR exchange rate. W hen the

as the rth currency per unit of currency j. For exam p le, with

euro strengthens, USD /EUR increases and Ejj(t) > 0. Holding

USD as the reporting currency, the exchange rate w here

all other things constant, this increases the total return on the

X jj[t)

equity position.

116

= U SD /EU R (/ is USD and j is EUR) is used to convert

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Portfolio Perform ance Evaluation Learning Objectives A fter com pleting this reading you should be able to: Differentiate between the tim e-weighted and dollar-weighted returns of a portfolio and describe their appropriate uses. Describe risk-adjusted perform ance m easures, such as Sharpe's m easure, Treynor's m easure, Jensen's measure (Jensen's alpha), and the information ratio, and identify the circum stances under which the use of each measure is most relevant. # Describe the uses for the M odigliani-squared and Treynor's measure in com paring two portfolios and the graphical representation of these m easures. Determ ine the statistical significance of a perform ance

D escribe style analysis. Explain the difficulties in measuring the perform ance of actively m anaged portfolios. D escribe perform ance manipulation and the problems associated with using conventional perform ance m easures. D escribe techniques to measure the m arket timing ability of fund m anagers with a regression and with a call option model and com pute return due to m arket tim ing. D escribe and apply perform ance attribution procedures, including the asset allocation decision, sector and security selection decision, and the aggregate contribution.

measure using standard error and the t-statistic.

E x c e rp t is C h a p ter 24 o f Investm ents, Twelfth Edition, by Zvi B o d ie, A le x Kane, and Alan J . M arcus.

MOST FINANCIAL ASSETS are m anaged by professional inves­

The left-hand side is the com pounded value of a $1 investm ent

tors, who thus at least indirectly allocate the lion's share of capi­

earning rG each year. We solve for 1 + rG as

tal across firm s. Efficient allocation therefore depends on the quality of these professionals and the ability of financial m arkets to identify and direct capital to the best stew ards. Therefore, if capital m arkets are to be reasonably efficient, investors must be able to measure the perform ance of their asset m anagers. How can w e evaluate investm ent perform ance? It turns out that even an average portfolio return is not as straightforward to measure as it might seem . In addition, adjusting average returns for risk presents a host of other problem s. In the end, perfor­ mance evaluation is far from trivial.

1 + rG = [(1 + r^d + r2) • • • (1 + r20)]1/20 Each return has an equal w eight in the geom etric average. For this reason, the geom etric average is referred to as a

time-weighted average.

Time-Weighted Returns versus DollarWeighted Returns To set the stage for the more subtle issues that follow, let's start with a trivial exam ple. Consider a stock paying a dividend of

W e begin this chapter with the m easurem ent of portfolio

$2 annually that currently sells for $50. You purchase the stock

returns. From there w e move on to conventional approaches to

today, collect the $2 dividend, and then sell the stock for $53 at

risk adjustm ent. W e consider the situations in which each of the

year-end. Your rate of return is

standard risk-adjusted perform ance m easures will be of most interest to investors and show how style analysis may be viewed as a generalization of the index model and the alpha statistic that it generates. Perform ance m easurem ent becom es far more difficult when m anagers change portfolio com position during the m easure­ ment period, so we also exam ine the com plications posed by changes in the risk characteristics of the portfolio. O ne particu­ lar way in which this may occur is when m anagers attem pt to tim e the broad m arket and adjust portfolio beta in anticipation

Total proceeds Income + Capital qain 2 + 3 -------- ------------ = ----------------- ----- -— = -------= .10, or 10% Initial investm ent 50 50 Another way to derive the rate of return that is useful in the more difficult multiperiod case is to set up the investment as a discounted cash flow problem. Call rth e rate of return that equates the present value of all cash flows from the investment with the initial outlay. In our example, the stock is purchased for $50 and generates cash flows at year-end of $2 (dividend) plus $53 (sale of stock). Therefore, we solve 50 = (2 + 53)/(l + r) to find again that r — .10, or 10%.

of m arket m ovem ents. M arket timing raises a wide range of

W hen we consider investm ents over a period during which cash

issues in perform ance evaluation.

was added to or withdrawn from the portfolio, measuring the

W e close the chapter with a look at perform ance attribution techniques. These are tools used to decom pose m anagers' perform ance into results that can be attributed to security selec­ tion, sector selection, and asset allocation decisions.

rate of return becom es more difficult. To continue our exam ple, suppose that you purchase a second share of the same stock at the end of the first year, and hold both shares until the end of year 2, at which point you sell each share for $54. Total cash outlays are shown below

8.1 THE CONVENTIONAL THEORY OF PERFORMANCE EVALUATION

Time

Outlay

0

$50 to purchase first share

Average Rates of Return

1

$53 to purchase second share a year later

Suppose we evaluate the perform ance of a portfolio over a

1

$2 dividend from initially purchased share

2

$4 dividend from the 2 shares held in the second year, plus

period of 20 years. The arithm etic average return is the sum of the 20 annual returns divided by 20. In contrast, the g eo m e tric average is the constant annual return over the 20 years that would provide the same total cum ulative return over the entire investm ent period. Therefore, the g e o m e tric average, rG, is defined by

The right-hand side of this equation is the com pounded final value of a $1 investm ent earning the 20 annual rates of return.

■

$108 received from selling both shares at $54 each Using the discounted cash flow (D CF) approach, we can solve for the average return over the two years by equating the pres­

(1 + Fg )20 = 0 + ri )0 + r2) • • • (1 + r20)

118

Proceeds

ent values of the cash inflows and outflows: 50 +

53

2

1 + r

-------------------

1 + r

112 +

d + r)2

Financial Risk Manager Exam Part II: Risk Management and Investment Management

resulting in r = 7.117% . This is the internal rate of return on the investm ent.1 The internal rate of return is called the dollar-weighted rate of

30

OThe Markowill Group ° S&P 500

25

return. It is "dollar w eighted" because the stock's perform ance in the second year, when two shares of stock are held, has a

20

greater influence on the average overall return than the firstyear return, when only one share is held. The tim e-weighted (geom etric average) return is 7.81% : 53 + 2 - 5 0

54 + 2 - 5 3

50

53

C£ 10

= 0.566 = 5.66%

when more money was invested, is lower.

.n .

o

O

o

1 Year

3 Years

.a .

5

The dollar-weighted average is less than the tim e-weighted average in this exam ple because the return in the second year,

o

■d.

rG = (1.10 X 1.0566)1/2 - 1 = .0781 = 7.81%

Concept Check 8.1

□

15

1 Quarter

Figure 8.1

5 Years

Universe com parison, periods ending

D ecem b er 31, 2025.

Shares of X YZ Corp, pay a $2 dividend

at the end of every year on D ecem ber 31. An investor buys

and bottom lines of each box are drawn at the rate of return of

two shares of the stock on January 1 at a price of $20 each,

the 95th and 5th percentile m anagers. The three dashed lines

sells one of those shares for $22 a year later on the next

correspond to the rates of return of the 75th, 50th (median), and

January 1, and sells the second share an additional year later

25th percentile m anagers. The diamond is drawn at the average

for $19. Find the dollar- and tim e-w eighted rates of return on

return of a particular fund and the square is drawn at the return

the 2-year investm ent.

of a benchm ark index, such as the S&P 500. The placem ent of the diamond within the box is an easy-to-read representation of

Adjusting Returns for Risk Evaluating perform ance based on average return alone is not very useful because returns must be adjusted for risk before they can be com pared m eaningfully. The sim plest and most popular way to make the adjustm ent is to com pare rates of return with those of other investm ent funds with similar risk characteristics. For exam ple, high-yield bond portfolios are grouped into one comparison universe, growth stock equity funds are grouped into another, and so on. Then the (usually tim e-weighted) average returns of each fund within the universe are ordered, and each portfolio m anager receives a percentile

the perform ance of the fund relative to the com parison universe. This com parison of perform ance with other m anagers of similar investm ent style is a useful first step in evaluating perform ance. However, such rankings can be m isleading. W ithin a particular universe, som e m anagers may concentrate on particular sub­ groups, so that portfolio characteristics are not truly com para­ ble. For exam ple, within the equity universe, one m anager may concentrate on high-beta or aggressive growth stocks. Sim i­ larly, within fixed-incom e universes, durations can vary across m anagers. A more fundam ental problem with the com parison universe

ranking of relative perform ance within the com parison group.

m ethodology is that the benchm ark perform ance is not an

For exam ple, the m anager with the ninth-best perform ance in

investable strategy. W hen we evaluate the perform ance of

a universe of 100 funds would be the 90th percentile m anager:

investm ent professionals and im plicitly ask if they have justified

Her perform ance was better than 90% of all com peting funds

their expenses, we would like to com pare their perform ance to

over the evaluation period.

what would have been available to a passive investor. M arket

These relative rankings are usually displayed in a chart such as that in Figure 8.1. The chart sum m arizes perform ance rankings over four periods: 1 quarter, 1 year, 3 years, and 5 years. The top

index portfolios, many of which are available as mutual funds or E T Fs, are natural benchm arks because investors can use these products to match the return on the index. In contrast, the median fund in Figure 8.1 cannot be known in advance. Because passive investors cannot reliably lock in the median return, it is

1 Excel's function XIRR calculates IRR. The function provides the IRR between any two dates given a starting value, cash flows at various dates in between (with additions given as negative numbers, and withdrawals as positive values), and a final value on the closing date.

an unsatisfactory benchm ark. These considerations suggest that a more precise means for risk adjustm ent is desirable.

Chapter 8 Portfolio Performance Evaluation

■

119

Risk-Adjusted Performance Measures M ethods of risk-adjusted perform ance evaluation using meanvariance criteria cam e on stage sim ultaneously with the capital asset pricing m odel. Ja ck Treynor,2 W illiam Sharpe,3 and Michael Je n se n 4 recognized im m ediately the im plications of the CAPM for rating the perform ance of m anagers. W ithin a short tim e, academ icians w ere in command of a battery of perform ance m easures, and a bounty of scholarly investigation of mutual fund perform ance was pouring from ivory tow ers. Shortly thereafter, agents em erged who were willing to supply rating services to portfolio m anagers and their clients.

4. Inform ation ratio: a P/cr{eP) The information ratio divides the alpha of the portfolio by nonsystematic risk, called "tracking error" in the industry. It measures abnormal return per unit of risk that in principle could be diversified away by holding a market index portfolio. (We should note that industry jargon tends to be a little loose concerning this topic. Some define the information ratio as excess return— rather than alpha— per unit of nonsystematic risk, using appraisal ratio to refer to the ratio of alpha to nonsystematic risk. Unfortunately, term inology in the profes­ sion is not fully uniform, and you may well encounter both of these definitions of the information ratio. We will consistently

But while w idely used, risk-adjusted perform ance m easures each

define it as we have done here, specifically as the ratio of

have their own lim itations. Moreover, their reliability requires

alpha to the standard deviation of residual returns.)

quite a long history of consistent m anagem ent with a steady level of perform ance and a representative sam ple of investm ent environm ents: bull as well as bear m arkets.

Each perform ance measure has som e appeal. But as C oncept Check 8.2 shows, these com peting measures do not necessarily provide consistent assessm ents of perform ance because the risk

We start by cataloging some common risk-adjusted performance

m easures used to adjust returns differ substantially. Therefore,

measures for a portfolio, P, and exam ine the circumstances in

we need to consider the circum stances in which each of these

which each might be most relevant.

m easures is appropriate.

1. Sharpe ratio: (rP — Tf)/crP

The Sharpe ratio divides average portfolio excess return

Concept Check 8.2

over the sam ple period by the standard deviation of returns

particular sam ple period:

Consider the following data for a

over that period. It m easures the reward to (total) volatility trade-off.5

2. Treynor m easure: (rP — ry)//3P

A verage return

Portfolio P

Market M

35%

28%

Like the Sharpe ratio, Treynor's measure gives excess return

Beta

per unit of risk, but it uses system atic risk instead of total risk.

Standard deviation

42%

30%

Tracking error (nonsystem atic risk), cr(e)

18%

0

3. Je n se n 's alpha: a P — rP — [ry + (3P (rM — ry)] Jensen's alpha is the average return on the portfolio over and above that predicted by the C A P M , given the portfolio's beta and the average m arket return.6

1.20

1.00

Calculate the following perform ance m easures for portfolio P and the m arket: Sharpe, Jensen (alpha), Treynor, information ratio. The T-bill rate during the period was 6%. By which

2 Jack L. Treynor, "How to Rate Management Investment Funds," Harvard Business Review 43 (January-February 1966). 3 William F. Sharpe, "Mutual Fund Performance," Journal o f Business 39 (January 1966). 4 Michael C. Jensen, "The Performance of Mutual Funds in the Period 1945-1964," Journal of Finance, May 1968; and Michael C. Jensen, "Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios," Journal of Business, April 1969. 5 We place bars over p as well as rp to denote the fact that because the risk-free rate may not be constant over the measurement period, we are taking a sample average, just as we do for rp. Equivalently, we may simply compute sample average excess returns. 6 In many cases performance evaluation assumes a multifactor market. For example, when the Fama-French 3-factor model is used, Jensen's alpha will be aP = rp - ry - /3P(rM - rf) - SPrSMB - hprHML, where sP is the loading on the SMB portfolio and hP is the loading on the HML portfolio.

120

■

m easures did portfolio P outperform the m arket?

The Sharpe Ratio for Overall Portfolios If investor preferences can be sum m arized by a mean-variance utility function, we can arrive at a relatively sim ple criterion. The particular utility function that we used is U = E(rP) —1/2 AcrP where A is the coefficient of risk aversion. With mean-variance preferences, the investor wants to maximize the Sharpe ratio [E(rP) — rf]/crP. The problem reduces to the search for the port­ folio with the highest possible Sharpe ratio. The Sharpe ratio is the slope of the capital allocation line, and investors will natu­ rally seek the portfolio that provides the greatest slope, that is,

Financial Risk Manager Exam Part II: Risk Management and Investment Management

the greatest increase in expected return for each unit increase in volatility.

Exam ple 8.1

M 2 Measure

Consider the perform ance of portfolio P and the m arket index

W e focus here on total volatility rather than system atic risk because we are looking at the full portfolio rather than a small com ponent of it. The benchm ark for acceptable perform ance is the Sharpe ratio of the m arket index because the investor can easily opt for a passive strategy by investing in an indexed equity mutual fund. The actively m anaged portfolio therefore must offer a higher Sharpe ratio than the m arket index if it is to be an acceptable candidate for the investor's optimal risky

portfolio, M from C o ncep t Check 8.2. Portfolio P had the higher return, but it also had higher risk, with the result that its Sharpe ratio was less than the m arket's. In Figure 8.2, we plot the aver­ age return and volatility of each portfolio and draw the capital allocation line for each. Portfolio P's C A L is less steep than the C M L, consistent with its lower Sharpe ratio. The adjusted portfolio P* is form ed by mixing bills with portfolio P We use w eights 30/42 = .714 in P a n d 1 - .714 = .286

portfolio.

in T-bills. By construction, the adjusted portfolio has exactly the sam e standard deviation as the m arket index:

The M2 Measure and the Sharpe Ratio

3 0 /4 2 X 42% = 30% . Despite its equal volatility, its return

W hile the Sharpe ratio can be used to rank portfolio performance, its numerical value is not easy to interpret. Com paring the ratios for portfolios M and P in Concept Check 8.2, you should have

would be only (.286 X 6%) + (.714 X 35%) = 26.7% , which is less than that of the m arket index. You can see in Figure 8.2 that portfolio P* is form ed by m ov­

found that S P = .69 and S M — .73. This suggests that portfolio P

ing down portfolio P's capital allocation line (by mixing P with

underperform ed the market index. But is a difference of .04 in the

T-bills) until we reduce the standard deviation by just enough

Sharpe ratio economically meaningful? We often compare rates

to match that of the m arket index. M2 is the vertical distance

of return, but these values are difficult to interpret.

betw een points M and P*. The M 2 of of portfolio P is therefore

An equivalent representation of Sharpe's ratio was proposed by

26.7% — 28% = —1.3% ; the negative M2 is consistent with the

Graham and Harvey, and later popularized by Leah Modigliani

inferior Sharpe ratio.

of Morgan Stanley and her grandfather Franco M odigliani, past winner of the Nobel Prize in Econom ics.7 Their approach has been dubbed the M 2 measure (for M odigliani-squared). Like the

The Treynor Ratio

Sharpe ratio, M2 focuses on total volatility as a measure of risk,

In many circum stances, you may have to select funds or port­

but its risk adjustm ent leads to an easy-to-interpret differential

folios that will be mixed together to form the investor's overall

return relative to the benchm ark index.

risky portfolio. For exam ple, the m anager in charge of a large

To com pute M 2, we imagine that an active portfolio, P, is mixed

pension plan might parcel out the total assets to several portfo­

with a position in T-bills so that the resulting "ad justed " portfo­

lio m anagers. Consider C alP ER S (the California Public Em ployee

lio m atches the volatility of a passive m arket index such as the S&P 500. For exam ple, if the active portfolio has 1.5 tim es the standard deviation of the index, you would mix it with T-bills using proportions of 1/3 in bills and 2/3 in the active portfolio. The resulting adjusted portfolio, which we call P*, would then have the same standard deviation as the index. (If the active portfolio had low er standard deviation than the index, it would be leveraged by borrowing money and investing the proceeds in the portfolio.) Because the m arket index and portfolio P* have the sam e standard deviation, we may com pare their perfor­ mance simply by com paring returns. This is the M2 measure for portfolio P:

M2 = rp* — Tm

(8.1)

7 John R. Graham and Campbell R. Harvey, "Grading the Performance of Market Timing Newsletters," Financial Analysts Journal 53 (November/ December 1997), pp. 54-66; and Franco Modigliani and Leah Modigliani, "Risk-Adjusted Performance," Journal of Portfolio Management, Winter 1997, pp. 45-54.

Figure 8.2

M2 of portfolio P is negative even though

its average return w as g reater than that of the m arket index, M.

Chapter 8 Portfolio Performance Evaluation

■

121

Retirem ent System ), which had a portfolio of about $350 billion

The SM L is the black line from the risk-free rate on the vertical

in early 2019. Like many large plans, it uses a funds o f funds

axis through point M . Its slope is the market's Treynor ratio, the

approach, allocating the endow m ent among a num ber of pro­

increase in return8 per increase in beta offered by portfolios that

fessional m anagers (funds). How should you com pare perfor­

mix the m arket index with T-bills.

mance across candidate m anagers in this context?

The line through point Q shows us all the beta-return combinations

W hen em ploying a num ber of m anagers, the nonsystem atic

that can be achieved by mixing bills with portfolio Q. The slope of

risk of each m anager will be largely diversified away, so only

this line is portfolio Q's Treynor ratio, so we call it the TQ-line. Simi­

system atic risk is relevant. The appropriate perform ance m etric

larly, the Tu-line goes from the origin through point U.

when evaluating co m p o n en ts of the full risky portfolio is now the Treynor m easure: This reward-to-risk ratio divides expected excess return by system atic risk (i.e., by beta).

A s always, the investor wants the portfolio that provides the best risk-return trade-off. W hen we measure risk using beta, that will be the portfolio with the steepest T-line, or, equivalently, the

Suppose the relevant data for two portfolios and the m arket

portfolio with the highest Treynor ratio. Therefore, we see that

index are given in Table 8.1. Portfolio Q has an alpha of 3.5% ,

despite its lower alpha, portfolio U actually will be preferred to

while that of portfolio U is 3% . It might appear that you would

portfolio Q. For any level of risk (beta), it provides the higher

prefer portfolio Q but this turns out not to be the case. To see

return.

why, turn to Figure 8.3. As in Figure 8.2, we plot portfolios on a return-risk graph, but now measure risk using beta.

Table 8.1

com bine portfolios with T-bills to match m arket risk so that we

Portfolio Perform ance Market

Risk-free Asset

Portfolio Q

Portfolio U

Index, M

Beta

0

1.3

0.8

1.0

A verage

6

22.0

17.0

16.0

0

16.0

11.0

10.0

0

3.5

3.0

0.0

return Excess return (%) Alpha (%)

We can measure the advantage of each portfolio com pared to the m arket index using a measure similar to M2. W e will again

Notes: Excess return = A verage return — Risk-free rate Alpha = A verage return — Beta X (M arket return — Risk-free rate)

can directly com pare rates of return. Here, however, w e use beta to measure risk, so we will form adjusted portfolios designed to match the beta of the m arket index (which, of course, is 1). We form the adjusted portfolio Q* by mixing Q with T-bills in pro­ portions wQ and (1 — wQ) . W e seek portfolio proportions that will make the beta of Q * equal to 1. Therefore, we choose W Q to satisfy /3q* = wQ X /3q + (1 - wQ) X jSbiHs = wQ X 1.25 + (1 — wQ) X 0 = 1.0 which implies that w Q = .8 . Because the systematic risk of the adjusted portfolio is constructed to match the market's, we can meaningfully compare their returns. The return on Q* is .8 X 22 + .2 X 6 = 18.8% , which beats the market return by 2.8% . This measure is analogous to the M2 mea­ sure, but it extends the Treynor rather than the Sharpe measure. Therefore, we will call it the T-square or T2 measure. The following example computes the T2 measure for portfolio U.

Exam ple 8.2

Equalizing Beta and the T2 Measure

Portfolio U has a beta of .8, which is less than the market beta of 1. Therefore, we will need to use leverage to increase systematic risk to match that of the market index. We choose w y to satisfy: Pit* ~ WU X f$u +

(1 —

WU) X A>ills -

x

.8 +

(1 — wu)

Beta

Fiaure 8.3

Treynor m easures of tw o portfolios and the m arket index.

122

■

x 0 — 1.0

8 We talk about return rather than expected return here because we are envisioning ourselves comparing the actual performance of a portfolio manager who earned a given return and took on a given level of risk to the risk-return combinations that we could have earned by mixing the market index with a risk-free asset.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

which im plies that w u = 1.25. So the adjusted portfolio (U*

W e can sum m arize the preceding discussion with the following

entails borrow ing at the risk-free rate, with all proceeds invested

table, which shows the definition of the various perform ance measures and the situations in which each is the relevant

in portfolio U.

perform ance measure.

The return on the adjusted portfolio U* is 1.25 X 17 — .25 X 6 — 19.75% , which beats the market's return by 3.75% . Portfolio U's higher T2 measure com pared to portfolio Q is consistent

Performance Measure

Definition

Application

with the steeper slope it displayed in Figure 8.3. W e can use either the T2 or the Treynor measure to rank portfolios when beta is the relevant

W hen choosing among portfolios com peting for the overall risky portfolio

Excess return

Sharpe

Standard deviation

measure of risk. Beta

The Information Ratio Here is another situation that calls for yet another perform ance criterio n. C o n sid er

Information ratio

W hen ranking many portfolios that will be mixed to form the overall risky portfolio

Excess return

Treynor

Alpha Residual standard deviation

W hen evaluating a portfolio to be mixed with the benchm ark portfolio

a pension fund with a largely passive and w ell-d iversified position— for exam p le, a portfolio that resem bles an indexed equity fund. Now the fund d ecid es to add a position in an active portfolio to its current position. For exam p le, a university m ight em ploy a hedge fund as a

Given the central role of alpha in the index model, the CAPM , and

possible addition to its core positions in more traditional

other models of risk versus return, you may be surprised that we

portfolios that w ere estab lished prim arily with concerns of

have not encountered a situation in which alpha is the criterion

diversificatio n in m ind. W hen the hedge fund (or another active position) is optim ally com bined with the baseline indexed portfolio, the im provem ent in the Sharpe measure will be determ ined by its information

- Sm +

used to choose one fund over another. But don't conclude from this that alpha does not matter! With some algebra, we can derive the relationship between the performance measures discussed so far and the alpha of the portfolio. The following table shows

ratio crH/cr(eH), according to c2

The Role of Alpha in Performance Measures

these relationships. In all cases, you can see that a positive alpha aH _cr[eH) _

is necessary to outperform the passive market index. Because ( 8 . 2)

superior performance requires positive alpha, it is the most widely used performance measure.

Equation 8.2 tells us that the appropriate perform ance measure for the hedge fund, H, is its infor­ mation ratio (IR). If you are looking for active m anagers to add to a

Treynor (Tp) Relation to alpha

want to select potential candidates with the best information ratios. The information ratio is yet another

E(rp) - r, _ a P , T A>

currently indexed position, you will Im provem ent com pared to m arket index

Sharpe* (Sp)

TP

Pp Tm -

E(rp) ~ rf m

P

Pp

(Tp

Sp

SM —

~

aP o-p

ap (Tp

Ratio

aP + P$M (1

P)S M

cr(ep)

aP cr(eP)

* p denotes the correlation coefficient between portfolio P and the market, and is less than 1.

version of a reward-to-risk ratio. In this context, the reward is the alpha of the active position. It is the

However, while positive alpha is necessary, it is not sufficient

expected return on that incremental portfolio over and above the

to guarantee that a portfolio will outperform the index:

risk premium that would normally correspond to its systematic risk.

Taking advantage of mispricing means departing from full

On the other hand, the incremental position tilts the total risky

diversification, which entails a cost in term s of nonsystem atic

portfolio away from the passive index, and therefore exposes it to

risk. A mutual fund can achieve a positive alpha, yet, at the same

risk that could, in principle, be diversified. The information ratio

tim e, its volatility may increase to a level at which its Sharpe

quantifies the trade-off between alpha and diversifiable risk.

ratio will actually fall.

Chapter 8 Portfolio Performance Evaluation

■

123

EXCEL APPLICATIONS

P e rfo rm a n c e M e a su re m e n t

The following perform ance m easurem ent spreadsheet

determ ine w hether the rankings are consistent using

com putes all the perform ance measures discussed in this

each m easure. W hat explains these results?

section. You can see how relative ranking differs according

2. W hich fund would you choose if you were considering

to the criterion selected. This Excel model is available in

investing the entire risky portion of your portfolio? W hat

C onnect or through your course instructor.

if you were considering adding a small position in one of these funds to a portfolio currently invested in the

Excel Questions

m arket index?

1. Exam ine the perform ance measures of the funds included in the spreadsheet. Rank perform ance and A 1

C

B

D

E

F

G

H

I

J

K

In f o r m a t io n

LEG EN D

P e rfo rm a n ce M e a su re m e n t

2

E n te r d a ta

3

V a lu e c a lc u la t e d

4

See com m ent

5 N on-

6 7 8 9 10 11 12 13 14 15 16 17

Fund

A lp h a O m ega O m icro n M illennium Big Value M o m en tu m W a tch e r Big P o ten tial S & P In d e x Return T-Bill Return

A v e ra g e

S ta n d a rd

B e ta

s y s t e m a t ic

S h a r p e 's

T r e y n e r 's

J e n s e n 's

M2

T2

R e tu rn

D e v ia t io n

C o e f f ic ie n t

R is k

M e a su re

M e a su re

M e a su re

M e a su re

M e a su re

R a tio

2 8 .0 0 % 3 1 .0 0 % 22. 00% 4 0 .0 0 % 1 5 .0 0 % 2 9 .0 0 % 1 5 .0 0 % 20. 00% 6. 00%

2 7 .0 0 % 2 6 .0 0 % 21. 00% 3 3 .0 0 % 1 3 .0 0 % 2 4 .0 0 % 11 . 00% 1 7 .0 0 %

1 .7 0 0 0 1 .6 2 0 0 0 .8 5 0 0 2 .5 0 0 0 0 .9 0 0 0 1 .4 0 0 0 0 .5 5 0 0

5 .0 0 % 6. 00% 2. 00% 2 7 .0 0 % 3 .0 0 % 1 6 .0 0 % 1 .5 0 % 0. 00%

0 .8 1 4 8 0 .9 6 1 5 0 .7 6 1 9 1 .0 3 0 3 0 .6 9 2 3 0 .9 5 8 3 0 .8 1 8 2 0 .8 2 3 5

0 .1 2 9 4 0 .1 5 4 3 0 .1 8 8 2 0 .1 3 6 0 0 .1 6 4 3 0 .1 6 3 6 0 .1 4 0 0

- 0 .0 1 8 0 0 .0 2 3 2 0 .0 4 1 0 - 0.0100 - 0 .0 3 6 0 0 .0 3 4 0 0 .0 1 3 0

- 0 .0 0 1 5 0 .0 2 3 5 - 0 .0 1 0 5 0 .0 3 5 2 - 0 .0 2 2 3 0 .0 2 2 9 - 0 .0 0 0 9

- 0 .0 1 0 6 0 .0 1 4 3 0 .0 4 8 2 - 0 .0 0 4 0 - 0 .0 4 0 0 0 .0 2 4 3 0 .0 2 3 6

- 0 .3 6 0 0 0 .3 8 6 7 2 .0 5 0 0 - 0 .0 3 7 0 - 1.2000 0 .2 1 2 5 0 .8 6 6 7

A v e ra g e

S ta n d a rd

B e ta

s y s t e m a t ic

S h a r p e 's

T r e y n o r 's

J e n s e n 's

M2

T2

In f o r m a t io n

R e tu rn

D e v ia t io n

C o e f f ic ie n t

R is k

M e a su re

M e a su re

M e a su re

M e a su re

M e a su re

R a tio

1.0000 0.0000

0.1000

0.0000

0.0000

0.0000

0.0000

18 R a n k in g B y S h a r p e 's M e a s u r e

19 20 21

Fund

N on-

Implementing Performance Measurement: An Example To illustrate som e of the calculations underlying portfolio evalua­ tion, let's look at the perform ance of portfolio P over the last

Table 8.2 Excess Returns for Portfolios P and Q and the Market Index M Over 12 Months Month 1

Portfolio P

Alternative Q

3.58%

2.81%

Index M 2 .20%

2

-4 .9 1

- 1 .1 5

-8 .4 1

well as those of an alternative portfolio Q and the m arket index

3

6.51

2.53

3.27

portfolio M. The bottom two rows in Table 8.2 provide the

4

11.13

37.09

14.41

5

8.78

12.88

7.71

6

9.38

39.08

14.36

7

- 3 .6 6

- 8 .8 4

- 6 .1 5

the sense that its beta is significantly higher (1.40 versus .70). A t

8

5.56

0.83

2.74

the sam e tim e, P's lower residual standard deviation indicates

9

- 7 .7 2

0.85

- 1 5 .2 7

that it is better diversified than Q (2.02% versus 9.81% ). Both

10

7.76

12.09

6.49

11

-4 .0 1

- 5 .6 8

- 3 .1 3

12

0.78

- 1 .7 7

1.41

Average

2.77

7.56

1.64

Standard deviation

6.45

15.55

8.84

12 months. Table 8.2 shows its excess return in each month as

sam ple average and standard deviation of each portfolio. From these, and regressions of P and Q on M , w e can com pute the necessary perform ance statistics. These appear in Table 8.3. Table 8.3 shows that portfolio Q is more aggressive than P, in

portfolios outperform ed the benchm ark m arket index, as is evi­ dent from their higher Sharpe ratios (and thus positive M2) and their positive alphas. Which portfolio is more attractive based on reported performance? If P or Q represents the entire investment fund, Q would be pref­ erable on the basis of its higher Sharpe measure (.49 vs. .43) and

124

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Table 8.3

To estim ate Jo e's portfolio alpha from the security characteristic

Performance Statistics

line (SCL), w e regress portfolio excess returns on the m arket

Portfolio P

Portfolio Q

Portfolio M

index. Suppose that we are in luck and (despite the underlying

Sharpe ratio

0.43

0.49

0.19

noise in investm ent returns) our regression estim ates precisely

M2

2.16

2.66

0.00

SCL regression statistics

match Jo e's true param eters. That means that our S C L estim ates for the N months are a — .2% ,

Alpha

1.63

5.26

0.00

Beta

0.70

1.40

1.00

Treynor

3.97

5.38

1.64

T2

2.34

3.74

0.00

cr(e)

2.02

9.81

0.00

Information ratio

0.81

0.54

0.00

R-square

0.91

0.64

1.00

(3 = 1.2,

A s outside evaluators who run such a regression, however, we do not know the true values. To assess w hether the alpha estim ate reflects true skill and not just luck due to statistical chance, w e com pute the t-statistic of the alpha estim ate to determ ine w hether we are justified in rejecting the hypothesis that Jo e 's true alpha is zero, that is, that he has no superior ability. The standard error of the alpha estim ate in the S C L regression is approxim ately £(e)

better M 2 (2.66% vs. 2.16%). For the second scenario, where Pand Q are competing for a role as one of a number of subportfolios, Q also dominates because its Treynor measure is higher (5.38 vs. 3.97). However, as an active portfolio to be mixed with the index portfolio, P is preferred because its information ratio [IR = a/a{e)] is higher

a(e) — 2%

V

n

where N is the number of observations and rf) correctly forecast.

tion decisions as well as more detailed sector and security allo­ cation decisions within asset classes. Perform ance attribution studies attem pt to decom pose overall perform ance into discrete com ponents that may be identified with a particular level of the

If we call P-i tthe proportion of the correct forecasts of bull mar­

portfolio selection process.

kets and P2 the proportion for bear m arkets, then P-, + P2 — 1 is

Attribution analysis starts from the broadest asset allocation

the correct measure of timing ability. For exam ple, a forecaster who always guesses correctly will have P-, = P2 = 1, and will show ability of Pi + P2 - 1 = 1 (100%). An analyst who always bets on a bear m arket will m ispredict all bull m arkets (P CD

(/) -4% Q LO u Q -8 %

•

-12%

-1 6

%

-

20 %

-10

0%

%

10%

20 %

High Yield Bond

Fiqure 9.10

Relative Value and Arbitrage-like Hedge Fund Styles: Fixed Income Arbitrage, Convertible Arbitrage, and Long/Short Equity There are three main styles in this cate­ gory separated by the m arket focus of

Risk factor in DJCS Distressed index: 1994-2010

the hedge fund m anagers. We begin

Source: Fung and Hsieh (2006) Figure 9 updated.

with those m anagers with a fixed income m arket focus. D JC S reports an

of corporations with very low credit ratings. W hile it is difficult to

index of F ix e d Incom e A rb itra g e H e d g e Funds. A description

obtain returns of nonm arketable securities, publicly traded high-

of the strategies utilized by funds included in this index is

yield bonds are a good proxy for exposure to low grade credit.

as follo w s:56

That turns out to be the case as shown in Figure 9.10.

The Dow Jo n e s Credit Suisse Fixed Income A rbitrage

The correlation between the D JC S Distressed index and high-

Hedge Fund lndexSM is a subset of the Dow Jo n e s Credit

yield bonds (as proxy by the Vanguard High Yield Corporate

Suisse Hedge Fund lndexSM that m easures the aggre­

bond fund) is 0.55. There is, however, some evidence of nonlin­

gate perform ance of fixed income arbitrage funds. Fixed

earity betw een the two return series, particularly at the extrem e

income arbitrage funds typically attem pt to generate

tails. Since Distressed hedge funds own securities that are much

profits by exploiting inefficiencies and price anom alies

less liquid than high-yield bonds, they may earn an extra liquid­

betw een related fixed incom e securities. Funds often

ity premium over high-yield bonds, and they may also incur a

seek to limit volatility by hedging out exposure to the

higher funding cost for carrying very illiquid securities. W hile

m arket and interest rate risk. Strategies may include

we have not found a good proxy for the funding cost of illiq­

leveraging long and short positions in sim ilar fixed

uid securities, we hypothesize that this cost would respond to

income securities that are related either m athem atically

extrem e credit m arket conditions, particularly when short-term

or econom ically. The sector includes credit yield curve

interest rates move dram atically. Indeed, a regression of the

relative value trading involving interest rate sw aps, gov­

D JC S Distressed index on the returns of high-yield bonds and

ernm ent securities and futures; volatility trading involv­

lookback straddles on the three-month Eurodollar deposit rate

ing options; and m ortgage-backed securities arbitrage

results in a positive coefficient to the form er and a negative

(the m ortgage-backed m arket is primarily US-based and

coefficient to the latter. This indicates that average returns of

over-the-counter).

Distressed hedge funds are lower during extrem e up and down

In an academ ic study, Fung and Hsieh (2002) analyzed a broad

moves in the three month Eurodollar deposit rate.

sam ple of hedge funds from several com m ercial databases

To sum m arize, the two major strategies in the Event-Driven

that are qualitatively classified as having a fixed income m arket

hedge fund style category both exhibit nonlinear returns characteristics— mostly as tail risk that shows up under extrem e m arket conditions. In the case of Risk A rb itrag e, the tail risk is

56 For more information go to http://www.hedgeindex.com/hedgeindex/ secure/en/indexperformance.aspx?indexname=CORE_FIARB&cy=USD.

Chapter 9 Hedge Funds

■

167

focus. For those hedge funds that are not classified with an arbitrage orien­ tation, convertible bond funds were strongly correlated to the C S FB (Credit Suisse/First Boston) Convertible Bond Index. High-yield funds were strongly correlated to the C S FB High-Yield Bond index. In addition, all styles, including fixed income arbitrage, have correla­ tions to changes in the default spread. Interpreting default spread as a measure of credit m arket condition, the central factor for most hedge funds with a fixed income m arket focus tend to be exposed to the credit m arket condi­ tions. This is intuitively appealing as most hedge funds with a fixed income orientation depend on leverage to enhance perform ance. Figure 9.11 provides support for this view. Here, we graph the then D JC S Fixed Income A rbitrage Index against the change in credit spread, as proxied

Change in Baa-10Y

Fiqure 9.11

Risk factor for DJCS fixed income arbitrage index: 1994-2010

Source: Fung and Hsieh (2006) Figure 5 updated.

by Moody's Baa yield over the tenyear Treasury constant maturity yield. A very sim ilar picture is

different secu rities (for exam p le, d eb t and equity) issued by

obtained if we use the HFRI Fixed Income (Total) index (which

the sam e com pany.

has been renamed HFRI Relative Value: M ulti-strategy index).

Duarte, Longstaff, and Yu (2007) found strong correlation

In a more recent study, D uarte, Longstaff, and Yu (2007) created

between the returns of these strategies and the returns of fixed

returns series of several fixed income arbitrage trades frequently

income arbitrage hedge funds. In addition, many of these strate­

used by hedge funds— swap spreads, yield-curve spreads,

gies have significant exposure to risks in the equity and bond

m ortgage spreads, fixed income volatility arbitrage, and capital

m arkets. D JC S reports an index of C on vertible A rb itra g e H e d g e

structure arbitrage. Essen tially, the sw ap spread trad e is a bet th at the fixed side of the spread (the d ifferen ce betw een the sw ap rate and

Funds. A description of the strategies utilized by funds included in this index is as follow s:57 The Dow Jo n e s C redit Suisse Convertible A rbitrage

the yield of the Treasury secu rity of the sam e m aturity) will

Hedqe Fund lndexSM is a subset of the Dow Jo n es Credit

rem ain higher than the floating side of the spread (the differ­

Suisse Hedge Fund lndexSM that m easures the aggre­

ence betw een LIB O R and the repo rate) w hile staying within a

gate perform ance of convertible arbitrage funds. C o n­

reasonable range that can be estim ated from historical data.

vertible arbitrage funds typically aim to profit from the

Yield-curve spread tra d e s are "b u tte rflie s", betting that bond

purchase of convertible securities and the subsequent

prices (which can be m apped to points along the yield curve)

shorting of the corresponding stock when there is a pric­

d eviate from the overall yield curve only fo r short-run, ta c ti­

ing error made in the conversion factor of the security.

cal liquidity reasons, which d issip ate over tim e. M ortgage

M anagers of convertible arbitrage funds typically build

spread trad es are bets on prep aym ent rates, consisting of a

long positions of convertible and other equity hybrid

long position on a pool of G N M A m ortgages financed using a

securities and then hedge the equity com ponent of

"d o llar ro ll", delta-hedged with a five-year interest rate sw ap. Fixed incom e vo latility trad es are bets that the im plied vo latil­ ity of interest rate caps tend s to be higher than the realized vo latility of the Eu ro d o llar futures co ntract. C ap ital-stru cture arb itrag e or cred it arb itrag e trad es on m ispricing am ong

168

■

57 For further information go to http://www.hedgeindex.com/ hedgeindex/secure/en/indexperformance.aspx?indexname=HEDG CVaRB&cy=USD.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

the long securities positions by

10%

shorting the underlying stock or options. The num ber of shares sold short usually reflects a delta

5%

neutral or m arket neutral ratio. As a result, under normal mar­ ket conditions, the arbitrageur

x (D ~o (U U) CD

generally expects the com bined position to be insensitive to fluctuations in the price of the underlying stock. Using a sample of US and Japanese convertible bonds, Agarwal et. al. (2010) created the return of a rulebased, passive convertible bond arbi­ trage strategy which they label as the

-M

JD < •

0%

_CD

-Q •— (U >

o u CD o —> Q

-5%

- 10%

"buy-and-hedge" strategy. The strat­ egy mimics the performance of pur­ chasing a broad portfolio of -10%

convertible bonds and mechanically

-

0%

5%

10%

Hedge Convertible Bonds

hedges the implicit equity exposure by shorting an appropriate amount of

-5%

Fiqure 9.12

stocks. This strategy resembles the

Risk factor for DJCS convertible arbitrage index: 1994-2010.

usual passive buy-and-hold strategy of conventional asset-class indi­

perform ance of long/short equity funds. Long/short

ces but for the addition of the equity hedge. Figure 9.12 presents a

equity funds typically invest in both long and short sides

simplified version of the Agarwal et. al. (2010) model by comparing

of equity markets, generally focusing on diversifying or

the hedged returns of a broad-based portfolio of convertible bonds

hedging across particular sectors, regions or market capi­

to the performance of the D JC S convertible arbitrage index.58

talizations. M anagers typically have the flexibility to shift

The results are consistent with the Agarw al et. al. (2010) findings and confirm s. O ne interpretation of the Agarw al et. al. (2010) results is that the return to convertible arbitrage hedge funds stem s from a liquidity premium paid by issuers of convertible bonds to the hedge fund com m unity for holding inventories of

from value to growth; small to medium to large capitaliza­ tion stocks; and net long to net short. M anagers can also trade equity futures and options as well as equity related securities and debt or build portfolios that are more con­ centrated than traditional long-only equity funds.

convertible bonds, managing the inherent risk by hedging the

This is an im portant hedge fund style categ o ry. The long/

equity content of these bonds.59

short equity style co nsistently accounts fo r 3 0 -4 0 % of the

D JC S reports an index of Long/Short Equity H ed g e Funds. A description of the strategy used by these managers is as follow s:60 The Dow Jo n es Credit Suisse Long/Short Equity Hedge

total num ber of hedge funds. A garw al and Naik (2004) studied a w ide range of equity-oriented hedge funds, and Fung and Hsieh (2011) focused on long/short equity funds. The em pirical evid ence show s that long/short equity funds have

Fund lndexSM is a subset of the Dow Jo nes Credit Suisse

directional exposure to the stock m arket as well as exposure

Hedge Fund lndexSM that measures the aggregate

to long sm all-cap/short large-cap positions, sim ilar to the SM B facto r in the Fam a and French (1992) three-facto r model

58 We used the Vanguard Convertible Securities Portfolio as a proxy for the convertible bond universe. The hedging is done by a rolling regres­ sion of the convertible bond portfolio to the Russell 2000 index to esti­ mate the amount of short equity index position needed. 59 This is analogous to the role played by market makers of securities. 60 For further information go to http://www.hedgeindex.com/ hedgeindex/secure/en/indexperformance.aspx?indexname=HEDG_ LOSHO&cy=USD.

for stocks. Figure 9.13 provides support for this view. Here, we use the previous twenty-four months of data to estim ate the expo­ sure of long/short equity funds (as proxied by the D JC SI Long/ Short Equity Index) to three market factors: the S&P 500 index, the Russell 2000 index, and the MSCI E A F E index. The esti­ mated coefficients are used to perform a one-month-ahead

Chapter 9 Hedge Funds

■

169

6%

The Dow Jo nes Credit Suisse Dedicated Short Bias Hedge Fund lndexSM is a subset of the Dow

4% -

Jones Credit Suisse Hedge Fund lndexSM that measures the aggre­

2%

gate perform ance of dedicated

-

short bias funds. Dedicated short 0%

bias funds typically take more short

-

positions than long positions and -

2%

earn returns by maintaining net -

short exposure in long and short equities. Detailed individual com ­

-4% -

pany research typically forms the core alpha generation driver of

-

6%

-

-

8%

-

dedicated short bias m anagers, and a focus on companies with weak cash flow generation is common. To affect the short sale, the manager typically borrows the stock from a

- 10% Jan-03

Jan-04

Fiqure 9.13

Jan-05

Jan-06

Jan-07

Jan-08

Jan-09

Jan-10

Actual and predicted returns for DJCS long/short equity index

counterparty and sells it in the mar­ ket. Short positions are som etim es implem ented by selling forward. Risk m anagem ent often consists of

Source: Fung and Hsieh (2006) Figure 6 updated.

offsetting long positions and stoploss strategies.

conditional forecast.61 The figure shows that the one-monthahead forecast is a very good predictor of the D JC S Long/Short

As exp ected , the D edicated Short Bias strategy is negatively

Equity index. An intuitive explanation of these results is as fol­

correlated to equities, which is shown in Figure 9.14. In the

lows. Typically, long/short equity hedge fund m anagers are stock

regression of the D JC S D edicated Short Bias index on the SNP

pickers with diverse opinions and ability. As such, the individual

index, the slope coefficient is -0 .8 1 (with a t-statistic of - 1 6 .1 )

perform ance of these m anagers is likely to be highly idiosyn­

and an R2 of 0.56.

cratic. However, all m anagers are subject to the basic phenom e­ non that "underpriced stocks", if they exist, are likely to be found among smaller, "under-researched" stocks, or foreign mar­

D JC S provides the following description of the Em erging Mar­ k e t strategy as follow s:63

kets (particularly emerging markets). On the short side, liquidity

The Dow Jo n es C redit Suisse Em erging M arkets Hedge

conditions in the stock-loan m arket make small stocks and for­

Fund lndexSM is a subset of the Dow Jo n es C redit Suisse

eign stocks much less attractive candidates for short sales.

Hedge Fund lndexSM that m easures the aggregate perform ance of em erging m arkets funds. Em erging

Niche Strategies: Dedicated Short Bias, Emerging Market and Equity Market Neutral The rem ainder of this section covers the other three D JC S strat­ egy indices. D JC S provides the following description of the Dedicated Short Bias strategy as follo w s.62 61 Specifically, the one-month-ahead conditional forecasts use the regression coefficients from the previous 24 months and the realized val­ ues of the regressors in the subsequent month. 62 For further information go to http://www.hedgeindex.com/hedgeindex/ secure/en/indexperformance.aspx?indexname=HEDG_DEDSH&cy=USD.

170

■

m arkets funds typically invest in currencies, debt instru­ ments, equities, and other instrum ents of countries with "em erging" or developing m arkets (typically measured by G D P per capita). Such countries are considered to be in a transitional phase between developing and devel­ oped status. Exam ples of em erging m arkets include China, India, Latin A m erica, much of Southeast Asia, parts of Eastern Europe, and parts of Africa.

63 For further information qo to http://www.hedqeindex.com/ hedgeindex/secure/en/indexperformance.aspx?indexname=HEDG EMMKT&cy=USD.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

30%

dram atically across different months. It appears that equity m arket neutral does not behave like a single niche strategy. Return behavior suggests that

20 %

different funds apply different trading

x < 1)

strategies with a similar goal of achiev­

c/) 10% CD CO t O

set of equity indices. W e therefore con­

"O

CO

ing almost zero beta(s) against a broad clude that there is no single common risk factor that drives the return behav­

0%

“O

Q) CD •U — "O < 1> Q m - 10% U O

ior of Equity M arket Neutral funds.

-M

-

W e have shown that, using a bottomup approach, alm ost all except one of the D JC S strategy indices can be linked to observable m arket risk factors. Some

20 %

of these are standard factors such as equity and bond indices. O thers are

■30% - 20 %

spread factors, such as the spread -1 5%

- 10%

-5%

0%

5%

10%

betw een Baa corporate bonds and

15%

10-year treasuries. There are also highly

S&P 500 Index

Figure 9.14

nonlinear factors like volatility factors

Risk factor in DJCS dedicated short bias index: 1994-2010

that behave like portfolios of straddles on bonds, currencies, and com m odi­

ties. W e will discuss the im plications of these factors on perfor­

The index has a num ber of subsectors, including arbi­

mance evaluation, portfolio construction and risk m anagem ent

trage, credit and event driven, fixed income bias, and

for hedge fund investors.

equity bias. Since it is often very difficult to

20%

short securities in the less devel­ oped econom ies, Em erging Mar­ ket hedge funds typically have

10%

a long bias. Figure 9.15 shows clearly that the D JC S Em erging M arket index is highly correlated

X

CD

“O

with the M SCI Em erging M arket

CD

index. The regression of the for­

CD

mer on the latter gives a slope coefficient of 0.49 (with a t-statistic of 18.6) and an R2 of 0.63. W hen we exam ined the collection of hedge funds in the Equity M arket Neutral strategy, we did not find a

0%

CD C

’ CD CD

E

LU

-

10%

-

20 %

CO

o o

single common com ponent in their returns. This tells us that there is not a single common strategy em ployed by many funds. Indeed, even index suppliers such as HFR or D JC S differ on which funds are "equity m arket neutral" funds. Their returns can differ

-30% -30%

-

20 %

-

10%

0%

10%

20 %

Emerging Market Index

Fiqure 9.15

Risk factor in DJCS emerging market index,

Chapter 9 Hedge Funds

■

171

9.4 W H ERE DO INVESTORS G O FROM H ER E?

divide this sam ple period into sub-periods to gain insight on how factor betas may have changed over tim e .65 The second and third columns of Table 9 .3 A report the regression results in

Portfolio Construction and Performance Trend

two sub-periods, 1990-1993 and 1994-1996 using 1994 as the

In the early days of the hedge fund industry, before the aca­

to changes in the m arket. Excep t for a persistent, significant

dem ic studies on publicly available hedge fund returns and the attendant risk factors, investors often viewed hedge funds as "black b o xe s", regarding them as a separate "asset class" that were not correlated to standard equity and bond indices. These early hedge fund investors had limited access to perform ance data and often had to rely on tools that were designed for eval­ uating long-bias funds investing predom inantly in conventional asset classes. It is perhaps not surprising that portfolio construc­ tion and risk m anagem ent often reduce to spreading risk capital across hedge fund m anagers with different sounding strategies.

break point for the analysis of tim e varying betas. The results are consistent with dynam ic adjustm ents to factor betas responding exposure to em erging m arkets, other factor betas show variabil­ ity over tim e. Alpha also appeared to be declining over tim e (from 2.11 % per month during the 1990-1993 period to 0.92% per month during the 1994-1996 period), but remained statisti­ cally significant at the 1% level in both sub periods.66 O verall, total return from the LHF27 portfolio appears to be sensitive to a persistent exposure to the em erging m arkets and opportunis­ tic bets on a number of other risk factors. It is noteworthy that there is no persistent directional exposure to the US equity m arket.

During these early days, m anager selection was primarily driven

How does the perform ance of the LHF27 portfolio com pare to

by the reputation of individual hedge fund m anagers. Knowing

its peers? Unfortunately we do not have reliable history for the

what we know today, how would we do things differently? Let us

D JC S index before 1994. W e can however answer this question

go back to the 27 large hedge funds identified in the Fung and

for the second sub-period 1994-1996. Table 9.3B reports the

Hsieh (2000b) and Fung, Hsieh, and Tsatsaronis (2000). Suppose

results of two statedependent regressions of LHF27 to the two

we are evaluating these m anagers for potential investm ents in

indices— D JC SI and HFRI over the period 1994-1996 by adding

1997 at the endpoint of these funds' perform ance history gath­

dummy variables that take on the value of 0 w henever the SNP

ered for the Fung and Hsieh studies. W hat additional insight can

return is greater than its median return over this sam ple period

new research undertaken since then add to this decision?

and the value of 1 otherwise.

W e begin by asking the question: are there system atic risk exp o ­

LHF27 = a + SN PD UM M Y + /3*lndex(DJCSI or HFRI)

sures in their perform ance? Table 9.3 reports the regression results of these 27 large funds as an equally w eighted portfolio (LHF27 for short) against the eight-factor model used to analyze

+ /31*SNPDUM M Y*lndex(DJCSI or HFRI) + e

(9.1)

This regression equation helps us answer the question of

hedge fund indices in Table 9.2. Table 9 .3 A tells us that over the

w hether there is peer group alpha relative to the average per­

period 1990-1996 this portfolio has no significant exposure to

form ance of the hedge fund industry (the hedge fund indices)

stocks and bonds.64 The regression results suggest that returns

and w hether it varies according to the stock m arket environm ent

are partially driven by exposure to directional bets on nonlinear

(is it a bull or bear m arket alpha)? The LHF27 portfolio has an

factors in the foreign exchange and com m odities m arkets

alpha of 1.89% (1.65% ) per month and a beta of 0.47 (0.21) ver­

(PTFSFX-R f and PTFSCO M -Rf) as well as on em erging markets

sus the D JC SI (HFRI) index; all coefficients are highly statistically

(IFC-Rf). As an equally w eighted portfolio, LHF27 has a highly

significant during months when the SNP index return is above

significant alpha of 1.48% per month. The monthly average total

its m edian. The corresponding figures for months when the SNP

return over this period is 1.58% which im plies that total returns

index return is below it median are an alpha of 1.37% (1.48%)

are not derived from static exposures to the set of risk factors in the eight-factor m odel. Hedge fund m anagers are primarily active m anagers, therefore, a static regression model like the eight-factor model used here can only capture the average exposures of these m anagers' fac­ tor bets (betas) over a given sam ple period. A ccordingly we 64 We chose 1990 as the starting point as some of the instruments used in constructing our dataset do not extend back beyond 1990.

172

■

65 Ideally one should explicitly model the time-varying behavior of factor-betas. However data limitations present serious challenges—see for example Bollen and Whaley (2009) and Patton and Ramadorai ( 2012 ). 66 The null hypothesis of equality of individual coefficients between the 1990-1993 and 1994-1996 sub-periods can be rejected at the 1% sig­ nificance level for the constant term and the bond straddle (PTFSFX-Rf). In addition, the joint test for the equality of all coefficients is rejected as well.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Regression of 27 Large Hedge Funds (LHF27), the DJCS and HFRI Indices on an Eight-Factor Table 9.3 Model Similar to That of Table 9.2: SP-Rf is the Excess Return of the S&P 500 Index. RL-SP is the Return of the Russell 2000 Index Minus the Return of the S&P500 Index. TY-Rf is the Excess Return of US Ten-Year Treasuries. BAA-TY is the Return of Moody's BAA Corporate Bonds Minus the Return of US Ten-Year Treasuries. PTFSBD-Rf is the Excess Return of a Portfolio of Bond Straddles. PTFSFX-Rf is the Excess Return of a Portfolio of FX Straddles. PTFSCOM-Rf is the Excess Return of a Portfolio of Commodity Straddles. IFCRf is the Excess Return of the International Finance Corporation's Emerging Market Index. Regression Equation (1): LHF27 = constant + SNPDUMMY + p*lndex + p*SNPDUMMY*lndex + e 3A. Sam ple P eriod

LHF27 1990-1996

1990-1993

1994-1996

0.0148

0.0211

0.0092

0.0020

0.0016

0.0028

7.4949

13.2255

3.2809

0.0606

0.0411

0.2347

0.0770

0.1072

0.1268

0.7869

0.3831

1.8508

0.0701

0.1299

0.0512

0.0573

0.0835

0.0851

1.2241

1.5556

0.6013

0.2733

- 0 .1 7 3 5

0.2069

0. 1502

0.1707

0.1212

1.8202

- 1 .0 1 6 3

1.7066

- 0 .1 6 2 4

- 1 .0 0 7 7

0.3309

0.2246

0.3006

0.3111

- 0 .7 2 2 8

-3 .3 5 2 7

1.0637

0.0272

0.0547

- 0 .0 0 1 4

0.0180

0.0105

0.0179

1.5134

5.1856

- 0 .0 7 6 3

0.0236

0.0119

0.0291

0.0088

0.0130

0.0105

2.6911

0.9151

2.7750

0.0499

0.0265

0.0522

0.0146

0.0167

0.0256

3.4235

1.5831

2.0357

0.1171

0.1268

0.1412

0.0281

0.0396

0.0605

4.1757

3.2067

2.3332

Adj R2

0.3345

0.3620

0.4303

D.W.

1.7778

1.8685

2.1050

Constant

SP-Rf

RL-SP

TY-Rf

BA A -TY

PTFSBD -R f

PTFSFX-Rf

PTFSC O M -R f

IFC-Rf

Source: Fung and Hsieh, 2000b.

Chapter 9 Hedge Funds

■

173

Table 9.3

Continued

3B. 1994-1996 D JC SI

HFRI

Index

SNPDUMMY* Index

Constant

SNPDUMMY

0.0188

- 0 .0 1 3 7

0.4657

0.3018

0.0026

0.0034

0.1249

7.2308

-4 .0 2 9 4

0.0165

Adj Rsq

Durbin Watson

0.3251

1.6430

p-Value of Test of Equality Constant

0.0000

0.1338

Slope

0.0241

3.7286

2.2556

Jo in t

0.0000

- 0 .0 1 4 8

0.2065

0.8193

Constant

0.0099

0.0045

0.0057

0.2297

0.2681

Slope

0.0022

3.6667

-2 .5 9 6 5

0.8990

3.0559

Jo in t

0.0031

0.1811

1.8115

SNPDUMMY = 1 (SP index return < = median); Newey-West (1987) standard errors with 6 lags in italics.

and a beta of 0.30 (0.82) versus the D JC SI (HFRI) index; all coefficients are highly statistically significant. The joint test of equality indicates that there is a nonlinear correlation betw een these large funds and the indices. Taken together these results are consistent with a superior perform ing portfolio, LH F27, relative to the m arket aver­ ages (hedge fund indices) achieved by dynam ically managing it risk exposure (betas) in response to changing equity m arket conditions. This is consistent with the eight-factor model results, which tell us that these large hedge funds take time-varying bets on dif­ ferent risk factors, and their overall risk profile relative to their peers (hedge fund index betas) is nonlinear and responsive to changing equity m arket conditions.

Fiau re 9.16 Cumulative return of DJCSI, HFRI indices and the LHF27 portfolio: 1994-1996.

Figure 9.16 plots the cum ulative per­ form ance of the LH F27, D JC S I, and H FRI. It shows that the LHF27 portfolio delivered a cum ulative return of 59.08% versus 42.24% and 53.18% respectively for the D JC S I and HFRI index. The respective annualized returns

How Much of the LHF27 Portfolio's Monthly Alpha of 2.11% (1990-1993) and 0.92% (1994-1996) Is Due to Measurement Bias?

for the period (1994-1996) are 15.88% , 12.20% , 14.42% for

In the absence of a com m ercially available hedge fund per­

LH F27, D JC S I, and HFRI with corresponding annualized stan­

form ance database, this would be a very difficult question to

dard deviations of 8.04% , 9.08% , and 4 .94 % . A s w e pointed

answ er in 1997. Let us see what hindsight would have told us

out, data prior to 1996 from com m ercial databases are suscep­

about two im portant biases that overshadow the reliability of

tive to backfilled and survivorship biases, w hereas the LHF27

the LHF27's historical alpha. Unfortunately the available data

portfolio suffers from ex post selection bias. Ju st how much will

over the 1997 to 2001 period is insufficient to support defini­

m easurem ent biases affect these im pressive historical perfor­

tive answers to this question. Given the hedge fund indus­

mance statistics?

try's change in investor clientele post 2001, it is instructive to

174

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

Table 9.4A Assets Under Management of the Top 50 Reporting Funds to Commercial Databases ($ billion): At the End of Each Formation Year, Funds Reporting to Three Commercial Databases (BarclayHedge, HFR, Lipper-TASS) are Sorted According to Their Assets Under Management (AUM). Duplicated Funds are Eliminated. Top 50 is the Sum of the AUM of the Top 50 Funds in This Ranking. All Other Funds Denotes the Sum of AUM of All Other Funds Below the Top 50 Formation Year AUM in $ billions All other funds Top 50 Total AUM Top 50/Total AUM (%)

2002

2001

2004

2003

2005

2006

2007

2008

2009

2010

132

168

231

350

456

570

842

539

541

666

70

94

113

133

166

209

265

233

228

278

202

262

343

483

622

779

1,107

772

769

945

34.65

35.88

32.94

27.54

26.69

26.83

23.94

30.18

29.65

29.42

Source: BarclayHedge, HFR, Lipper-TASS.

Table 9.4B AUM Range of Top 50 Reporting Funds to Commercial Databases ($ Million) Versus Overall Median Fund Size. At the End of Each Calendar Year Funds are Ranked by AUM to Identify the Top 50 Hedge Funds Formation Year Break Points in $ millions O verall median fund size

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

25

29

30

33

33

35

43

23

28

23

693

806

1,066

1,476

1,748

2,300

3,042

2,456

2,381

2,638

Top 50— largest

7,878

8,557

9,534

7,793

16,580

16,045

11,685

13,986

12,500

22,662

Sm allest/M edian

27.72

27.79

35.53

44.73

52.97

65.71

70.74

106.78

85.04

114.70

315.12

295.07

317.80

236.15

502.42

458.43

271.74

608.09

446.43

985.30

Top 50— sm allest

Largest/M edian

Source: BarclayHedge, HFR, Lipper-TASS.

exam ine this perform ance persistency question using a dataset

are many tim es bigger than the median fund in our consolidated

that spans the recent decade. Table 9.4 tracks the Top 50 funds

database— ranging from 27.72 tim es (sm allest Top 50 in 2001)

ranked by AUM in each of the sam ple year based on end of year

to 985.30 tim es (largest Top 50 in 2010). This size divergence

figures reported to the three consolidated com m ercial data­

betw een the largest fund and the median fund has been steadily

bases BarclayH edge, HFR, Lipper-Tass.

growing in this first decade of the millennium.

A t the end of each year, we identify a set of unique funds that

Table 9 .4 C tabulates the rate of entry and exit of funds in our

report to the three com m ercial databases by elim inating all

consolidated database. W hen a fund exits com m ercial data­

duplicated funds w hereby creating a consolidated database

bases, there are typically two broad categories of reasons. O ne,

almost free of doubted counted funds. We then sort all these

it is being dropped by the database vendor because it no longer

hedge funds in the consolidated database by AUM and identify

meets the vendor's inclusion criteria. Two, the fund m anager

the Top 50 funds. Dividing the total sam ple into two sets of

elects to stop reporting. In the first category, database vendors

funds— the Top 50 and all others— we record the total year end

attem pt to flag those exiting funds that w ent out of business but

AUM for each set and tabulate them in Table 9.4A . Table 9.4B

the information is generally incom plete. In the second category,

reports the median fund's year end AUM and the AUM range

the reasons can be many and varied; ranging from a dying fund

(sm allest and largest) of the Top 50 subset for each sam ple year

whose m anager no longer finds reporting bad news to a data­

2001 to 2010. The results show that the Top 50 funds consis­

base to be a business priority, to successful funds who have

tently manage between 23.94% to 35.88% of the hedge fund

reached their AUM capacity limit and find the burden of report­

industry's total A U M . Table 9.4B shows that the Top 50 funds

ing perform ance to the generally public a costly exercise with

Chapter 9 Hedge Funds

■

175

Entry, Exit, and Survival Rates of Top 50 and All Other Funds. At the End of Each Calendar Year, We Table 9.4C Compute the Fraction of New Funds Entering Into, Surviving Funds From Last Year, Liquidated and Unknown Exits from Our Combined Database Relative to the Total Number of Unique Funds in Our Sample Formation Year

All others

Top 50

2001

2002

2003

2004

2005

2006

2007

2008

2009

New Entry in Form ation Year

0.07

0.08

0.08

0.11

0.10

0.09

0.08

0.06

0.06

Survive N ext Year

0.86

0.85

0.87

0.85

0.83

0.81

0.72

0.76

0.82

Exit N ext Year/Liquidated

0.08

0.08

0.07

0.10

0.10

0.09

0.14

0.11

0.01

Exit N ext Year/Unknown

0.06

0.07

0.05

0.06

0.07

0.11

0.15

0.13

0.17

Total Exit

0.14

0.15

0.13

0.15

0.17

0.20

0.29

0.24

0.18

New Entry in Form ation Year

0.00

0.00

0.00

0.00

0.00

0.00

0.02

0.00

0.00

Survive N ext Year

0.98

0.92

0.94

0.98

0.88

0.84

0.82

0.94

0.88

Exit N ext Year/Liquidated

0.00

0.00

0.00

0.00

0.00

0.00

0.04

0.00

0.00

Exit N ext Year/Unknown

0.02

0.08

0.06

0.02

0.12

0.16

0.14

0.06

0.12

Total Exit

0.02

0.08

0.06

0.02

0.12

0.16

0.18

0.06

0.12

diminishing benefits.67 Suffice to say that large hedge funds are

when its AUM falls below the threshold for that year. It is not

likely to fall into this second category. Therefore, when a large

always clear that dem oted funds necessarily underperform pro­

fund drops out of a database, it does not necessarily carry the

moted funds that took their places from year to year. We pro­

negative interpretation of the usual em pirical studies on survi­

vide som e insight to this question later. For now, the em pirical

vorship bias. In fact, the bias can easily go the other way. The

evidence thus far, when taken together, points to a sm aller m ea­

results in Table 9.4C illustrate this point. Com paring the two

surem ent bias in the estim ated 1.48% monthly alpha of the

"N ew Entry to Database in Form ation Year" rows, we see the

27 large-hedge fund portfolio than that of the average hedge

rate at which new funds enter the database for all other funds

fund. If these im pressive high-teen returns with limited persis­

whereas only once in 2007 we had a new Top50 fund that first

tent exposure to system ic risks (factor betas) cannot be easily

reports perform ance to the databases that year.68 Com paring

accounted for by m easurem ent bias it begs the question

the two "E x it N ext Year/Liquidated" rows, we see that only once

"is the attractive perform ance of large hedge funds a sustain­

we saw eight funds (4%) of the 2007 Top 50 funds met with liq­

able proposition?"

uidation the following year (2008). In all other cases, exits from the Top 50 subset tend to be selfselected for reasons unknown to the database vendors. The evidence suggests that large funds are better at retaining investors' assets and staying in business than sm aller funds.69 However, there still exists the pos­ sibility that a Top 50 fund in any given year can get dem oted

Simulating the Performance of Investing in Large Funds To gain insight into the strategy of investing into a portfolio of large hedge funds, we synthesize a com parable experim ent to the LHF27 portfolio by constructing an equally w eighted portfo­ lio of the largest 50 hedge funds (TO P50 for short) using more

67 There are other reasons such as those funds that change the vendors they report to etc. See Fung and Hsieh (2009) for a discussion on non­ reporting funds.

recent data— 2002-2010. W e do this in two ways. First, to mini­ mize ex post selection bias, we construct a T O P 5 0 portfolio as follows. Starting at the end of 2001, take the Top 50 funds

68 The entry to Table 9.4C shows a 2% figure which is one fund for the Top 50 subset.

ranked by 2001 year end AUM to create an equally w eighted

69 This is consistent with the conclusion reached in Fung and Hsieh (2009) and some recent results in an unpublished paper in Edelman, Fung and Hsieh (2011). Because large funds tend to stay large, the loo­ kahead bias of selecting large funds ex-post is also less severe. However we caution the reader that our conjecture is derived from available data which remains incomplete to-date.

the following year.70*The process is repeated at the end of each

176

■

portfolio (TO P50) of these 50 funds and observe their returns for

70 In the event of one of these Top 50 funds exiting the databases, its capital is reinvested in cash to be conservative in our simulation.

Financial Risk Manager Exam Part II: Risk Management and Investment Management

year until the end of 2009, resulting in a return series mimicking

alpha during months when the SNP index return is below its

the perform ance of a strategy of investing in the Top 50 hedge

m edian. O verall, the results indicate that the strategy of buying

funds in equal dollar am ounts while rebalancing at the end

large hedge funds delivers superior perform ance to investing in

of each calendar year resulting in a return series spanning

indices (or the industry average). In term s of dynam ic risk-taking

2002-2010. Second, we create a TO P 5 0 _2 0 1 0 portfolio by com ­

behavior the results hint at a nonlinear, stock m arket dependent

puting the pro forma returns of the Top 50 hedge funds created

shift for the TO P 5 0 _2 0 1 0 portfolio. This is a subject w orthy of

at the end of the sam ple period based on 2010 year end AU M .

further investigation as we accum ulate more data after the 2008

This second portfolio has a sim ilar ex-post selection bias to the

financial crisis.72

LHF27 portfolio, in that the identities of the top 50 large funds at the end of the sam ple period is not known during the earlier years. Com paring the TO P 50 and TO P 5 0 _2 0 1 0 portfolios gives us a lower and upper bound of the perform ance investors can achieve by simply adopting the strategy of investing equally into the Top 50 large funds and rebalancing each year (lower bound) and that of a foresight-assisted portfolio TO P 5 0 _2 0 1 0 (upper bound).

C um ulatively, over this 2 0 0 2 -2 0 1 0 period, all of the portfo­ lios T O P 5 0 , D JC S I and HFRI outperform ed the equity m arket (proxy by the SN P index) as Figure 9.17 sh o w s.73 These results taken to g eth er are supportive of the continuing inter­ est of institutional investors in hedge funds; and especially in large hedge funds. Capital continues to flow into the hedge fund industry after the 2008 financial crisis. The total industry AUM figures in Table 9 .5 A show the 2010 AUM figure is once

Table 9.5 reports the perform ance characteristics of the T O P 5 0 ,

again on the rise after a pause follow ing the 2008 crisis.

D JC S I, and HFRI versus the eight-factor model in the same for­

Although the Top 50 hedge funds' total AUM rem ains

mat as Table 9.3. Table 9 .5 A shows the TO P 50 portfolio to have

around 30% of total industry A U M , the size of these larger

no statistically significant alpha whereas the foresight-assisted

hedge funds relative to the median of our data universe

portfolio T O P 5 0 _2 0 1 0 shows a monthly alpha of 0.53% and is

continues to expand in favor of larger funds. O ur analysis of

statistically significant at the one percent level. This is a signifi­

large hedge funds shows perform ance statistics consistent

cant decline from the results we saw with the LHF27 portfolio.

with m anagers of these funds continuing to deliver alpha rela­

However, it must be noted that there is no significant negative

tive to their peers and having low exposure to the US equity

alpha. This is im portant as the returns we used for the TO P 50

m arket which helps to explain their success in attracting insti­

portfolio is net of all fees and expenses whereas no trading cost

tutional investors' capital. Later, w e discuss other m arket

is factored into the returns of the risk factors in the regression

structural issues that reinforces the persistency of this capital

m odel. This micro effect of trading friction will be discussed fur­

form ation trend.

ther in a later sectio n.71 The decline in monthly alpha from 2.11% (1990-1994) to 0.92% (1994-1996) for the LHF27 portfo­ lio and now to 0% and 0.52% respectively for the TO P 50 and TO P 5 0 _2 0 1 0 portfolios over the recent decade (2002-2010) is consistent with the com bined effect of rising com petition in a

9.5 RISK M AN AGEM EN T AND A TALE O F TW O RISKS

hedge fund industry that experienced alm ost a ten-fold increase

An im portant feature that attracts investors to the hedge fund

in AUM since 1996— an outcom e that is anticipated by the theo­

industry is the variety of strategies hedge fund m anagers deploy

retical model of Berk and Green (2004). In term s of risk factor

and the diversity of assets to which these strategies are applied.

exposures, like the LH F27, the T O P 5 0 and the TO P 5 0 _2 0 1 0

Even at an aggregated level, long-term historical return patterns

portfolios continue to exhibit highly significant betas to the

reveal several categories of trading styles with low return corre­

em erging m arket factor (IFC-Rf). W hile both portfolios have no

lations. Com m ercial index providers like D JC S reports ten dis­

significant beta to the US equity factors, they both have a highly

tinct style-specific sub-indices.74 Under normal circum stances,

significant credit-factor (BAA-TY) beta. Relative to their peers, Table 9.5B shows that both the TO P 50 and the TO P 5 0 _2 0 1 0 portfolios have statistically significant alpha relative to the hedge fund indices— D JC SI and HFRI. The SN PD U M M Y variable shows a significant lowering of the D JC SI

72 We also ran a similar regression to Equation (9.1) using the credit spread variable (BAA-TY) as the conditioning risk factor instead of the SNP. The results are similar. 73 The cumulative returns are 76.62%, 91.55%, 86.70%, and 30.59% respectively for TOP50, DJCS, HFRI and SNP

71 A similar finding was reported in Fung et. al. (2008) and Edelman et. al. (2012) who also reported a similar trend decline of historical alpha.

74 See http://www.hedgeindex.com/hedgeindex/en/indexoverview .aspx?indexname=HEDG&cy=USD for more details, excluded are those sub-indices that are combinations of other specialist styles.

Chapter 9 Hedge Funds

■

177

Table 9.5 In Panel A Regression of TOP50 and TOP50_10 Indices on Eight-Factor Model Similar to that of Table 9.2: SP-Rf is the Excess Return of the S&P 500 Index. RL-SP is the Return of the Russell 2000 Index Minus the Return of the S&P 500 Index. TY-Rf is the Excess Return of US Ten-Year Treasuries. BAA-TY is the Return of Moody's BAA Corporate Bonds Minus the Return of US Ten-Year Treasuries. PTFSBD-Rf is the Excess Return of a Portfolio of Bond Straddles. PTFSFX-Rf is the Excess Return of a Portfolio of FX Straddles. PTFSCOM-Rf is the Excess Return of a Portfolio of Commodity Straddles. IFC-Rf is the Excess Return of the International Finance Corporation's Emerging Market Index, and in Panel B We Run the Regression Equation (1) Using: TOP50(TOP50_2010) = constant + SNPDUMMY + p*lndex + p*SNPDUMMY*lndex + e 5A.

TO P50

Sam ple P eriod Constant

SP-Rf

RL-SP

TY-Rf

BA A -TY

PTFSBD -Rf

PTFSFX-Rf

PTFSC O M -R f

IFC-Rf

T O P 5 0 _ 1 0 Pro Fo rm a 2002-2010

2002-2010

0.0007

0.0053

0.0011

0.0009

0.6291

5 .8 6 2 4

0.0170

0.0071

0.0342

0.0431

0.4981

0.1655

0.0176

0.0258

0.0456

0.0458

0.3863

0.5631

- 0 .0 3 1 2

0.0199

0.0564

0.0627

- 0 .5 5 2 6

0.3169

0.1286

0.1107

0.0466

0.0337

2 .7 6 2 4

3.2831

- 0 .0 1 6 5

- 0 .0 0 7 3

0.0093

0.0090

- 1 .7 8 6 4

- 0 .8 0 9 7

0.0079

0.0129

0.0034

0.0050

2 .3 3 2 5

2 .5 5 3 3

0.0048

0.0019

0.0074

0.0058

0.6466

0.3284

0.1091

0.1377

0.0199

0.0268

5 .4 7 1 1

5 .1 3 1 0

Adj R2

0.5402

0.5421

D.W .

1.9186

1.9674

Newey-West (1987) standard errors with 6 lags in italics.

178

■

Financial Risk Manager Exam Part II: Risk Management and Investment Management

5B.

TOP50

In dex = Sam ple P eriod

H FRI

TOP50_2010 D JC S

HFRI

2002-2010 Constant

D JC S

2002-2010 0.0031

0.0063

0.0078

0.0009

0.007 7

0.0072

0.0072

2.6667

2.8182

5.2500

6.5000

- 0 .0 0 2 4

- 0 .0 0 2 9

- 0.0021

- 0 .0 0 3 7

0.0075

0.0076

0.0075

0.0077

- 1 .6 0 0 0

- 1 .8 1 2 5

- 1 .4 0 0 0

-2 .1 7 6 5

0.544

0.4207

0.6281

0.4484

0.0496

0.0470

0.0752

0.0657

9.9677

8.9511

8.3524

6.8250

-0 .0 3 3 1

- 0 .0 3 1 5

- 0 .1 4 7 8

- 0 .0 9 9

0.0680

0.0539

0.0789

0.0598

- 0 .4 8 6 8

- 0 .5 8 4 4

- 1 .8 7 3 3

- 1 .6 5 5 5

Adj R2

0.7053

0.6952

0.7162

0.6531

D.W.

1.6547

1.6052

1.687

1.6323

Constant

0.1048

0.0625

0.1663

0.0302

Slope

0.6261

0.5588

0.0609

0.0981

Jo in t Test

0.2351

0.0862

0.0352

0.0087

DUM SP

Index

In d e x * DUM SP

0.0024

p-value of test of equality

SNPDUMMY = 1 (SP index return < median); Newey and West (1987) standard errors with

6

lags in italics.

these sub-indices perform quite independently of each other as

Reserve. The next episode occurred in August 1998 leading up

som e of the risk factor analysis shows. However, periodically,

to the collapse of LTCM . In this month, eight out of the ten niche

m arket events occur during which seem ingly different strategies

D JC S style sub-indices suffered sizeable losses ranging from

can undergo stress at the same tim e. W hen this occurs, an oth­

—23.03% for emerging market hedge funds to —0.85% for

erwise diverse portfolio of hedge funds can converge in term s of

equity market neutral hedge funds. The exception being Short

risk, or its portfolio diversification im plodes. To gain insight on

Sellers and Managed Futures funds which returned 22.71% and

how convergence of risk factors can be m anaged we analyze

9.95% respectively. Much has been written about the events

som e of these incidents to underscore the special nature of

leading up to the collapse of LTCM ,75 suffice it to say that the

hedge fund strategies.

commonly accepted causes are market-wide liquidation of risky

The first such recorded event occurred during the March to April period in 1994. Seven out of the ten style-specific sub-indices in the D JC S fam ily lost money in these two months. The exceptions being Short Sellers and M anaged Futures which delivered posi­ tive perform ance in both months, Risk A rbitrage with a positive return in March and Equity M arket Neutral with a positive return in April. The overall D JC S Broad index is negative for both these

assets and the bloated balance sheet of LTCM from aggressive use of leverage. W hile wholesale liquidation of risky assets can occur globally for a variety of reasons inflicting stress on conven­ tional long-biased strategies as well as hedge funds, it is the effect of leverage that makes hedge fund investm ent risk differ­ ent from conventional long-bias strategies. Put differently, man­ aging hedge fund investm ent risk applies to both sides of the

two months. The reason for the negative perform ance across strategies is generally attributed to liquidation of leveraged posi­ tions following the unexpected rate hike by the US Federal

7 5

See for example Lowenstein (2001).

Chapter 9 Hedge Funds

■

179

3.0

margin requirem ents, borrowing costs and investors withdrawing their equity. In short, there was a crisis on the liability side of most hedge funds' balance sheet irrespective of the type of assets (risk factors) they hold (are exposed to) and their trading strategy. No major strategy category was spared. For exam ple, a historically low volatility strategy like Convertible A rbitrage lost over 12% a month for both Septem ber and O ctober of 2008 according to the D JC S style index for that strateg y.78 These were the two left tail data points of this strat­ egy shown in Figure 9.12. Under normal m arket conditions, shorting the equity content of a convertible bond will elim i­ nate most of the day-to-day price fluctu­

Fiau re 9.17 Cumulative return of DJCS, HFRI, SNP indices, and the TOP50 and TOP50_2010 portfolios: 2002-2010.

ation thus creating a low risk portfolio to take advantage of perceived mispricing of convertible bonds. However, when these positions are leveraged, the latent

balance sheet— asset as well as liability— in that a diversified set

risk of rolling over these positions can prove to be extrem ely

of risk factor exposures from the asset side of the balance sheet

costly in a credit crunch.

is no guarantee that funding risk is simultaneously diversified.

Can funding risk be m itigated in part or in w hole? It is now

Events leading up to the 2008 financial crisis are a stark illustra­

alm ost four years since the 2008 financial crisis and the im pact

tion of the dam age that a m arket-wide funding crisis can inflict

of global deleveraging is still unfolding with no end in sight.

on leveraged positions. August 2007 marked the first ever

The profitability of most hedge fund strategies is driven by

month in the reported history of D JC S 's hedge fund indices in

effective use of leverage. Therefore the risk of another funding

which all nine specialist style sub-indices lost money— the only

crisis sim ilar in character to what we experienced in the sum m er

exception being the positive return from specialist funds with a

of 2008 is som ething that cannot, and should not, be over­

short focus or short sellers. Some authors have attributed the

looked. It is also a risk that cannot be easily m itigated by sim ply

event to "firesale liquidation of sim ilar portfolios that happened

spreading one's capital to different hedge fund strategies. The

to be quantitatively constructed." 76 This, however, would not

need to consider hedging a credit-driven tail risk event in a

explain how all other hedge fund styles lost money as well.

hedge fund portfolio is clear; however, a com plete solution to

A nother clue lies with the extraordinary events leading up to the

this problem remains beyond our grasp and lies beyond the

dem ise of Bear Stearns.77 Bear Stearns was among the first

scope of this chapter. N onetheless, we offer the readers a few

major W all-Street victim s of the credit contagion em anating

"em pirical fruits" for thought. M anaged futures, as a hedge

from what we know with hindsight as the US housing m arket cri­

fund style, has historically been a strategy that delivers a convex

sis. Around the peak period of the 2008 financial crisis between

perform ance profile relative to other hedge fund strateg ies.79*

Ju ly and O cto b er of 2008, there were unprecedented consecu­

Unfortunately, on the w hole, the D JC S M anaged Futures index

tive months, Ju ly to Septem ber, during which all hedge fund

failed to deliver m itigating perform ance during the losing

styles excep t short sellers lost money. The precise reasons why

months of August and Septem ber of 2008. H ow ever the replica­

different specialist hedge fund styles lost money are likely to be

tion of trend following as a sub category of this strategy group

many and varied. The one common them e is the "forced liquida­

could be an interesting substitute to the D JC S M anaged

tion" of leveraged positions driven by a com bination of rising 7 8 7 6

See Khandani and Lo (2007, 2011).

7 7

See Hajim and Lashinsky (2007).

See Palazzolo (2009) for more detailed discussions.

See for example Figure 9.6, and for more discussions on this see Fung and Hsieh (2004b).

7 9

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Financial Risk Manager Exam Part II: Risk Management and Investment Management

Futures in d ex.80 The subject of replicating and separating risk

fund returns began to emerge. After several years of develop­

factors inherent in risk hedge fund strategy will be taken up fur­

ment, these hedge fund (strategy) beta products are becoming

ther. Suffice to say that the risk m anagem ent of hedge fund

ubiquitous. For exam ple, Credit Suisse overviews their products in

portfolios must take into consideration nonlinear risks such as

this space, Liquid Alternative Betas (LAB), as follows:

rare but dram atic m arket events the m anifestation of which can

Liquid Alternative Beta (LAB) is a series of indices that aim

take place on either the asset side and/or the liability side of a

to replicate the aggregate return profiles of alternative

hedge fund's balance sheet.

investments strategies using liquid, tradable instruments. LAB benefits directly from Credit Suisse's experience in the alternative investment space, and is supported by a

9.6 ALPHA-BETA SEPARATION, REPLICATION PRODUCTS, AND FEES

comprehensive quantitative platform with a focus on deliv­ ering alternative returns with liquidity and transparency. LAB strategies utilize quantitative processes in order to

Much has been written about the generous fee structure which

provide similar risk/return characteristics to alternative

hedge funds com m and. A fter two decades of nearly unabated

indices and strategies by identifying and sizing exposure

growth, the hedge fund industry is much larger (in AUM terms)

to proxy factors and/or system atically im plem enting

and dom inated by sophisticated institutional investors— inves­ tors who are not known for their generosity when it com es to

trades typically used by alternative investm ent m anagers.

fees. Yet, there is little sign that hedge fund fees are falling at a

Source: http://alternativebeta.credit-suisse.com/altbeta/en/ ab_home.aspx?cy=USD.

pace com parable to the industry's asset growth. In this section we discuss some of the perceived value of investing in hedge fund strategies, and how the supply side of hedge fund prod­ ucts has responded and evolved to changing investors' dem ands. The earlier sections of this chapter laid out a fram e­ w ork for analyzing hedge fund perform ance and concluded that hedge fund returns com e packaged with an alpha-like com po­ nent mixed with system ic risk exposures (betas). Some of these betas can be traced to asset-class factors that can be accessed via lower cost vehicles.81 For exam ple Table 9.2 shows that the eight-factor model explains 78.38% of monthly return variation of a hedge fund index like the HFRI. To the extent that the return from a persistent exposures to a factor beta represents the risk premium earned from placing capital at risk, it raises the question: can th ese risk prem ia from d ifferen t factors b e ca p­

Today, Credit Suisse offers a suite of these LAB products mim­ icking the factor-related returns of the D JC SI as well as sub-indi­ ces like Event-Driven, Long/Short Equity, Risk A rbitrage, and M anaged Futures. These products typically offer liquidity term s com parable to mutual funds and charge much lower fees than hedge funds. O ther variations to the Credit Suisse's LAB that mimic a broad-based index like the D JC SI are w idely available— see for exam ple the Goldm an Sachs Absolute Return Tracker (ART) Fund offer in a US mutual fund form at, Barclays Hedge Fund Replicator Fund offer in a European (UCITS) mutual fund form at and ProShares offer HDG Hedge Replication, an E T F based on the Merrill Lynch Factor Model of hedge fund b etas.82 It is too early to conclude w hether these products offer a more cost-effective way to access the system atic com ponent of hedge

tured via low er co st alternatives to h e d g e fund veh icles?

fund strategies' perform ance. However, their existence offers a

Let us take a bottom-up approach to analyze this question. It

way of separating the alpha com ponent of a hedge fund portfo­

shows that some of the more mature hedge fund strategies can

lio's return from its betas in a practical tradable form . The debut

be replicated with rule-based models using liquid assets that are

of these products also adds to the risk m anagem ent tool kit

readily executable in the market place. Therefore, a rule-based

available to hedge fund investors. Figure 9.3 shows the convex

representation of a given hedge fund strategy can be thought of

return characteristics of managed futures strategies (or trend fol­

as the beta factor of that strategy or its strategy beta. Collectively,

lowers). Hedge fund investors concerned with their portfolio's

these strategies are often referred to as alternative betas. Towards

tail risk exposure can modify the return convexity of their portfo­

the second half of 2007 products attempting to replicate hedge

lio via these liquid, low cost products that have the flexibility of a publicly traded fund like E T F s .83 If alpha and beta can be

See for example http://faculty.fuqua.duke.edu/~dah7/HFRFData .htm; and http://faculty.fuqua.duke.edu/%7Edah7/DataLibrary/TF-Fac .xls which show very large positive returns in August and September of 2008.

See http://www.goldmansachs.com/gsam/advisors/products/featured_ funds/art-fund/index.html and http://www.proshares.com/funds/hdg .html.

This is not to say that hedge fund managers physically transact in these factors, but that combinations of these risk factors can closely mimic the performance of a variety of matured hedge fund strategies.

Recall that most hedge fund vehicles require cumbersome redemp­ tion notice and only allow periodic subscriptions, whereas these alterna­ tive products are generally deals at daily Net Asset Value (NAV).

8 0

81

8 2

8 3

Chapter 9 Hedge Funds

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181

satisfactorily separated, it begs the question: what are the im pli­

depending on the actual target tracked. W e believe two major

cations on fe e s levied by conventional h e d g e fund veh icles?

factors contribute to these tracking errors. First, investable indi­

To gain insight on the historical trend on the cost of hedge fund investing, we begin by observing the experience of the early institutional investors in hedge funds at the turn of the century. As noted, most of these early institutional investors outsourced the lion's share of the portfolio m anagem ent function to fundsof-hedge funds. FO H Fs offer a one-stop vehicle that delivers m anager selection, due diligence, portfolio construction, adm in­ istration, reporting, and risk m anagem ent of a diverse group of hedge fund m anagers located in different parts of the world engaging in leveraged, dynam ic strategies transaction in finan­ cial centers globally. Prima facie this appears to be a reasonable step to take to access a then new, unfamiliar class of investm ent strategies. As is always the case, the value of such a service depends on a com parison of the lower net return to an investor versus the cost of engaging the services of FO H Fs. W e turn now to m ulti-manager hedge fund products. Fung et. al. (2008) found that only a small fraction of FO H Fs delivered

ces offer better liquidity term s than the typical hedge fund. Therefore one would exp ect returns from investable indices to underperform their target by a liquidity premium. Second, hedge fund indices are statistical constructs and as such, they carry index construction rules that cannot be im plem ented in practice. For exam ple, the HFRI index assum es rebalancing at the end of each month to maintain equal dollar invested in each of its index com ponents. This is clearly not possible as nearly all hedge funds require advance notification for exiting investors ranging from 30 days to 90 days, and in som e cases, redem p­ tions are only perm itted on an annual basis while others carry an early exit penalty— see Fung and Hsieh (2004b) for more discus­ sions on this to p ic.84 We now return to our simulation of the large hedge fund portfo­ lio to see how these new hedge fund products help to evaluate the rule-based strategy of investing into large hedge funds. Equation (9.1) gives us a general structure which sim plifies to :85

positive and statistically significant alpha above the seven-factor model of Fung and Hsieh (2004a). Interestingly, though, almost no FO H Fs delivered negative and statistically significant alpha. Basically, the m ajority of FO H Fs had no alpha, which is not alto­ gether a bad outcom e when com pared with mutual funds, the vast m ajority of which produced negative alpha relative to their respective benchm arks. Yet, the observation that few FO H Fs

TO P50 = alpha + b eta*lnd ex(D JC SI or

to 0.24% per relative to the D JC S I. But neither the D JC SI nor the HFRI is an investable proposition. Since the arrival of invest­ able indices, we can replace them by their investable counter­ part. For exam ple, we can w rite for the D JC SI index: T O P 5 0 = alpha + beta*(tracking error + (all-hedge-beta)*D JCS AIIH edge Index)

and the FO H Fs accounted for all excess returns (or alpha) gener­ ated before fees. N onetheless, the lack of persistent negative

*D JC S A LLH edge Index

Total Peer G roup Alpha for TO P 50 = alpha + beta*tracking error

new hedge fund products will em erge to offer lower fee hedge sive, rule-based m ulti-manager hedge fund products began to em erge com peting for investors' capital. Today, C redit Suisse offers a suite of m ulti-manager portfolios (All Hedge Indexes) that mimics the fam ily of D JC S hedge fund indices— see http:// w w w .hedgeindex.com /hedgeindex/en/indexoverview . aspx?indexnam e= SECT& cy= U SD . Hedge Fund Research (HFR) offers a number of similar multi-manager portfolios, see https:// w w w .hedgefundresearch.com /hfrx_reg/index.php7fuseH ogin_

(9.4)

and

theoretical m odel. However, in a general equilibrium context, fund vehicles. It is perhaps not surprising that around 2003, pas­

(9.3)

D JC SI = tracking error + (all-hedge-beta)

alpha does imply that hedge fund m anagers do generate alphas non consistent with the prediction of Berk and Green (2004)'s

(9.2)

Table 9.5B tells us that over the period 2002-2010, alpha com es

delivered alpha means that the fees charged by the hedge funds

before fees which vanished after adjusting for fees; a phenom e­

HFRI)

(9.5)

Equations (9.2), (9.3), (9.4), and (9.5) give us a fram ew ork for evaluating the value of investing in a m ulti-manager hedge fund portfolio such as TO P 50 (or a FO H F) com pared to a passive, investable hedge fund index portfolio. For instance, the total peer group alpha in Equation (9.5) can be interpreted as the sum of a m anager selection premium relative to the industry average (peer-group alpha) and a liquidity premium in that by investing into the Top 50 hedge fund m anagers investors are

bd. Since their inception, the tracking errors of these passive investable hedge fund indices have been consistently positive, in the sense that the target index consistently outperform ed the tracker portfolio. Actual operational costs of these portfolios alone cannot com pletely explain the sizeable tracking errors, which average over 2% per annum since their inception

182

■

Unrealistic rebalancing rules amount to adding an additional liquidity premium to the index's return.

8 4

Both the TOP50 and TOP50_2010 will recommend the same choice of funds going into 2011. The difference between the two lies with the expected alpha and beta relative to either DJCSI or HFRI.

8 5

Financial Risk Manager Exam Part II: Risk Management and Investment Management

accepting inferior liquidity term s com pared to the D JC S All

infer from observable data a persistent concentration of industry

Hedge product. The existence of passive investable indices

AUM in the hands of a small number of large funds. In other

allows investors to determ ine how much of a multi-manager

w ords, success begets more success. It is a pattern that may well

portfolio strategy's added value com es from superior m anager

have been in existence from the early 1990s as shown in early

choice and how much is just a liquidity prem ium .86

studies by Fung and Hsieh (2000b) and Fung, Hsieh, and Tsatsar-

Finally, by com paring an investable index, which is a passive rule-based m ulti-manager portfolio, to an appropriate portfolio of LA Bs, investors can assess w hether on average hedge fund m anagers add value to a portfolio of beta-bets. The hedge fund industry is m aturing. The availability of perform ance data has substantially improved the quality and depth of perform ance benchm arks, leading to the developm ent of passively invest­ able index-like products. This encouraged academ ic research on hedge fund risk factors to develop which in turn sparked the developm ent of beta-like hedge fund products adding to

onis (2000). Table 9.4B reports a continuing divergence between the AUM of the top funds relative to the industry's m edian. Towards the end of 2010, the largest fund in the observable data universe is almost 1,000 tim es bigger than the median fund. The em pirical evidence supports the conjecture that the unobserved AUM in the hedge fund industry is mostly in the hands of large hedge funds. It is for this reason we chose to develop our overview of hedge fund perform ance focusing on large hedge funds. O ver the past two decades, the hedge fund industry's path to

investors' risk m anagem ent tools. In the next section we present

success was punctuated by a number of landm ark events, and

som e concluding remarks and conjectures on future develop­

follow ed the industry's evolution along this event-oriented time

ment and areas of research interest, drawing from our observa­

line. The convergence of risky bets in 1994 and the collapse of

tions on capital form ation and product developm ent trends.

LTCM in 1998 were valuable lessons in risk m anagem ent and portfolio construction. These events were touched upon and

CO N CLUDIN G REM ARKS

illustrate the system ic effect of funding risk has on leveraged strategies around the 2008 financial crisis. The arrival of com ­ mercial databases around 1994, incom plete as they may be,

In the beginning of this chapter we posited an em pirical m etric

spurred much of the developm ent in hedge fund benchm arks

for measuring the success of an asset m anagem ent com pany—

and academ ic research on hedge fund betas. O ne section is

its ability to grow and retain investors' capital. Rooted in the

devoted to these topics— hedge fund strategy benchm arks and

world of private wealth m anagem ent, confidentiality and privacy

their inherent risk factors. Since then, investable hedge fund

remain a common trait among hedge fund m anagers, many of

indices and funds that replicate hedge fund betas evolved.

whom do not release their perform ance data to the general public. Table 9.1 confirms that com m ercial hedge fund data­ bases capture data from less than half of the hedge fund assets serviced by fund adm inistrators and consistently so from 2003 to 2010. This raises an im portant and challenging question for researchers: do the u n o b se rve d a ssets behave in a similar way to their o b serva b le cou n terp a rts? W e noted that the high degree of correlation betw een FO H Fs perform ance with database dependent hedge fund indices hints at potential sim ilarity between these two sets of hedge fund data— reporting versus nonreporting.87 N onetheless, until a more com prehensive answer to this question presents itself, the existence of such a large data gap casts a long shadow over the existing body of em pirical hedge fund research. In this chapter we pull together em pirical evidence and research from different sources to pro­ vide some insight to this im portant question. Specifically we

Perhaps the most im portant event that shaped the modern day hedge fund industry was the arrival of institutional investors. This major shift in investor clientele had a profound im pact on the supply of hedge fund products. The corporate governance requirem ent of institutional investors worked in favor of large hedge fund m anagem ent com panies shaping the capital for­ mation trend of the industry since the turn of the century. We believe that the concentration trend of AUM in the hands of a small number of mega hedge fund m anagem ent com panies is pervasive. If this is the case, then the data gap we noted betw een AUM serviced by hedge fund adm inistrators and AUM reported to com m ercial databases com es mostly from success­ ful, large hedge fund m anagers who elected not to disclose data to databases. Insight on the properties of this data gap is not only im portant to m odels of hedge fund strategies and per­ form ance, but may potentially affect the future of hedge fund regulation. A fter all, regulating a small num ber of large m anage­ ment com panies is quite a different proposition from regulating

8 6

Investable indices typically carry lower fees than regular hedge funds.

We note that FOHFs are not limited to investing only in hedge funds that are available in commercial databases. 8 7

thousands of small private asset m anagers. However, if AUM concentration does continue without bounds, the probability of a convergence of risky bets like 1994 will rise, as increasing

Chapter 9 Hedge Funds

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183

amounts of leverage-able capital are concentrated in the hands

variation. The problem arises when the incentive fee which hedge

of a few hedge fund m anagers. A convergence of opinions on

fund managers are entitled to, typically at 15-20% of new profits

certain risky assets could potentially lead to m arket disrupting

(or profits above a high w ater mark— HWM), ends up enticing a

events. More work is needed in this area of research.

fund manager to take unreasonable bets. This can occur when the

W e return to the discussion of analyzing perform ance. The con­ tinuing growth of industry AUM attests to the relative attractive­ ness of hedge fund strategies on average com pared to their attendant risk (betas). The continuing success (in attracting AUM ) of large hedge funds attests to the positive perception of value that large funds bring relative to their peers. The im pres­ sive AUM growth of the hedge fund industry has to be coinci­ dental to delivering attractive perform ance relative to com peting risky assets elsew here in the global m arkets. To this end, Table 9 .2 A tells us that on average (based on reported indi­ ces like D JC SI and HFRI) the hedge fund industry returned sta­ tistically significant alphas adjusting for a broad range of risk factors. For investors searching for an alternative source of return to equities, Figure 9.4 provides justification for being attracted to hedge fund products over the period of 1996 to 2010. However, Table 9.2D tells us that alpha may be evaporat­ ing during the more recent period of 2002 to 2010. This is where large funds cam e to our rescue. We show that not only do the 27 large hedge funds used in the (Fung and Hsieh, 2000b) study deliver sizeable alpha relative to the eight risk factors (Table 9.3A ), it also has substantial peer group alpha relative to the hedge fund indices (Table 9.3B). Therefore while alpha may have dissipated for the average hedge fund (or index) the same observation may not hold for the large hedge funds. W e track the perform ance of the Top 50 hedge funds ranked by year end A U M . Although the passive strategy of investing in the past year's Top 50 funds consistently delivered alpha with respect to peer-group hedge fund indices, it failed to generate alpha with respect to the eight-factor m odel. However, the foresightassisted portfolio of investing in the Top 50 hedge funds based on 2010 AUM rankings produced highly significant factor-based alpha as well as peer-group alpha. W hile this latter portfolio TO P 5 0 _2 0 1 0 is not achievable without foresight, its perfor­ mance illustrates that winners exist among large hedge funds, which is consistent with the belief that m anager selection m at­ te rs.88 The fact that some large hedge funds can continue to outperform their peers reinforces the im portance of better understanding the data gap from non-reporting hedge funds. Finally, much has been written about the asymmetry in risk shar­ ing between principal and agent inherent in variable com pensa­ tion schem es of which hedge fund style incentive fees is one such

current loss-carry-forward (HWM) gets to a point that new profits only becom e viable when very large bets pay off. The cost of taking unreasonable bets is to further increase future loss-carriedforward should large bets fail. Faced with such a dilemma, a man­ ager may be tem pted to take an unreasonable risk so long as the option of closing shop and restarting in a new business (thereby resetting the loss-carryforward burden) if a large bet goes wrong is a feasible proposition. Historically, there are many incidents of fund managers re-emerging from a failed fund to raise fresh capital for new hedge fund ventures. However, closing shop and starting again clearly depends on the opportunity cost to the manager of closing a fund. It would be reasonable to assume that the larger the hedge fund m anagem ent company, and the size as well as the age of the fund in question, the more costly it is for a fund manager to exercise the closure option— both in term s of the value of the track record of an operating fund and the repu­ tation risk to the fund manager (or m anagem ent company). The cost of fund closure being higher for large funds does partially mitigate this principal (investor) and agent (manager) conflict. In addition, from the early days of the hedge fund industry, inves­ tors have a preference for funds in which the agents (fund manag­ ers) invest a sizeable amount of their own wealth. This remains a common feature among successful hedge funds, one that helps align the interests of hedge fund investors and managers. This type of contractual arrangem ent has survived from the early days of the hedge fund industry. Taken together, these considerations tend to favor large hedge fund m anagem ent companies and can provide some relief to the com plex principal-agent conflict inherent in hedge fund compensation models. However, a formal model encompassing all of these features on how hedge fund managers are com pensated has yet to em erge.

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of hedge funds. Jou rn a l o f Em pirical Finance, 7(1), 1-36.

Econom ics, 84(1), 229-264.

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Lowenstein, R. (2001). W hen genius failed: The rise and fall o f

Palazzolo, C . (2009). The con vertible b o n d m arket dislocation o f

long-term capital m anagem ent. New York : Random House.

2008: Creating op p o rtu n ities in 2009 and b eyo n d . W hite Paper:

M erton, R. (1981). On m arket timing and investm ent perfor­

A Q R Capital M anagem ent LLC.

mance I: An equilibrium theory of value for m arket forecasts.

Patton, A . (2009). Are 'm arket neutral' hedge funds really mar­

Jou rn al o f Business, 54(3), 363-407.

ket neutral?. R eview o f Financial Stu d ies, 22(7), 2496-2530.

M itchell, M., & Pulvino, T. (2001). Characteristics of risk in risk

Patton, A ., & Ram adorai, T. (2012). On the high frequency

arbitrage. Jou rn a l o f Finance, 56(6), 2135-2175. N A C U B O (National Association of C olleg e and University Busi­

dynam ics of hedge fund risk exposures. Jou rn a l o f Finance (forthcoming).

ness O fficers), Endow m ent Study, 1998-2008.

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N A C U B O (National Association of C ollege and University Busi­

Sharpe, W. F. (1992). A sset allocation: M anagem ent style and

ness O fficers)— Com m onfund, Study of Endow m ent, 2009-2010.

perform ance m easurem ent. Jou rn a l o f Portfolio M anagem ent,

N ewey, W ., & W est, K. (1987). A sim ple, positive sem i-definite,

18(2), 7-19.

heteroskedasticity and autocorrelation consistent covariance

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m atrix. Econ om etrica, 55(3), 703-708.

nal o f Eco n om ics P ersp ective, 21(2), 175-194.

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Learning Objectives A fter com pleting this reading you should be able to: Identify reasons for the failures of hedge funds in the past. Explain elem ents of the due diligence process used to assess investm ent m anagers. Identify them es and questions investors can consider when evaluating a hedge fund manager. Describe criteria that can be evaluated in assessing a

Explain how due diligence can be perform ed on a hedge fund's operational environm ent. Explain how a hedge fund's business model risk and its fraud risk can be assessed. D escribe elem ents that can be included as part of a due diligence questionnaire.

hedge fund's risk m anagem ent process.

E x c e rp t is C h a p ter 12 o f Hedge Fund Investing: A Practical Approach to Understanding Investor M otivation, M anager Profits, and Fund Perform ance, S e co n d Edition, by Kevin R. M irabile.

This chapter is concerned with the process of perform ing due

and allows investors to ask the type of open-ended questions

diligence on a specific m anager that is being considered for

needed to assess the attitudes and culture of a m anager and

investm ent. Due diligence is the term used to describe the

the consistency of m essage or a process throughout an entire

process of evaluation and analysis that an investor follow s to

organization.

get com fortable with a strategy, a m anager, and a fund prior to making an investm ent. It includes all the steps that are needed to get to know why and how a fund cam e into being; the skills

This chapter organizes the due diligence process into four sections:

its founders or current partners claim to have m astered; the

1. Investm ent process

evaluation of the tim eliness, accuracy, and consistency of man­

2. Risk m anagem ent

ager and fund inform ation; the reliability and independence of service providers; and far more. The chapter is designed to describe som e of the common procedures used to investigate

3. O perational environm ent 4. Business model assessm ent

a m anager's trading and investm ent skill; ability to manage

In each section, we cover a few of the more im portant quantita­

operations, credit, and liquidity risk; and im portantly, the ability

tive or check-the-box criteria, as well as those qualitative and

to run a business.

subjective criteria that very often help an investor expose a

Investors would be wise to assess all three skill sets needed to

m anager's underlying strength or w eakness.

run a modern-day hedge fund— investm ent, operational, and

However, before diving into the investm ent, risk m anagem ent,

business skills— before com m itting capital to any fund. Those

or operational or business model risk assessm ent for any man­

who do lower the risk of surprise and improve the prospects of

ager or fund, a few words of caution are worth noting. Each of

getting what they anticipated from any opportunity. M anag­

the following axiom s provides a word or two of caution about

ers today are rarely good at all three things. In fact, due to the

the due diligence process. If they are follow ed, investors will at

changing dem ands of institutional investors and the failure of

least position them selves for the best possible outcom e, given

2008, it is most often im possible for any one person or leader

any set of idiosyncratic circum stances or m arket outcom es that

to process a high level of com petency in all three areas. This has

may arise. Hopefully, they will elim inate at least some of the less

profound im plications for how hedge funds are run today.

fortunate surprises that inevitably occur when investing in lightly

Founders who are the C IO and C E O and who also manage a

regulated private vehicles such as hedge funds.

fund's risk and business model them selves are, quite frankly, considered dinosaurs today. Today's top m anagers are very often making the choice to either be the C IO and share the C E O role or, where they are serving both roles, to bring in senior partners who can add depth and have specialized risk, accounting, operations, or trading skills beyond their own. Investors in hedge funds now are quite focused on making sure the organization can provide all three skills at a very high level, even though any one founder cannot. Many firms with great investm ent ideas lack risk controls or business skills. O thers who are control oriented and can run a business may not be able to generate the returns that are needed. Finding the best com bi­ nation of return and infrastructure without excessive business risk is som etim es more of an art than a science. Investors need to think about perform ing due diligence in a way that is com prehensive and holistic. This means that it must cover the investm ent process, operational environm ent, and business acumen of a m anager and a fund. It should also be

10.1 BE PREPARED First and forem ost, an investor must be well prepared when trying to assess any investm ent opportunity. This is particularly true in trying to evaluate the skill of a hedge fund m anager or the attractiveness of any investm ent process. Being prepared means having a firm understanding of why you are considering a particular type of investm ent style or strategy. It means knowing how that style should react to various m arket conditions. By fully understanding the strategy beta, you will be able to focus more tim e and attention on the m anager's ability to generate alpha relative to peers in the same strategy.

10.2 LEARN FROM THE PAST— FROM BOTH SU CCESSES AND FAILURES

both quantitative and qualitative. Q uantitative analysis ensures

G ettin g caught up in the past success o f hedge fund in vest­

that every aspect of due diligence is covered and nothing obvi­

ing is quite easy. In fa ct, very often an investor's previous

ous gets missed. This is som etim es referred to as the check­

success or past association with an industry legend can create

list approach. Q ualitative analysis is much more investigative

ju st enough hubris to get the investor in trouble in the future.

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Investors like to b elieve they have found the next G e o rg e

their work escalate their concerns. If something in a manager's

Soros, Jim Sim ons, or Paul Tudor Jo n e s. Th ey rarely like to

track record, background, or pedigree comes into question, ana­

m ention when they end up having found the next M adoff

lysts must raise their hands and speak their minds. Very often, the

or allo cated capital to yet ano ther frau d ste r with supposed

most notorious frauds and funds that were behaving badly were

investm ent su p erio rity or acum en.

quite obvious to those in direct contact with the manager. Often

So why do funds fail? There are many reasons. Investors should remind them selves of those reasons and seek answers about previous fund failures in the strategy they are considering as part of the due diligence process. Funds can fail as a result of bad investm ent decisions. Funds can make several com pounded bad decisions or just a few concentrated calls on the m arkets or individual securities that perform very poorly. Funds can also

only in retrospect is everyone able to see what should have been obvious to all. In the end, no matter how uncom fortable, escala­ tion of questionable information will benefit the organization and will be appreciated. If things don't feel right or just don't pass the smell test, then they should be voiced within the research team before ever getting to the investm ent com m ittee for allocation decisions or approval.

fail due to all sorts of frauds, including accounting frauds, valu­ ation frauds, or m isappropriation of funds. Funds can fail due to excessive leverage, im probable probabilities, unexpected events, and tail risk. Funds can fail due to a flood of unan­ ticipated withdrawals of capital at the least opportune tim e. Funds can get caught in squeezes by the street or by other hedge funds. Funds can fail as a result of a lack of supervision or com pliance controls related to insider trading. Funds can fail because of their own actions or the acts of others. A prime bro­ ker like Lehman or MF Global can go bankrupt and take a fund with it. Funds can fail when liquidity dries up, and they can't m eet redem ptions and must sell into a m arket that no longer exists, at least at that moment. Investors need to evaluate each strategy and each m anager with open eyes and take great care not to be blinded by the past success of any one person or strategy. The more an inves­ tor assum es things can and will go w rong, the better the due diligence process and the more likely it is that an investor will uncover problem s and/or ensure that attractive opportunities have a higher probability of success.

10.4 REM EM BER, IT'S STILL ABOUT RETURNS! So much media and regulatory focus has been placed on the need for hedge funds to raise their standards and adhere to best practices, particularly related to operations, credit risk, and liquidity, that it is entirely possible for som e investors to actu­ ally overem phasize some aspects of the due diligence process. Investors may place so much em phasis on operational due diligence alone that they end up picking m anagers with great controls that actually don't add much return to the portfolio at all. Investors should be mindful not to overw eight infrastructure and business model risks. There needs to be a good balance betw een the investm ent opportunity and the risk profile of the fund. A set of minimum standards or bright lines is helpful to ensure that the balance doesn't shift too far in the other direc­ tion, resulting in the selection of m anagers with great strategies and poor controls or business risk. The need for independent adm inistration, audits, and top-tier service providers is generally not negotiable. However, infrastructure and business m odels

10.3 IF IT LO O KS TO O G O O D TO BE TRUE, IT PROBABLY IS

should be strategy and life cycle specific. A recently launched equity variable bias fund operating in the United States may not need multiple prime brokers, real-time disaster recovery, and a hot backup or succession plan, certainly not all on day one! The

The individual em ployees who are performing investm ent due

reason investors invest is to increase return and to reduce risk.

diligence should always rem em ber to trust their own judgm ent.

As sim ple as that sounds, it can easily be forgotten.

If it looks too good to be true, it probably is. Too often, firms make allocation decisions by com m ittee. In this setting, it is easy for one voice, perhaps one's boss, to direct the decisions of the team . Individuals may feel too intimidated to speak out or to

10.5 COM M ON ELEM EN TS O F THE DUE D ILIG EN CE PROCESS

communicate details that may reflect negatively on a manager who is well known to the firm or who has established a high-level

The due diligence process today is very different than it was

relationship with the C IO or other members of the organization. It

in the past. In the past, m anager reputation and perform ance

is essential that people who come across facts, figures, opinions,

were the most im portant factors. Investors did little digging into

references, or any other relevant information uncovered during

the how and why of perform ance and the safeguards in place to

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protect assets. This was due in part to the lack of leverage that individual investors had with the m anagers. They w ere often considered "lucky" just to have gotten into a well-known fund with limited capacity. Institutions had relatively small exposures to hedge funds at the beginning and needed to have a high return to have the investm ent m atter to the portfolio. Finally, m anagers were rather selective and if you asked too many ques­ tions you would simply be told to go elsew here. As the industry matured and as more institutions came into the m arket, not to mention some very high-profile frauds, the due diligence process expanded. Today, both m anagers and investors spend a great deal of tim e trying to learn where a manager's "e d g e " is coming from and that their investm ent is safeguarded and properly valued. The due diligence process involves two separate but closely related evaluations. O ne evaluation is of the firm's investm ent process and related risk controls. The other is related to the fund's operations and business m odel. Today both are consid­ ered alm ost equally im portant and are often interrelated.

10.6 INVESTMENT MANAGEMENT This section is a high-level summary of some of the common them es and questions investors use to perform due diligence on a fund's investm ent process. It is by no means com prehen­ sive and is intended to provide a sam ple of the types of issues that investors are facing when trying to determ ine the value and quality of a fund's investm ent process them selves, indepen­ dently from the docum entation and high-level representations of senior m anagem ent. Most if not all of the questions related to a fund's investm ent process should be done in person with as many people of mixed seniority as possible. The goal is to find out what is really going on at the fund and not just have a pitch book recitation by the investor relations staff. Rem em ber that if you cannot get access to the actual decision makers when you are trying to invest, it is unlikely you will have access if som e­ thing goes wrong! Hearing it directly from the firm's founder and lieutenants is always best, but getting the same m essage from a diverse number of people who perform certain tasks on a dayto-day basis or should be fam iliar with them is also quite useful.

What Is Your Strategy, and How Does It Work?

1. W hat is the m anager's self-described style, and how does it fit within a particular classification schem e? 2 . W hat are the current them es included in the portfolio, and what are the fund's highest convictions or most concen­ trated positions? 3 . How has the portfolio evolved over the past several quar­ ters, and what is the outlook for any changes, given current m arket conditions? 4 . Does the firm manage the fund to specific gross and net exposure targets, and if so, where does the fund stand today versus those targets and why? 5 . W hat is the portfolio turno ver and num ber of days to liq­ uidate, and w hat are the trig g ers that result in a reversal and a sell or buy to co ver or e xit d ecisio n? A re the trig ­ gers hard coded into the risk m anagem ent process or just guid elines?

6 . How are stop losses used to manage risk? Are they used at the position level, portfolio level, or both? Are they always executed or are there exceptions? 7 . How quantitative is the investm ent process, and how much does the firm rely upon proprietary m odels? If so, what are they based on, and how are they developed, back-tested, and allocated capital, or decom m issioned when failing to perform ?

8 . How are short sales used— as hedges, alpha generators, or both? Has the firm ever been hurt by a short squeeze, recall, or buy-in on borrowed shares? 9 . How are listed or O T C derivatives used in the portfolio? 1 0 . How is trading organized? Does the firm have a central trading desk for all external order flow? 1 1 . Is the strategy capacity constrained? 1 2 . Has the fund ever held private investm ents, and if so, why and how do they support the core investm ent strategy? 1 3 . Is the firm more return oriented, asset growth oriented, or both? 1 4 . How does it manage the conflict between generating returns for existing investors versus growing the assets under m anagem ent? 1 5 . Has the fund ever been soft or hard closed or returned capital to investors? O nce this initial set of questions about the firm and the fund has

Investors who are evaluating a m anager often start with high-

been answ ered, the investor can begin to drill down into more

level questions that provide them with som e context about the

specific questions about the firm and the process follow ed to

firm , its investm ent strategy, and how it works.

manage investing.

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How Is Equity Ownership Allocated among the Portfolio Management, Trading, and Research Teams?

The ability to verify a new manager's prior em ploym ent is just

Understanding the firm's ownership structure and how things

the trigger puller or acting in a support role? Did they gener­

get done is critical. The participation of the investm ent team in some form of ownership is a critical area of differentiation among firm s. Som e firms do not share equity ownership among the portfolio m anagers or traders in the firm . O ther firm s use equity ownership as a key feature of their professional talent retention program and to attract and groom new talent for future leadership positions. O ne model is not necessarily better than the other. Each has its pros and cons. Investors often have a view one w ay or another. The key thing is to understand the firm's philosophy and how it im pacts perform ance, talent acqui­ sition, and retention.

investors, and experiences other investors have had, including both positive and negative over the life of the fund. the beginning. Did they do what they described? W ere they ate ideas or im plem ent ideas? Did they operate individually or within a group? O ften, the best way to find out is to ask form er colleagues, partners, m anagers, clients, or other independent parties. Investors perform ing reference checks can think of the process as a 360-degree review of what a person has claimed about the past or even about his or her current skill set. If enough people are saying the sam e thing about a person or a firm , then an investor can take some com fort. If significant dif­ ferences of opinion about a person or a m anager are uncovered, they should be thoroughly vetted and then discussed directly with the manager. Most often, there is a good explanation— but not always!

Is the Track Record Reliable? A fter an initial set of questions about the firm , an investor will want to dig a bit deeper into the m anager's and the specific fund's track record. According to a recent report on hedge fund due diligence perform ed by the not-for-profit organization the G reenw ich Roundtable, investors should inquire w hether the track record is com parable to similar strategies, has been audited, and is long enough for statistical evaluation and infer­ ence, w hether returns were im pacted by fund size, and if the team that produced the historical track record is still in place today. Additional questions about the track record should include how it perform ed during periods of m arket stress and

Hedge fund scandals and blowouts over the past 10 years have also changed the way investors need to think about the people they are entrusting with their assets. The high-profile blowups of several hedge funds, including Bayou M anagem ent and Madoff, have raised im portant questions about what can be done to uncover fraud in advance of getting hurt. Background checks can certainly be obtained. Most investors can get a pretty com prehensive report on a m anager for as little as $750. More depth requires more m oney, but in som e cases, it certainly may be worth it. Very often there is information just below the surface that can be used to discover m anagers who have had trouble in the past.

how it relates to the portfolio manager's experience at previous

In many hedge fund frau d s, investors could sim ply have

firm s, if applicable.

searched public d atab ases and found litig atio n, crim inal accusatio ns, or civil disputes that may have at least been

Who Are the Principals, and Are They Trustworthy? Investors who are thinking about a particular m anager need to allocate resources to both references and background checks.

used to raise questions about the m anager's integ rity or past d eed s. M any fraud s sim ply go und etected because of a lack of p roper due d ilig en ce. A fte r the fa ct, it is easy to point to sm oking guns or indicators that som ething may have been w rong.

N ew er m anagers are a bit trickier than established ones. New

Either on their own or using independent resources, investors

m anagers need to have references from previous hedge funds

should always consider calling form er em ployers, track down

or banks verified, both those that are on the manager's refer­

credit reports, and contact auditors, adm inistrators, and prime

ence list and those that the investor can obtain independently.

brokers to verify what a m anager is representing in fund docu­

More established m anagers w on't need to be interrogated

ments or through verbal com m unication. An investor should

about previous firm s or em ployers from the distant past as

include searches of w ebsites maintained by the S E C and read

much as start-ups or firm s lacking a reliable track record. W hen

the m anager's Form A D V in detail before deciding to invest.

interviewing established m anagers or talking to their references,

Information about bankruptcy, federal or appeals court records,

focus the dialogue more on the manager's m otivation, behav­

or other sources to uncover information about a m anager are

ior during crisis or stress periods, ability to com m unicate to

readily available.

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Investors should always look for related party activity when

technology. M odern-day hedge funds use com plex processes

doing background searches. Does the m anager or the principal

to originate and control risk. Investors should inquire about the

own other business activities that do business with the fund? A

process used by the firm to choose a single or multiple sets of

fund that uses affiliated brokers or adm inistrators can lead to

risk platform s and the consistency of risk m easurem ent between

real problem s, especially if the m anager did not disclose it in

the traders, portfolio m anagers, and investors.

advance.

G reat care should be taken to understand the inputs and

Investors need to make sure they have access to the people

assum ptions used in the firm's risk m odels and w hether the

at the top of the firm . It is also im portant that investors deal

portfolio is stress-tested on a regular basis to m easure the

directly with the actual risk takers and decision makers and not

im pact of changing assum ptions. Too often, traders use a dif­

just investor relations, salespeople, or junior staff at the fund.

ferent system with different inputs and outputs to m onitor their risk than the firm is using to report risk to investors. This can

10.7 RISK MANAGEMENT PROCESS Evaluating the risk m anagem ent process and procedures entails hybrid questions that should be answered by all levels of man­ agem ent of the firm . Portfolio m anagers and traders, as well as operations staff and risk m anagers, all have valuable insight for investors. Risk m anagem ent-related questions should be asked as part of both the evaluation of the investm ent process and the operational environm ent of the firm.

How Is Risk Measured and Managed? Risk m anagem ent is an em erging discipline at many funds. That is not to say risk was not m anaged well in the past. It is more a reflection of the fact that risk m easurem ent and reporting and the decision to take action is evolving toward a more indepen­ dent model that segregates risk taking and investing from risk m easurem ent and m anagem ent. Today, many funds have dedi­ cated risk m anagers who report to the C IO or the C E O inde­ pendently from the portfolio m anagers and traders. Many firms also em ploy independent risk service providers to report risk to investors com pletely independently from the firm . Some use fund accountants and adm inistrators to achieve this goal. Investors must first inquire about the potential risks that a strat­ egy will expose them to in the normal course of business and then inquire about the additional idiosyncratic risks presented by a specific m anager within a strategy. Investors next might want to ask if there are written policies and procedures to monitor and measure each of the applicable risks and w hether there is a risk com m ittee to which each of the m ea­ sured risks gets reported on a daily, w eekly, or monthly basis. Is there a risk m anagem ent culture in the firm , and do traders and portfolio m anagers, as well as back-office and support staff, understand and participate in risk m anagem ent and m itigation?

result in a significant m iscom m unication and lead to problem s when things go wrong. Im portantly, each style of hedge fund strategy has a unique and som etim es mutually exclusive set of risks. An equity fund has beta exposure, whereas a credit arbitrage fund may have credit spread exposure. Event funds may be exposed to very specific catalysts that can have a significant im pact on perform ance. Global macro funds have more inflation, interest rate, and cur­ rency exposure than most single-strategy funds that trade a specific asset class. The information made available to investors needs to cover both the generic risks common to many funds and the particular risk associated with a single strategy and a specific fund.

How Are Securities Valued? A firm's valuation policy is another critical area that investors need to exam ine when considering a fund. W hat percentage of the fund's assets are exchange traded and marked to m arket via exchange prices versus model prices or broker quotes? Does the adm inistrator take responsibility for valuation, or does the m anager retain responsibility? W ho can override prices, and is there a formal docum ented process to do so?

What Is the Portfolio Leverage and Liquidity? An investor needs to evaluate the current and historical changes in leverage, the sources of leverage, and the liquidity of the fund's portfolio over tim e. In doing so, understand where the particular m anager may deviate from peers or exhibit lever­ age or illiquidity that can cause perform ance to deviate from the expectation of the strategy. Some strategies such as global macro have fairly uniform leverage term s and liquidity based on the products they trade. O thers, such as fixed income and con­

An evaluation of a fund's risk and its process to measure and

vertibles, use varying degrees of leverage and have very differ­

monitor risk inevitably morphs into a discussion of system s and

ent liquidity profiles from firm to firm . An investor who expects

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to earn the mean return of an index, such as a convertible index,

Investors should inquire about the fees, high-water mark, and

can get very different results depending on the m anager's lever­

hurdle rate related to any investm ent. Is the fee appropriate

age and liquidity or orientation. Depending on the answers to

and in line with peers? How is the hurdle rate calculated and by

questions about leverage and liquidity, investors may need to

whom ? Is the high-water mark reset annually, or is it perpetual?

adjust their expectations for returns that w ere initially based on

Does the portfolio's liquidity match the liquidity offered to inves­

the strategy or a com parable index. Investors should inquire

tors, and if not, is the gap a reasonable one? Is there a lock-up

how the current leverage and liquidity in the existing portfolio

period before redem ptions are allow ed? Can the fund gate or

com pares to previous quarters. Liquidity will also have a direct

suspend redem ptions?

effect on a fund's capacity and ability to handle larger amounts of investor capital.

Does the Strategy Expose the Investor to Tail Risk?

10.8 FUND OPERATING ENVIRONMENT, DOCUMENTATION, FINANCIALS, AND SERVICE PROVIDERS

Certain strategies may expose investors to unanticipated tail

This section provides a high-level sum m ary of som e of the

risk. Investors need to perform their own analysis of a fund's

common them es and questions investors use to perform due

data and determ ine its skew ness or kurtosis. They should also

diligence on a fund's operational environm ent. This includes

inquire w hether the m anager believes that tail risk exists and, if

validation of a fund's internal procedures and its relationships

so, get an explanation of how it is hedged or w hether investors

or exposure to im portant service providers. O nce again, it

need to accept or hedge it on their own.

is by no means com prehensive and is intended to provide a

How Often Do Investors Get Risk Reports, and What Do They Include?

trying to independently assess the quality of a fund's operating

Investors are always entitled to periodic reporting from the

eral im portant aspects of how a hedge fund is managed and

fund. The fund offering docum ents and m aterials normally state

how its interaction with the fund itself is controlled. The primary

sam ple of the types of issues that investors are facing when environm ent. An operational due diligence program includes review of sev­

explicitly when and what is provided. Some funds report on risk

purpose of operational due diligence is to ensure that no signifi­

using a standard package produced by a third-party risk pro­

cant additional risk of loss is being created for investors related

vider or include key risk statistics in their monthly fact sheet or

to the settlem ent of securities, process of corporate actions,

periodic investor letter. Investors should obtain this inform ation,

m isappropriation or theft by em ployees or agents, or any other

ensure they com pletely understand it, and com pare it to peers

breakdown in the m anager's confirm ation, verification, valuation,

and/or strategy-level indices for consistency and to identify

and reconciliation process.

unique risk taking by the fund prior to investing.

An investor performing operational due diligence generally focuses on assessing the adequacy of a manager's internal con­

Do the Fund Terms Make Sense for the Strategy?

trols, consistency of fund documents and legal representations,

Investors want to assess if the term s make sense for the strategy

Internal Control Assessment

that is being offered. A long-only m anager getting a 2 and 20

and the risks of loss due to counterparty or service provider failure.

fee or a liquid long and short equity strategy with a one-year

A review of a manager's control environm ent includes many

lock-up can be red flags. Investors can com pare any specific

item s. Some of the more im portant items that investors can

m anager or fund to its peers to see if the term s make sense.

review include the qualifications of people at the fund, the qual­

Law firm s, accountants, and many commercial databases are

ity of the written procedures, and the ability of the team to e xe ­

good sources to collect com parative data on fund term s. Inves­

cute them each day and clear any breaks of exceptions that may

tors who give away term s such as lock-up to m anagers are not

occur, as well as the fund's exposure to derivative counterparties

getting com pensated for the risk they are taking. Investors who

and the protections provided by its governance structure. It is

pay high fees for m arket beta are overpaying for som ething that

not enough to have a good plan. The people must be qualified,

could be more cheaply replicated on its own.

and the process must be follow ed every day.

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Let's start with a brief discussion of the qualifications of the

MF G lobal, and Refco failures all resulted in hedge funds losing

people who run the firm and are em pow ered to act on behalf

money that belonged to the funds they m anaged. W hen a fund

of the fund. Does the C E O support a culture of control and

has cash being held with a dealer and the dealer goes bust, it

com pliance, or is he a person who doesn't really like to follow

may not get the money back— ever! A t a minimum, there may

the rules? The m essage from the top down needs to be one of

be a lengthy court battle, and then recovery may only be 30 or

safeguarding assets, where following a process is supported

40 percent of the amount they thought was safe and secure as

and, more than anything, investors are valued and treated with

cash on the balance sheet or a receivable from a dealer. Hedge

respect. An assessm ent must be made w hether the opera­

funds have to diversify this risk among several firm s, take action

tions, accounting, treasury, technology, com pliance, and other

to move any excess cash out of firm s that may be at risk, and

personnel are truly qualified for the positions they hold and

have a process in place to monitor the risks of these counterpar­

the products the fund is trading. Investors must ask w hether

ties every day.

the m anagers have experience managing and w hether they them selves are qualified to get the job done correctly. It is not unusual for background checks to be done on the firm's C O O , C F O , accounting m anagers, or other key back and middle office personnel, in addition to the checks normally done on the investm ent and research team m em bers. Does the firm hire people with experience, and how do they train their staff and maintain and grow their skill set and knowledge base outside the big-firm environm ent from which most people cam e? A review of the fund's written procedures related to trading,

Finally, is there a governance structure that extends beyond the C E O ? If so, does it have any teeth? Increasingly, investors are holding fund directors and advisors accountable for the deci­ sions a fund m anager makes related to service providers and the actions that a fund takes that lead to style drift or even fraud.

Documents and Disclosures An investor needs to verify with the listed law firm in the fund docum ents that they were responsible for the original content

derivatives, cash and securities processing, and position servic­

and for any updates. Investors generally rely on the quality of

ing can be perform ed during a site visit to the firm . It is now

the law firm that has created or am ended fund docum ents. On

routine for investors to inspect docum ents outlining firm pro­

some occasions, m anagers have been known to make changes

cedures and evaluate those procedures to see evidence of how

to their fund docum ents without the consent or even knowledge

the written policies are being follow ed. Unfortunately, these

of the law firm that drafted the docum ents. An investor can

sorts of docum ents and process reviews are not really com pre­

actually check the docum ent to see if any changes w ere made

hensive or efficient. In reality, it only gives investors a sense of

after the as-of date on the face of the docum ent. Changes made

w hether the m anagem ent of the hedge fund takes the whole

after that date should be discussed with the m anager im m edi­

control process seriously. Some hedge fund m anagers have

ately and with the law firm . In addition, verify that the law firm

made real progress in this area and have gone as far as to get an

cited in the fund docum ents is still under a retainer agreem ent

outside audit firm to evaluate their procedures and controls on

with the m anager or fund. Most law firm s will at least indicate

a periodic basis and issue an opinion of w hether the controls are

w hether they currently represent the fund.

sufficiently well designed and have been tested and are operat­ ing effectively.

N ext, it is very im portant to ensure that the fund offering memo, subscription agreem ent, limited partnership agreem ent, invest­

Com pliance is another critical area of investigation. Most firms

ment m anagem ent agreem ent, Form ADV, and w ebsite are all

today have either their own in-house com pliance function or

saying the same thing at the same point in tim e. Very often,

an outsourced relationship with a com pliance service provider.

these docum ents can change after a fund launch, and some may

All but the sm allest of firm s have some resources dedicated to

no longer match the term s of the offering memo that ultimately

com pliance. Com pliance practices that can be verified include

governs an investor's rights and obligations. Particular attention

the existence of a code of ethics, prohibition of related-party

must be paid to fees, liquidity, side pockets, gates, suspension

transactions, and restrictions related to em ployee trading. Counterparty risk related to the use of O T C derivatives and other trade counterparties is now a topic routinely covered

rights, creation of subfunds or SPVs, and change in offshore investm ent m anagers. Investors in hedge funds must carefully consider the conflicts

in the operational due diligence function. Funds have varying

of interest section of the fund's offering memo (OM ). This is

exposure to the firm s they trade with. Firms holding up-front

where the law firm drafting the docum ents most clearly states

margin have failed and closed out fund positions without any

any concern about nonstandard arrangem ents with m anagers,

return of the margin paym ent held in the account. The Lehman,

co-investors, and others. Be sure to query these representations,

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Financial Risk Manager Exam Part II: Risk Management and Investment Management

especially if they are vaguely w orded, such as "certain princi­

to the gross negligence, bad faith, fraud, or willful m isconduct

pals or affiliates of the m anager may maintain relationships with

of the manager.

certain fund counterparties but will always operate on an arm'slength basis." This can mean anything from "our adm inistrator also does som e accounting for Citibank, where we hold our operating accounts" to "the m anager takes a personal rebate from the prime broker." Caution is advised when there are either insufficient or extrem ely broad risk disclosures. Insufficient risk factors are more of a red flag than too many. In addition, overly broad and irrelevant risk factors are also a red flag. In the latter case, the law firm may not have adequately looked at the m anager's pro­ gram or is drafting the OM so broadly that it is looking primarily to protect itself, not the investor.

The docum ents should also clearly state the manager's obli­ gations for reporting to investors, including audited financial statem ents and any tax im plications associated with the fund's investm ents that can im pact fund investors. Financial statem ents are also im portant docum ents for investors to evaluate when considering a particular fund. Analysis of the fund's last financial statem ents can provide investors with valu­ able information about the m anager and the fund. A review of the financial statem ents should start with reading the opinion and confirming that it is, in fact, "unqualified." This basically means the independent auditor has reviewed the company's records and issued the statem ents without any material caveats

Also be sure to check registration and com pliance language with independent counsel specializing in the regulation of the strategy mix that the m anager trades. Investm ent advisors may or may not cover com m odities. Foreign advisors may not be exem pt from U.S. registration, even if you are investing through a feed er fund. The scope of exem ptions from registration is con­ stantly changing and should be current.

or concerns. An investor can exam ine the balance sheet and income state­ ment to see if it makes sense based on the fund's trading strat­ egy. Equity funds should look very different than global macro funds or fixed-incom e funds. An equity fund that purports to have a low level of leverage that has been declining year over year should not report a high level of interest expense that is

Docum ent review should include a com plete read of all the fund

rising year over year in its financial statem ents. A global macro

docum ents to ensure that the term s are reflective of the discus­

fund most likely has interest income earned in its income state­

sions the investor has had with the manager. Very often, term s

ment. Investors can quickly learn to expect certain patterns in

are om itted or not discussed in person, yet later are uncovered

the balance sheet and income statem ents of funds pursuing

at the last minute when docum ents are being reviewed or,

specific strategies. If a particular fund doesn't make sense, then

w orse yet, being com pleted. Redem ption right, liquidity, notice

questions need to be asked im m ediately. Leverage on the bal­

period for redem ptions, hard or soft lock-ups, early redem ption

ance sheet can be recalculated and com pared to the leverage

fees, the ability of the m anager to gate or generally suspend

expected by the strategy or represented by the manager. In

redem ptions, and the amount and timing of payouts following

addition, funds that have a long-term buy-and-hold strategy

redem ption (there may be a 5 to 10 percent holdback pending

should not be generating large amounts of realized gains or

annual audit) should all be confirm ed with the m anager verbally

losses each year; they should have sizable unrealized gains or

and reconciled to the fund docum ents, The same holds true for

losses instead.

m anagem ent and incentive fees subject to a high-water mark or hurdle rate and the expenses that a fund will bear related to start-up costs, m arket data, or other costs. Finally, subscription rights (timing of subscriptions, minimum subscription amounts, limits or com m itm ents on capacity) should be reviewed and agreed upon with the manager. O ther im portant considerations when reviewing fund docu­ ments include the pow ers of the m anager: Are they very broad or relatively narrow? A re there any restrictions related to the use of leverage or concentration in the docum ents? Can the m anager amend fund docum ents, such as the limited partner­ ship agreem ent? W hat are the key man event rights or notice

Any unusual line items that raise a red flag should be discussed with the m anager or even the auditor. Material items that are unique or different are usually explained in the footnotes. Reading the footnotes is critical, as it is often where the really im portant items get clarified, such as the use of derivatives or litigation. Investors can and should recalculate the fees paid by the fund to the m anager and make sure they make sense. Fees should be com pared to the pitch book and other fund docum ents such as the O M . There should never be incentive fees earned in years when the fund lost money.

to investors? Does the fund have indem nification provisions,

Finally, check the equity section to see if the general partner is

and to w hat extent does the fund itself indem nify the m anager

continuing to invest in the fund. W ithdraw als or reductions in

and any directors? Typical indem nifications should not extend

equity are a big red flag. Investors should thoroughly discuss

Chapter 10 Performing Due Diligence on Specific Managers and Funds

■

195

and understand the changes in the capital accounts of the gen­

A white paper written in 2011 by Merlin Securities, a prime

eral partner and any significant key people who run the fund.

broker that caters to hedge funds managing less than $1 bil­

Service Provider Evaluation

today with respect to the business of running a hedge fund. The

lion, captures many of the challenges that m anagers are facing

Investors should expect that a hedge fund will make all of the key contacts at their service providers available to them so they can verify the scope of any services being provided. Investors can also obtain internal control letters and audited financial statem ents from the fund's service providers to make sure there is an independent check on the service providers them selves. It is not uncommon for investors today to interview service provid­ ers and discuss the role they play in executing trades, providing technology, perform ing valuations or verification, and safe­ guarding assets.

executive summary reads: 2010 was a transform ative year for the hedge fund industry and served as a strong rem inder that m anag­ ing money is not the same as running a business. The significant num ber of sm all, mid-size, and large fund closures already in 2011 provides continuing evidence of the m aterial, m ultifaceted challenges facing operators of hedge fund businesses. M anagers who understand the distinction betw een managing money and running a business and who execute both effectively are best positioned to maintain a sustainable and prosperous business— to achieve not only investm ent alpha, but also

10.9 BUSINESS MODEL RISK

enterprise alpha. M anagers who take business model risk seriously and who are

This section of the text deals with the risks encom passed in

actively modifying their business to adapt will be successful.

sim ply running the business of being a hedge fund. It is an

Those who do not adapt will not be successful. Given the m as­

entrepreneurial activity that is now being held to institutional

sive changes in this industry over the past five years, it is virtu­

best practices as standards. It is a business that has risks that are sim ilar to many others. Will there be adequate cash on hand, where does the working capital come from , and is it organized properly? Is there a succession plan? W hat happens if too many investors redeem at the sam e tim e? These and many other questions are relatively new to hedge fund m anagers. During the early stages of the industry's growth, hedge fund m anag­ ers rarely had to face these sorts of issues. They benefited from relatively low barriers to entry, and much of the tim e there were even relatively low barriers to success. Capital was plentiful, leverage was available, m arkets were rising, rates were low, and spreads w ere narrowing! Today, there are much higher barriers to entry, and the barriers to success have gotten much higher. Not everyone succeeds. In fact, over the past several years, as many as or in some cases more funds have failed than have been launched. This rarely occurred in the past, if ever. The im plication to investors can be significant. A fund that fails needs to be liquidated, often in adverse conditions. Capital may be tied up; w orst case, there may be litigation and em barrassm ent or a loss of confidence in the investor's decisions. No investor wants to give money to a m anager who then closes suddenly, having run out of cash

ally im possible for a m anager to simply stand still and still be successful. Since 2008, understanding the cost base and the revenue and exp ense model of any fund has becom e critical to predicting w hether a fund will survive. M anagers need to spend a great deal of effort to design a sustainable business m odel that can survive under a w ide range of perform ance scenarios and that can support the ever-increasing dem ands of investors. Not all funds are able to do this w ell. In fact, many funds have decided to sim ply return capital or close rather than evolve to m eet the dem ands of the m arket and of their changing investor base. A manager's ability to control costs and predict revenues, while not easy, is essential for a firm to survive. Firms that overrely on variable incentive or perform ance fees have increased business risk unless there is a working capital facility in place. Firms with significant assets, where m anagem ent fees far exceed operating costs, have less business model risk. Larger firm s, however, may unfortunately have perform ance challenges, particularly if they have grown beyond the strategy's capacity or diluted perfor­ mance just to gain or gather assets.

to run the business. Many hedge fund m anagers are simply

According to the Merlin study, "There is still no one-size-fits-all

not prepared for this brave new w orld. They often have never

business model for hedge funds, but there are several common

needed to develop the business building, financial planning, and

factors and best practices that have developed to ensure the

strategic planning skills needed to launch a business, retain tal­

m anager is engaged in a sustainable business. A fund o perat­

ent, and grow a business over an extended period of tim e.

ing in the red zone is dependent on outsized perform ance to

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Financial Risk Manager Exam Part II: Risk Management and Investment Management

cover its expenses; a fund in the yellow zone requires minimal perform ance; and a green zone fund can sustain itself when High Fixed Expenses

its perform ance is lower than exp ected , nonexistent, or even, negative. Funds that structure their business model to operate in the green zone are better positioned to navigate through downturns and therefore

Medium Fixed Expenses

have higher survival rates over the long term ." Figure 10.1 highlights the basic revenue and expense scenarios for three types of

Low Fixed Expenses

hedge fund operating m odels analyzed in the Merlin report: red zone, yellow zone, and green zone. The Merlin study noted that it is the perform ance fee effect that makes the hedge fund model so powerful. Tradi­ tional asset m anagem ent m odels derive

Source: Wells Fargo Securities, "The Business of Running a Hedge Fund Best Practices for Get­ ting to the 'Green Zone,'" February 2011.

revenues almost exclusively based on assets, w hereas a hedge fund's revenues

30%

include perform ance incentives. Figure 10.2 m ent com pany with $3 million in operating costs

CD

under a range of perform ance and asset under

c ru

m anagem ent scenarios, som e positive and others negative, that was used in the study. Figure 10.3 sim ply shows the pow er of incentive or perfor­

r

25%

shows the profitability of a hypothetical m anage­ u

20 %

15% E o 10% CD

Q_

0%

mance fee growth relative to m anagem ent fees

WS4.5M

In addition to being aware of the firm's strategic

-15

come up regarding its business m odel, an investor can and should ask questions designed to uncover any additional business model risk. Investors can ask additional questions specifically designed to

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__________________________________

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Assets under Management (US$ Millions)

Fiqure 10.2

Merlin ADM/Performance MAP.

Source: Wells Fargo Securities, "The Business of Running a Hedge Fund: Best Practices for Getting to the 'Green Zone,"' February 2011.

evaluate a fund's business model risk throughout the entire due diligence process. Q uestions might include several of the following:

6 . Does the fund use any outsourced solutions? W hy or why not?

7. W hat is the m anagem ent com pany's break-even AU M ?

1. W hat is the firm's strategic vision?

2. Do you have a m ultiyear budget? Many do not! 3. How many months of cash flow do you have in the bank? 4. W hat steps can the fund take or is it taking to lower its cost base?

8 . W hat is the fund perform ance needed to break even at the existing AUM level?

9. W hat is the capacity of the existing staff to handle addi­ tional assets?

10. Does the fund have key man insurance and, if so, on

5. W hen was the last tim e the fund renegotiated its term s with its key service providers?

A U s 18.75M

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positioning, business plan, and other issues that

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