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ALLAN M. MALZ





















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Models, History, and Institutions


ALLAN M. MALZ



WILEY

John Wiley & Sons, Inc.











Copyright © 2011 by Allan M. Malz. All rights reserved.

Published by John Wiley 8t Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Malz, Allan M.

Financial risk management: models, history, and institution : models, history, and
institution / Allan M. Malz.

p. cm. - (Wiley finance series)

Includes bibliographical references and index.

ISBN 978-0-470-48180-6 (cloth); ISBN 978-1-118-02291-7 (ebk);

ISBN 978-1-118-02290-0 (ebk); ISBN 978-1-118-02289-4 (ebk)

1. Financial risk management. I. Title.

HD61.M256 2011

332-dc22 2010043485

Printed in the United States of America


10 987654321


To

Karin, Aviva, and Benjamin
with love



Contents


List of Figures

xvii

Preface

xxi

CHAPTER 1


Financial Risk in a Crisis-Prone World

1

1.1

Some History: Why Is Risk a Separate Discipline Today?

i


1.1.1 The Financial Industry Since the 1960s

2


1.1.2 The “Shadow Banking System”

1.1.3 Changes in Public Policy Toward the

9


Financial System

15


1.1.4 The Rise of Large Capital Pools

1.1.5 Macroeconomic Developments Since the

17


1960s: From the Unraveling of Bretton

Woods to the Great Moderation

20

1.2

The Scope of Financial Risk

34


1.2.1 Risk Management in Other Fields

34


Further Reading

41

CHAPTER 2


Market Risk Rasies

43

2.1

Arithmetic, Geometric, and Logarithmic Security Returns

44

2.2

Risk and Securities Prices: The Standard Asset



Pricing Model

2.2.1 Defining Risk: States, Security Payoffs, and

49


Preferences

50


2.2.2 Optimal Portfolio Selection

54


2.2.3 Equilibrium Asset Prices and Returns

56


2.2.4 Risk-Neutral Probabilities

61


VII


CONTENTS


viii


2.3 The Standard Asset Distribution Model 63

2.3.1 Random Walks and Wiener Processes 64

2.3.2 Geometric Brownian Motion 71

2.3.3 Asset Return Volatility 74

2.4 Portfolio Risk in the Standard Model 75

2.4.1 Beta and Market Risk 76

2.4.2 Diversification 82

2.4.3 Efficiency 85

2.5 Benchmark Interest Rates 88

Further Reading 91

CHAPTER 3

Value-at-Risk 93

3.1 Definition of Value-at-Risk 94

3.1.1 The User-Defined Parameters 97

3.1.2 Steps in Computing VaR 98

3.2 Volatility Estimation 99

3.2.1 Short-Term Conditional Volatility Estimation 99

3.2.2 The EWMA Model 104

3.2.3 The GARCH Model 106

3.3 Modes of Computation 108

3.3.1 Parametric 108

3.3.2 Monte Carlo Simulation 109

3.3.3 Historical Simulation 111

3.4 Short Positions 113

3.5 Expected Shortfall 114

Further Reading 116

CHAPTER 4

Nonlinear Risks and the Treatment of Ronds and Options 119

4.1 Nonlinear Risk Measurement and Options 121

4.1.1 Nonlinearity and VaR 123

4.1.2 Simulation for Nonlinear Exposures 126

4.1.3 Delta-Gamma for Options 127

4.1.4 The Delta-Gamma Approach for General

Exposures 134

4.2 Yield Curve Risk 136

4.2.1 The Term Structure of Interest Rates 138

4.2.2 Estimating Yield Curves 141

4.2.3 Coupon Bonds 144



Contents


IX


4.3 VaR for Default-Free Fixed Income Securities Using

The Duration and Convexity Mapping 148

4.3.1 Duration 149

4.3.2 Interest-Rate Volatility and Bond Price Volatility 150

4.3.3 Duration-Only VaR 152

4.3.4 Convexity 154

4.3.5 VaR Using Duration and Convexity 155

Further Reading 156

CHAPTER 5

Portfolio VaR for Market Risk 159

5.1 The Covariance and Correlation Matrices 160

5.2 Mapping and Treatment of Bonds and Options 162

5.3 Delta-Normal VaR 163

5.3.1 The Delta-Normal Approach for a Single

Position Exposed to a Single Risk Factor 164

5.3.2 The Delta-Normal Approach for a Single

Position Exposed to Several Risk Factors 166

5.3.3 The Delta-Normal Approach for a Portfolio

of Securities 168

5.4 Portfolio VAR via Monte Carlo simulation 174

5.5 Option Vega Risk 175

5.5.1 Vega Risk and the Black-Scholes Anomalies 176

5.5.2 The Option Implied Volatility Surface 180

5.5.3 Measuring Vega Risk 183

Further Reading 190

CHAPTER 6

Credit and Counterparty Risk 191

6.1 Defining Credit Risk 192

6.2 Credit-Risky Securities 193

6.2.1 The Economic Balance Sheet of the Firm 193

6.2.2 Capital Structure 194

6.2.3 Security, Collateral, and Priority 195

6.2.4 Credit Derivatives 196

6.3 Transaction Cost Problems in Credit Contracts 196

6.4 Default and Recovery: Analytic Concepts 199

6.4.1 Default 199

6.4.2 Probability of Default 200

6.4.3 Credit Exposure 201



X


CONTENTS


6.4.4 Loss Given Default 201

6.4.5 Expected Loss 202

6.4.6 Credit Risk and Market Risk 204

6.5 Assessing creditworthiness 204

6.5.1 Credit Ratings and Rating Migration 204

6.5.2 Internal Ratings 207

6.5.3 Credit Risk Models 207

6.6 Counterparty Risk 207

6.6.1 Netting and Clearinghouses 209

6.6.2 Measuring Counterparty Risk for Derivatives

Positions 209

6.6.3 Double Default Risk 211

6.6.4 Custodial Risk 211

6.6.5 Mitigation of Counterparty Risk 212

6.7 The Merton model 213

6.8 Credit Factor Models 222

6.9 Credit Risk Measures 226

6.9.1 Expected and Unexpected Loss 228

6.9.2 Jump-to-Default Risk 229

Further Reading 229

CHAPTER 7

Spread Risk and Default Intensity Models 231

7.1 Credit Spreads 231

7.1.1 Spread Mark-to-Market 233

7.2 Default Curve Analytics 235

7.2.1 The Hazard Rate 237

7.2.2 Default Time Distribution Function 239

7.2.3 Default Time Density Function 239

7.2.4 Conditional Default Probability 240

7.3 Risk-Neutral Estimates of Default Probabilities 241

7.3.1 Basic Analytics of Risk-Neutral Default Rates 242

7.3.2 Time Scaling of Default Probabilities 245

7.3.3 Credit Default Swaps 246

7.3.4 Building Default Probability Curves 250

7.3.5 The Slope of Default Probability Curves 259

7.4 Spread Risk 261

7.4.1 Mark-to-Market of a CDS 261

7.4.2 Spread Volatility 262

Further Reading 264



Contents


XI


CHAPTER 8

Portfolio Credit Risk 265

8.1 Default Correlation 266

8.1.1 Defining Default Correlation 266

8.1.2 The Order of Magnitude of Default Correlation 270

8.2 Credit Portfolio Risk Measurement 270

8.2.1 Granularity and Portfolio Credit Value-at-Risk 270

8.3 Default Distributions and Credit VaR with the

Single-Factor Model 275

8.3.1 Conditional Default Distributions 275

8.3.2 Asset and Default Correlation 279

8.3.3 Credit VaR Using the Single-Factor Model 281

8.4 Using Simulation and Copulas to Estimate Portfolio

Credit Risk 284

8.4.1 Simulating Single-Credit Risk 286

8.4.2 Simulating Joint Defaults with a Copula 288

Further Reading 295

CHAPTER 9

Structured Credit Risk 297

9.1 Structured Credit Basics 297

9.1.1 Capital Structure and Credit Losses in a

Securitization 301

9.1.2 Waterfall 305

9.1.3 Issuance Process 307

9.2 Credit Scenario Analysis of a Securitization 309

9.2.1 Tracking the Interim Cash Flows 309

9.2.2 Tracking the Final-Year Cash Flows 314

9.3 Measuring Structured Credit Risk via Simulation 318

9.3.1 The Simulation Procedure and the Role of

Correlation 318

9.3.2 Means of the Distributions 323

9.3.3 Distribution of Losses and Credit VaR 327

9.3.4 Default Sensitivities of the Tranches 333

9.3.5 Summary of Tranche Risks 336

9.4 Standard Tranches and Implied Credit Correlation 337

9.4.1 Credit Index Default Swaps and Standard

Tranches 338

9.4.2 Implied Correlation 340

9.4.3 Summary of Default Correlation Concepts 341



XII


CONTENTS


9.5 Issuer and Investor Motivations for Structured Credit 342

9.5.1 Incentives of Issuers 343

9.5.2 Incentives of Investors 345

Further Reading 346

CHAPTER 10

Alternatives to the Standard Market Risk Model 349

10.1 Real-World Asset Price Behavior 349

10.2 Alternative Modeling Approaches 363

10.2.1 Jump-Diffusion Models 363

10.2.2 Extreme Value Theory 365

10.3 The Evidence on Non-Normality in Derivatives Prices 372

10.3.1 Option-Based Risk-Neutral Distributions 372

10.3.2 Risk-Neutral Asset Price Probability

Distributions 380

10.3.3 Implied Correlations 387

Further Reading 390

CHAPTER 11

Assessing the Quality of Risk Measures 393

11.1 Model Risk 393

11.1.1 Valuation Risk 395

11.1.2 Variability of VaR Estimates 395

11.1.3 Mapping Issues 397

11.1.4 Case Study: The 2005 Credit Correlation

Episode 399

11.1.5 Case Study: Subprime Default Models 405

11.2 Backtesting of VaR 407

11.3 Coherence of VaR Estimates 414

Further Reading 419

CHAPTER 12

Liquidity and Leverage 421

12.1 Funding Liquidity Risk 422

12.1.1 Maturity Transformation 422

12.1.2 Liquidity Transformation 423

12.1.3 Bank Liquidity 425

12.1.4 Structured Credit and Off-Balance-Sheet

Funding 429

12.1.5 Funding Liquidity of Other Intermediaries 432

12.1.6 Systematic Funding Liquidity Risk 434



Contents


xiii


12.2 Markets for Collateral 437

12.2.1 Structure of Markets for Collateral 438

12.2.2 Economic Function of Markets for Collateral 441

12.2.3 Prime Brokerage and Hedge Funds 443

12.2.4 Risks in Markets for Collateral 445

12.3 Beverage and Forms of Credit in Contemporary Finance 448

12.3.1 Defining and Measuring Beverage 448

12.3.2 Margin Foans and Beverage 454

12.3.3 Short Positions 455

12.3.4 Derivatives 456

12.3.5 Structured Credit 460

12.3.6 Asset Volatility and Beverage 460

12.4 Transactions Fiquidity Risk 461

12.4.1 Causes of Transactions Fiquidity Risk 461

12.4.2 Characteristics of Market Fiquidity 463

12.5 Fiquidity Risk Measurement 464

12.5.1 Measuring Funding Fiquidity Risk 464

12.5.2 Measuring Transactions Fiquidity Risk 466

12.6 Fiquidity and Systemic Risk 469

12.6.1 Funding Fiquidity and Solvency 469

12.6.2 Funding and Market Fiquidity 471

12.6.3 Systemic Risk and the “Plumbing” 471

12.6.4 “Interconnectedness” 473

Further Reading 474

CHAPTER 13

Risk Control and Mitigation 477

13.1 Defining Risk Capital 478

13.2 Risk Contributions 480

13.2.1 Risk Contributions in a Fong-Only Portfolio 481

13.2.2 Risk Contributions Using Delta Equivalents 485

13.2.3 Risk Capital Measurement for

Quantitative Strategies 490

13.3 Stress Testing 499

13.3.1 An Example of Stress Testing 501

13.3.2 Types of Stress Tests 504

13.4 Sizing Positions 506

13.4.1 Diversification 506

13.4.2 Optimization and Implied Views 507

13.5 Risk Reporting 509

13.6 Hedging and Basis Risk 512

Further Reading 516



XIV


CONTENTS


CHAPTER 14

Financial Crises 517

14.1 Panics, Runs, and Crashes 519

14.1.1 Monetary and Credit Contraction 519

14.1.2 Panics 528

14.1.3 Rising Insolvencies 535

14.1.4 Impairment of Market Functioning 537

14.2 Self-Reinforcing Mechanisms 539

14.2.1 Net Worth and Asset Price Declines 540

14.2.2 Collateral Devaluation 542

14.2.3 Risk Triggers 543

14.2.4 Accounting Triggers 547

14.3 Behavior of Asset Prices During Crises 548

14.3.1 Credit Spreads 549

14.3.2 Extreme Volatility 551

14.3.3 Correlations 556

14.4 Causes of Financial Crises 562

14.4.1 Debt, International Payments, and Crises 563

14.4.2 Interest Rates and Credit Expansion 570

14.4.3 Procyclicality: Financial Causes of Crises 575

14.4.4 Models of Bubbles and Crashes 578

14.5 Anticipating Financial Crises 583

14.5.1 Identifying Financial Fragility 583

14.5.2 Macroeconomic Predictors of Financial

Crises 585

14.5.3 Asset-Price Predictors of Financial

Crises 585

Further Reading 591

CHAPTER 15

Financial Regulation 597

15.1 Scope and Structure of Regulation 598

15.1.1 The Rationale of Regulation 598

15.1.2 Regulatory Authorities 601

15.2 Methods of Regulation 605

15.2.1 Deposit Insurance 606

15.2.2 Capital Standards 608

15.2.3 Bank Examinations and Resolution 619

15.3 Public Policy Toward Financial Crises 621

15.3.1 Financial Stability Policies 621

15.3.2 Lender of Last Resort 628



Contents


XV


15.4 Pitfalls in Regulation 635

15.4.1 Moral Hazard and Risk Shifting 636

15.4.2 Regulatory Evasion 643

15.4.3 Unintended Consequences 645

Further Reading 647

APPENDIX A

Technical Notes 653

A.l Binomial Distribution 653

A.2 Quantiles and Quantile Transformations 654

A.3 Normal and Lognormal Distributions 656

A.3.1 Relationship between Asset Price Levels

and Returns 656

A.3.2 The Black-Scholes Distribution Function 657

A.4 Hypothesis Testing 661

A.5 Monte Carlo Simulation 662

A.5.1 Fooled by Nonrandomness: Random

Variable Generation 663

A.5.2 Generating Nonuniform Random Variates 664

A.6 Homogeneous Functions 664

Further Reading 666

APPENDIX B

Abbreviations 667

APPENDIX C

References 671

Index 701




List of Figures


1.1 Disintermediation in the U.S. Financial System 1980-2010 4

1.2 Share of Financial Services Industry in U.S. Output 5

1.3 OTC Derivatives Markets 1998-2010 9

1.4 Intermediation by Sector 1959-2008 12

1.5 Traditional and Innovative Intermediation 1951-2010 13

1.6 Securitization of Commercial Real Estate Lending 1960-2010 14

1.7 Hedge Fund Assets under Management 18

1.8 Growth of World Income 1950-2006 21

1.9 Growth of World International Trade 1971-2009 22

1.10 U.S. Labor Productivity 1947-2010 23

1.11 U.S. Inflation 1958-2010 24

1.12 U.S. Current Account Balance 1960-2010 25

1.13 Growth of International Monetary Reserves 26

1.14 Real Fed Funds Rate 1971-2009 27

1.15 U.S. Growth Rate and Its Volatility 1947-2009 28

1.16 U.S. Savings Rate 1946-2010 29

1.17 Corporate Leverage in the United States 29

2.1 Approximating Logarithmic by Arithmetic Returns 48

2.2 Sample Path of a Random Walk 66

2.3 Convergence of a Random Walk to a Brownian Motion 67

2.4 Convergence of a Random Walk to a Brownian Motion 69

2.5 Geometric Brownian Motion: Asset Price Level 73

2.6 Geometric Brownian Motion: Daily Returns 74

2.7 Joint Distribution of EUR and JPY Returns 78

2.8 Correlation and Beta 79

2.9 Volatility and Beta 80

2.10 Diversification, Volatility, and Correlation 84

2.11 Minimum-Variance and Efficient Portfolios 87

3.1 Definition of VaR 96

3.2 The EWMA Weighting Scheme 105

3.3 Comparison of Volatility Estimators 107

3.4 Comparison of Simulation Approaches 112

4.1 Monotonicity and Option Risk Measurement 124


xvii


XViii LIST OF FIGURES


4.2 Delta-Gamma and VaR for an Unhedged Long Call 130

4.3 Delta-Gamma and VaR for a Hedged Call 132

4.4 Option Combinations 133

4.5 Delta-Gamma and Full-Repricing VaR for a Risk Reversal 135

4.6 Spot, Forward, and Discount Curves 145

4.7 Bond Price and Yield Volatility 152

4.8 Approximating the Bond Price-Yield Relationship 155

5.1 Time Variation of Implied Volatility 176

5.2 Option Vega 178

5.3 S&P 500 Implied Volatility Smile 181

5.4 EUR-USD Volatility Surface 182

5.5 Impact of Vega Risk 184

5.6 Euro Foreign Exchange Implied Volatilities 186

5.7 Vega and the Smile 188

5.8 Euro Implied Volatilities, Risk Reversals, and Strangle Prices 189

6.1 Default Rates 1920-2010 206

6.2 Merton Model 220

6.3 Asset and Market Index Returns in the Single-Factor Model 225

6.4 Distribution of Bond Value in the Merton Model 227

6.5 Credit VaR in the Merton Model 228

7.1 Computing SpreadOl for a Fixed-Rate Bond 234

7.2 SpreadOl a Declining Function of Spread Level 235

7.3 Intensity Model of Default Timing 238

7.4 CDS Curves 247

7.5 Estimation of Default Curves 258

7.6 Spread Curve Slope and Default Distribution 260

7.7 Morgan Stanley CDS Curves, select dates 261

7.8 Measuring Spread Volatility: Citigroup Spreads 2006-2010 263

8.1 Distribution of Defaults in an Uncorrelated Credit Portfolio 272

8.2 Distribution of Losses in an Uncorrelated Credit Portfolio 274

8.3 Default Probabilities in the Single-Factor Model 277

8.4 Single-Factor Default Probability Distribution 279

8.5 Conditional Default Density Function in the

Single-Factor Model 280

8.6 Distribution of Losses in the Single-Factor Model 285

8.7 Density Function of Portfolio Losses in the

Single-Factor Model 286

8.8 Estimated Single-Credit Default Risk by Simulation 287

8.9 Shifting from Uniform to Normal Distribution Simulations 288

8.10 Distribution of Losses in the Single-Factor Model 292

8.11 Simulating Multiple Defaults 294

9.1 Values of CLO Tranches 326



List of Figures


XIX


9.2 Distribution of Simulated Equity Tranche Values 328

9.3 Distribution of Simulated Mezzanine Bond Tranche Losses 328

9.4 Distribution of Simulated Senior Bond Tranche Losses 329

9.5 Default Sensitivities of CLO Tranches 335

10.1 Normal and Non-Normal Distributions 351

10.2 S&P 500 Daily Returns 1928-2011 353

10.3 Statistical Properties of Exchange Rates 356

10.4 Kernel Estimate of the Distribution of VIX Returns 360

10.5 QQ Plot of USD Exchange Rates against the

Euro and Turkish Lira 362

10.6 Jump-Diffusion Process: Asset Price Level 364

10.7 Jump-Diffusion: Daily Returns 365

10.8 Elan Corporation Stock Price 366

10.9 QQ Plot of the S&P 500 367

10.10 Constructing a Long Butterfly 378

10.11 State Prices and the Risk Neutral Density 379

10.12 Fitted Implied Volatility Smile 384

10.13 Estimated Risk-Neutral Density 385

10.14 Risk-Neutral Implied Equity Correlation 389

11.1 Convexity of CLO Liabilities 401

11.2 Correlation Risk of the Convexity Trade 404

11.3 Implied Correlation in the 2005 Credit Episode 405

11.4 ABX Index of RMBS Prices 407

11.5 Chi-Square Distribution 410

11.6 Backtest of a Normal Distribution 411

11.7 Likelihood-Ratio Test 412

11.8 Elistorical Backtesting 413

11.9 Failure of Subadditivity 417

12.1 Short-Term Commercial Paper of Financial Institutions 430

12.2 Convertible Bond Cheapness 437

12.3 U.S. Broker-Dealer Repo 1980-2010 444

12.4 Repo Rates and Spreads 2006-2009 447

13.1 Risk Contributions in a Long-Only Strategy 486

13.2 Allocation, Volatility, and Constant Risk Contribution 487

13.3 Simulated Fledge Fund Strategy Returns 494

13.4 Citigroup CDS Basis 2007-2010 514

14.1 Net Borrowing in U.S. Credit Markets 1946-2010 520

14.2 Growth in U.S. Bank Credit 1947-2011 521

14.3 Tightening of Credit Terms 1990-2011 523

14.4 U.S. Bank Lending during the Subprime Crisis 2006-2011 524

14.5 Outstanding Volume of Commercial Paper 2001-2011 527

14.6 U.S. Bond Issuance 1996-2010 527



XX


LIST OF FIGURES


14.7 Institutional Investor Assets in MMMFs 2008-2010 529

14.8 Citigroup Credit Spreads during the Subprime Crisis 532

14.9 Three-Month TED Spread 1985-2011 533

14.10 Libor-OIS Spread 2006-2011 534

14.11 U.S. Dollar Overnight Rates 2006-2011 535

14.12 U.S. Commercial Bank Charge-Off and Delinquency

Rates 1985-2010 536

14.13 Settlement Fails in the Treasury Market 1990-2010 538

14.14 U.S. Credit Spreads 1997-2014 549

14.15 U.S. Dollar Swap Spreads 1988-2011 551

14.16 S&P 500 Prices 1927-2011 552

14.17 U.S. Equity Implied Volatility 1990-2011 554

14.18 Equity Volatility Dispersion 554

14.19 Proxy Fledging and the ERM Crisis 1992-1993 557

14.20 On- vs. Off-the-Run Rate Correlation 558

14.21 Changing Equity Betas during the Subprime Crisis 559

14.22 Implied Credit Correlation 2004-2010 561

14.23 Gold and the U.S. Dollar at the End of Bretton Woods 568

14.24 Sterling in the European Monetary System 569

14.25 U.S. Leverage 1947-2010 583

14.26 Behavior of Implied and Historical Volatility in Crises 589

15.1 U.S. House Prices and Homeownership 1987-2011 623

15.2 Citigroup Credit Spreads during the Subprime Crisis 641

A.l Convergence of Binomial to Normal Distribution 654

A.2 The Black-Scholes Probability Density Function 660

A.3 Transforming Uniform into Normal Variates 665



Preface


F inancial Risk Management started as one thing and has ended as another. I
took up this project with the primary aim of making risk measurement and
management techniques accessible, by working through simple examples,
and explaining some of the real-life detail of financing positions. I had
gotten fairly far along with it when the subprime crisis began and the world
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