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CAD $114.00

Financial Risk Management: Models, History, and Institutions

Allan M. Malz

ISBN: 978-0-470-48180-6 September 2011 752 Pages

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Financial RISK Management

Models, History, and Institutions

"The need for sensible and realistic risk management becomes more obvious daily, and achieving it requires familiarity with both quantitative economic models and regulatory policy. Allan Malz's wide experience on Wall Street and at the Fed provides him with the perfect background for writing this important and uniquely comprehensive book."
—Emanuel Derman, Professor of Professional Practice, Columbia University's Industrial Engineering and Operations Research Department; author of My Life as a Quant: Reflections on Physics and Finance

"Finance is all about risk and reward. Investors are pretty good at measuring reward—at least after the fact—but many, including more than a few of the most 'sophisticated' are not very good at assessing risk before the fact, which is when of course it matters! There is a better way. Allan Malz provides the road map that investors need to understand the risks they take with the investment decisions they make. Malz has a unique perspective: as an academic, a central banker, and a risk manager—he has been there and done that. His book should be required reading for investors and practitioners alike."
—Richard Clarida, C. Lowell Harriss Professor of Economics, Columbia University

"It is almost cliché now to point out that the practice of risk management is as much art as it is science. For those new to the field, however, while there are excellent guides to the science and models of risk, there are none that connect the models to the markets, the economy, the banking system, and the history of all of these. Allan Malz's new book does this, providing a perspective that is critical to managing risk in the post-financial crisis world."
—Christopher Finger, Executive Director, MSCI Inc.

"Allan Malz has done a wonderful job of surveying the challenges that face those who labor in the vineyard of financial risk management. He brings a wealth of experience and insight to this work. The first chapter, which tackles the history of financial market innovation and risks, is a tour de force and may well be worth the price of the book itself."
—Galen Burghardt, Director of Research, Newedge USA; coauthor of Managed Futures for Institutional Investors: Analysis and Portfolio Construction

"This book provides a wealth of information on the theory and practice of risk management. In clearly written chapters, Malz progresses from simple asset pricing theory to complex derivatives including credit derivatives and CDO tranches. Institutional and historical description is rich and plentiful with a broad discussion of the financial crisis and new regulatory issues."
—Robert Engle, 2003 Nobel Laureate in Economics and Michael Armellino Professor of Finance, Stern School of Business, New York University

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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? 1

1.1.1 The Financial Industry Since the 1960s 2

1.1.2 The “Shadow Banking System” 9

1.1.3 Changes in Public Policy Toward the Financial System 15

1.1.4 The Rise of Large Capital Pools 17

1.1.5 Macroeconomic Developments Since the 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 Basics 43

2.1 Arithmetic, Geometric, and Logarithmic Security Returns 44

2.2 Risk and Securities Prices: The Standard Asset Pricing Model 49

2.2.1 Defining Risk: States, Security Payoffs, and 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

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 Bonds 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

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

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

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

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

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 Leverage and Forms of Credit in Contemporary Finance 448

12.3.1 Defining and Measuring Leverage 448

12.3.2 Margin Loans and Leverage 454

12.3.3 Short Positions 455

12.3.4 Derivatives 456

12.3.5 Structured Credit 460

12.3.6 Asset Volatility and Leverage 460

12.4 Transactions Liquidity Risk 461

12.4.1 Causes of Transactions Liquidity Risk 461

12.4.2 Characteristics of Market Liquidity 463

12.5 Liquidity Risk Measurement 464

12.5.1 Measuring Funding Liquidity Risk 464

12.5.2 Measuring Transactions Liquidity Risk 466

12.6 Liquidity and Systemic Risk 469

12.6.1 Funding Liquidity and Solvency 469

12.6.2 Funding and Market Liquidity 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 Long-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

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

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.1 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

Praise for Financial Risk Management

"The need for sensible and realistic risk management becomes more obvious daily, and achieving it requires familiarity with both quantitative economic models and regulatory policy. Allan Malz's wide experience on Wall Street and at the Fed provides him with the perfect background for writing this important and uniquely comprehensive book."
Emanuel Derman, Professor of Professional Practice, Columbia University's Industrial Engineering and Operations Research Department; author of My Life as a Quant: Reflections on Physics and Finance

"Finance is all about risk and reward. Investors are pretty good at measuring reward—at least after the fact—but many, including more than a few of the most 'sophisticated' are not very good at assessing risk before the fact, which is when of course it matters! There is a better way. Allan Malz provides the road map that investors need to understand the risks they take with the investment decisions they make. Malz has a unique perspective: as an academic, a central banker, and a risk manager—he has been there and done that. His book should be required reading for investors and practitioners alike."
Richard Clarida, C. Lowell Harriss Professor of Economics, Columbia University

"It is almost cliché now to point out that the practice of risk management is as much art as it is science. For those new to the field, however, while there are excellent guides to the science and models of risk, there are none that connect the models to the markets, the economy, the banking system, and the history of all of these. Allan Malz's new book does this, providing a perspective that is critical to managing risk in the post-financial crisis world."
Christopher Finger, Executive Director, MSCI Inc.

"Allan Malz has done a wonderful job of surveying the challenges that face those who labor in the vineyard of financial risk management. He brings a wealth of experience and insight to this work. The first chapter, which tackles the history of financial market innovation and risks, is a tour de force and may well be worth the price of the book itself."
Galen Burghardt, Director of Research, Newedge USA; coauthor of Managed Futures for Institutional Investors: Analysis and Portfolio Construction

"This book provides a wealth of information on the theory and practice of risk management. In clearly written chapters, Malz progresses from simple asset pricing theory to complex derivatives including credit derivatives and CDO tranches. Institutional and historical description is rich and plentiful with a broad discussion of the financial crisis and new regulatory issues."
Robert Engle, 2003 Nobel Laureate in Economics and Michael Armellino Professor of Finance, Stern School of Business, New York University

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