Business Snapshots xvii

Preface xix

CHAPTER 1 Introduction 1

1.1 Risk vs. Return for Investors 2

1.2 The Efficient Frontier 5

1.3 The Capital Asset Pricing Model 8

1.4 Arbitrage Pricing Theory 13

1.5 Risk vs. Return for Companies 13

1.6 Risk Management by Financial Institutions 16

1.7 Credit Ratings 18

Summary 18

Further Reading 19

Practice Questions and Problems 19

Further Questions 20

CHAPTER 2 Banks 21

2.1 Commercial Banking 22

2.2 The Capital Requirements of a Small Commercial Bank 24

2.3 Deposit Insurance 26

2.4 Investment Banking 27

2.5 Securities Trading 32

2.6 Potential Conflicts of Interest in Banking 33

2.7 Today’s Large Banks 34

2.8 The Risks Facing Banks 37

Summary 38

Further Reading 38

Practice Questions and Problems 38

Further Questions 39

CHAPTER 3 Insurance Companies and Pension Plans 41

3.1 Life Insurance 41

3.2 Annuity Contracts 45

3.3 Mortality Tables 46

3.4 Longevity and Mortality Risk 50

3.5 Property-Casualty Insurance 51

3.6 Health Insurance 53

3.7 Moral Hazard and Adverse Selection 55

3.8 Reinsurance 56

3.9 Capital Requirements 56

3.10 The Risks Facing Insurance Companies 58

3.11 Regulation 58

3.12 Pension Plans 59

Summary 62

Further Reading 64

Practice Questions and Problems 64

Further Questions 65

CHAPTER 4 Mutual Funds and Hedge Funds 67

4.1 Mutual Funds 67

4.2 Hedge Funds 74

4.3 Hedge Fund Strategies 79

4.4 Hedge Fund Performance 83

Summary 84

Further Reading 85

Practice Questions and Problems 85

Further Questions 86

CHAPTER 5 Trading in Financial Markets 89

5.1 The Markets 89

5.2 Long and Short Positions in Assets 90

5.3 Derivatives Markets 92

5.4 Plain Vanilla Derivatives 93

5.5 Clearing Houses 103

5.6 Margin 104

5.7 Non-Traditional Derivatives 107

5.8 Exotic Options and Structured Products 111

5.9 Risk Management Challenges 114

Summary 115

Further Reading 115

Practice Questions and Problems 116

Further Questions 118

CHAPTER 6 The Credit Crisis of 2007 121

6.1 The U.S. Housing Market 121

6.2 Securitization 124

6.3 The Crisis 131

6.4 What Went Wrong? 131

6.5 Lessons from the Crisis 133

Summary 134

Further Reading 135

Practice Questions and Problems 136

Further Questions 136

CHAPTER 7 How Traders Manage Their Risks 137

7.1 Delta 137

7.2 Gamma 144

7.3 Vega 146

7.4 Theta 148

7.5 Rho 149

7.6 Calculating Greek Letters 150

7.7 Taylor Series Expansions 151

7.8 The Realities of Hedging 152

7.9 Hedging Exotic Options 153

7.10 Scenario Analysis 154

Summary 156

Further Reading 156

Practice Questions and Problems 156

Further Questions 157

CHAPTER 8 Interest Rate Risk 159

8.1 The Management of Net Interest Income 159

8.2 LIBOR and Swap Rates 162

8.3 Duration 164

8.4 Convexity 168

8.5 Generalization 169

8.6 Nonparallel Yield Curve Shifts 172

8.7 Interest Rate Deltas in Practice 174

8.8 Principal Components Analysis 176

8.9 Gamma and Vega 179

Summary 179

Further Reading 180

Practice Questions and Problems 181

Further Questions 181

CHAPTER 9 Value at Risk 183

9.1 Definition of VaR 183

9.2 Examples of the Calculation of VaR 185

9.3 VaR vs. Expected Shortfall 186

9.4 VaR and Capital 188

9.5 Coherent Risk Measures 190

9.6 Choice of Parameters for VaR 191

9.7 Marginal VaR, Incremental VaR, and Component VaR 195

9.8 Euler’s Theorem 196

9.9 Aggregating VaRs 197

9.10 Back-Testing 197

Summary 200

Further Reading 201

Practice Questions and Problems 201

Further Questions 202

CHAPTER 10 Volatility 205

10.1 Definition of Volatility 205

10.2 Implied Volatilities 208

10.3 Are Daily Percentage Changes in Financial

Variables Normal? 209

10.4 The Power Law 211

10.5 Monitoring Daily Volatility 213

10.6 The Exponentially Weighted Moving Average Model 216

10.7 The GARCH(1,1) Model 218

10.8 Choosing Between the Models 220

10.9 Maximum Likelihood Methods 220

10.10 Using GARCH(1,1) to Forecast Future Volatility 225

Summary 229

Further Reading 229

Practice Questions and Problems 230

Further Questions 231

CHAPTER 11 Correlations and Copulas 233

11.1 Definition of Correlation 233

11.2 Monitoring Correlation 235

11.3 Multivariate Normal Distributions 238

11.4 Copulas 240

11.5 Application to Loan Portfolios: Vasicek’s Model 246

Summary 252

Further Reading 253

Practice Questions and Problems 253

Further Questions 254

CHAPTER 12 Basel I, Basel II, and Solvency II 257

12.1 The Reasons for Regulating Banks 257

12.2 Bank Regulation Pre-1988 258

12.3 The 1988 BIS Accord 259

12.4 The G-30 Policy Recommendations 262

12.5 Netting 263

12.6 The 1996 Amendment 265

12.7 Basel II 268

12.8 Credit Risk Capital Under Basel II 269

12.9 Operational Risk Capital Under Basel II 277

12.10 Pillar 2: Supervisory Review 278

12.11 Pillar 3: Market Discipline 278

12.12 Solvency II 279

Summary 280

Further Reading 281

Practice Questions and Problems 281

Further Questions 283

CHAPTER 13 Basel 2.5, Basel III, and Dodd–Frank 285

13.1 Basel 2.5 285

13.2 Basel III 289

13.3 Contingent Convertible Bonds 295

13.4 Dodd–Frank Act 296

13.5 Legislation in Other Countries 298

Summary 299

Further Reading 300

Practice Questions and Problems 300

Further Questions 301

CHAPTER 14 Market Risk VaR: The Historical Simulation Approach 303

14.1 The Methodology 303

14.2 Accuracy 308

14.3 Extensions 309

14.4 Computational Issues 313

14.5 Extreme Value Theory 314

14.6 Applications of EVT 317

Summary 319

Further Reading 320

Practice Questions and Problems 320

Further Questions 321

CHAPTER 15 Market Risk VaR: The Model-Building Approach 323

15.1 The Basic Methodology 323

15.2 Generalization 326

15.3 Correlation and Covariance Matrices 327

15.4 Handling Interest Rates 330

15.5 Applications of the Linear Model 334

15.6 Linear Model and Options 335

15.7 Quadratic Model 338

15.8 Monte Carlo Simulation 340

15.9 Non-Normal Assumptions 341

15.10 Model-Building vs. Historical Simulation 342

Summary 343

Further Reading 343

Practice Questions and Problems 343

Further Questions 345

CHAPTER 16 Credit Risk: Estimating Default Probabilities 347

16.1 Credit Ratings 347

16.2 Historical Default Probabilities 349

16.3 Recovery Rates 351

16.4 Credit Default Swaps 352

16.5 Credit Spreads 357

16.6 Estimating Default Probabilities from Credit Spreads 360

16.7 Comparison of Default Probability Estimates 362

16.8 Using Equity Prices to Estimate Default Probabilities 367

Summary 370

Further Reading 371

Practice Questions and Problems 371

Further Questions 373

CHAPTER 17 Counterparty Credit Risk in Derivatives 375

17.1 Credit Exposure on Derivatives 375

17.2 Bilateral Clearing 376

17.3 Central Clearing 380

17.4 CVA 382

17.5 The Impact of a New Transaction 385

17.6 CVA Risk 387

17.7 Wrong Way Risk 388

17.8 DVA 389

17.9 Some Simple Examples 389

Summary 394

Further Reading 395

Practice Questions and Problems 395

Further Questions 396

CHAPTER 18 Credit Value at Risk 399

18.1 Ratings Transition Matrices 400

18.2 Vasicek’s Model 402

18.3 Credit Risk Plus 403

18.4 CreditMetrics 405

18.5 Credit VaR in the Trading Book 406

Summary 410

Further Reading 410

Practice Questions and Problems 411

Further Questions 411

CHAPTER 19 Scenario Analysis and Stress Testing 413

19.1 Generating the Scenarios 413

19.2 Regulation 419

19.3 What to Do with the Results 423

Summary 426

Further Reading 426

Practice Questions and Problems 427

Further Questions 428

CHAPTER 20 Operational Risk 429

20.1 What is Operational Risk? 430

20.2 Determination of Regulatory Capital 431

20.3 Categorization of Operational Risks 433

20.4 Loss Severity and Loss Frequency 434

20.5 Implementation of AMA 435

20.6 Proactive Approaches 439

20.7 Allocation of Operational Risk Capital 440

20.8 Use of Power Law 441

20.9 Insurance 442

20.10 Sarbanes-Oxley 443

Summary 444

Further Reading 445

Practice Questions and Problems 445

Further Questions 446

CHAPTER 21 Liquidity Risk 447

21.1 Liquidity Trading Risk 447

21.2 Liquidity Funding Risk 454

21.3 Liquidity Black Holes 462

Summary 468

Further Reading 469

Practice Questions and Problems 470

Further Questions 470

CHAPTER 22 Model Risk 473

22.1 Marking to Market 473

22.2 Models for Linear Products 475

22.3 Physics vs. Finance 476

22.4 How Models are Used for Pricing Standard Products 478

22.5 Hedging 484

22.6 Models for Nonstandard Products 485

22.7 Dangers in Model Building 486

22.8 Detecting Model Problems 487

Summary 488

Further Reading 488

Practice Questions and Problems 489

Further Questions 489

CHAPTER 23 Economic Capital and RAROC 491

23.1 Definition of Economic Capital 491

23.2 Components of Economic Capital 493

23.3 Shapes of the Loss Distributions 495

23.4 Relative Importance of Risks 497

23.5 Aggregating Economic Capital 498

23.6 Allocation of Economic Capital 501

23.7 Deutsche Bank’s Economic Capital 503

23.8 RAROC 503

Summary 505

Further Reading 506

Practice Questions and Problems 506

Further Questions 507

CHAPTER 24 Risk Management Mistakes to Avoid 509

24.1 Risk Limits 509

24.2 Managing the Trading Room 512

24.3 Liquidity Risk 514

24.4 Lessons for Nonfinancial Corporations 517

24.5 A Final Point 518

Further Reading 519

Appendix A Compounding Frequencies for Interest Rates 521

Appendix B Zero Rates, Forward Rates, and Zero-Coupon Yield Curves 525

Appendix C Valuing Forward and Futures Contracts 529

Appendix D Valuing Swaps 531

Appendix E Valuing European Options 533

Appendix F Valuing American Options 535

Appendix G Taylor Series Expansions 539

Appendix H Eigenvectors and Eigenvalues 543

Appendix I Principal Components Analysis 547

Appendix J Manipulation of Credit Transition Matrices 549

Appendix K Valuation of Credit Default Swaps 551

Appendix L Synthetic CDOs and Their Valuation 555

Answers to Questions and Problems 559

Glossary 595

DerivaGem Software 615

Table for N(x) when x ≤ 0 621

Table for N(x) when x ≥ 0 623

Index 625