Handbook of Asset and Liability Management (eBook)

Front cover 1
Title page 4
Copyright page 5
Introduction to the Series 6
Contents of the Handbook 8
Preface 10
Contents 14
Chapter 1. Enterprise-Wide Asset and Liability Management: Issues, Institutions, and Models 22
Abstract 23
1. Introduction 24
1.1. What is enterprise risk management 25
1.2. Example: Enterprise-wide view of credit risks in a bank 26
2. A conceptual framework for enterprise risk management 27
2.1. The management of a single line of business 28
2.2. The management of a business portfolio 30
2.3. Integrating design, pricing, funding, and capitalization 30
2.4. Components of enterprise risk management 31
2.5. Why is enterprise risk management important 36
3. Asset and liability management in enterprise risk management 38
3.1. Components of asset and liability management 38
4. Models for asset and liability management 40
References 42
Chapter 2. Term and Volatility Structures 46
Abstract 47
Keywords 47
1. Term structure 48
1.1. An example 48
1.2. BootStrapping 51
1.3. Nelson-Siegel and Svensson's extension 55
1.4. Maximum smoothness 57
1.5. Forward-rates via geometric programming 58
1.6 EpiCurves 59
1.7 A comparison for U.S. Treasury curves 72
2. Volatility structure 78
2.1. Setting the stage 78
2.2. Some tree-based valuation models 81
2.3. The EpiVolatility model 82
2.4. Implementation 83
2.5. Summary 86
References 88
Chapter 3. Protecting Investors Against Changes in Interest Rates 90
1. Basic concepts for valuation and immunization of bond portfolios in continuous time 94
1.1. The instantaneous forward rate 94
1.2. The continuously compounded spot rate 96
1.3. Introducing the missing link: The continuously compounded total return 98
1.4. Relationships between the total return, the forward rate and the spot rate 101
1.5. Theorems on the behavior of the forward rate and the total return 102
1.6. The spot rate curve as a spline and its corresponding forward rate curve 105
2. Immunization: A first approach 111
2.1. The continuously compounded horizon rate of return 112
2.2. A geometrical representation of the horizon rate of return 112
2.3. Existence and characteristics of an immunizing horizon 114
2.4. The Macaulay concept of duration, its properties and uses 115
2.5. A second-order condition 120
2.6. The immunization problem 121
3. Protecting investors against any shift in the interest rate structure-A general immunization theorem 123
3.1. Notation 123
3.2. Present values at time 0 125
3.3. Future values at time 0 126
3.4. Present values at time epsilon 126
3.5. Future values at time epsilon 127
3.6. Further concepts for immunization: the moments of order k of a bond and a bond portfolio 127
3.7. A general immunization theorem 130
3.8. The nature of the cash flows of an immunizing portfolio 139
4. Applications 139
4.1. The spot structures and their shifts 140
4.2. Building immunizing portfolios 143
4.3. Immunization results 145
4.4. How large should we set the immunization parameter K? 147
4.5. Infinity of solutions 149
4.6. How sensitive are immunizing portfolios to changes in horizon H? 151
4.7. How sensitive are immunizing portfolios to a change in the basket of available bonds? 152
5. Conclusion and suggestions 154
6. Notes to references 158
References 158
Chapter 4. Risk-Return Analysis 160
Abstract 161
Keywords 162
1. Introduction 163
2. The ``general'' mean-variance model 165
3. Applications of the general model 167
3.1. Asset liability modeling 167
3.2. Factor models 168
3.3. Other constraints 169
3.4. Tracking error 169
4. Examples of mean-variance efficient sets 170
4.1. Critical lines and corner portfolios 170
4.2. Efficient EV and Esigma combinations 171
4.3. All feasible Esigma combinations 173
4.4. Possible features 174
5. Solution to the ``general'' mean-variance problem 177
5.1. Preliminaries 177
5.2. The critical line algorithm 177
5.3. Getting started 179
5.4. The critical line algorithm with upper bounds 182
5.5. The critical line algorithm with factor and scenario models of covariance 183
5.6. Notes on computing 186
6. Separation theorems 187
6.1. The Tobin-Sharpe separation theorems 187
6.2. Two-funds separation 190
6.3. Separation theorems not true in general 190
6.4. The Elton, Gruber, Padberg algorithm 191
6.5. An alternate EGP-like algorithm 192
7. Alternate risk measures 194
7.1. Semideviation 194
7.2. Mean absolute deviation (MAD) 196
7.3. Probability of loss and value at risk (Gaussian Rp) 197
7.4. Probability of loss and Value at Risk (non-Gaussian Rp) 199
7.5. Conditional value at risk (CVaR) 201
8. Choice of criteria 201
8.1. Exact conditions 201
8.2. Mean-variance approximations to expected utility 202
8.3. Significance of MV approximations to EU 205
9. Risk-return analysis in practice 205
9.1. Choice of criteria 206
9.2. Tracking error or total variability 207
9.3. Estimates for asset classes 208
9.4. Estimation of expected returns for individual equities 208
9.5. Black-Litterman 209
9.6. Security analyst recommendations 210
9.7. Estimates of covariance 210
9.8. Parameter uncertainty 211
10. Epilogue 213
References 214
Chapter 5. Dynamic Asset Allocation Strategies Using a Stochastic Dynamic Programming Approach 220
Abstract 221
Keywords 221
1. Introduction 222
2. Approaches for dynamic asset allocation 225
2.1. Multi-stage stochastic programming 225
2.2. Stochastic dynamic programming 227
3. Single-period portfolio choice 228
4. Utility functions 230
5. A general approach to modeling utility 232
6. Dynamic portfolio choice 235
6.1. Dynamic stochastic programming and Monte Carlo sampling 236
6.2. Serially dependent asset returns 237
6.3. A fast method for normally distributed asset returns 238
7. Numerical results 238
7.1. Data assumptions 238
7.2. An investment example 243
7.3. The performance of dynamic strategies 255
7.4. Dynamic strategies for hedging downside risk 259
7.5. Downside risk protection at every period 262
7.6. Computation times 267
8. Comparison to multi-stage stochastic programming 268
Acknowledgements 269
References 269
Chapter 6. Stochastic Programming Models for Asset Liability Management 274
Abstract 275
1. Introduction 276
2. Stochastic programming 277
2.1. Basic concepts in stochastic programming 277
2.2. Stochastic programming model for portfolio management 282
3. Scenario generation and tree construction 288
3.1. Scenarios for the liabilities 288
3.2. Scenarios for economic factors and asset returns 291
3.3. Methods for generating scenarios 293
3.4. Constructing event trees 298
3.5. Options, bonds and arbitrage 304
4. Comparison of stochastic programming with other methods 308
4.1. Mean-variance models and downside risk 308
4.2. Discrete-time multi-period models 309
4.3. Continuous-time models 311
4.4. Stochastic programming 312
5. Applications of stochastic programming to ALM 312
6. Solution methods and computations 317
7. Summary and open issues 318
References 320
Chapter 7. Bond Portfolio Management via Stochastic Programming 326
Abstract 327
1. Introduction 328
2. The bond portfolio management model 332
3. Input data 336
4. Scenario reduction and scenario tree construction 341
5. Numerical results 342
6. Stress testing via contamination: Add worst-case scenarios 346
7. Conclusions 355
Acknowledgements 356
References 356
Chapter 8. Perturbation Methods for Dynamic Portfolio Allocation Problems 358
Abstract 359
1. Introduction 360
2. General problem formulation 361
2.1. Investment opportunity set 362
2.2. Utility function 365
3. Exact solution for unit elasticity of intertemporal substitution 366
3.1. General results 366
3.2. Example 1: Time-varying expected returns (finite horizon) 370
3.3. Example 2: Time-varying expected returns (infinite horizon) 373
4. Approximate solution for general elasticity of intertemporal substitution 374
4.1. Perturbation around unit elasticity of substitution 374
4.2. Perturbation around mean of consumption/wealth ratio 381
5. Example 387
5.1. Time-varying volatility 388
5.2. Time-varying interest rates 399
6. Conclusions 403
References 404
Chapter 9. The Kelly Criterion in Blackjack Sports Betting, and the Stock Market 406
Abstract 407
Keywords 407
1. Introduction 408
2. Coin tossing 409
3. Optimal growth: Kelly criterion formulas for practitioners 413
3.1. The probability of reaching a fixed goal on or before n trials 413
3.2. The probability of ever being reduced to a fraction x of this initial bankroll 415
3.3. The probability of being at or above a specified value at the end of a specified number of trials 416
3.4. Continuous approximation of expected time to reach a goal 417
3.5. Comparing fixed fraction strategies: the probability that one strategy leads another after n trials 417
4. The long run: when will the Kelly strategy ``dominate''? 419
5. Blackjack 420
6. Sports betting 422
7. Wall street: the biggest game 426
7.1. Continuous approximation 427
7.2. The (almost) real world 430
7.3. The case for ``fractional Kelly'' 432
7.4. A remarkable formula 435
8. A case study 436
8.1. The constraints 437
8.2. The analysis and results 437
8.3. The recommendation and the result 438
8.4. The theory for a portfolio of securities 439
9. My experience with the Kelly approach 440
10. Conclusion 441
Acknowledgements 441
References 449
Chapter 10. Capital Growth: Theory and Practice 450
Abstract 451
Keywords 452
1. Introduction 453
2. Capital accumulation 455
2.1. Asset prices 456
2.2. Decision criteria 456
2.3. Timing of decisions 457
3. Asset prices 457
3.1. Pricing model 459
3.2. Estimation 461
3.3. Comparison 463
4. Growth strategies 465
4.1. The Kelly strategy 466
4.2. Stochastic dominance 470
4.3. Bi-criteria problems: Fractional Kelly strategies 472
4.4. Growth-security trade-off 478
5. Timing of decisions 484
5.1. Control limits 484
6. Legends of capital growth 486
6.1. Princeton Newport Partners 487
6.2. Kings College Chest Fund 487
6.3. Berkshire-Hathaway 489
6.4 Hong Kong Betting Syndicate 490
References 490
Author Index 496
Subject Index 504