HANDBOOK OF ASSET AND LIABILITY MANAGEMENT VOLUME 1:THEORY AND METHODOLOGY

CONTENTS
Introduction to the Series v
Contents of the Handbook vii
Preface ix
Chapter 1
Enterprise-Wide Asset and Liability Management: Issues, Institutions, and Models
DAN ROSEN and STAVROS A. ZENIOS 1
Abstract 2
1. Introduction 3
1.1. What is enterprise risk management 4
1.2. Example: Enterprise-wide view of credit risks in a bank 5
2. A conceptual framework for enterprise risk management 6
2.1. The management of a single line of business 7
2.2. The management of a business portfolio 9
2.3. Integrating design, pricing, funding, and capitalization 9
2.4. Components of enterprise risk management 10
2.5. Why is enterprise risk management important 15
3. Asset and liability management in enterprise risk management 17
3.1. Components of asset and liability management 17
4. Models for asset and liability management 19
References 21
Chapter 2
Term and Volatility Structures
ROGER J.-B. WETS and STEPHEN W. BIANCHI 25
Abstract 26
Keywords 26
1. Term structure 27
1.1. An example 27
1.2. BootStrapping 30
1.3. Nelson–Siegel and Svensson’s extension 34
1.4. Maximum smoothness 36
1.5. Forward-rates via geometric programming 37
1.6. EpiCurves 38
1.7. A comparison for U.S. Treasury curves 51

2. Volatility structure 57
2.1. Setting the stage 57
2.2. Some tree-based valuation models 60
2.3. The EpiVolatility model 61
2.4. Implementation 62
2.5. Summary 65
References 67
Chapter 3
Protecting Investors against Changes in Interest Rates
OLIVIER DE LA GRANDVILLE 69
1. Basic concepts for valuation and immunization of bond portfolios in continuous
time 73
1.1. The instantaneous forward rate 73
1.2. The continuously compounded spot rate 75
1.3. Introducing the missing link: The continuously compounded total return 77
1.4. Relationships between the total return, the forward rate and the spot rate 80
1.5. Theorems on the behavior of the forward rate and the total return 81
1.6. The spot rate curve as a spline and its corresponding forward rate curve 84
2. Immunization: A first approach 90
2.1. The continuously compounded horizon rate of return 91
2.2. A geometrical representation of the horizon rate of return 91
2.3. Existence and characteristics of an immunizing horizon 93
2.4. The Macaulay concept of duration, its properties and uses 94
2.5. A second-order condition 99
2.6. The immunization problem 100
3. Protecting investors against any shift in the interest rate structure—A general
immunization theorem 102
3.1. Notation 102
3.2. Present values at time 0 104
3.3. Future values at time 0 105
3.4. Present values at time ε 105
3.5. Future values at time ε 106
3.6. Further concepts for immunization: the moments of order k of a bond and a bond portfolio 106
3.7. A general immunization theorem 109
3.8. The nature of the cash flows of an immunizing portfolio 118
4. Applications 118
4.1. The spot structures and their shifts 119
4.2. Building immunizing portfolios 122
4.3. Immunization results 124
4.4. How large should we set the immunization parameter K? 126
4.5. Infinity of solutions 128
4.6. How sensitive are immunizing portfolios to changes in horizon H? 130

4.7. How sensitive are immunizing portfolios to a change in the basket of available bonds? 131
5. Conclusion and suggestions 133
6. Notes to references 137
References 137
Chapter 4
Risk-Return Analysis
HARRY M. MARKOWITZ and ERIK VAN DIJK 139
Abstract 140
Keywords 141
1. Introduction 142
2. The “general” mean-variance model 144
3. Applications of the general model 146
3.1. Asset liability modeling 146
3.2. Factor models 147
3.3. Other constraints 148
3.4. Tracking error 148
4. Examples of mean-variance efficient sets 149
4.1. Critical lines and corner portfolios 149
4.2. Efficient EV and Eσ combinations 150
4.3. All feasible Eσ combinations 152
4.4. Possible features 153
5. Solution to the “general” mean-variance problem 156
5.1. Preliminaries 156
5.2. The critical line algorithm 156
5.3. Getting started 158
5.4. The critical line algorithm with upper bounds 161
5.5. The critical line algorithm with factor and scenario models of covariance 162
5.6. Notes on computing 165
6. Separation theorems 166
6.1. The Tobin–Sharpe separation theorems 166
6.2. Two-funds separation 169
6.3. Separation theorems not true in general 169
6.4. The Elton, Gruber, Padberg algorithm 170
6.5. An alternate EGP-like algorithm 171
7. Alternate risk measures 173
7.1. Semideviation 173
7.2. Mean absolute deviation (MAD) 175
7.3. Probability of loss and value at risk (Gaussian Rp) 176
7.4. Probability of loss and Value at Risk (non-Gaussian Rp) 178
7.5. Conditional value at risk (CVaR) 180
8. Choice of criteria 180
8.1. Exact conditions 180

8.2. Mean-variance approximations to expected utility 181
8.3. Significance of MV approximations to EU 184
9. Risk-return analysis in practice 184
9.1. Choice of criteria 185
9.2. Tracking error or total variability 186
9.3. Estimates for asset classes 187
9.4. Estimation of expected returns for individual equities 187
9.5. Black–Litterman 188
9.6. Security analyst recommendations 189
9.7. Estimates of covariance 189
9.8. Parameter uncertainty 190
10. Epilogue 192
References 193
Chapter 5
Dynamic Asset Allocation Strategies Using a Stochastic Dynamic Programming
Approach
GERD INFANGER 199
Abstract 200
Keywords 200
1. Introduction 201
2. Approaches for dynamic asset allocation 204
2.1. Multi-stage stochastic programming 204
2.2. Stochastic dynamic programming 206
3. Single-period portfolio choice 207
4. Utility functions 209
5. A general approach to modeling utility 211
6. Dynamic portfolio choice 214
6.1. Dynamic stochastic programming and Monte Carlo sampling 215
6.2. Serially dependent asset returns 216
6.3. A fast method for normally distributed asset returns 217
7. Numerical results 217
7.1. Data assumptions 217
7.2. An investment example 222
7.3. The performance of dynamic strategies 234
7.4. Dynamic strategies for hedging downside risk 238
7.5. Downside risk protection at every period 241
7.6. Computation times 246
8. Comparison to multi-stage stochastic programming 247
Acknowledgements 248
References 248

Chapter 6
Stochastic Programming Models for Asset Liability Management
ROY KOUWENBERG and STAVROS A. ZENIOS 253
Abstract 254
1. Introduction 255
2. Stochastic programming 256
2.1. Basic concepts in stochastic programming 256
2.2. Stochastic programming model for portfolio management 261
3. Scenario generation and tree construction 267
3.1. Scenarios for the liabilities 267
3.2. Scenarios for economic factors and asset returns 270
3.3. Methods for generating scenarios 272
3.4. Constructing event trees 277
3.5. Options, bonds and arbitrage 283
4. Comparison of stochastic programming with other methods 287
4.1. Mean-variance models and downside risk 287
4.2. Discrete-time multi-period models 288
4.3. Continuous-time models 290
4.4. Stochastic programming 291
5. Applications of stochastic programming to ALM 291
6. Solution methods and computations 296
7. Summary and open issues 297
References 299
Chapter 7
Bond Portfolio Management via Stochastic Programming
M. BERTOCCHI, V. MORIGGIA and J. DUPAˇCOVÁ 305
Abstract 306
1. Introduction 307
2. The bond portfolio management model 311
3. Input data 315
4. Scenario reduction and scenario tree construction 320
5. Numerical results 321
6. Stress testing via contamination: Add worst-case scenarios 325
7. Conclusions 334
Acknowledgements 335
References 335
Chapter 8
Perturbation Methods for Dynamic Portfolio Allocation Problems
GEORGE CHACKO and KARL NEUMAR 337
Abstract 338
1. Introduction 339

2. General problem formulation 340
2.1. Investment opportunity set 341
2.2. Utility function 344
3. Exact solution for unit elasticity of intertemporal substitution 345
3.1. General results 345
3.2. Example 1: Time-varying expected returns (finite horizon) 349
3.3. Example 2: Time-varying expected returns (infinite horizon) 352
4. Approximate solution for general elasticity of intertemporal substitution 353
4.1. Perturbation around unit elasticity of substitution 353
4.2. Perturbation around mean of consumption/wealth ratio 360
5. Example 366
5.1. Time-varying volatility 367
5.2. Time-varying interest rates 378
6. Conclusions 382
References 383
Chapter 9
The Kelly Criterion in Blackjack Sports Betting, and the Stock Market
EDWARD O. THORP 385
Abstract 386
Keywords 386
1. Introduction 387
2. Coin tossing 388
3. Optimal growth: Kelly criterion formulas for practitioners 392
3.1. The probability of reaching a fixed goal on or before n trials 392
3.2. The probability of ever being reduced to a fraction x of this initial bankroll 394
3.3. The probability of being at or above a specified value at the end of a specified number of
trials 395
3.4. Continuous approximation of expected time to reach a goal 396
3.5. Comparing fixed fraction strategies: the probability that one strategy leads another after n
trials 396
4. The long run: when will the Kelly strategy “dominate”? 398
5. Blackjack 399
6. Sports betting 401
7. Wall street: the biggest game 405
7.1. Continuous approximation 406
7.2. The (almost) real world 409
7.3. The case for “fractional Kelly” 411
7.4. A remarkable formula 414
8. A case study 415
8.1. The constraints 416
8.2. The analysis and results 416

8.3. The recommendation and the result 417
8.4. The theory for a portfolio of securities 418
9. My experience with the Kelly approach 419
10. Conclusion 420
Acknowledgements 420
References 428
Chapter 10
Capital Growth: Theory and Practice
LEONARD C. MACLEAN and WILLIAM T. ZIEMBA 429
Abstract 430
Keywords 431
1. Introduction 432
2. Capital accumulation 434
2.1. Asset prices 435
2.2. Decision criteria 435
2.3. Timing of decisions 436
3. Asset prices 436
3.1. Pricing model 438
3.2. Estimation 440
3.3. Comparison 442
4. Growth strategies 444
4.1. The Kelly strategy 445
4.2. Stochastic dominance 449
4.3. Bi-criteria problems: Fractional Kelly strategies 451
4.4. Growth-security trade-off 457
5. Timing of decisions 463
5.1. Control limits 463
6. Legends of capital growth 465
6.1. Princeton Newport Partners 466
6.2. Kings College Chest Fund 466
6.3. Berkshire–Hathaway 468
6.4. Hong Kong Betting Syndicate 469
References 469
Author Index 475
Subject Index 483

 

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