发帖
雷达卡
Portfolio Optimization and Performance Analysis (Chapman Financial Mathematics Series)
by Jean-Luc Prigent (Author)
Book Description
In answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, contains a precise overview of standard portfolio optimization, provides a review of the main results for static and dynamic cases, and shows how theoretical results can be applied to practical and operational portfolio optimization. Divided into four sections that mirror the book's aims, this resource first describes the fundamental results of decision theory, including utility maximization and risk measure minimization. Covering both active and passive portfolio management, the second part discusses standard portfolio optimization and performance measures. The book subsequently introduces dynamic portfolio optimization based on stochastic control and martingale theory. It also outlines portfolio optimization with market frictions, such as incompleteness, transaction costs, labor income, and random time horizon. The final section applies theoretical results to practical portfolio optimization, including structured portfolio management. It details portfolio insurance methods as well as performance measures for alternative investments, such as hedge funds. Taking into account the different features of portfolio management theory, this book promotes a thorough understanding for students and professionals in the field.
In answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, contains a precise overview of standard portfolio optimization, provides a review of the main results for static and dynamic cases, and shows how theoretical results can be applied to practical and operational portfolio optimization. Divided into four sections that mirror the book's aims, this resource first describes the fundamental results of decision theory, including utility maximization and risk measure minimization. Covering both active and passive portfolio management, the second part discusses standard portfolio optimization and performance measures. The book subsequently introduces dynamic portfolio optimization based on stochastic control and martingale theory. It also outlines portfolio optimization with market frictions, such as incompleteness, transaction costs, labor income, and random time horizon. The final section applies theoretical results to practical portfolio optimization, including structured portfolio management. It details portfolio insurance methods as well as performance measures for alternative investments, such as hedge funds. Taking into account the different features of portfolio management theory, this book promotes a thorough understanding for students and professionals in the field.
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Contents
List of Tables XIII
List of Figures XV
I Utility and risk analysis 1
1 Utility theory 5
1.1 Preferences under uncertainty . . . . . . . . . . . . . . . . . 7
1.1.1 Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 Axioms on pref erences . . . . . . . . . . . . . . . . . . 8
1.2 Expected utility . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Risk aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Arrow-Pratt measures ofri sk aversion . . . . . . . . . 13
1.3.2 Standard utility functions . . . . . . . . . . . . . . . . 15
1.3.3 Applications to portfolio allocation . . . . . . . . . . . 17
1.4 Stochastic dominance . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Alternative expected utility theory . . . . . . . . . . . . . . . 24
1.5.1 Weighted utility theory . . . . . . . . . . . . . . . . . 25
1.5.2 Rank dependent expected utility theory . . . . . . . . 27
1.5.3 Non-additive expected utility . . . . . . . . . . . . . . 32
1.5.4 Regret theory . . . . . . . . . . . . . . . . . . . . . . . 33
1.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Riskmeasures 37
2.1 Coherent and convex risk measures . . . . . . . . . . . . . . 37
2.1.1 Coherent riskmeasures . . . . . . . . . . . . . . . . . 38
2.1.2 Convex riskmeasures . . . . . . . . . . . . . . . . . . 39
2.1.3 Representation ofri sk measures . . . . . . . . . . . . . 40
2.1.4 Risk measures and utility . . . . . . . . . . . . . . . . 41
2.1.5 Dynamic riskmeasures . . . . . . . . . . . . . . . . . 43
2.2 Standard riskmeasures . . . . . . . . . . . . . . . . . . . . . 48
2.2.1 Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.2 CVaR . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.3 Spectral measures of risk . . . . . . . . . . . . . . . . 59
2.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 62
X Portfolio Optimization and Performance Analysis
II Standard portfolio optimization 65
3 Static optimization 67
3.1 Mean-variance analysis . . . . . . . . . . . . . . . . . . . . . 68
3.1.1 Diversification effect . . . . . . . . . . . . . . . . . . . 68
3.1.2 Optimal weights . . . . . . . . . . . . . . . . . . . . . 71
3.1.3 Additional constraints . . . . . . . . . . . . . . . . . . 78
3.1.4 Estimation problems . . . . . . . . . . . . . . . . . . . 82
3.2 Alternative criteria . . . . . . . . . . . . . . . . . . . . . . . 85
3.2.1 Expected utility maximization . . . . . . . . . . . . . 85
3.2.2 Risk measure minimization . . . . . . . . . . . . . . . 93
3.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Indexed funds and benchmarking 103
4.1 Indexed funds . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.1.1 Tracking error . . . . . . . . . . . . . . . . . . . . . . 104
4.1.2 Simple index tracking methods . . . . . . . . . . . . . 105
4.1.3 The threshold accepting algorithm . . . . . . . . . . . 106
4.1.4 Cointegration tracking method . . . . . . . . . . . . . 112
4.2 Benchmark portf olio optimization . . . . . . . . . . . . . . . 117
4.2.1 Tracking-error definition . . . . . . . . . . . . . . . . . 118
4.2.2 Tracking-errorminimization . . . . . . . . . . . . . . . 119
4.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 127
5 Portfolio performance 129
5.1 Standard performance measures . . . . . . . . . . . . . . . . 130
5.1.1 The Capital Asset Pricing Model . . . . . . . . . . . . 130
5.1.2 The three standard performance measures . . . . . . . 132
5.1.3 Other performance measures . . . . . . . . . . . . . . 140
5.1.4 Beyond the CAPM . . . . . . . . . . . . . . . . . . . . 145
5.2 Perf ormance decomposition . . . . . . . . . . . . . . . . . . . 151
5.2.1 The Fama decomposition . . . . . . . . . . . . . . . . 151
5.2.2 Other performance attributions . . . . . . . . . . . . . 153
5.2.3 The external attribution . . . . . . . . . . . . . . . . . 153
5.2.4 The internal attribution . . . . . . . . . . . . . . . . . 155
5.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . 163
III Dynamic portfolio optimization 165
6 Dynamic programming optimization 169
6.1 Control theory . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.1.1 Calculus ofv ariations . . . . . . . . . . . . . . . . . . 169
6.1.2 Pontryagin and Bellman principles . . . . . . . . . . . 175
6.1.3 Stochastic optimal control . . . . . . . . . . . . . . . . 182
6.2 Lifetime portfolio selection . . . . . . . . . . . . . . . . . . . 187
Contents XI
6.2.1 The optimization problem . . . . . . . . . . . . . . . . 187
6.2.2 The deterministic coefficients case . . . . . . . . . . . 188
6.2.3 The general case . . . . . . . . . . . . . . . . . . . . . 195
6.2.4 Recursive utility in continuous-time . . . . . . . . . . 203
6.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 205
7 Optimal payoff profiles and long-term management 207
7.1 Optimal payoffs as functions of a benchmark . . . . . . . . . 207
7.1.1 Linear versus option-based strategy . . . . . . . . . . 207
7.2 Application to long-term management . . . . . . . . . . . . . 214
7.2.1 Assets dynamics and optimal portfolios . . . . . . . . 214
7.2.2 Exponential utility . . . . . . . . . . . . . . . . . . . . 220
7.2.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . 223
7.2.4 Distribution ofthe optimal portfolio return . . . . . . 225
7.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 226
8 Optimization within specific markets 229
8.1 Optimization in incomplete markets . . . . . . . . . . . . . . 230
8.1.1 General result based on martingale method . . . . . . 230
8.1.2 Dynamic programming and viscosity solutions . . . . 238
8.2 Optimization with constraints . . . . . . . . . . . . . . . . . 242
8.2.1 General result . . . . . . . . . . . . . . . . . . . . . . . 242
8.2.2 Basic examples . . . . . . . . . . . . . . . . . . . . . . 249
8.3 Optimization with transaction costs . . . . . . . . . . . . . . 256
8.3.1 The infinite-horizon case . . . . . . . . . . . . . . . . . 256
8.3.2 The finite-horizon case . . . . . . . . . . . . . . . . . . 260
8.4 Other f rameworks . . . . . . . . . . . . . . . . . . . . . . . . 263
8.4.1 Labor income . . . . . . . . . . . . . . . . . . . . . . . 263
8.4.2 Stochastic horizon . . . . . . . . . . . . . . . . . . . . 272
8.5 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 276
IV Structured portfolio management 279
9 Portfolio insurance 281
9.1 The Option Based Portfolio Insurance . . . . . . . . . . . . . 282
9.1.1 The standard OBPI method . . . . . . . . . . . . . . . 284
9.1.2 Extensions oft he OBPI method . . . . . . . . . . . . 286
9.2 The Constant Proportion Portfolio Insurance . . . . . . . . . 294
9.2.1 The standard CPPI method . . . . . . . . . . . . . . . 295
9.2.2 CPPI extensions . . . . . . . . . . . . . . . . . . . . . 303
9.3 Comparison between OBPI and CPPI . . . . . . . . . . . . . 305
9.3.1 Comparison at maturity . . . . . . . . . . . . . . . . . 305
9.3.2 The dynamic behavior ofOBPI and CPPI . . . . . . . 310
9.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 318
XII Portfolio Optimization and Performance Analysis
10 Optimal dynamic portfolio with risk limits 319
10.1 Optimal insured portfolio: discrete-time case . . . . . . . . . 321
10.1.1 Optimal insured portfolio with a fixed number of assets 321
10.1.2 Optimal insured payoffs as functions of a benchmark . 326
10.2 Optimal Insured Portfolio: the dynamically complete case . . 333
10.2.1 Guarantee atmaturity . . . . . . . . . . . . . . . . . . 333
10.2.2 Risk exposure and utility function . . . . . . . . . . . 335
10.2.3 Optimal portfolio with controlled drawdowns . . . . . 337
10.3 Value-at-Risk and expected shortfall based management . . . 340
10.3.1 Dynamic saf ety criteria . . . . . . . . . . . . . . . . . 340
10.3.2 Expected utility under VaR/CVaR constraints . . . . 347
10.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 350
11 Hedge funds 351
11.1 The hedge funds industry . . . . . . . . . . . . . . . . . . . . 351
11.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 351
11.1.2 Main strategies . . . . . . . . . . . . . . . . . . . . . . 352
11.2 Hedge f und perf ormance . . . . . . . . . . . . . . . . . . . . 354
11.2.1 Return distributions . . . . . . . . . . . . . . . . . . . 354
11.2.2 Sharpe ratio limits . . . . . . . . . . . . . . . . . . . . 355
11.2.3 Alternative performance measures . . . . . . . . . . . 362
11.2.4 Benchmarks for alternative investment . . . . . . . . . 368
11.2.5 Measure oft he performance persistence . . . . . . . . 369
11.3 Optimal allocation in hedge funds . . . . . . . . . . . . . . . 370
11.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 371
A Appendix A: Arch Models 373
B Appendix B: Stochastic Processes 381
References 397
Symbol Description 431
Index 433
List of Tables XIII
List of Figures XV
I Utility and risk analysis 1
1 Utility theory 5
1.1 Preferences under uncertainty . . . . . . . . . . . . . . . . . 7
1.1.1 Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 Axioms on pref erences . . . . . . . . . . . . . . . . . . 8
1.2 Expected utility . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Risk aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Arrow-Pratt measures ofri sk aversion . . . . . . . . . 13
1.3.2 Standard utility functions . . . . . . . . . . . . . . . . 15
1.3.3 Applications to portfolio allocation . . . . . . . . . . . 17
1.4 Stochastic dominance . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Alternative expected utility theory . . . . . . . . . . . . . . . 24
1.5.1 Weighted utility theory . . . . . . . . . . . . . . . . . 25
1.5.2 Rank dependent expected utility theory . . . . . . . . 27
1.5.3 Non-additive expected utility . . . . . . . . . . . . . . 32
1.5.4 Regret theory . . . . . . . . . . . . . . . . . . . . . . . 33
1.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Riskmeasures 37
2.1 Coherent and convex risk measures . . . . . . . . . . . . . . 37
2.1.1 Coherent riskmeasures . . . . . . . . . . . . . . . . . 38
2.1.2 Convex riskmeasures . . . . . . . . . . . . . . . . . . 39
2.1.3 Representation ofri sk measures . . . . . . . . . . . . . 40
2.1.4 Risk measures and utility . . . . . . . . . . . . . . . . 41
2.1.5 Dynamic riskmeasures . . . . . . . . . . . . . . . . . 43
2.2 Standard riskmeasures . . . . . . . . . . . . . . . . . . . . . 48
2.2.1 Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.2 CVaR . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.3 Spectral measures of risk . . . . . . . . . . . . . . . . 59
2.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 62
X Portfolio Optimization and Performance Analysis
II Standard portfolio optimization 65
3 Static optimization 67
3.1 Mean-variance analysis . . . . . . . . . . . . . . . . . . . . . 68
3.1.1 Diversification effect . . . . . . . . . . . . . . . . . . . 68
3.1.2 Optimal weights . . . . . . . . . . . . . . . . . . . . . 71
3.1.3 Additional constraints . . . . . . . . . . . . . . . . . . 78
3.1.4 Estimation problems . . . . . . . . . . . . . . . . . . . 82
3.2 Alternative criteria . . . . . . . . . . . . . . . . . . . . . . . 85
3.2.1 Expected utility maximization . . . . . . . . . . . . . 85
3.2.2 Risk measure minimization . . . . . . . . . . . . . . . 93
3.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Indexed funds and benchmarking 103
4.1 Indexed funds . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.1.1 Tracking error . . . . . . . . . . . . . . . . . . . . . . 104
4.1.2 Simple index tracking methods . . . . . . . . . . . . . 105
4.1.3 The threshold accepting algorithm . . . . . . . . . . . 106
4.1.4 Cointegration tracking method . . . . . . . . . . . . . 112
4.2 Benchmark portf olio optimization . . . . . . . . . . . . . . . 117
4.2.1 Tracking-error definition . . . . . . . . . . . . . . . . . 118
4.2.2 Tracking-errorminimization . . . . . . . . . . . . . . . 119
4.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 127
5 Portfolio performance 129
5.1 Standard performance measures . . . . . . . . . . . . . . . . 130
5.1.1 The Capital Asset Pricing Model . . . . . . . . . . . . 130
5.1.2 The three standard performance measures . . . . . . . 132
5.1.3 Other performance measures . . . . . . . . . . . . . . 140
5.1.4 Beyond the CAPM . . . . . . . . . . . . . . . . . . . . 145
5.2 Perf ormance decomposition . . . . . . . . . . . . . . . . . . . 151
5.2.1 The Fama decomposition . . . . . . . . . . . . . . . . 151
5.2.2 Other performance attributions . . . . . . . . . . . . . 153
5.2.3 The external attribution . . . . . . . . . . . . . . . . . 153
5.2.4 The internal attribution . . . . . . . . . . . . . . . . . 155
5.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . 163
III Dynamic portfolio optimization 165
6 Dynamic programming optimization 169
6.1 Control theory . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.1.1 Calculus ofv ariations . . . . . . . . . . . . . . . . . . 169
6.1.2 Pontryagin and Bellman principles . . . . . . . . . . . 175
6.1.3 Stochastic optimal control . . . . . . . . . . . . . . . . 182
6.2 Lifetime portfolio selection . . . . . . . . . . . . . . . . . . . 187
Contents XI
6.2.1 The optimization problem . . . . . . . . . . . . . . . . 187
6.2.2 The deterministic coefficients case . . . . . . . . . . . 188
6.2.3 The general case . . . . . . . . . . . . . . . . . . . . . 195
6.2.4 Recursive utility in continuous-time . . . . . . . . . . 203
6.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 205
7 Optimal payoff profiles and long-term management 207
7.1 Optimal payoffs as functions of a benchmark . . . . . . . . . 207
7.1.1 Linear versus option-based strategy . . . . . . . . . . 207
7.2 Application to long-term management . . . . . . . . . . . . . 214
7.2.1 Assets dynamics and optimal portfolios . . . . . . . . 214
7.2.2 Exponential utility . . . . . . . . . . . . . . . . . . . . 220
7.2.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . 223
7.2.4 Distribution ofthe optimal portfolio return . . . . . . 225
7.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 226
8 Optimization within specific markets 229
8.1 Optimization in incomplete markets . . . . . . . . . . . . . . 230
8.1.1 General result based on martingale method . . . . . . 230
8.1.2 Dynamic programming and viscosity solutions . . . . 238
8.2 Optimization with constraints . . . . . . . . . . . . . . . . . 242
8.2.1 General result . . . . . . . . . . . . . . . . . . . . . . . 242
8.2.2 Basic examples . . . . . . . . . . . . . . . . . . . . . . 249
8.3 Optimization with transaction costs . . . . . . . . . . . . . . 256
8.3.1 The infinite-horizon case . . . . . . . . . . . . . . . . . 256
8.3.2 The finite-horizon case . . . . . . . . . . . . . . . . . . 260
8.4 Other f rameworks . . . . . . . . . . . . . . . . . . . . . . . . 263
8.4.1 Labor income . . . . . . . . . . . . . . . . . . . . . . . 263
8.4.2 Stochastic horizon . . . . . . . . . . . . . . . . . . . . 272
8.5 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 276
IV Structured portfolio management 279
9 Portfolio insurance 281
9.1 The Option Based Portfolio Insurance . . . . . . . . . . . . . 282
9.1.1 The standard OBPI method . . . . . . . . . . . . . . . 284
9.1.2 Extensions oft he OBPI method . . . . . . . . . . . . 286
9.2 The Constant Proportion Portfolio Insurance . . . . . . . . . 294
9.2.1 The standard CPPI method . . . . . . . . . . . . . . . 295
9.2.2 CPPI extensions . . . . . . . . . . . . . . . . . . . . . 303
9.3 Comparison between OBPI and CPPI . . . . . . . . . . . . . 305
9.3.1 Comparison at maturity . . . . . . . . . . . . . . . . . 305
9.3.2 The dynamic behavior ofOBPI and CPPI . . . . . . . 310
9.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 318
XII Portfolio Optimization and Performance Analysis
10 Optimal dynamic portfolio with risk limits 319
10.1 Optimal insured portfolio: discrete-time case . . . . . . . . . 321
10.1.1 Optimal insured portfolio with a fixed number of assets 321
10.1.2 Optimal insured payoffs as functions of a benchmark . 326
10.2 Optimal Insured Portfolio: the dynamically complete case . . 333
10.2.1 Guarantee atmaturity . . . . . . . . . . . . . . . . . . 333
10.2.2 Risk exposure and utility function . . . . . . . . . . . 335
10.2.3 Optimal portfolio with controlled drawdowns . . . . . 337
10.3 Value-at-Risk and expected shortfall based management . . . 340
10.3.1 Dynamic saf ety criteria . . . . . . . . . . . . . . . . . 340
10.3.2 Expected utility under VaR/CVaR constraints . . . . 347
10.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 350
11 Hedge funds 351
11.1 The hedge funds industry . . . . . . . . . . . . . . . . . . . . 351
11.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 351
11.1.2 Main strategies . . . . . . . . . . . . . . . . . . . . . . 352
11.2 Hedge f und perf ormance . . . . . . . . . . . . . . . . . . . . 354
11.2.1 Return distributions . . . . . . . . . . . . . . . . . . . 354
11.2.2 Sharpe ratio limits . . . . . . . . . . . . . . . . . . . . 355
11.2.3 Alternative performance measures . . . . . . . . . . . 362
11.2.4 Benchmarks for alternative investment . . . . . . . . . 368
11.2.5 Measure oft he performance persistence . . . . . . . . 369
11.3 Optimal allocation in hedge funds . . . . . . . . . . . . . . . 370
11.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . 371
A Appendix A: Arch Models 373
B Appendix B: Stochastic Processes 381
References 397
Symbol Description 431
Index 433
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