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Portfolio optimization and performance analysis

Author: Prigent, Jean-Luc Series: Financial mathematics series Publisher: Chapman and Hall, 2007. ; CRC, 2007.Language: EnglishDescription: 434 p. : Graphs ; 24 cm.ISBN: 9781584885788Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print HG4529.5 .P75 2007
(Browse shelf)
001235468
Available 001235468
Total holds: 0

Includes bibliographical references and index

Digitized

Portfolio Optimization and Performance Analysis Contents List of Tables List of Figures XIII XV I Utility and risk analysis 1 Utility theory 1 5 1.1 Preferences under uncertainty ......................................................... 7 1.1.1 Lotteries .................................................................................. 7 1.1.2 Axioms on preferences ............................................................ 8 1.2 Expected utility 9 1.3 Risk aversion .................................................................................... 11 1.3.1 Arrow-Pratt measures of risk 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 Risk measures 2.1 Coherent and convex risk measures ............................................... 2.1.1 Coherent risk measures ..................................................... 2.1.2 Convex risk measures ......................................................... 2.1.3 Representation of risk measures ......................................... 2.1.4 Risk measures and utility ................................................... 2.1.5 Dynamic risk measures ...................................................... 2.2 Standard risk measures ................................................................ 2.2.1 Value-at-Risk ....................................................................... 2.2.2 CVaR ........................................................................................ 2.2.3 Spectral measures of risk ................................................... 2.3 Further reading ............................................................................ 37 37 38 39 40 41 43 48 48 54 59 62 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 portfolio optimization .................................................. 117 4.2.1 Tracking-error definition ..................................................... 118 4.2.2 Tracking-error minimization ............................................... 119 4.3 Further reading ............................................................................ 127 5 Portfolio performance 5.1 Standard performance measures .................................................. 5.1.1 The Capital Asset Pricing Model .......................................... 5.1.2 The three standard performance measures ....................... 5.1.3 Other performance measures ............................................. 5.1.4 Beyond the CAPM................................................................... 5.2 Performance decomposition ............................................................ 5.2.1 The Fama decomposition ..................................................... 5.2.2 Other performance attributions ......................................... 5.2.3 The external attribution ..................................................... 5.2.4 The internal attribution ..................................................... 5.3 Further Reading ............................................................................ 129 130 130 132 140 145 151 151 153 153 155 163 III Dynamic portfolio optimization 165 169 169 169 175 182 187 6 Dynamic programming optimization 6.1 Control theory ................................................................................. 6.1.1 Calculus of variations ......................................................... 6.1.2 Pontryagin and Bellman principles ..................................... 6.1.3 Stochastic optimal control .................................................. 6.2 Lifetime portfolio selection ................................................................ 6.2.1 The optimization problem .................................................... 6.2.2 The deterministic coefficients case ...................................... 6.2.3 The general case .................................................................. 6.2.4 Recursive utility in continuous-time ................................... 6.3 Further reading ............................................................................ 187 188 195 203 205 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 of the 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 frameworks ........................................................................... 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 of the 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 of OBPI and CPPI.............................. 310 9.4 Further reading ............................................................................ 318 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 at maturity ..................................................... 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 safety 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 fund performance .............................................................. 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 of the performance persistence .......................... 369 11.3 Optimal allocation in hedge funds ............................................... 370 11.4 Further reading .......................................................................... 371 A Appendix A: Arch Models B Appendix B: Stochastic Processes References Symbol Description Index 373 381 397 431 433

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