Introduction to Modern Portfolio Optimization With NUOPT and S-PLUS

Contents
Preface ...............................................................................................................vii
List of Code Examples.....................................................................................xix
1 Linear and Quadratic Programming.....................................................1
1.1 Linear Programming: Testing for Arbitrage..............................................1
1.2 Quadratic Programming: Balancing Risk and Return ...............................6
1.3 Dual Variables and the Impact of Constraints.........................................17
1.4 Analysis of the Efficient Frontier ............................................................24
Exercises..........................................................................................................30
Endnotes ..........................................................................................................32
2 General Optimization with SIMPLE .....................................................35
2.1 Indexing Parameters and Variables .........................................................35
2.2 Function Optimization.............................................................................45
2.3 Maximum Likelihood Optimization........................................................50
2.4 Utility Optimization ................................................................................54
2.5 Multistage Stochastic Programming........................................................61
2.6 Optimization within S-PLUS ....................................................................69
Exercises..........................................................................................................79
Endnotes ..........................................................................................................80
3 Advanced Issues in Mean-Variance Optimization .............................81
3.1 Nonstandard Implementations.................................................................81
3.2 Portfolio Construction and Mixed-Integer Programming........................90
3.3 Transaction Costs ....................................................................................98
Exercises........................................................................................................106
Endnotes ........................................................................................................108
4 Resampling and Portfolio Choice.......................................................109
4.1 Portfolio Resampling.............................................................................109
4.2 Resampling Long-Only Portfolios ........................................................114
4.3 Introduction of a Special Lottery Ticket ...............................................115
4.4 Distribution of Portfolio Weights..........................................................120
4.5 Theoretical Deficiencies of Portfolio Construction via Resampling .....126
4.6 Bootstrap Estimation of Error in Risk-Return Ratios............................129
Exercises........................................................................................................136
Endnotes ........................................................................................................139
5 Scenario Optimization: Addressing Non-normality.........................141
5.1 Scenario Optimization...........................................................................141
5.2 Mean Absolute Deviation......................................................................153
5.3 Semi-variance and Generalized Semi-variance Optimization ...............158
5.4 Probability-Based Risk/Return Measures..............................................164
5.5 Minimum Regret ...................................................................................170
5.6 Conditional Value-at-Risk.....................................................................174
5.7 CDO Valuation using Scenario Optimization .......................................189
Exercises........................................................................................................193
Endnotes ........................................................................................................194
6 Robust Statistical Methods for Portfolio Construction....................195
6.1 Outliers and Non-normal Returns .........................................................195
6.2 Robust Statistics versus Classical Statistics ..........................................200
6.3 Robust Estimates of Mean Returns .......................................................202
6.4 Robust Estimates of Volatility ..............................................................209
6.5 Robust Betas..........................................................................................218
6.6 Robust Correlations and Covariances ...................................................221
6.7 Robust Distances for Determining Normal Times versus
Hectic Times .........................................................................................226
6.8 Robust Covariances and Distances with Different Return Histories.....233
6.9 Robust Portfolio Optimization ..............................................................238
6.10 Conditional Value-at-Risk Frontiers: Classical and Robust..................261
6.11 Influence Functions for Portfolios.........................................................276
Exercises........................................................................................................294
Endnotes ........................................................................................................297
7 Bayes Methods .....................................................................................299
7.1 The Bayesian Modeling Paradigm ........................................................299
7.2 Bayes Models for the Mean and Volatility of Returns ..........................303
7.3 Bayes Linear Regression Models ..........................................................346
7.4 Black-Litterman Models .......................................................................359
7.5 Bayes-Stein Estimators of Mean Returns..............................................375
7.6 Appendix 7A: Inverse Chi-Squared Distributions.................................380
7.7 Appendix 7B: Posterior Distributions for Normal Likelihood
Conjugate Priors....................................................................................384
7.8 Appendix 7C: Derivation of the Posterior for Jorion’s
Empirical Bayes Estimate .....................................................................384
Exercises........................................................................................................387
Endnotes ........................................................................................................389
Bibliography....................................................................................................393
Index ................................................................................................................401


Another Optimization Books
Download