Scherer B., Martin R.D. Introduction to Modern Portfolio Optimization with NuOpt, S-Plus and S+Bayes

Springer – 2005, 410 pages
ISBN 0387210164In recent years portfolio optimization and construction methodologies have become an increasingly critical ingredient of asset and fund management, while at the same time portfolio risk assessment has become an essential ingredient in risk management, and this trend will only accelerate in the coming years. Unfortunately there is a large gap between the limited treatment of portfolio construction methods that are presented in most university courses with relatively little hands-on experience and limited computing tools, and the rich and varied aspects of portfolio construction that are used in practice in the finance industry. Current practice demands the use of modern methods of portfolio construction that go well beyond the classical Markowitz mean-variance optimality theory and require the use of powerful scalable numerical optimization methods. This book fills the gap between current university instruction and current industry practice by providing a comprehensive computationally-oriented treatment of modern portfolio optimization and construction methods. The computational aspect of the book is based on extensive use of S-Plus, the S+NuOPT optimization module, the S-Plus Robust Library and the S+Bayes Library, along with about 100 S-Plus scripts and some CRSP sample data sets of stock returns. A special time-limited version of the S-Plus software is available to purchasers of this book.List of Code Examples
Linear and Quadratic Programming
Linear Programming: Testing for Arbitrage
Quadratic Programming: Balancing Risk and Return
Dual Variables and the Impact of Constraints
Analysis of the Efficient Frontier
Exercises
Endnotes
General Optimization with SIMPLE
Indexing Parameters and Variables
Function Optimization
Maximum Likelihood Optimization
Utility Optimization
Multistage Stochastic Programming
Optimization within S-PLUS
Exercises
Endnotes
Advanced Issues in Mean-Variance Optimization
Nonstandard Implementations
Portfolio Construction and Mixed-Integer Programming
Transaction Costs
Exercises
Endnotes
Resampling and Portfolio Choice
Portfolio Resampling
Resampling Long-Only Portfolios
Introduction of a Special Lottery Ticket
Distribution of Portfolio Weights
Theoretical Deficiencies of Portfolio Construction via Resampling
Bootstrap Estimation of Error in Risk-Return Ratios
Exercises
Endnotes
Scenario Optimization: Addressing Non-normality
Scenario Optimization
Mean Absolute Deviation
Semi-variance and Generalized Semi-variance Optimization
Probability-Based Risk/Return Measures
Minimum Regret
Conditional Value-at-Risk
CDO Valuation using Scenario Optimization
Exercises
Endnotes
Robust Statistical Methods for Portfolio Construction
Outliers and Non-normal Returns
Robust Statistics versus Classical Statistics
Robust Estimates of Mean Returns
Robust Estimates of Volatility
Robust Betas
Robust Correlations and Covariances
Robust Distances for Determining Normal Times versus
Hectic Times
Robust Covariances and Distances with Different Return Histories
Robust Portfolio Optimization
Conditional Value-at-Risk Frontiers: Classical and Robust
Influence Functions for Portfolios
Exercises
Endnotes
Bayes Methods
The Bayesian Modeling Paradigm
Bayes Models for the Mean and Volatility of Returns
Bayes Linear Regression Models
Black-Litterman Models
Bayes-Stein Estimators of Mean Returns
Appendix A: Inverse Chi-Squared Distributions
Appendix B: Posterior Distributions for Normal Likelihood
Conjugate Priors
Appendix C: Derivation of the Posterior for Jorion’s
Empirical Bayes Estimate
Exercises
Endnotes