Introduction To Modern Portfolio Optimization With NUOPT And S-PLUS

by SCHERER, BERND MICHAEL; MARTIN, R. DOUGLAS

• ISBN13: 9780387210162
• ISBN10: 0387210164
• Format: Hardcover
• Copyright: 2005-04-30
• Publisher: Springer Verlag

Summary

In 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-PlusA?, the S+NuOPTa?? optimization module, the S-Plus Robust Library and the S+Bayesa?? Library, along with about 100 S-Plus scripts and some CRSPA? sample data sets of stock returns. A special time-limited version of the S-Plus software is available to purchasers of this book. a??For money managers and investment professionals in the field, optimization is truly a can of worms rather left un-opened, until now! Here lies a thorough explanation of almost all possibilities one can think of for portfolio optimization, complete with error estimation techniques and explanation of when non-normality plays a part. A highly recommended and practical handbook for the consummate professional and student alike!a?? Steven P. Greiner, Ph.D., Chief Large Cap Quant & Fundamental Research Manager, Harris Investment Management a??The authors take a huge step in the long struggle to establish applied post-modern portfolio theory. The optimization and statistical techniques generalize the normal linear model to include robustness, non-normality, and semi-conjugate Bayesian analysis via MCMC. The techniques are very clearly demonstrated by the extensive use and tight integration of S-Plus software. Their book should be an enormous help to students and practitioners trying to move beyond traditional modern portfolio theory.a?? Peter Knez, CIO, Global Head of Fixed Income, Barclays Global Investors a??With regard to static portfolio optimization, the book gives a good survey on the development from the basic Markowitz approach to state of the art models and is in particular valuable for direct use in practice or for lectures combined with practical exercises.a?? Short Book Reviews of the International Statistical Institute, December 2005

Table of Contents

Preface	vii
List of Code Examples	xix
1 Linear and Quadratic Programming	1	(34)
1.1 Linear Programming: Testing for Arbitrage	1	(5)
1.2 Quadratic Programming: Balancing Risk and Return	6	(11)
1.3 Dual Variables and the Impact of Constraints	17	(7)
1.4 Analysis of the Efficient Frontier	24	(6)
Exercises	30	(2)
Endnotes	32	(3)
2 General Optimization with SIMPLE	35	(46)
2.1 Indexing Parameters and Variables	35	(10)
2.2 Function Optimization	45	(5)
2.3 Maximum Likelihood Optimization	50	(4)
2.4 Utility Optimization	54	(7)
2.5 Multistage Stochastic Programming	61	(8)
2.6 Optimization within S-PLUS	69	(10)
Exercises	79	(1)
Endnotes	80	(1)
3 Advanced Issues in Mean-Variance Optimization	81	(28)
3.1 Nonstandard Implementations	81	(9)
3.2 Portfolio Construction and Mixed-Integer Programming	90	(8)
3.3 Transaction Costs	98	(8)
Exercises	106	(2)
Endnotes	108	(1)
4 Resampling and Portfolio Choice	109	(32)
4.1 Portfolio Resampling	109	(5)
4.2 Resampling Long-Only Portfolios	114	(1)
4.3 Introduction of a Special Lottery Ticket	115	(5)
4.4 Distribution of Portfolio Weights	120	(6)
4.5 Theoretical Deficiencies of Portfolio Construction via Resampling	126	(3)
4.6 Bootstrap Estimation of Error in Risk-Return Ratios	129	(7)
Exercises	136	(3)
Endnotes	139	(2)
5 Scenario Optimization: Addressing Non-normality	141	(54)
5.1 Scenario Optimization	141	(12)
5.2 Mean Absolute Deviation	153	(5)
5.3 Semi-variance and Generalized Semi-variance Optimization	158	(6)
5.4 Probability-Based Risk/Return Measures	164	(6)
5.5 Minimum Regret	170	(4)
5.6 Conditional Value-at-Risk	174	(15)
5.7 CDO Valuation using Scenario Optimization	189	(4)
Exercises	193	(1)
Endnotes	194	(1)
6 Robust Statistical Methods for Portfolio Construction	195	(104)
6.1 Outliers and Non-normal Returns	195	(5)
6.2 Robust Statistics versus Classical Statistics	200	(2)
6.3 Robust Estimates of Mean Returns	202	(7)
6.4 Robust Estimates of Volatility	209	(9)
6.5 Robust Betas	218	(3)
6.6 Robust Correlations and Covariances	221	(5)
6.7 Robust Distances for Determining Normal Times versus Hectic Times	226	(7)
6.8 Robust Covariances and Distances with Different Return Histories	233	(5)
6.9 Robust Portfolio Optimization	238	(23)
6.10 Conditional Value-at-Risk Frontiers: Classical and Robust	261	(15)
6.11 Influence Functions for Portfolios	276	(18)
Exercises	294	(3)
Endnotes	297	(2)
7 Bayes Methods	299	(94)
7.1 The Bayesian Modeling Paradigm	299	(4)
7.2 Bayes Models for the Mean and Volatility of Returns	303	(43)
7.3 Bayes Linear Regression Models	346	(13)
7.4 Black-Litterman Models	359	(16)
7.5 Bayes-Stein Estimators of Mean Returns	375	(5)
7.6 Appendix 7A: Inverse Chi-Squared Distributions	380	(4)
7.7 Appendix 7B: Posterior Distributions for Normal Likelihood Conjugate Priors	384	(1)
7.8 Appendix 7C: Derivation of the Posterior for Jorion's Empirical Bayes Estimate	384	(3)
Exercises	387	(2)
Endnotes	389	(4)
Bibliography	393	(8)
Index	401