Introduction To Modern Portfolio Optimization With NUOPT And S-PLUS

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Format: Hardcover
Pub. Date: 2005-04-30
Publisher(s): Springer Verlag
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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

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