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Robust portfolio optimization: a conic programming approach

Robust portfolio optimization: a conic programming approach The Markowitz Mean Variance model (MMV) and its variants are widely used for portfolio selection. The mean and covariance matrix used in the model originate from probability distributions that need to be determined empirically. It is well known that these parameters are notoriously difficult to estimate. In addition, the model is very sensitive to these parameter estimates. As a result, the performance and composition of MMV portfolios can vary significantly with the specification of the mean and covariance matrix. In order to address this issue we propose a one-period mean-variance model, where the mean and covariance matrix are only assumed to belong to an exogenously specified uncertainty set. The robust mean-variance portfolio selection problem is then written as a conic program that can be solved efficiently with standard solvers. Both second order cone program (SOCP) and semidefinite program (SDP) formulations are discussed. Using numerical experiments with real data we show that the portfolios generated by the proposed robust mean-variance model can be computed efficiently and are not as sensitive to input errors as the classical MMV’s portfolios. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Optimization and Applications Springer Journals

Robust portfolio optimization: a conic programming approach

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Optimization; Operations Research, Management Science; Operation Research/Decision Theory; Statistics, general; Convex and Discrete Geometry
ISSN
0926-6003
eISSN
1573-2894
DOI
10.1007/s10589-011-9419-x
Publisher site
See Article on Publisher Site

Abstract

The Markowitz Mean Variance model (MMV) and its variants are widely used for portfolio selection. The mean and covariance matrix used in the model originate from probability distributions that need to be determined empirically. It is well known that these parameters are notoriously difficult to estimate. In addition, the model is very sensitive to these parameter estimates. As a result, the performance and composition of MMV portfolios can vary significantly with the specification of the mean and covariance matrix. In order to address this issue we propose a one-period mean-variance model, where the mean and covariance matrix are only assumed to belong to an exogenously specified uncertainty set. The robust mean-variance portfolio selection problem is then written as a conic program that can be solved efficiently with standard solvers. Both second order cone program (SOCP) and semidefinite program (SDP) formulations are discussed. Using numerical experiments with real data we show that the portfolios generated by the proposed robust mean-variance model can be computed efficiently and are not as sensitive to input errors as the classical MMV’s portfolios.

Journal

Computational Optimization and ApplicationsSpringer Journals

Published: Jun 23, 2011

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