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Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach

Author

Listed:
  • Laurent El Ghaoui

    (Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720)

  • Maksim Oks

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720)

  • Francois Oustry

    (INRIA Rhone-Alpes ZIRST, 655 avenue de l'Europe 38330 Montbonnot Saint-Martin, France)

Abstract

Classical formulations of the portfolio optimization problem, such as mean-variance or Value-at-Risk (VaR) approaches, can result in a portfolio extremely sensitive to errors in the data, such as mean and covariance matrix of the returns. In this paper we propose a way to alleviate this problem in a tractable manner. We assume that the distribution of returns is partially known, in the sense that only bounds on the mean and covariance matrix are available. We define the worst-case Value-at-Risk as the largest VaR attainable, given the partial information on the returns' distribution. We consider the problem of computing and optimizing the worst-case VaR, and we show that these problems can be cast as semidefinite programs. We extend our approach to various other partial information on the distribution, including uncertainty in factor models, support constraints, and relative entropy information.

Suggested Citation

  • Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:4:p:543-556
    DOI: 10.1287/opre.51.4.543.16101
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    References listed on IDEAS

    as
    1. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, University Library of Munich, Germany.
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    3. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
    4. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer;Western Finance Association, vol. 12(2), pages 201-242, October.
    5. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    Full references (including those not matched with items on IDEAS)

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