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Portfolio Optimization Under a Minimax Rule

Author

Listed:
  • Xiaoqiang Cai

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

  • Kok-Lay Teo

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Xiaoqi Yang

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Xun Yu Zhou

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

Abstract

This paper provides a new portfolio selection rule. The objective is to minimize the maximum individual risk and we use an l \infty function as the risk measure. We provide an explicit analytical solution for the model and are thus able to plot the entire efficient frontier. Our selection rule is very conservative. One of the features of the solution is that it does not explicitly involve the covariance of the asset returns.

Suggested Citation

  • Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:7:p:957-972
    DOI: 10.1287/mnsc.46.7.957.12039
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    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    3. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
    4. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    5. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    6. Best, Michael J. & Grauer, Robert R., 1992. "Positively Weighted Minimum-Variance Portfolios and the Structure of Asset Expected Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(4), pages 513-537, December.
    Full references (including those not matched with items on IDEAS)

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