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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
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    File URL: http://dx.doi.org/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. 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," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    3. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
    4. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
    5. 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(04), pages 513-537, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
    2. Deng, Xiao-Tie & Li, Zhong-Fei & Wang, Shou-Yang, 2005. "A minimax portfolio selection strategy with equilibrium," European Journal of Operational Research, Elsevier, vol. 166(1), pages 278-292, October.
    3. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.
    4. repec:spr:mathme:v:86:y:2017:i:1:d:10.1007_s00186-017-0582-4 is not listed on IDEAS
    5. Huang, Xiaolin & Shi, Lei & Pelckmans, Kristiaan & Suykens, Johan A.K., 2014. "Asymmetric ν-tube support vector regression," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 371-382.
    6. Polak, George G. & Rogers, David F. & Sweeney, Dennis J., 2010. "Risk management strategies via minimax portfolio optimization," European Journal of Operational Research, Elsevier, vol. 207(1), pages 409-419, November.
    7. repec:pal:jorsoc:v:55:y:2004:i:1:d:10.1057_palgrave.jors.2601648 is not listed on IDEAS
    8. repec:spr:annopr:v:256:y:2017:i:1:d:10.1007_s10479-016-2176-6 is not listed on IDEAS
    9. Li, Xiang & Qin, Zhongfeng, 2014. "Interval portfolio selection models within the framework of uncertainty theory," Economic Modelling, Elsevier, vol. 41(C), pages 338-344.
    10. Huang, Xiaoxia, 2007. "Two new models for portfolio selection with stochastic returns taking fuzzy information," European Journal of Operational Research, Elsevier, vol. 180(1), pages 396-405, July.
    11. Yu, Mei & Takahashi, Satoru & Inoue, Hiroshi & Wang, Shouyang, 2010. "Dynamic portfolio optimization with risk control for absolute deviation model," European Journal of Operational Research, Elsevier, vol. 201(2), pages 349-364, March.
    12. W. Hare & J. Nutini, 2013. "A derivative-free approximate gradient sampling algorithm for finite minimax problems," Computational Optimization and Applications, Springer, vol. 56(1), pages 1-38, September.

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