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A Minimax Portfolio Selection Rule with Linear Programming Solution

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  • Martin R. Young

    (University of Michigan School of Business, Department of Statistics and Management Science, Ann Arbor, Michigan 48109-1234)

Abstract

A new principle for choosing portfolios based on historical returns data is introduced; the optimal portfolio based on this principle is the solution to a simple linear programming problem. This principle uses minimum return rather than variance as a measure of risk. In particular, the portfolio is chosen that minimizes the maximum loss over all past observation periods, for a given level of return. This objective function avoids the logical problems of a quadratic (nonmonotone) utility function implied by mean-variance portfolio selection rules. The resulting minimax portfolios are diversified; for normal returns data, the portfolios are nearly equivalent to those chosen by a mean-variance rule. Framing the portfolio selection process as a linear optimization problem also makes it feasible to constrain certain decision variables to be integer, or 0-1, valued; this feature facilitates the use of more complex decision-making models, including models with fixed transaction charges and models with Boolean-type constraints on allocations.

Suggested Citation

  • Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
  • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:5:p:673-683
    DOI: 10.1287/mnsc.44.5.673
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    References listed on IDEAS

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    1. Elton, Edwin J & Gruber, Martin J & Padberg, Manfred W, 1976. "Simple Criteria for Optimal Portfolio Selection," Journal of Finance, American Finance Association, vol. 31(5), pages 1341-1357, December.
    2. Sharpe, William F., 1971. "A Linear Programming Approximation for the General Portfolio Analysis Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1263-1275, December.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. 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.
    5. Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problemâ€," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
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