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A Minimax Portfolio Selection Rule with Linear Programming Solution

Martin R. Young
Management Science
Vol. 44, No. 5 (May, 1998), pp. 673-683
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/2634472
Page Count: 11
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A Minimax Portfolio Selection Rule with Linear Programming Solution
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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.

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