A minimax portfolio selection rule with linear programming solution

A minimax portfolio selection rule with linear programming solution

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Article ID: iaor19991838
Country: United States
Volume: 44
Issue: 5
Start Page Number: 673
End Page Number: 683
Publication Date: May 1998
Journal: Management Science
Authors:
Keywords: investment, values, optimization
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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