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Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function

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Abstract

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimization.

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Authors and Affiliations

  1. Maître de Conférences, JEREM, Université de Perpignan, Perpignan, France

    W. Briec

  2. Chargé de Recherche, CNRS-LABORES, URA 362, IESEG, Lille, France

    K. Kerstens

  3. Directeur de Recherche, GREQAM-CNRS, UMR 6579, Université de la Méditerranée, Aix-Marseille, France

    J. B. Lesourd

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  1. W. Briec
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  2. K. Kerstens
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  3. J. B. Lesourd
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Briec, W., Kerstens, K. & Lesourd, J.B. Single-Period Markowitz Portfolio Selection, Performance Gauging, and Duality: A Variation on the Luenberger Shortage Function. Journal of Optimization Theory and Applications 120, 1–27 (2004). https://doi.org/10.1023/B:JOTA.0000012730.36740.bb

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