Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function

Walter Briec () and Kristiaan Jesourd Jean-Baptiste Kerstens
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Walter Briec: UPVD - Université de Perpignan Via Domitia

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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.

Date: 2004-01-01
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Published in Journal of Optimization Theory and Applications, 2004, 120 (1), pp.1-27

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05623484

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