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

W. Briec, Kristiaan Kerstens and J. B. Lesourd
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W. Briec: Université de Perpignan
J. B. Lesourd: Université de la Méditerranée

Journal of Optimization Theory and Applications, 2004, vol. 120, issue 1, No 1, 27 pages

Abstract: 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.

Keywords: Shortage function; efficient frontier; risk aversion; mean-variance portfolios (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (54)

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DOI: 10.1023/B:JOTA.0000012730.36740.bb

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