Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach

Walter Briec, Kristiaan Kerstens () and Octave Jokung
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Walter Briec: UPVD - Université de Perpignan Via Domitia
Kristiaan Kerstens: LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique

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Abstract: This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, nonconvex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.

Date: 2007-01
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Published in Management Science, 2007, 53 (1), pp.135-149. ⟨10.1287/mnsc.1060.0596⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05623607

DOI: 10.1287/mnsc.1060.0596

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