EDHEC RISK AND ASSET MANAGEMENT RESEARCH CENTRE 393-400 promenade des Anglais 06202 Nice Cedex 3 Tel.: +33 (0)4 93 18 32 53 E-mail:
[email protected] Web: www.edhec-risk.com Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach September 2005 Walter Briec Maître de conférences, University of Perpignan Kristiaan Kersten Chargé de recherche, CNRS-LABORES, IESEG Octave Jokung Professor, EDHEC Business School 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 makes it possible to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, non-convex 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. JEL: G11 Keywords: shortage function, efficient frontier, mean-variance-skewness portfolios, risk aversion, prudence. EDHEC is one of the top five business schools in France. Its reputation is built on the high quality of its faculty (110 professors and researchers from France and abroad) and the privileged relationship with professionals that the school has cultivated since its establishment in 1906.