Single Period Markowitz Portfolio Selection, Performance Gading and Duality: A Variation on Luenberger'a Shortage Function

Walter Briec (), Kristiaan Kerstens and Jean Baptiste Lesourd ()
Additional contact information
Walter Briec: Université de Perpignan.
Jean Baptiste Lesourd: GREQAM, Centre de la Vieille Charit.

No 203, Working Papers from Departament Empresa, Universitat Autònoma de Barcelona

Abstract: Markowitz portfolio theory (1952) has induced 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 generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of 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 thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Keywords: shortage function; efficience frontier; risk aversionm mean-variance portfolios. (search for similar items in EconPapers)
Pages: 38 pages
Date: 2001-12, Revised 2002-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Published in Working Papers at the Department of Business, April 2002 pages 1-38

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