TITLE:
On Some Class of Distance Functions for Measuring Portfolio Efficiency
AUTHORS:
Carlos Barros, Walter Briec, Hermann Ratsimbanierana
KEYWORDS:
Distance Functions, Portfolio Selection, Efficient Frontier, Dualities, Risk Aversion
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.1 No.2,
August
25,
2011
ABSTRACT: Morey and Morey [1] have developed an approach for gauging portfolio efficiencies in the context of the Markowitz model. Following some recent contributions [2,3], this paper analyzes the axiomatic properties of distance functions extending an earlier approach proposed by Morey and Morey. The paper also focusses on the hyperbolic measure and the McFadden gauge function [4]. Among other things, overall, allocative and portfolio improvements possibilities (in term of return expansion or/and risk contraction) based upon the indirect mean-variance utility function are analyzed. Along this line, duality results are established in each case. This enables us to calculate the degree of risk aversion maximizing the investor indirect mean-variance utility function in either return expansion or risk contraction. An empirical illustration is provided and reveal ranking of preferred risks aversion for some “CAC40” assets.