Author(s)

M. Di Pierro & J. Mosevich

Abstract

In this paper we discuss the issue of portfolio ranking for a rational risk averse investor with and without the option to buy a risk free asset. We find that in the former case the use of Sharpe, Omega, Sortino, and Kappa rankings are all justified although they follow from different definitions. We also find that for portfolios with Gaussian distributed returns these rankings, as well as the Stutzer ranking, are equivalent to each other. Finally we prove that without a risk free asset all the above rankings are incompatible with being a rational risk averse investor and a different ranking is required. We propose an exact analytical formula as well as an approximate formula for practical use. Keywords: portfolio ranking, skewness, kurtosis, Omega, non-Gaussian disributions. 1 Introduction In this paper we discuss the issue of portfolio ranking and selection. We will concentrate on selecting one portfolio among a finite set of portfolios, where each portfolio is characterized by its own distribution of returns p(x). This distribution may be inferred from past performances and assumed to be persistent, or it may be derived by some model of future performances. We distinguish two main cases: CASE #1 An amount A must be invested and it can be distributed between a risk free asset (that pays a risk free rate r) and the selected portfolio. CASE #2 An amount A must be invested exclusively in the selected portfolio.

Keywords

portfolio ranking, skewness, kurtosis, Omega, non-Gaussian disributions.