Hedge Fund Investment Management
With contributions from some of the most prominent and successful Hedge Fund managers in the world, this book explains the different styles of funds and summarizes the key issues in every one.
TABLE OF CONTENTS Hedge Fund Investment Management
Chapter 9: On Ranking Schemes and Portfolio Selection
MASSIMO DI PIERRO AND JACK W. MOSEVICH
ABSTRACT
There are now in use several risk-return indicators, which are utilized to rank historical returns of portfolios. Some popular ones are the Sharpe Ratio, the Sortino Ratio, Omega and the Stutzer Index, among others. It is well known that portfolio log-returns, especially of alternative assets, are not normally (Gaussian) distributed. This is the reason for the development of indicators other than the Sharpe Ratio. The purpose of this paper is to evaluate the relationships between these indicators for both Gaussian and non-Gaussian distributions. We prove mathematically that rankings are essentially the same for these indicators in a Gaussian environment, and different in a non-Gaussian one, which is as it should be. We are able to compute an implied utility function for the indicators and find that it is the same for all of them, something not very intuitive. We then propose a utility function, which corresponds more with what we expect investors to desire. We conclude by showing how to relate our results to the Markowitz MPT.
9.1 INTRODUCTION
In this paper we discuss different criteria for ranking portfolios including the Sharpe ratio (Sharpe, 1964), the Sortino ratio (Sortino and Van Der Meer, 1991; Sortino and Price, 1994; Sortino and Forsey, 1996), the kappa ratio (Kaplan and Knowles, 2004), the omega ratio (Shadwick and Keating, 2002; Sortino, 2001; Wilmott, 2000) and the Stutzer index (Amenc, Malaise, Martellini and Vaisse). We prove that in a world where portfolio returns are Gaussian distributions, all...
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