Does the choice of performance measure influence the evaluation of hedge funds

                           Journal of Banking & Finance 31 (2007) 2632–2647                          

www.elsevier.com/locate/jbf

Does the choice of performance measure influence the evaluation of hedge funds?

Martin Eling ^a,*, Frank Schuhmacher ^b,1

a  Institute of Insurance Economics, University of St. Gallen, Kirchlistrasse 2, 9010 St. Gallen, Switzerland

b  Department of Finance, University of Leipzig, Jahnallee 59, 04109 Leipzig, Germany

Received 21 March 2006; accepted 11 September 2006

Available online 31 January 2007

Abstract

The Sharpe ratio is adequate for evaluating investment funds when the returns of those funds are normally distributed and the investor intends to place all his risky assets into just one investment fund. Hedge fund returns differ significantly from a normal distribution. For this reason, other performance measures for hedge fund returns have been proposed in both the academic and practiceoriented literature. In conducting an empirical study based on return data of 2763 hedge funds, we compare the Sharpe ratio with 12 other performance measures. Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.  2007 Elsevier B.V. All rights reserved.

JEL classification: D81; G10; G11; G29

Keywords: Asset management; Hedge funds; Performance measurement; Rank correlation; Sharpe ratio

1. Introduction

Financial analysts and, often, individual investors themselves rely heavily on riskadjusted return (i.e., ‘‘performance’’) measures to select among available investment funds.

*

Corresponding author. Tel.: +41 71 243 40 93; fax: +41 71 243 40 40.

E-mail addresses: martin.eling@unisg.ch (M. Eling), schuhmacher@wifa.uni-leipzig.de (F. Schuhmacher).

1

Tel.: +49 341 973 36 70; fax: +49 341 973 36 79.

0378-4266/$ - see front matter  2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jbankfin.2006.09.015

The most widely known performance measure is the Sharpe ratio, which measures the relationship between the risk premium and the standard deviation of the returns generated by a fund (see Sharpe, 1966). The Sharpe ratio is an adequate performance measure if the returns of the funds are normally distributed^[1] and the investor wishes to place all his risky assets in just one fund.^[2] However, there are many other performance measures and there are two good arguments for the application of performance measures other than the Sharpe ratio.

First, a performance measure adequate for an investor who invests all his risky assets in just one fund may not be appropriate for an investor who splits the risky assets, e.g., between a market index and an investment fund (see, e.g., Bodie et al., 2005). The Sharpe ratio is appropriate in the first case, while in the second case, a performance measure that also takes into account the correlation between the market index and the respective fund would be more suitable.^[3] Such measures include the Treynor and Jensen measures (see Treynor, 1965; Jensen, 1968).^[4]

The second argument (put forth by many authors) for using another performance measure than the Sharpe ratio is that the choice of an adequate performance measure depends on the fund’s return distribution. In case of normally distributed returns, performance measures that rely on the first two moments of the return distribution (expected value, standard deviation), as does the Sharpe ratio, are appropriate. As hedge funds frequently generate returns that have a nonnormal distribution, it is commonly believed that these funds cannot be adequately evaluated using the classic Sharpe ratio (see, e.g., Brooks and Kat, 2002; Mahdavi, 2004; Sharma, 2004). Consideration of this issue has led to the development of new performance measures, which are currently under debate in the hedge fund literature.

In the following we analyze and compare 13 different performance measures: the Sharpe’s, Treynor’s, and Jensen’s measures, as well as Omega, the Sortino ratio, Kappa 3, the upside potential ratio, the Calmar ratio, the Sterling ratio, the Burke ratio, the excess return on value at risk, the conditional Sharpe ratio, and the modified Sharpe ratio. Using these measures, we analyze 2763 hedge funds to find an answer to the question of whether the ranking of the funds depends in a critical way on the choice of the performance measure.

The motivation for the analysis comes from recent research in which the choice of a particular measure has no significant influence on the ranking of an investment. Pfingsten et al. (2004) compared rank correlations for various risk measures on the basis of an investment bank’s 1999 trading book. In doing so, they found that different measures result in a largely identical ranking. Pedersen and Rudholm-Alfvin (2003) compared risk-adjusted performance measures for various asset classes over the period from 1998 to 2003. They found a high rank correlation between the performance measures’ rankings. In the hedge fund context, Eling and Schuhmacher (2006) found a high rank correlation between different performance measures using hedge fund indices data from 1994 to 2003.