Does the choice of performance measure influence the evaluation of hedge funds, страница 2

This study builds on these earlier studies as follows. In contrast to Pedersen and Rudholm-Alfvin (2003), we concentrate on hedge funds as an asset class, performance measures proposed for hedge funds, and the related debate concerning the suitability of classic and newer measures for the evaluation of hedge funds. In contrast to Eling and Schuhmacher (2006), we analyze individual hedge fund data instead of indices. Furthermore, we analyze the situation in which the fund under consideration represents the entire risky investment as well as the situation in which the fund represents only a portion of the investor’s wealth.

The result of our analysis can be summarized as follows: Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to other measures results in virtually identical rank ordering across the hedge funds.

The remainder of the paper is organized as follows. In Section 2, the performance measures are presented. Section 3 and 4 comprise an empirical study where all 13 measures are employed for determining the performance of 2763 hedge funds. In Section 3, we consider the decision-making situation where the fund under evaluation represents the entire risky investment. In Section 4, we examine the decision-making situation where the fund under evaluation represents only a portion of the investor’s wealth. In both sections, the data and the methodology are explained (Sections 3.1 and 4.1), the results of the performance measurement are presented (Sections 3.2 and 4.2), and robustness tests are conducted (Sections 3.3 and 4.3). The results of the study are summarized in Section 5.

2. Classic and newer approaches to measuring performance

2.1. Classic performance measurement – the Sharpe ratio

In hedge fund analysis, the Sharpe ratio is frequently chosen as performance measure and a comparison is made with the Sharpe ratios of other funds or market indices (see, e.g., Ackermann et al., 1999; Liang, 1999; Schneeweis et al., 2002). Using historical monthly returns r_i1, ... ,r_iT for investment fund i, the Sharpe ratio can be calculated as follows:

rdi  rf

Sharpe ratio_i ¼ ;            ð1Þ r_i

where r^d_i ¼ ðr_i1 þ  þ r_iT Þ=T represents the average monthly return for security i, r_f the risk-free monthly interest rate, and r_i ¼ ðððr_i1  r^d_i Þ² þ  þ ðr_iT  r_i^d Þ²Þ=ðT  1ÞÞ^0:5 the standard deviation of the monthly return. However, use of the Sharpe ratio in hedge fund performance measurement is the subject of intense criticism because hedge fund returns do not display a normal distribution (see Kao, 2002; Amin and Kat, 2003; Gregoriou and Gueyie, 2003). For example, the use of derivative instruments results in an asymmetric return distribution, as well as fat tails, leading to the danger that the use of standard risk and performance measures will underestimate risk and overestimate performance (see Kat, 2003; McFall Lamm, 2003; Geman and Kharoubi, 2003). To avoid this problem, newer performance measures that illustrate the risk of loss are recommended (see Pedersen and Rudholm-Alfvin, 2003; Lhabitant, 2004).

2.2. Newer approaches to performance measurement

2.2.1. Measuring performance on the basis of lower partial moments

Lower partial moments (LPMs) measure risk by negative deviations of the returns realized in relation to a minimal acceptable return s. The LPM of order n for security i is calculated as

                                    1 XT                                    n

              LPM_niðsÞ ¼            max½s  r_it;0 :

T

t¼1