Does the choice of performance measure influence the evaluation of hedge funds, страница 5

We obtained hedge fund data from ehedge, a German financial services company founded in 2000 by the LCF Rothschild Group and bmp Venture Capital. The company provides hedge fund information and other services to institutional investors (see www. ehedge.de). As of July 2005, the ehedge database contained 2763 individual hedge funds reporting monthly net-of-fee returns for the time period from 1985 to 2004.^[7] The database contains additional information on each fund, such as company name, strategy description, assets under management, and management fees. The database includes 2106 (76.22%) surviving funds and 657 (23.78%) dissolved funds. The total assets under management are about $229.47 billion, which is approximately one-quarter of the worldwide hedge fund market volume of $950 billion (for the hedge fund market volume, see Van,

2005).^[8]

Table 1

Descriptive statistics for 2763 hedge fund return distributions

The return distributions of the hedge funds are analyzed in Table 1. The table shows the mean, the median, the standard deviation, the minimum, and the maximum of the first four moments of the return distribution (mean value, standard deviation, skewness, and excess kurtosis). On basis of the Jarque-Bera test, the assumption of normally distributed hedge fund returns must be rejected for 39.12% (44.08%) of the funds at the 1% (5%) significance level.

The findings reported in the following section were generated by first using the measures presented in Sections 2.1 and 2.2 to determine hedge fund performance. For the LPM-based performance measures we assume that the minimal acceptable return is equal to the risk-free monthly interest rate (s = 0.35%).^[9] For the Sterling and Burke ratios, the five largest drawdowns are considered (N = 5). The value-at-risk-based performance measures were calculated using a significance level of a= 0.05. Next, for each performance measure the funds were ranked on the basis of the measured values. Finally, the rank correlations between the performance measures were calculated.

3.2. Findings

In Table 2, we present the Spearman rank correlation coefficients between the performance measures.^[10]

All performance measures display a very high rank correlation with respect to the Sharpe ratio as well as in relation to each other. The rank correlation coefficient for the Sharpe ratio varies between 0.93 (Sterling ratio) and 1.00 (excess return on value at risk). On average, the rank correlation of the Sharpe ratio in relation to the other performance measures amounts to 0.97. There is also a very high correlation between the Sharpe ratio, Omega, the Sortino ratio, the Sterling ratio, Kappa 3, and the conditional Sharpe ratio (rank correlation greater than 0.98 in each case).

We also find high rank correlations when comparing the new performance measures to each other. The highest possible rank correlation of 1.00 can be found when comparing Kappa 3 and the Sortino ratio, while the lowest value of 0.92 is found with the modified Sharpe ratio and the Sterling ratio. The average rank correlation between the performance measures is 0.96.

Table 2

Rank correlation based on different performance measures