Does the choice of performance measure influence the evaluation of hedge funds, страница 14

[7] For some hedge funds in the database there is also return data prior to 1985, but we choose to start our investigation in 1985 as there are too few observations before this point in time.

[8] Like other hedge fund databases, the ehedge database suffers from some data biases. Survivorship bias is calculated as the difference in fund returns between all funds and the surviving funds. In the ehedge database, this difference amounts 0.06% per month, which is comparable to other values found in the literature. See, e.g., Ackermann et al. (1999) and Liang (2000). There also might be a backfilling bias, as fund returns are in the database before its starting point in 2000. To take these bias problems into account, we conducted our investigation separately for surviving and for dissolved funds and for the time period from 2000 to 2004 (see Section 3.3). However, none of these variations influence our main result.

[9] A constant risk-free interest rate of 0.35% per month was used. This corresponds to the interest rate on 10year US Treasury bonds at 30th December 2004 (4.28% per annum). Alternatively, a rolling interest rate, an average interest rate for the period under consideration, or the interest rate at the beginning of the investigation period could be used. All three approaches yield almost identical results.

[10] In this and the following Table 5 we only display and calculate the bottom left triangle of the symmetric matrix, not the values on the diagonal (1.00) or in the mirror image on the upper-right triangle of the matrix.

[11] Note that the second test is much stronger than the first test. Nevertheless, we report the results of the first test because it is more widely known than the second test. We have not tested the hypothesis of unit correlation because even for normally distributed returns we would not expect all correlations to be equal to 1.

[12] The only noticeable deviation from the Sharpe ratio rankings can be found with the LPM-based measures if the minimal acceptable return is higher than 0.50%. This is due to the way these performance measures are constructed: as the minimum return increases, those strategies that display a high volatility of returns are favored because only those strategies have a sufficient number of returns that exceed the minimum return. This results in changes in performance values and in considerable changes in rankings and rank correlation.

[13] To calculate the correlation-based Treynor ratio and Jensen measure, we need to restrict ourselves to those 841 funds that have the full time series of 60 monthly returns between 2000 and 2004. The ranking of the Treynor ratio is also unique in that we first eliminate all funds with negative excess return from the analysis and then use the reciprocal of the negative Treynor ratio to rank the remaining funds. See Breuer et al. (2004, p. 393).

[14] See Ingersoll (1987, p. 104). If the return vector of individual securities is elliptically distributed, then the return distribution of any portfolio from these securities is characterized by its expected return and variance. In this case, the specific return distribution of the portfolio is of only secondary interest. Therefore, one does not need distributions having stability or reproduction characteristics, like the normal distribution, in order to found the mean-variance rule.