Does the choice of performance measure influence the evaluation of hedge funds, страница 10

We used the test statistics described in Section 3.2 to check the statistical significance of the rank correlations. The hypothesis of independence of the measurement series was again rejected for all correlation coefficients at a significance level of a = 0.01. We also again checked the hypothesis that the rank correlation is smaller than a certain given number x. For a significance level of a = 0.01, the hypothesis that the rank correlation is smaller than x is rejected for all x smaller than 0.916. We thus conclude that it does not much matter which measure (except the Treynor ratio) is used to assess portfolio performance, as nearly all measures produce similar results.

4.3. Robustness of the findings

We examined the robustness of the results using the tests described in Section 3.3. None of the changes listed in that section had a crucial influence on the results given in Section 4.2 (the results of these five tests are available upon request). However, for the modified decision-making situation under consideration here, two additional robustness tests were made.

First, we altered the portion of hedge funds in the investor’s portfolio from between 1% and 10%. Table 6 shows the resulting rank correlations of the performance measures in relation to the Sharpe ratio. For example, the third column of Table 6 shows rank correlations for the situation where the investor wants to shift exactly 2% of his portfolio into hedge funds (we also show the situation where the portfolio is invested 100% in hedge funds, which is the decision-making situation discussed in Section 3).

Table 6

Results of robustness tests

Performance measure	Rank correlation in relation to the Sharpe ratio when the portion of hedge funds is...											stocks is...
	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	100%	40%
Omega	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.99	1.00
Sortino ratio	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.99	1.00
Kappa 3	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.98	1.00
Upside potential ratio	0.93	0.93	0.93	0.94	0.94	0.94	0.94	0.94	0.94	0.94	0.95	0.91
Calmar ratio	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.99	0.99	0.97	0.96
Sterling ratio	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.98	0.98
Burke ratio	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.98	0.96
Excess return on value at risk	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.99	1.00
Conditional Sharpe ratio	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.98	0.99
Modified Sharpe ratio	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.91	1.00
Jensen measure	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.69	1.00
Treynor ratio	0.34	0.35	0.36	0.37	0.37	0.38	0.39	0.40	0.41	0.41	0.44	0.13
Average	0.94	0.94	0.94	0.94	0.94	0.94	0.94	0.94	0.94	0.94	0.90	0.89