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An alternative route to performance hypothesis testing Authors: Bernd Scherer Source: Journal of Asset Management Date: June 2004 |
The determination of confidence intervals is a non-negligible step in a performance analysis problem, in addition to the calculation of risk-adjusted ratios. However, confidence bands are difficult to determine in the presence of arbitrary risk-adjusted returns, sample sizes and distribution.
Scherer uses a bootstrapping method as a generalized method to obtain a bootstrap sampling distribution. It is on the basis of this resampled distribution that the normality of small samples will be judged.
From January 1990 to April 2003, the Sharpe and Sortino ratios of the HFR Fund of Funds index are calculated. While the resampled distribution of the Sharpe ratio is normal, the Sortino ratio exhibits a non-normal distribution. Using a 95 per cent confidence band, both ratios are significantly different from zero.
To verify the relevance of this confidence interval, a double bootstrap procedure is conducted. Again, the Sortino ratio displays a non-normal distribution.
However, the author stresses that the bootstrapping method has to be adapted to the autocorrelation of returns in the hedge fund universe. Neither resulting Sortino or Sharpe ratios are statistically different from zero on a larger number of series than expected with a lower confidence bound of 2.5 per cent.
