A great deal of recent literature discusses the persistence of skewness and non-normality in hedge fund returns (see, e.g., Mitchell and Pulvino, Journal of Finance, 2001; Darius et al., Quantitative Finance, 2002; Agarwal and Naik, Review of Financial Studies, 2004). The aim of this paper is to add three new aspects to this discussion: First, we first show via goodness-of-fit tests that hedge fund returns can be well described by skew-normal distributions. Second, we rewrite the most common traditional performance ratios (e.g., Sharpe ratio, Omega) in a closed-form using the skew-normal distribution. We empirically compare the traditional performance ratios with the new skew normal ratios and derive common characteristics. Our skew-normal ratios spotlight the influence of the shape parameters on hedge fund performance. However, as long as we deal with performance ratios for moderate investor style, such as the Sharpe ratio or Omega, the skew-normal formulae of ratios provide virtually equal results than the empirical ones. Vice versa, as we use ratios tailored to a more aggressive investment style, such as Rachev ratios, the traditional and skew-normal formulas no longer correspond well. Finally, we show that the normalized shape parameter from the skew-normal distribution (also called Azzalini’s skewness parameter) can be used to grasp immediate perception of how the empirical returns differ from being Gaussian and how this discrepancy may impact performance.
Performance Ratios for Skew-normal Hedge Funds
TIBILETTI, Luisa
2008-01-01
Abstract
A great deal of recent literature discusses the persistence of skewness and non-normality in hedge fund returns (see, e.g., Mitchell and Pulvino, Journal of Finance, 2001; Darius et al., Quantitative Finance, 2002; Agarwal and Naik, Review of Financial Studies, 2004). The aim of this paper is to add three new aspects to this discussion: First, we first show via goodness-of-fit tests that hedge fund returns can be well described by skew-normal distributions. Second, we rewrite the most common traditional performance ratios (e.g., Sharpe ratio, Omega) in a closed-form using the skew-normal distribution. We empirically compare the traditional performance ratios with the new skew normal ratios and derive common characteristics. Our skew-normal ratios spotlight the influence of the shape parameters on hedge fund performance. However, as long as we deal with performance ratios for moderate investor style, such as the Sharpe ratio or Omega, the skew-normal formulae of ratios provide virtually equal results than the empirical ones. Vice versa, as we use ratios tailored to a more aggressive investment style, such as Rachev ratios, the traditional and skew-normal formulas no longer correspond well. Finally, we show that the normalized shape parameter from the skew-normal distribution (also called Azzalini’s skewness parameter) can be used to grasp immediate perception of how the empirical returns differ from being Gaussian and how this discrepancy may impact performance.
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