Skewness in hedge funds returns: classical skewness coefficients vs Azzalini's skewness parameter

Recent literature discusses the persistence of skewness and tail risk in hedge fund returns. The aim of this paper is to suggest an alternative skewness measure, Azzalini's skewness parameter delta, which is derived as the normalized shape parameter from the skew-normal distribution. The paper seeks to analyze the characteristics of this skewness measure compared with other indicators of skewness and to employ it in some typical risk and performance measurements. The paper first provides an overview of the skew-normal distribution and its mathematical formulation. Then it presents some empirical estimations of the skew-normal distribution for hedge fund returns and discusses the characteristics of using delta with respect to classical skewness coefficients. Finally, it illustrates how delta can be used in risk management and in a performance measurement context. The results highlight the advantages of Azzalini's skewness parameter delta, especially with regard to its interpretation. Delta has a limpid financial interpretation as a skewness shock on normally distributed returns. The paper also derives some important characteristics of delta, including that it is more stable than other measures of skewness and inversely related to popular risk measures such as the value-at-risk (VaR) and the conditional value-at-risk (CVaR). The contribution of the paper is to apply the skew-normal distribution to a large sample of hedge fund returns. It also illustrates that using Azzalini's skewness parameter delta as a skewness measure has some advantages over classical skewness coefficients. The use of the skew-normal and related distributions is a relatively new, but growing, field in finance and not much has been published on the topic. Skewness itself, however, has been the subject of a great deal of research. Therefore, the results contribute to three fields of research: skewed distributions, risk measurement, and hedge fund performance.