Tail Risk in Hedge Funds: 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 which is derived as the normalized shape parameter from the skew-normal distribution. We empirically fit a large sample of hedge fund returns to the skew-normal distribution and illustrate that the skew-normal distribution is better able to catch the characteristics of hedge fund returns than the normal distribution. We then derive characteristics of the skewness parameter which has a number of advantages compared to common measures of skewness. For example, it has a limpid financial interpretation as a skewness shock on normally distributed returns. Furthermore, we show that measures tail risk coherently with two of the most popular risk measures—value-at-risk and conditional value-at-risk—and we therefore derive the inverse relationship between and these two risk measures.