The Tail that Wags the Hedge Fund Dog

Abstract

We consider a portfolio of hedge funds as a portfolio of insurance policies against a set of risk factors. We highlight some deficiencies of linear estimation procedures and apply several nonlinear approaches to an individual hedge fund and also to a set of investable hedge fund indices. We apply Extreme Value Theory to the estimation of hedge funds tail risk. We find that although some hedge fund indices may apparently be well-fit by short-, medium-, and long-tailed classes of Generalized Extreme Value distributions, in practice it is more conservative to use the longest-tailed class of GEV for which statistically significant goodness-of-fit may be attained. In particular we find that, examining the monthly returns of twelve HFRX investable hedge fund indexes over the ten-year period from January 1998 through December 2007, seven indexes are well-fit by long-tailed distributions including the generalized Pareto and the Cauchy, while five indexes are well-fit by the medium-tailed Gamma distribution. Care should be taken because seven of the twelve indexes also appear to be well-fit by the normal distribution, and we caution that for purposes of tail-risk estimation, acceptance of the normal distribution would prove illusory and hazardous.