The Performance Evaluation of Hedge Funds: are Investors Mislead by Standard Mean-Variance Statistics?

This paper shows that hedge fund returns may suffer from excess smoothness, positive kurtosis and negative skewness. We argue that these distribution properties cause standard mean-variance statistics to underestimate the true variability and beta, and overrate the true performance. We discuss alternatives that do take into account excess smoothness, kurtosis and skewness, such as unsmoothed returns, summed betas and VaR modifications based on the Cornish-Fisher expansion. We conclude that the investor is, partly, mislead by standard mean-variance statistics as the performance of the hedge funds under consideration turns out to be significantly lower if higher moments and excess smoothness are taken into account. We end with a short digression on the hidden risks of hedge funds that are, to our knowledge, not taken into account by any performance model at the moment.

Keywords:hedge funds, skewness, modified VAR, Cornish-Fisher