Abstract: The monthly return distributions of many hedge fund indices exhibit highly unusual skewness and kurtosis properties as well as first-order serial correlation. This has important consequences for investors. We demonstrate that although hedge fund indices are highly attractive in mean-variance terms, this is much less the case when skewness, kurtosis and autocorrelation are taken into account. Sharpe Ratios will substantially overestimate the true risk-return performance of (portfolios containing) hedge funds. Similarly, mean-variance portfolio analysis will over-allocate to hedge funds and overestimate the attainable benefits from including hedge funds in an investment portfolio. We also find substantial differences between indices that aim to cover the same type of strategy. Investors? perceptions of hedge fund performance and value added will therefore strongly depend on the indices used.