In the literature, hedge funds often are evaluated by Markowitz portfolio selection theory, under which hedge funds appear to be a remarkable opportunity, seeing as they are characterized by low correlations to stock and bond markets and therefore offer the chance of better portfolio diversification. However, this approach neglects three problems concerning the returns of this alternative type of investment. When comparing the returns of hedge funds to those of traditional investments, the former show a significant extent of autocorrelation, bias, and fat tails. When these problems are incorporated in a performance evaluation of hedge funds, this type of fund loses most of its attraction.