This paper provides a simple method to predict how the (higher order) return properties of a single strategy fund of hedge funds will vary as one or more funds are added to, or removed from, the portfolio. Our model-free approach uses average co-moments obtained from the universe of available funds to develop a functional relationship between portfolio return distributions and the number of funds in the portfolio. We show that some single strategy funds of hedge funds may be under-diversified and that covariance, coskewness, and cokurtosis, rather than variance, skewness and kurtosis, matter most in portfolio diversification.