Existing portfolio combination rules that optimize the out-of-sample performance under parameter uncertainty assume multivariate normally distributed returns. However, we show that this assumption is not innocuous because fat tails in returns lead to poorer out-of-sample performance of the sample mean–variance and sample global minimum-variance (GMV) portfolios relative to normality. Consequently, when returns are fat-tailed, portfolio combination rules should allocate less to the sample mean–variance and sample GMV portfolios, and more to the risk-free asset, than the normality assumption prescribes. Empirical evidence shows that accounting for fat tails in the construction of optimal portfolio combination rules significantly improves their out-of-sample performance.