Risk managers use portfolios to diversify away the unpriced risk of individual securities. In this article we compare the benefits of portfolio diversification for downside risk in case returns are normally distributed with the case of fat-tailed distributed returns. The downside risk of a security is decomposed into a part which is attributable to the market risk, an idiosyncratic part, and a second independent factor. We show that the fat-tailed-based downside risk, measured as value-at-risk (VaR), should decline more rapidly than the normal-based VaR. This result is confirmed empirically.