Portfolio Diversification Effects of Downside Risk

Risk managers use portfolios to diversify away the unpricedrisk of individual securities. In this article we compare thebenefits of portfolio diversification for downside risk in casereturns are normally distributed with the case of fat-taileddistributed returns. The downside risk of a security is decomposedinto a part which is attributable to the market risk, an idiosyncraticpart, and a second independent factor. We show that the fat-tailed-baseddownside risk, measured as value-at-risk (VaR), should declinemore rapidly than the normal-based VaR. This result is confirmedempirically.