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Risk managers use portfolios to diversify away the un-priced risk of individual securities. In this paper we compare the bene...ts of portfolio diversi...cation for downside risk in case returns are normally distributed with the case 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-Riskdoi:10.2139/ssrn.653064 fatcat:vjzplbfow5e6hiyaymqdzxycwi