Aggregation of downside risk and portfolio selection

This article refines Markowitz’s classical portfolio theory by replacing standard deviation with a below-target deviation measure referred to as downside risk , in which only returns below the safe return of the market contribute to the quantification of risk. Downside risk is economically intuitive but neither a general deviation nor a coherent risk measure. We establish the existence and uniqueness of downside-efficient portfolios that aggregate the downside risks of finitely many assets. The tractability of downside-efficient portfolios allows for a risk analysis that parallels the classical mean–variance analysis. We show that all central tenets carry over if standard deviation is substituted with downside risk. A numerical example illustrates when downside-efficient portfolios outperform mean–variance efficient portfolios.