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 financial 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 when the standard deviation is replaced with our downside-risk measure. Among these is a downside security market line along with a linear pricing rule , which, contrary to the mean-variance case, provides arbitrage-free asset prices. A numerical investigation illustrates when downside-efficient portfolios outperform mean-variance efficient portfolios.