Portfolio Construction with Downside Risk

Abstract

Portfolio construction seeks an optimal trade-off between a portfolio’s mean return and its associated risk. Since risk may not be properly described by return volatility we optimize portfolios with respect to various measures of downside risk in an empirical out-of-sample setting. These optimizations are successful for most of the investigated measures when assuming perfect foresight of expected returns, moreover, these findings still hold when using more naive return estimates. The reductions in downside risk are most convincing for semivariance, semideviation, CVaR and loss penalty while value at risk and measures related to skewness appear rather useless for portfolio construction purposes.

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