Portfolio selection with a systematic skewness constraint

•We examine the impact of systematic skewness on portfolio selection.•The systematic skewness is achieved at the expense of mean-variance efficiency.•The systematic skewness constraint enhances the skewness of efficient portfolios.

This paper investigates portfolio selection within a mean-variance-systematic skewness framework. We derive the composition of efficient portfolios in our model, and analyze the properties of these efficient portfolios. We show that the required systematic skewness is achieved at the expense of traditional mean-variance efficiency, and that a more stringent systematic skewness constraint induces a greater loss in mean-variance efficiency. Our numerical analysis demonstrates that the presence of the systematic skewness constraint helps improve the skewness of efficient portfolios in our model over the skewness of traditional efficient portfolios.