Controlling portfolio skewness and kurtosis without directly optimizing third and fourth moments

•We propose a new mean-variance approach that can control higher moments.•Our model does not directly impose higher moment terms in the formulation.•Our model employs robust formulation with a specific choice of uncertainty set.•We provide analytical proofs showing our model can control higher moments.•We present empirical results supporting the validity of our model.

In spite of their importance, third or higher moments of portfolio returns are often neglected in portfolio construction problems due to the computational difficulties associated with them. In this paper, we propose a new robust mean-variance approach that can control portfolio skewness and kurtosis without imposing higher moment terms. The key idea is that, if the uncertainty sets are properly constructed, robust portfolios based on the worst-case approach within the mean-variance setting favor skewness and penalize kurtosis.