Distributionally Robust Portfolio Optimization

In this paper we consider the problem of portfolio optimization involving uncertainty in the probability distribution of the assets returns. Starting with an estimate of the mean and covariance matrix of the returns of the assets, we define a class of admissible distributions for the returns and show that optimizing the worst-case risk of loss can be done in a numerically efficient way. More precisely, we show that determining the asset allocation that minimizes the distributionally robust risk can be done using quadratic programming and a one line search. Effectiveness of the proposed approach is shown using academic examples.