Robust empirical optimization is almost the same as mean-variance optimization

We formulate a distributionally robust optimization problem where the deviation of the alternative distribution is controlled by a ϕ-divergence penalty in the objective, and show that a large class of these problems are essentially equivalent to a mean-variance problem. We also show that while a “small amount of robustness” always reduces the in-sample expected reward, the reduction in the variance, which is a measure of sensitivity to model misspecification, is an order of magnitude larger.