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

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Abstract 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.

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