Data-Driven Portfolio Management with Quantile Constraints

We investigate an iterative, data-driven approximation to a problem where the investor seeks to maximize the expected return of her portfolio subject to a quantile constraint, given historical realizations of the stock returns. Our approach involves solving a series of linear programming problems and thus can be solved quickly for problems of large scale. We compare its performance to that of methods commonly used in the finance literature, such as fitting a Gaussian distribution to the returns ([1],[2]). We also analyze the resulting efficient frontier and extend our approach to the case where portfolio risk is measured by the inter-quartile range of its return.