Algorithms and Learning for Fair Portfolio Design

ABSTRACTIn this paper we initiate the study of financial asset design with fairness as an explicit goal. We consider a variation on the classical problem of optimal portfolio design. In our setting, an individual consumer is specified by her risk tolerance, which corresponds to the variance in returns she is willing to accept in exchange for higher expected returns. We must design a (small) collection of portfolios and assign each consumer to a portfolio at lower or approximately equal risk than her tolerance. Fairness is imposed by demanding that the portfolios designed do not discriminate (in terms of expected returns) against less wealthy clients (or other specified protected groups). Our main results are algorithms for optimal and near-optimal portfolio design for both social welfare and fairness objectives, both with and without assumptions on the underlying group structure. We describe an efficient algorithm based on an internal two-player zero-sum game that learns near-optimal fair portfolios ex ante and show experimentally that it can be used to obtain a small set of fair portfolios ex post as well. For the special but natural case in which group structure coincides with risk tolerances (which models the reality that wealthy consumers generally tolerate greater risk), we give an efficient and optimal fair algorithm. We also provide generalization guarantees for the underlying risk distribution that has no dependence on the number of portfolios and illustrate the theory with simulation results.