Algorithms and Learning for Fair Portfolio Design

TL;DR

This paper develops algorithms for designing fair and optimal portfolios for diverse consumer groups, balancing social welfare and fairness, with theoretical guarantees and practical experimental validation.

Contribution

It introduces algorithms for fair portfolio design that optimize social welfare and fairness, including special cases with group-risk alignment, supported by theoretical analysis and experiments.

Findings

Efficient algorithms for near-optimal fair portfolios.

Theoretical guarantees on generalization of risk distributions.

Experimental validation demonstrating practical effectiveness.

Abstract

We consider a variation on the classical finance problem of optimal portfolio design. In our setting, a large population of consumers is drawn from some distribution over risk tolerances, and each consumer must be assigned to a portfolio of lower risk than her tolerance. The consumers may also belong to underlying groups (for instance, of demographic properties or wealth), and the goal is to design a small number of portfolios that are fair across groups in a particular and natural technical sense. 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.