Multiobjective portfolio optimization via Pareto front evolution

Abstract

Portfolio optimization is about building an investment decision on a set of candidate assets with finite capital. Generally, investors should devise rational compromise to return and risk for their investments. Therefore, it can be cast as a biobjective problem. In this work, both the expected return and conditional value-at-risk (CVaR) are considered as the optimization objectives. Although the objective of CVaR can be optimized with existing techniques such as linear programming optimizers, the involvement of practical constraints induces challenges to exact mathematical methods. Hence, we propose a new algorithm named F-MOEA/D, which is based on a Pareto front evolution strategy and the decomposition based multiobjective evolutionary algorithm. This strategy involves two major components, i.e., constructing local Pareto fronts through exact methods and picking the best one via decomposition approaches. The empirical study shows F-MOEA/D can obtain better approximations of the test instances against several alternative multiobjective evolutionary algorithms with a same time budget. Meanwhile, on two large instances with 7964 and 9090 assets, F-MOEA/D still performs well given that a multiobjective mathematical method does not finish in 7 days.