Mean–Absolute Deviation Portfolio Models with Discrete Choice Constraints

Abstract

In this paper, we consider the problem of incorporating a wide set of real-world trading constraints to the mean-variance portfolio framework. Instead of using the mean-variance model directly, we use the equivalent Mean-Absolute Deviation (MAD) linear programming formulation. The addition of the trading constraints transforms the MAD model to a mixed-integer linear programming problem. We solve both the mean-variance and MAD models with the various trading constraints using a commercial solver and find that MAD model is substantially more tractable. In addition, a heuristic is developed for the extended MAD model to provide solutions for larger problem instances.