Portfolio optimization using robust mean absolute deviation model: Wasserstein metric approach

Abstract

Portfolio optimization can lead to misspecified stock returns that follow a known distribution. To investigate tractable formulations of the portfolio selection problem, we study these problems with the ambiguity set defined by the Wasserstein metric. Robust optimization with Wasserstein models protects against ambiguity in the distribution when analyzing decisions. This study considers portfolio optimization using a robust mean absolute deviation model consistent with the Wasserstein metric. The core of our idea is to consider the sets of distributions that lie within a certain distance from an empirical distribution. However, since information in financial markets is often unclear, we extend this structure to the weighted mean absolute deviation model when the underlying probability distribution is not precisely known. We then construct a decomposition algorithm based on the Benders decomposition approach to solve such problems. For more efficient comparison, the acquired optimization programs are applied to real data.