Multi-objective optimization using evolutionary algorithms: An antifragile approach to portfolio selection

Abstract

Considering the documented difficulties in empirically applying widely recognized portfolio selection models that use mean-variance relationships as central features, as proposed by Markowitz and later extended in CAPM by Sharpe, this study aims to extend these theories. Drawing upon contributions from Keating and Shadwick, which highlight CAPM's limitations in handling non-normal distributions, the study introduces non-convex attributes into a multi-objective optimization framework using evolutionary algorithms. Additionally, an antifragile metric known as CVIX is implemented to assess conditional correlation with the VIX, thereby addressing questions concerning the feasibility of market portfolios outperforming CAPM's theoretical market portfolio. Optimizations were carried out on U.S. markets, using time frames from 1994 to 2022. The results are encouraging; in contrast to optimizations that employed solely convex attributes, which yielded inferior outcomes in all scenarios compared to the OCAPM model, applying the antifragile metric along with non-convex attributes in multi-objective optimization produced superior results.

DOI:https://doi.org/10.56238/sevened2024.010-024