A Hierarchical Approach to a Tri-Objective Portfolio Optimization Problem Considering an ESG Index

Traditional portfolio construction primarily revolves around a bi-objective approach, focusing on minimizing portfolio variance while maximizing expected returns. However, this approach leaves out other objectives that could interest decision makers. In this work, we incorporate an extra objective, namely the environmental, social, and governance index (ESG), as a secondary objective. This addition empowers investors to customize their portfolios by defining explicit trade-off thresholds between expected returns and risk, considering the ESG index. To achieve this goal, we make use of external archiving techniques and evolutionary algorithms. In particular, we first find approximate solutions to the bi-objective problem; then, we look for efficient solutions for ESG. We tested our approach with data on the Dow Jones, S&P500, and Nasdaq100 from Yahoo Finance. The results show that the proposed methodology can identify portfolios with good returns and risks considering ESG.