A four-objective mean-variance-CVaR-ESG model for portfolio selection problem

Environmental, Social, and Governance, or simply ESG, has become an increasingly important topic in recent years. On the other side, the conditional value-at-risk (CVaR) is often used to quantify losses beyond the value-at-risk (VaR). In this work, we propose a four-objective portfolio optimization model, where the portfolio choice is made based on four criteria: the expected portfolio return, the portfolio variance, the portfolio CVaR, and the portfolio ESG score. The four-objective problem is transformed into a single-objective problem using the ϵ-constraint technique. The resulting single-objective problem consists in minimizing the portfolio variance with constraints on the target levels of the expected portfolio return, portfolio CVaR, and portfolio ESG score. Assuming a discrete probability space, the above problem is formulated as a convex quadratic programming problem. We compare the out-of-sample performance of the proposed portfolio optimization model against two competitive models. The datasets used to evaluate the out-of-sample performance are the Dow Jones Industrial Average (DJIA) and the Euro Stoxx 50. Our analysis demonstrates that our model is a valid alternative to existing models in the literature.