Managing ESG ratings disagreement in sustainable portfolio selection

In sustainable portfolio selection, investors have a twofold objective: they want to achieve the best compromise between portfolio risk and return, but they also want to take into account the sustainability of their investment, assessed through some Environmental, Social, and Governance (ESG) evaluation criteria. The inclusion of sustainable goals in the portfolio selection process may have an impact on the portfolio financial performance. ESG scores provided by the rating agencies are generally considered good proxies for the sustainability performance of an investment, as well as appropriate measures for Socially Responsible Investments (SRI). In this framework, the lack of alignment between ratings provided by different agencies is a crucial issue that inevitably undermines the robustness and reliability of these evaluation measures. In fact, the ESG rating disagreement may produce conflicting information, implying difficulty for the investors in the ESG evaluation of their portfolios. This may cause underestimation or overestimation of the market opportunities for a sustainable investment. In this paper, we deal with a multi-criteria portfolio selection problem, taking into account risk, return, and ESG criteria. For the ESG evaluation of the securities, we consider more than one agency and propose a new approach to overcome the problem related to the disagreement between the ESG ratings given by different agencies. For our three-criteria portfolio selection problem, we present an optimization model which adopts the so-called sum operator to formulate a concise ESG evaluation measure. The natural formulation of the model, in which the portfolio risk is measured by the variance of its returns, leads to a nonlinear program, but we show that it can be reformulated as an equivalent convex quadratic model. We also show that the model can be generalized to include any convex portfolio risk measures. An extensive empirical analysis of the out-of-sample performance of this model is provided on real-world financial data sets. From a theoretical viewpoint, our work extends the use of sum methodology to quadratic programming.