Responsible investing and portfolio selection: a shapley-CVaR approach

Socially responsible investments represent the heart of a sustainable and inclusive economy. The goals set by the regulatory framework have encouraged the integration of responsible concerns into the corporate business strategy. In this paper, we present an operation research design under a risk management perspective that adjusts the portfolio selection problem for the ethical values of investors. We focus on the firms of the Euro Stoxx 50 during the years 2007-2019 and cluster the companies according to the Environmental Score (E). For each cluster, we build a portfolio that minimizes the Conditional Value-at-Risk (CVaR) introducing the constraint on the E into the optimization problem. We compute the Shapley Value for each portfolio using the minimized CVaR and the optimized E as the characteristic functions to yield, respectively, the contribution of the portfolios to the public welfare in terms of the exposure to the tail market risk and the required environmental commitment to mitigate it. The cluster analysis shows that the efforts of the firms to embrace environmental concerns are paid off with generally lower contribution to the tail market risk. From the two characterizations of the Shapley Value, the computation of well-known measures of financial performance (Sharpe, Sortino, and Calmar ratios) reveals that optimal portfolio choices should prioritize the environmental commitment of the companies.