The environmental, social, and governance (ESG) rating of firms is a useful tool for stakeholders and investment decision-makers. This paper develops a rough set model to relate ESG scores to popular corporate financial performance measures. This methodology permits handling with information in an uncertain, ambiguous, and imperfect context. A large database was gathered, including ESG scores, as well as industry sector and financial variables for publicly traded European companies during the period 2013–2018. We carried out 500 simulations of the rough set model for different values in the discretization parameter and different grouping scenarios of firms regarding ESG scores. The results suggest that the variables considered are useful in the prediction of ESG rank when firms are clustered in three or four equally balanced groups. However, the prediction power vanishes when a larger number of groups is computed. This would suggest that industry sector and financial variables serve to find big differences across firms regarding ESG, but the significance of the model drops when small differences in ESG performance are scrutinized.

We propose a multi-objective approach for portfolio selection, which allows investors to consider not only return and downside risk criteria but also to include environmental, social and governance (ESG) scores in the investment decision-making process. Owing to the uncertain environment of portfolio selection, the return and ESG score of each asset are considered as independent L-R power fuzzy variables. To make the model more realistic, we take budget, floor ceiling and cardinality constraints into account. In order to select the optimal portfolio along the efficient frontier, we apply the Sortino ratio in a credibilistic environment. The subsequent empirical application uses a data set from Bloomberg's ESG Data in combination with US Dow Jones Industrial Average data. The experimental results show that the proposed model offers promising results for socially responsible investors seeking ethical and sustainability goals beyond the return-risk trade-off and its ability to beat the benchmark.

The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio’s performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.

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