Nowadays, there is an uprising social pressure on big companies to incorporate into their decisionmaking process elements of the so-called social responsibility. Among the many implications of this fact, one relevant one is the need to include this new element in classic portfolio selection models. This paper meets this challenge by formulating a model that combines goal programming with "goal games" against nature in a scenario where the social responsibility is defined through the introduction of a battery of sustainability indicators amalgamated into a synthetic index. In this way, we have obtained an efficient model that only implies solving a small number of linear programming problems. The proposed approach has been tested and illustrated by using a case study related to the selection of securities in international markets.