Regret theory-based fuzzy multi-objective portfolio selection model involving DEA cross-efficiency and higher moments

Abstract This paper deals with fuzzy portfolio selection problems under the framework of bounded rationality, in which the higher moments and DEA cross-efficiency are taken into consideration. To this end, a regret cross-efficiency (RCE) evaluation model is first proposed to evaluate cross-efficiency scores of all assets by integrating several important financial information: return on equity, earnings per share, current ratio, price/earnings ratio, price/book ratio, and beta value. Then, by incorporating cross-efficiency into the mean–variance-skewness framework, a regret theory-based multi-objective portfolio selection model is developed. The model aims to maximize investor’s perceived utility (composed of utility, regret, and rejoice functions) with respect to the four objectives, namely mean–variance-skewness-efficiency, bounded by several realistic constraints. Additionally, considering the inherent uncertainty in data, the criteria related to RCE evaluation as well as asset returns are characterized as fuzzy variables. The current study not only empowers investors with an overall control over the preferences regarding all portfolio objectives, but also gives investors an opportunity to tweak their intrinsic behavioral tendencies from the perspective of regret aversion and rejoice preference, thus achieving the results that are compatible with the actual preferences of investors. A real-world empirical application is presented to demonstrate the effectiveness of the proposed model.