A sequential goal programming model with fuzzy hierarchies to sustainable and responsible portfolio selection problem

Abstract

Sustainable and responsible (SR) investors have to address two criteria types: both financial ones and those pertaining to sustainability and social responsibility. We present a comfortable tool for SR investors that allow them to express their preferences at two levels: first, by comparing criteria of the same nature, and second, via the comparison between the two superior level criteria (the financial and the SR objectives). Owing to the difficulty involved in determining a precise preference between the conflicting objectives, we address this by goal programming with fuzzy hierarchies (GPFH) modelling. This methodology is a modification of the lexicographic GP approach whereby the relative importance relations among the criteria are modelled by fuzzy relations. The proposed sequential handling for the SR portfolios selection provides information to the investors on the best result they can achieve in regard to their goals. An application to a set of UK-SR mutual funds is presented.

Keywords:

• goal programming with fuzzy hierarchies
• socially responsible investment fund
• portfolio selection
• fuzzy sets

Acknowledgements

The authors wish to gratefully acknowledge the financial support from the Spanish Ministry of Education, Project ECO2015-66521, and would like to thank the anonymous reviewers and the editor for their valuable comments and suggestions to improve the quality of the paper.

Notes

1 This application has been carried out using the MATLAB R2013a environment.

2 The value of fuzzy number with respect to a reduction function s(α), denoted by , is defined as: . In this work, s(α)=α.

3 We consider the equally probable scenarios, therefore: π_j=1/J.