DEA based fuzzy portfolio evaluation models integrated with TOPSIS techniques to rank the efficient Portfolios under different risk indicators

Abstract

Abstract Data Envelopment Analysis models estimates the relative efficiency of a group of identical Decision-Making Units (DMUs) with multiple inputs and outputs. Since the rank of all efficient DMUs in DEA is one, thus there is no other method to distinguish their performance. Now, as all the efficient DMUs may be considered an alternative, the ranking of all efficient units is required. Here, we made an attempt to assess the portfolios from two perspectives: efficiency and performance. Accordingly, the portfolios have been ranked through a two-stage process using DEA-based fuzzy portfolio estimation models in stage 1 and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method in stage 2. To evaluate the portfolio efficiency in a fuzzy environment, two types of portfolios are considered, having possibilistic mean return as output and possibilistic variance and possibilistic semi-variance as input criteria, respectively. As an output variable can take positive as well as negative values, the Range Directional Measure (RDM) model of DEA has been extended to fuzzy environment and used to rank all the portfolios as per their efficiency score. By utilizing the properties and advantages of both methods, this paper proposed a hybrid approach (DEA-TOPSIS method) which provides the complete ranking of all efficient fuzzy portfolios. Detailed numerical illustrations are presented here to authenticate the proposed approach, and the obtained results are compared with other existing DEA methods that validate the accuracy and feasibility of the proposed technique.