Multiobjective Fuzzy Portfolio Performance Evaluation Using Data Envelopment Analysis Under Credibilistic Framework

Abstract

In this article, two different multiobjective fuzzy portfolio selection models are presented. The significant criteria considered for portfolio selection are risk (variance or conditional value at risk), return, liquidity, and entropy. Here, the return of the portfolio is considered to be satisfied by a minimum return threshold constraint. Also, to introduce some degree of diversification in the model, a lower and upper bound constraint on investment in an asset is used along with the capital budget and no short selling constraints. Trapezoidal fuzzy returns are considered to incorporate the inherent uncertainty of the stock market, which is handled by using the credibility theory. The weighted sum approach is used to aggregate the objectives and characterize different investor attitudes. Random sample portfolios with progressively increasing sample sizes are generated that obey the constraints of the portfolio models. These random sample portfolios with multiple inputs (risk and entropy) and multiple outputs (return and liquidity) are evaluated in terms of their performance by using data envelopment analysis. Furthermore, a frontier improvement technique existing in the literature is used to rebalance the inefficient random sample portfolios to make them efficient, so that an investor may have more avenues to select efficient portfolios. A detailed numerical illustration with a simulation study using different sample sizes is presented to substantiate the proposed study.