Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable

Abstract

Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.