A novel approach to incorporate investor’s preference in fuzzy multi-objective portfolio selection problem using credibility measure

Abstract

Investment decision making is usually a multi-objective optimization problem in an uncertain environment. In a real-life scenario, an investor aims to choose a portfolio based on his/her preferences for each objective. Credibility theory has been attributed as one of the most effective ways to model uncertain portfolio attributes. LR fuzzy numbers based credibilistic moments have been used successfully in the recent past to model portfolio selection problems in uncertain environments. Traditionally, the preferences on portfolio attributes are reflected as user defined threshold values. This work proposes a novel way to integrate the investor’s preferences in the portfolio selection model. Investor’s preferences are specified as LR fuzzy numbers corresponding to the portfolio’s expected return and illiquidity distributions. The portfolio models formulated in this study attempt to attain them to the best possible extent. Four new models are presented considering uncertain portfolio attributes, namely, fuzzy return and fuzzy illiquidity. The models are solved using the MIBEX-SM Genetic Algorithm (GA) and ECE methodology. In order to demonstrate the efficient working of the proposed models, practical applications of portfolio selection problem using historical time series data of National Stock Exchange (NSE) is presented. Credibilistic Sharpe Ratio (CSR) has been used to compare the efficiency of models among themselves as well as with the Nifty−50 index.