Multi-criteria Fuzzy Portfolio Optimization

Abstract

In this chapter, we describe fuzzy portfolio selection models using five criteria: short term return, long term return, dividend, risk and liquidity. For portfolio return, we consider short term return (average performance of the asset during a 12-month period), long term return (average performance of the asset during a 36-month period) and annual dividend. This is done in order to capture subjective preferences of the investors for portfolio return. For a given expected return, the negative semi-absolute deviation is penalized which quantifies portfolio risk. Further, we categorize all individual investor attitudes towards bearing portfolio risk into one of the following two distinct classes: aggressive (weak risk aversion attitude) and conservative (strong risk aversion attitude). The nonlinear S-shape membership functions are employed to express vague aspiration levels of the investor regarding the multiple criteria used for portfolio selection.