Portfolio optimization of equity mutual funds with fuzzy return rates and risks

Portfolio selection is an important issue for researchers and practitioners. Focusing on equity mutual funds, this paper proposes a basic portfolio selection model in which future return rates and future risks of mutual funds are represented by triangular fuzzy numbers. Firstly, a cluster analysis is proposed to categorize the huge amount of equity mutual funds into several groups based on four evaluation indices: rates of return, standard deviation, turnover rate, and Treynor index, in order to aid investors in making the investment decision. The fuzzy optimization model is proposed to determine the optimal investment proportion of each cluster. The portfolio optimization problem is developed in two ways: to maximize the future expected return subject to the given greatest future risk, and to minimize the future risk subject to a required lowest future expected return. The proposed approaches are demonstrated by Taiwan equity mutual funds.