Application of Fuzzy Theory to the Investment Decision Process

In the present paper, we propose a new approach to portfolio optimization that allows portfolio managers to construct portfolios that reflect their views about risk assets by applying fuzzy theory. The proposed approach to the investment decision process is based on the mean-variance approach proposed by Markowitz (1952,1959) and uses the concept of asset market equilibrium proposed by Sharpe (1964). For portfolio managers, it is very meaningful to use the equilibrium expected excess returns associated with the capital market as a reference. The proposed approach enables a new method for incorporating the views of portfolio managers to aid in the investment decision process. Moreover, in order to estimate the distribution of an unknown true membership function of the views of portfolio managers concerning risk assets, we propose a fuzzy information criterion to evaluate the fitness of the distribution between an unknown true membership function and a hypothetical membership function. In particular, the proposed approach enables a group of portfolio managers of pension funds to obtain an important solution that realizes optimal expected excess returns of risk assets by specifying the vague views of portfolio managers as a fuzzy number.