A fuzzy nonlinear model approach with CAPM for portfolio optimization

In the stocks markets, main factors which have to be considered to make accurate investment decisions are return and risk. Since the knowledge related this couple is not certain and precise, deterministic and stochastic models used in portfolio optimization are not sufficient for investment decisions. In this study, a new fuzzy nonlinear portfolio model is proposed by means of membership functions developed for return and risk. In construction of the mentioned model, Konno and Yamazaki’s model is taken as reference model. As a second stage, expected return of this model is assumed to be fuzzy. Since the expected return is taken as fuzzy, the values of objective function which denote risk can also be accepted as fuzzy. For this reason the nonlinear programming model with fuzzy source and objective is constituted. Besides, in order to consider stocks market trend, the constraint, which includes sensitivity of market, is added in this model by means of membership function of portfolio beta that is consistent with Capital Asset Pricing Model (CAPM). In application part, using the closure data of stocks operated in ISE30 index, the performance of the proposed model is compared with ones of Markowitz and Konno-Yamazaki model