Guaranteed Rate of Return for Excess Investment in a Fuzzy Portfolio Analysis

With increasing profit in securities investment, portfolio analysis has become a major topic for investors. We propose a fuzzy portfolio model as it is an efficient portfolio selection method associated with uncertain or vague returns. Although many researchers focus on studying the fuzzy portfolio model, they do not consider excess investment based on the selected guaranteed rates of return for some securities. To manage such an investment, a new fuzzy return function—where some securities are considered for excess investment based on the selected guaranteed rate of return—is introduced to improve the possibilistic mean and variance values, leading to a revised fuzzy portfolio model. Accordingly, to set certain securities for excess investment in the fuzzy return function, efficient portfolios for each selected guaranteed rate of return can be obtained under different levels of investment risk. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model. This example shows that the expected rate of return of a lower guaranteed rate of return is larger than that of a higher guaranteed rate of return under different levels of investment risks. The portfolio analysis with some guaranteed rate of returns can provide more invested risk selection.