Comparison between Fuzzy and Not Fuzzy Portfolio Optimization under Downside Risk Measures

Wilma Handayani, Sulaiman, Suvriadi Panggabean, Liza Setyaning Pertiwi, Dr. Sutarman M. Sc

Abstract: This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained so that a given expected return should be achieved. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. And then we compare those with a given not fuzzy portfolio one. Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form.

Keywords: Portfolio, Expected return, Fuzzy expected return, Interval-valued expectation, Downside risk