Fuzzy optimal portfolio selection based on multi-objective Mean-Variance-Skewness model by using NSGA-II algorithm

Abstract

Constructing an optimal portfolio is a critical decision for investors. The classic portfolio models generally consider mean and variance of return criteria, which are mostly intended single objective and have been analyzed and studied under conditions of certainty. But, in the real world problem of portfolio selection, is a multi-objective problem and in addition to the criteria of mean and variance of return, other criteria such as liquidity risk should also be considered. On the other hand, in practice, we are faced with a vague inaccurate data and portfolio selection problem must be studied under conditions of fuzzy uncertainty. In this paper, we have developed a new fuzzy multi-objective programming model based on mean-variance-skewness model for optimal portfolio selection under fuzzy uncertainty. The objective functions include maximizing the expected return, maximizing skewness or the chance to gain expected returns and minimizing liquidity risk. Rates of return, rates of turnover, and the maximum number of types of stocks included in the portfolio have been considered as triangular fuzzy numbers. To solve this problem an elitist non-dominated sorting genetic algorithm (NSGA-II) has been developed. Vector evaluated genetic algorithm (VEGA) and non-dominated sorting genetic algorithm (NSGA) were used to compare and evaluate the performance of the proposed solving method. Finally, the results obtained from the algorithms output are compared and analyzed, which indicates a higher efficiency of the proposed solving method compared to other methods.