A polynomial goal programming model for portfolio optimization based on entropy and higher moments

Portfolio selection is a critical factor in investment. Having considered a number of risky assets, fund managers must choose the optimum portfolio. Stock values can be affected by different types of events such as governmental crises, economic turmoil and industrial improvements. Due to the vague nature of these events, it is difficult to estimate the future value of stocks. However, Markowitz's Modern portfolio theory, which is principally focused on portfolio risk, has introduced a novel model for stock diversification. According to this approach, an investor can decrease portfolio risk basically by holding mixtures of assets that are not highly positively correlated. Meanwhile, an efficient portfolio can only be obtained by focusing on return and risk simultaneously. When the normality assumption of return series of assets are not valid, higher moments can also be added to ensure the efficiency of the Markowitz model. In this study, a new approach for polynomial goal programming which is based on a mean-variance-skewness-kurtosis-entropy model is proposed. Two real data sets were used in experiments to verify the effectiveness of the proposed model. Based on a variety of portfolio optimization model, the out-of-sample performance of two entropy measures- Shannon entropy and Gini-Simpson entropy- were compared in the portfolio selection. The results indicate that the proposed approach is well-suited especially for portfolio models with higher moments.