Higher moment of portfolio optimization with Polynomial Goal Programming approach

Abstract

The mean-variance (MV) model has been introduced in portfolio optimization to minimize the risk and achieve the target rate of return in the investment. However, the higher moment skewness and kurtosis are not considered in this model. The investors prefer portfolio with high skewness value and low kurtosis value so that the probability of getting extreme negative rates of return will be reduced. Therefore, the MV model has been extended to the mean-variance-skewness-kurtosis (MVSK) model by incorporating the skewness and kurtosis factor. The objective of this study is to construct the optimal portfolio of the MVSK model by using the polynomial goal programming (GP) approach. The data of this study comprises technology companies that listed in Malaysian stock market. In the fourth industrial revolution, technology companies play an important role in the development of a country. The results of this study show that the optimal portfolio of MVSK model outperforms the MV model by giving higher portfolio skewness value and lower portfolio kurtosis value. This study is significant because the investors can maximize the portfolio skewness value and minimize the portfolio kurtosis value with the MVSK model.