Higher moment portfolio management with downside risk

Abstract

Variance is the common risk measure that has been used in portfolio optimization since the introduction of the mean-variance model. However, the mean-variance model penalizes not only the downside deviation but also the upside deviation. The upside deviation is desirable to the investors. The objective of this study is to compare the compositions and performances of optimal portfolios by replacing variance with lower partial moment. The lower partial moment is the downside risk that focuses on the deviation below the specified target rate of return which better matches investor's perception towards risk. Incorporating skewness, this study employs the polynomial goal programming method. This method is flexible to incorporate different degree of investor's preference for mean return and skewness. Skewness is important because increasing skewness reduces the probability of getting negative rates of return. The empirical results demonstrate that the optimal portfolios compositions base on lower partial moment are different to the optimal portfolios compositions based on variance. Furthermore, at the same level of downside risk, optimal portfolios that based on lower partial moment are found to give higher expected return and skewness than the optimal portfolios that are based on variance. This implies that the optimal portfolios that are based on lower partial moment dominate those based on variance at the same level of downside risk. Lower partial moment is a more appropriate risk measure for the investors because it only penalizes the downside deviation.