Mean-semivariance approach for portfolio optimisation

Abstract

The mean-variance method is hugely used for portfolio management. However, this approach assumes normality in the distribution of the assets' returns, which is not always observed in reality. Furthermore, using the variance as a measure of risk penalises the upside deviations of the returns, which investors consider as profit. Alternatives such as the semivariance measure has been proposed to overcome these drawbacks. This study aims to investigate the performance of the portfolios using semivariance as a measure of risk. A sample of ten companies from the Johannesburg Stocks Exchange Top 40 index is used for analysis. Using the Lagrange method for op-timisation, the optimal portfolios from the mean-variance and the mean-semivariance approaches are constructed. The results show that the optimisation using the semi-variance as a measure of risk produces desirable benefits: the optimal portfolios constructed achieve less risk and higher returns than those constructed using optimisa-tion with the variance as a measure of risk. Furthermore, a tracking error analysis for portfolio performance indicates that the minimum-risk portfolio constructed by the mean-semivariance approach has less tracking error as compared to the minimum-risk portfolio constructed by the mean-variance method.