A new higher moment portfolio optimisation model with conditional value at risk

Variance is a common risk measure used for constructing portfolios. However, variance strictly depends on the assumptions that the returns of assets are not normally distributed or investor's function is quadratic. Moreover, variance not only penalises the downside deviations below the mean return but also the upside deviation, variance, thus, does not match investor's desire to maximise the upside deviation and minimise the downside deviation. The objective of this paper is to propose a new four moment mean-conditional-value-at-risk-skewness-kurtosis model and empirically test the model. In this proposed model, variance is replaced with conditional value at risk as the risk measure. The polynomial goal programming method is used in this study as it is flexible to incorporate different degree of investor's preference on mean, skewness and kurtosis. Results of this study demonstrate that the mean-CVaR-skewness-kurtosis model gives higher mean return and skewness and provides better performance than the mean-variance-skewness-kurtosis model for all combinations of degree of preferences. This implies that CVaR is a better risk measure than variance in portfolio optimisation.