Prospect Theory and Higher Moments

The paper relates cumulative prospect theory to the moments of returns distributions, e.g. skewness and kurtosis, assuming returns are normal inverse Gaussian distributed. The normal inverse Gaussian distribution parametrizes the first- to forth-order moments, making the investigation straightforward. Cumulative prospect theory utility is found to be positively related to the skewness. However, the relation is negative when probability weighting is set aside. This shows that cumulative prospect theory investors display a prefer-ence for skewness through the probability weighting function. Furthermore, the investor’s utility is inverse hump-shape related to the kurtosis. Conse-quences for portfolio choice issues are studied. The findings, among others, suggest that optimal cumulative prospect theory portfolios are not mean-variance efficient under the normal inverse Gaussian distribution