• PORTFOLIO RANKING EFFICIENCY (I)

Abstract

Equations of squared skewness and kurtosis as well as sharp inequalities between these quantities are derived for the normal bilateral gamma (NBG) convolution and the important normal variance gamma (NVG) sub-family. Application to portfolio selection with CARA utility is considered. With the NVG as test return distribution, it is analyzed whether a recent approximate ranking function with cubic mean-variance-skewness-kurtosis trade-off should be preferred to the original Gaussian ranking function with linear mean-variance trade-off or not. Based on an appropriate ranking efficiency measure and a simulation study, one notes, up to some exceptional cases, a systematic efficiency increase of the approximate ranking versus the Gaussian ranking. An empirical data analysis for eight different sets of returns from the Swiss Market and the Standard & Poors 500 stock indices, fitted to the NVG with the moment method, confirms the results from the simulation study. For this, full analytical solutions to the moment equations of the variance gamma and the normal variance gamma turn out to be very useful.