• PORTFOLIO RANKING EFFICIENCY (III), NORMAL TEMPERED STABLE RETURNS

Abstract

The five parameter normal tempered stable (NTS) distribution is studied. The domain of variation between skewness and excess kurtosis is derived and a full analytical solution of the moment equations is displayed. Application to portfolio selection with CARA utility is considered. With the NTS 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 an empirical data analysis, one notes a systematic efficiency increase of the approximate ranking versus the Gaussian ranking. Comparisons with the normal variance gamma (NVG) and the truncated Lévy flight (TLF) distributions as test return distribution are included.