Lower Partial Moments und Value-at-Risk: Eine Synthese

This paper investigates the relation between the Value at Risk-Measure and the asymmetrical Lower Partial Moments (LPM), which have become increasingly popular in the recent financial literature. It will be shown that - based on the first-order LPM - the classical VaR-Framework can be extended to a Shortfall-VaR, measuring the expected loss for an investor, if the loss realization exceeds the classical VaR. The final part of the paper illustrates the important influence of the higher distributional moments, namely skewness and kurtosis, on both the VaR- and Shortfall-VaR using nonparametrical Spearman rank correlation tests. Especially, there is some evidence that a VaR-based perception of risk is unsatisfactory for return distributions, which deviate from the normal distribution assumption.