The stable Paretian hypothesis and the frequency of large returns: An empirical investigation

This paper provides an analysis of daily returns for thirty German stocks forming the DAX share index as well as the DAX itself during the period 1988 to 1994. Estimating the parameters of the stable laws and performing standard tests for fit some evidence in favor of the stable Paretian hypothesis can be found. However, application of a more recently developed semi-parametric technique for analysis of the behaviour in tails of a distibution (Hill's tail index estimator) gives results incompatible with the stable laws and leads to the rejection of the Paretian hypothesis for all stocks considered. Furthermore, strong similarity in the extremal behaviour of the thirty series is found and the hypothesis of identical limit laws of their extreme value distribution can not be rejected.