An Empirical Examination of Daily Stock Return Distributions for U.S. Stocks

This article investigates whether the Gaussian distribution hypothesis holds 382 U.S. stocks and compares it to the stable Paretian hypothesis. The daily returns are examined in the framework of two probability models – the homoskedastic independent, identical distributed model and the conditional heteroskedastic ARMA-GARCH model. Consistent with other studies, we strongly reject the Gaussian hypothesis for both models. We find out that the stable Paretian hypothesis better explains the tails and the central part of the return distribution. Acknowledgement: Prof Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft and the Deutscher Akademischer Austausch Dienst.