Earlier studies which applied the family of stable Paretian distributions to financial data are inconclusive and contradictory. In this article I estimate the parameters of the model by the Feuerverger-McDunnough method which enables the application of maximum likelihood rhethods. Based on inferential statistics, stable Paretian distributions can be rejected with monthly data. In order to confirm this result, the model is extended to the family of distributions with regularly varying tails. The result that stable Paretian distributions are not applicable is indeed confirmed by estimating the coefficient of regular variation.