Empirical distributions of stock returns: european securities markets, 1990-95

Abstract

The assumption that daily stock returns are normally distributed has long been disputed by the data. In this article we test (and clearly reject) the normality assumption using time series of daily stock returns for thirteen European securities markets. More importantly, we fit to the data four alternative specifications, find overall support for the scaled-t distribution (and partial support for a mixture of two Normal distributions), and quantify the magnitude of the error that stems from predicting the probability of obtaining returns in specified intervals by using the Normal distribution. We conclude by arguing that normality may be a plausible assumption for monthly (but not for daily) stock returns.