Robust Properties of Stock Return Tails

This paper explores the tail features of daily stock returns. Recently developed versions of the Hill estimator are used to measure the extreme positive and negative returns for a small set of individual daily stocks covering the period of 1926 through 2004. The findings report many of the accepted stylized facts about stock returns. Scaling exponents are reliably near 3, and generally stable over time and across positive and negative tails. A simple measure of tail behavior, the Gaussian crossing point, is introduced which gives further information on tail behavior including some intriguing results suggesting that positive tails may be fatter than negative ones. JEL Classification: G12, C10, C32