The Angular Distribution of Asset Returns in Delay Space

Abstract

In Chapter 7 I reported on a GARCH study of Yeager’s ruble data. At least two considerations limit the value of that study. First, the GARCH model assumes that the underlying error term is normally distributed. But, as Broussard and Koppl (1999) report, Yeager’s ruble returns exhibit kurtosis. The distribution of returns has fat tails; it is not a normal distribution. Second, the model assumes the data are continuous, not discrete. But the ruble data are discrete. The price of hundred-ruble notes moved in jumps of 0.05 marks. It is possible to overcome these two difficulties with non-parametric tools designed to handle discrete data. This chapter reports on a test for herding and contra-herding that uses such tools. It builds on Crack and Ledoit’s (1996) analysis of the “compass rose.”

This chapter is a modified version of Koppl and Nardone (2001).