Fat Tails in Small Sample

Abstract:     
It is a well-known stylized fact that financial returns are non-normal and tend to have fat-tailed distributions. This paper presents a methodology that accurately estimates the degree of fat-tailedness, characterized by the tail-index, in small samples. We present a simple approach based on the Hill estimator. Our estimator is a weighted average of a set of Hill estimators, with weights obtained by using simple least squares techniques. The estimator produces unbiased estimates for the tail-index in small samples and we also provide appropriate standard errors. Using this estimator we produce tail-index estimates for returns on stocks and exchange rates that are close to estimates obtained from extremely large datasets. The results indicate that many documented conclusions about the tail behavior of financial series have over-estimated their fat-tailedness in small samples.

Number of Pages in PDF File: 38

JEL Classification: C13, C40, G10, F31

working papers series