Tail Index Estimates in Small Samples

Financial returns are known to be nonnormal and tend to have fat-tailed distributions. This article presents a simple methodology that accurately estimates the degree of tail fatness, characterized by the tail index, in small samples. Our method is a weighted average of Hill estimators for different threshold values that corrects for the small-sample bias apparent in the latter. Using this estimator we produce tail-index estimates for returns on exchange rates that are close to nonbiased estimates obtained from extremely large datasets. The results indicate that many documented conclusions concerning the tail behavior of financial series are likely to have overestimated the tail fatness in small samples.