Estimating the Tail Index of Conditional Distribution of Asset Returns

Abstract

Massive stock market failures in the past decades cast a doubt on the standard normality assumption of many economic models. Despite decent research on the non-Gaussian characteristics of many financial time series, the question of tail heaviness still remains open. We conduct diagnostic analysis on the conditional distribution of asset returns of small/large companies (Russell 2000 and S&P 500) to look for clear evidence on the presence of heavy tails. We employ extreme value (EVT) tools in order to estimate the shape parameter () of Generalized Pareto distribution (GPD) using a well-known “Hill estimator”. It turns out that the shape parameter lies in the interval  implying that the conditional distribution of asset returns supposedly has finite mean and variance. We also find an evidence that the tail estimates experience structural breaks during 2008 Global Financial Crisis.