Fat tails in small samples

Abstract

The tail of financial returns is typically governed by a power law (i.e. “fat tails†). However,the constancy of the so-called tail index α which dictates the tail decay has been hardlyinvestigated. We study the finite sample properties of some recently proposed endogenous tests forstructural change in α. Given that the finite sample critical values strongly depend on the tailparameters of the return distribution we propose a bootstrap-based version of the structuralchange test. Our empirical application spans a wide variety of long-term developed and emergingfinancial asset returns. Somewhat surprisingly, the tail behavior of emerging stock markets is notmore strongly inclined to structural change than their developed counterparts. Emergingcurrencies, on the contrary, are more prone to shifts in the tail behavior than developedcurrencies. Our results suggest that extreme value theory (EVT) applications in hedging tail risksor in assessing the (changing) propensity to financial crises can assume stationary tail behaviorover long time spans provided one considers portfolios that solely consist of stocks or bonds.However, our break results also indicate it is advisable to use shorter estimation windows whenapplying EVT methods to emerging currency portfolios.