Extreme Value Theory and Fat Tails in Equity Markets


Blake LeBaron and Ritirupa Samanta
May 2004

Abstract

Equity market crashes or booms are extreme realizations of the underlying return distribution. This paper questions whether booms are more or less likely than crashes and whether emerging markets crash more frequently than developed equity markets. We apply Extreme Value Theory (EVT) to construct statistical tests of both of these questions. EVT elegantly frames the problem of extreme events in the context of the limiting distributions of sample maxima and minima. This paper applies generalized extreme value theory to understand the probability of extreme events and estimate the level of “fatness” in the tails of emerging and developed markets.

We disentangle the major “tail index” estimators in the literature and evaluate their small sample properties and sensitivities to the number of extreme observations. We choose to use the Hill index to measure the shape of the distribution in the tail. We then apply nonparametric techniques to assess the significance of differences in tail thickness between the positive and negative tails of a given market and in the tail behavior of the developed and emerging region. We construct Monte Carlo and Wild Bootstrap tests of the null of tail symmetry and find that negative tails are statistically significantly fatter than positive tails for a subset of markets in both regions. We frame group bootstrap tests of universal tail behavior for each region and show that the tail index is statistically similar across countries within the same region. This allows us to pool returns and estimate region wide tail behavior. We form bootstrapping tests of pooled returns and document evidence that emerging markets have fatter negative tails than the developed region. Our findings are consistent with prevalent notions of crashes being more in the emerging region than among developed markets. However our results of asymmetry in several markets in both regions, suggest that the risk of market crashes varies significantly within the region. This has important implications for any international portfolio allocation decisions made with a regional view.