Developed and emerging equity market tail risk: Is it constant?

The tail of equity returns is typically governed by a power law, however, the constancy of the so-called tail index αα, which dictates the tail decay, has been hardly studied. Using the Hill estimator to estimate the tail index, we study the finite sample properties of endogenous stability tests for αα. We show that the finite sample critical values strongly depend on the underlying distributional assumptions for the stock returns. We therefore recommend a bootstrap-based version of the stability test as an alternative to the test’s asymptotic distribution. Upon applying this stability test to return tails of developed and emerging equity markets, the evidence for structural shifts is found to be rather weak. This is reassuring news for the proponents of Extreme value Theory (EVT). They typically assume stationary tail behavior when applying tail index and extreme quantile estimators to the downside risk of equity portfolios.