Using a generalized autoregressive conditional heteroskedasticity model to explain away the volatility clustering of volatility effect and extreme value theory to analyse the residuals' left and right tails, we study the tail thickness of 22 developed and 19 emerging equity market indices. In‐sample and out‐of‐sample tests indicate that exponential tails of the residuals cannot be strongly rejected. We study the dispersion of extremes of developed and emerging markets, and we report a statistically significant tail asymmetry in both types of markets and a significant change in both tail risk and tail asymmetry of emerging markets after the financial crisis of 2008.