Risk management critically depends on the assumptions made about the distribution of stock returns. This paper applies extreme value methods to investigate the limiting distribution of the extreme returns of the NIKKEI225, FTSE100 and S&P500 indices as well as the indices of some of largest sectors in Japan, UK and US. The results indicate that the much celebrated Generalised Extreme Value distribution does not provide the most accurate description of the minima since the Generalised Logistic distribution performs better due to its ability to better capture the fat tails of returns. The time varying nature of extremes is also confirmed while a simulation exercise adds to the robustness of our results. It is also shown that the findings may have important implications for risk models, such as VaR and Expected Shortfall, since risk measures which cannot capture the fatness of tails of the empirical distribution function of returns may lead to serious underestimation of downside risk.