This study examines the issue of detecting permanent shifts in the volatility of emerging stock market indexes returns. We show that standard tests have no power in disentangling conditional heteroscedasticity versus jumps in the variance of stock returns. We propose two methods to detect jumps in the variance when there is conditional heteroscedasticity. The first one is based on the properties of temporal aggregation of GARCH (1, 1) models. The second one consists in filtering the stock returns series with a GARCH (1, 1) model in conjunction with the ICSS algorithm. We show that jumps in variance are less frequent than previously believed. Moreover, the jumps are country specific so that they can be diversified