Back to normal? A study of the behaviour of volatility in the Indian stock market

In this paper, we undertake a study of the structure of volatility in stock returns in the Indian stock market, as also the impact of the global financial crisis of 2008 on the stock market. Ordinarily, this would be answered by comparing the level of volatility before and after the event of interest, but we attempt to go beyond this and understand what structural change there has been in volatility. We make our point in this paper by proposing a new statistic called the “Vol Ratio”, which allows us to infer the behaviour of the volatility of volatility (Vol of vol) at various horizons.

We find that there has been a dramatic change caused by the global financial crisis of 2008. In particular, we find that the volatility of volatility does not die down or takes a very long time to do so in the Nifty index, subsequent to the global financial crisis. By way of contrast, prior to the crisis, the Vol of vol exhibits a rapid decline with respect to the horizon.

We analysed the data over k-day moving windows, such as when k =1, the original series was taken as it was and consisted of daily return data. When k = 2, observations 1 & 2, 2 & 3, and so on were added to form a new series of k-day returns. Based on this series, Vol Ratio and Vol of vol were calculated for each k ranging from 1 to 20. Prior to the crisis, the Vol of vol of long-term stock returns converges to zero for k-day ≥ 10, and so the k-day returns are normally distributed starting from k-day = 10. However, during the post-crisis period, the picture is completely different, in that the Vol of vol of long-term stock returns does not die down to zero even for k-day = 20. Hence, long-term returns are not normally distributed but remain a mixture of normals.