The volatility in both the cash and futures markets both for NIFTY index and selected ten blue chip stocks are compared with the help of some descriptive statistical measures first and then through measures of conditional variance modeled in different ARCH family of frameworks.
The descriptive statistical measures are presented in Tables 1 and 2 for cash market and futures market respectively. Though there are different descriptive measures included in the table, our focus will be only on measures of volatility like standard deviation, skewness and kurtosis. These measures represent variability in return series as well as the chances of positive or negative deviations from the mean and the chances of very large deviations.
Comparing with standard deviation of NIFTY spot and futures indices, it is observed that variability in the daily return series is more in futures market compared to that of spot market. Now, as far as the symmetricity of the return distribution is concerned, both the spot and futures index returns are found to be negatively skewed where the chances of negative deviations or drop in return than the mean is more. Looking at the kurtosis figures, both the return series are found to have a kurtosis of more than three and therefore found to be leptokurtic, the degree of peakedness is being found to be lesser for the spot index return.
The standard deviation measure of all stocks reveal that the variability in stock return of majority seven no. of stocks is low in spot market than the futures market except for INFOSYS, HINDALCO and TELCO. If we look into the skewness figures for all the stocks, then it is found that eight out of ten stocks show negatively skewed returns except for stocks like HINDALCO and TISCO which show positively skewed returns. Therefore, the chances of negative return deviation is more for almost all the stocks in both spot and futures markets. The kurtosis figures also reveal the same fact as skewness. Though the degrees of kurtosis are different for different stocks, these are nearly close for the same stock in spot and futures markets. All these figures represent a minor difference among the volatility in spot and futures markets in India, both at the underlying stock and index level.
Again, volatility in spot and futures markets for NIFTY index and ten underlying stocks are measured by using different ARCH family of models. Tables 3 and 4 represent spot and futures return volatility for underlying NIFTY index and stocks respectively measured through ARCH (1) process. The results of conditional variance equation clearly reveal that the ARCH coefficient for spot index is found to be significant. But the ARCH coefficients of underlying stocks in the spot market are found to be
significant for majority seven out of ten stocks except securities like HINDUSTHAN UNILEVER, HDFC and SBI. As far as futures market volatility is concerned, the ARCH coefficient for futures index return is observed to be statistically significant. Again, the ARCH coefficient for measuring volatility of stock futures returns is found to be significant for same seven stocks as was observed in case of spot market volatility.
Similarly, volatility results for NIFTY index and stocks in a GARCH (1,1) framework are presented in tables 5 and 6 for spot market and near month futures market respectively. Since GARCH (1,1) model is most parsimonious and widely applicable framework to model conditional volatility of returns, it has been observed that the GARCH coefficient for NIFTY index alike as ARCH coefficient is found to be statistically significant in both spot and futures market. The interesting observation here is that GARCH coefficient for all the stocks is found to be significant in the spot as well as futures market. If we compare the significance of ARCH and GARCH coefficients for the underlying stocks, then GARCH coefficient is significant for all the stocks whereas ARCH coefficient is significant for seven out of ten underlying stocks. This represents the stronger impact of old news comparative to the recent news in Indian spot market volatility.
Taking the GARCH (1,1) model as base, we have calculated the conditional and unconditional volatility in spot and futures markets as represented in tables 7 and 8 respectively. By comparing the unconditional and conditional volatility in both the markets, it can be inferred as to which market has a higher amount of unconditional and conditional volatility. The market with a lower figure is found to be significant. The comparison among spot and futures market clearly reveal that both the unconditional and conditional volatility is observed to be lower for futures index returns than NIFTY spot. Now, as far as the stock level results are considered, both the conditional and unconditional volatility have been found to be lower in futures market for nine out of ten underlying stocks except only the case for HINDALCO. Therefore, it can be said that on a whole, both the conditional and unconditional volatility are less in futures comparative to spot market in Indian scenario.
After estimating conditional and unconditional volatility in spot and futures markets, another attempt has been made to test the forecasting power of ARCH and GARCH family of models used as a measure of volatility forecasting. The test is made for returns in index and underlying stocks in both spot and near month futures markets.
Dynamic volatility forecasting techniques are presented in tables 9, 10, 11 and 12 for spot and futures returns under ARCH (1) and GARCH (1,1) models for underlying index and stocks respectively. As far as the forecasting results for the index as well as stock returns are considered, most of the test statistics reveal that GARCH (1,1) model has lesser forecasting error compared to ARCH (1) framework, though the difference is very marginal. Volatility forecasting for stocks in both spot and futures markets are observed to have little difference in the forecasting error among the ARCH (1) and GARCH (1,1) frameworks and also the result vary from one stock to another and also different in spot and futures markets respectively.