Modelling S&P 100 Volatility : The Information Content of Stock Returns

Hitherto, index volatility has been modelled using the history of index returns but not the returns histories of the stocks that define the index. Theoretical models that relate volatility to the quantity of information are extended to a multi-asset setting and it is deduced that stock returns may or may not have incremental information when modelling index volatility, depending on the sources of information that move stock prices. The first empirical study that can help resolve this theoretical uncertainty is presented. A detailed analysis of a daily volatility of the Samp;P 100 index from 1983 to 1992 shows there is some incremental volatility information in the returns from the 100 shares that define the index. ARCH models are estimated, that incorporate leverage effects, dummy variables for the 1987 crash and aggregate measures of stock return volatility. Parameter estimates for several stock measures reject the null hypothesis that these measures are irrelevant, at the 5% level, for the ten years considered. Mixed results are obtained for sub-periods. Significant differences between estimated volatilities are found, leaving open the possibility that the new volatility estimates may price options differently, by amounts that are of economic significance