The asymmetric impact of firm-specific and of index returns on the volatility processes of individual stocks

This article examines the volatility processes of the 30 constituent stocks of the Dow Jones Industrial Average (DJIA) from 1998 to 2007. Estimating the standard Glosten, Jagannathan and Runkle (GJR) model across the DJIA's components confirms previous empirical findings of individual stocks' conditional variances being less asymmetric than that of the parent index. A modified specification is then tested, termed the GJR-I, where lagged signed market returns have replaced firm-specific returns. The results suggest that individual stock volatility is significantly correlated with past signed index returns and that the asymmetry phenomenon is more pronounced with respect to market news compared to firm-specific news. This result still holds after estimating an extended specification where the conditional variance responds both to idiosyncratic and systematic innovations. The fact that individual stock volatility responds more asymmetrically to market returns than to firm specific returns stands in contrast to the 'leverage effect' as well as 'volatility feedback' explanations, but it is consistent with the hypothesis of the volatility asymmetry phenomenon being a 'down market effect'.