We show that there is an asymmetry in the predictability of the volatilities of large versus small firms. Using both univariate and multivariate ARMA–GARCH-M parameterizations, we find that volatility surprises to large market value firms are important to the future dynamics of their own returns as well as the returns of smaller firms. Conversely, however, shocks to smaller firms have no impact on the behavior of either the mean or the variance of the returns of larger capitalization companies.

[We show that there is an asymmetry in the predictability of the volatilities of large versus small firms. Using both univariate and multivariate ARMA-GARCH-M parameterizations, we find that volatility surprises to large market value firms are important to the future dynamics of their own returns as well as the returns of smaller firms. Conversely, however, shocks to smaller firms have no impact on the behavior of either the mean or the variance of the returns of larger capitalization companies.]