Studies that fit volume-augmented GARCH models often find support for the hypothesis that trading volume explains ARCH effects in daily stock returns. We show that this finding is due to an unrecognized constraint imposed by the GARCH specification used for the analysis. Using a more flexible specification, we find no evidence that inserting volume into the conditional variance function of the model reduces the importance of lagged squared returns in capturing volatility dynamics. Volume is strongly correlated with contemporaneous return volatility, but the correlation is driven largely by transitory volatility shocks that have little to do with the highly persistent component of volatility captured by standard volatility models.