This article studies how the spot-futures conditional covariance matrix responds to positive and negative innovations. The main results of the article are achieved by obtaining the Volatility Impulse Response Function (VIRF) for asymmetric multivariate GARCH structures, extending Lin (1997) findings for symmetric GARCH models. This theoretical result is general and can be applied to analyze covariance dynamics in any financial system. After testing how multivariate GARCH models clean up volatility asymmetries, the Asymmetric VIRF is computed for the Spanish stock index IBEX-35 and its futures contract. The empirical results indicate that the spot-futures variance system is more sensitive to negative than positive shocks, and that spot volatility shocks have much more impact on futures volatility than vice versa. Additionally, evidence is obtained showing that optimal hedge ratios are insensitive to the well-known asymmetric volatility behavior in stock markets. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:1019–1046, 2003