We develop a new multivariate GARCH parameterization that is suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity. The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time-to-maturity effects.