Hedging strategies for commodity prices largely rely on dynamic models to compute optimal hedge ratios. This paper illustrates the importance of considering the commodity inventory effect (effect by which the commodity price volatility increases more after a positive shock than after a negative shock of the same magnitude) in modelling the variance-covariance dynamics. We show by in-sample and out-of-sample forecasts that a commodity price index portfolio optimized by an asymmetric BEKK-GARCH model outperforms the symmetric BEKK, static (OLS) or naïve models. Robustness checks on a set of commodities and by an alternative mean-variance optimization framework confirm the relevance of taking into account the inventory effect in commodity hedging strategies.