Most research on hedging has disregarded both the long-run cointegrating relationship between financial assets and the dynamic nature of the distributions of the assets. This study argues that neglecting these affects the hedging performance of the existing models and proposes an alternative model that accounts for both of them. Using a bivariate error correction model with a GARCH error structure, the risk-minimizing futures hedge ratios for several currencies are estimated. Both within-sample comparisons and out-of-sample comparisons reveal that the proposed model provides greater risk reduction than the conventional models. Furthermore, a dynamic hedging strategy is proposed in which the potential risk reduction is more than enough to offset the transactions costs for most investors.