The hedging effectiveness of dynamic strategies is compared with static (traditional) ones using futures contracts for the leading five currencies. The traditional hedging model assumes time invariance in the joint distribution of spot and futures price changes thus leading to a constant optimal hedge ratio (OHR). However, if this timeinvariance assumption is violated, time-varying OHRs are appropriate for hedging purposes. A bivariate GARCH model is employed to estimate the joint distribution of spot and futures currency returns and the sequence of dynamic (time-varying) OHRs is constructed based upon the estimated parameters of the conditional covariance matrix. The empirical evidence strongly supports time-varying OHRs but the dynamic model provides superior out-of-sample hedging performance, compared to the static model, only for the Canadian dollar.