This paper deals with the estimation of optimal hedge ratios. Three alternative hedging strategies are considered: duration matching, least squares hedge estimator and asymmetric multivariate GARCH. Hedging performance comparisons, in terms of ex-post variance portfolio reduction, are conducted. The portfolio analysed is composed by Italian Government Bonds. The hedging instrument is the nearby futures contract traded on LIFFE. Eventually, a dynamic hedging strategy is proposed in which the potential risk reduction is more than enough to offset the transaction costs.