We derive the optimal hedging ratios for a portfolio of assets driven by a Cointegrated Vector Autoregressive model with general cointegration rank. Our hedge is optimal in the sense of minimum variance portfolio. We consider a model that allows for the hedges to be cointegrated with the hedged asset and among themselves. We nd that the minimum variance hedge for assets driven by the CVAR, depends strongly on the portfolio holding period. The hedge is dened as a function of correlation and cointegration parameters. For short holding periods the correlation impact is predominant. For long horizons, the hedge ratio should overweight the cointegration parameters rather then short-run correlation information. In the innite horizon, the hedge ratios shall be equal to the cointegrating vector. The hedge ratios for any intermediate portfolio holding period should be based on the weighted average of correlation and cointegration parameters. The results are general and can be applied for any portfolio of assets that can be modeled by the CVAR of any rank and order.