Traditional hedges of bond duration and convexity are non-optimal.We derive correct hedge ratios by capturing the neglected volatility linkage between Treasury futures and cheapest-to-deliver Treasuries.Our hedge-ratio equations specify each hedge instrument's contribution against short-term spot and forward rate exposures.Numerical analysis indicates that traditional hedge substantially over-hedges.The relative over-hedge is especially large in hedging high coupon bond when the hedge horizon is long,the te...