关于duration hedge, 计算optimal hedging ratio, 为什么不用现在的久期，而用到期时的久期？？
原题:
John Holt is managing a fixed-income portfolio worth USD１0 million. The duration of the portfolio today is 5.9 years and in six months it is expected to be 6.2 years. The 6-month Treasury bond futures contract is trading at USD 98.47. The bomd that is expected to be cheapest-to-deliver has a duration of 4.0 years today and an expected duration of 4.8 years ate maturity of the futures contract. How many futures contracts should John short to hedge against changes in interest rates over the next six months ?   
参考答案的计算用的久期是6.2和4.8，而不是5.9和4，不解。。。