这里的久期不是年为单位的，应该是麦考利久期，而不是修正久期？

NO.PZ2016082404000022 问题如下 On June 2, a funmanager with US10 million investein government bon is concernethinterest rates will highly volatile over the next three months. The manager cis to use the September Treasury bonfutures contrato hee the portfolio. The current futures priis US95.0625. Eacontrais for the livery of US100,000 favalue of bon. The ration of the manager’s bonportfolio in three months will 7.8 years. The cheapest-to-liver (CT bonin the Treasury bonfutures contrais expecteto have a ration of 8.4 years maturity of the contract. the maturity of the Treasury bonfutures contract, the ration of the unrlying benchmark Treasury bonis nine years. Whposition shoulthe funmanager unrtake to mitigate his interest rate risk exposure?   Short 94 contracts   Short 98 contracts   Short 105 contracts   Short 113 contracts ANSWER: BThe number of contracts to short is N∗=−∗S∗F=−(7.8×10,000,000)8.4×95.0625×1,000=−97.7N\ast=-\frac{S^\ast S}{F^\ast F}=\frac{-(7.8\times10,000,000)}{8.4\times95.0625\times1,000}=-97.7N∗=−∗​F∗​S​=8.4×95.0625×1,000−(7.8×10,000,000)​=−97.7, or 98 contracts. Note ththe relevant ration for the futures is thof the CT other numbers are irrelevant. the maturity of the Treasury bonfutures contract, the ration of the unrlying benchmark Treasury bonis nine years.思路和老师的一样，但是看到这句话就不敢做了，不知道这里的ration怎么套到公式里面

NO.PZ2016082404000022 问题如下 On June 2, a funmanager with US10 million investein government bon is concernethinterest rates will highly volatile over the next three months. The manager cis to use the September Treasury bonfutures contrato hee the portfolio. The current futures priis US95.0625. Eacontrais for the livery of US100,000 favalue of bon. The ration of the manager’s bonportfolio in three months will 7.8 years. The cheapest-to-liver (CT bonin the Treasury bonfutures contrais expecteto have a ration of 8.4 years maturity of the contract. the maturity of the Treasury bonfutures contract, the ration of the unrlying benchmark Treasury bonis nine years. Whposition shoulthe funmanager unrtake to mitigate his interest rate risk exposure?   Short 94 contracts   Short 98 contracts   Short 105 contracts   Short 113 contracts ANSWER: BThe number of contracts to short is N∗=−∗S∗F=−(7.8×10,000,000)8.4×95.0625×1,000=−97.7N\ast=-\frac{S^\ast S}{F^\ast F}=\frac{-(7.8\times10,000,000)}{8.4\times95.0625\times1,000}=-97.7N∗=−∗​F∗​S​=8.4×95.0625×1,000−(7.8×10,000,000)​=−97.7, or 98 contracts. Note ththe relevant ration for the futures is thof the CT other numbers are irrelevant. 分母为什么*1000，这个1000是一份合约里有多少个标的物的意思吗》是如何确定的？

NO.PZ2016082404000022问题如下 On June 2, a funmanager with US10 million investein government bon is concernethinterest rates will highly volatile over the next three months. The manager cis to use the September Treasury bonfutures contrato hee the portfolio. The current futures priis US95.0625. Eacontrais for the livery of US100,000 favalue of bon. The ration of the manager’s bonportfolio in three months will 7.8 years. The cheapest-to-liver (CT bonin the Treasury bonfutures contrais expecteto have a ration of 8.4 years maturity of the contract. the maturity of the Treasury bonfutures contract, the ration of the unrlying benchmark Treasury bonis nine years. Whposition shoulthe funmanager unrtake to mitigate his interest rate risk exposure?   Short 94 contracts   Short 98 contracts   Short 105 contracts   Short 113 contracts ANSWER: BThe number of contracts to short is N∗=−∗S∗F=−(7.8×10,000,000)8.4×95.0625×1,000=−97.7N\ast=-\frac{S^\ast S}{F^\ast F}=\frac{-(7.8\times10,000,000)}{8.4\times95.0625\times1,000}=-97.7N∗=−∗​F∗​S​=8.4×95.0625×1,000−(7.8×10,000,000)​=−97.7, or 98 contracts. Note ththe relevant ration for the futures is thof the CT other numbers are irrelevant.这个知识点是哪个知识点，久期乘以价格等于啥，这个对冲公式是那个点

NO.PZ2016082404000022 On June 2, a funmanager with US10 million investein government bon is concernethinterest rates will highly volatile over the next three months. The manager cis to use the September Treasury bonfutures contrato hee the portfolio. The current futures priis US95.0625. Eacontrais for the livery of US100,000 favalue of bon. The ration of the manager’s bonportfolio in three months will 7.8 years. The cheapest-to-liver (CT bonin the Treasury bonfutures contrais expecteto have a ration of 8.4 years maturity of the contract. the maturity of the Treasury bonfutures contract, the ration of the unrlying benchmark Treasury bonis nine years. Whposition shoulthe funmanager unrtake to mitigate his interest rate risk exposure?   Short 94 contracts   Short 98 contracts   Short 105 contracts   Short 113 contracts ANSWER: B The number of contracts to short is N∗=−∗S∗F=−(7.8×10,000,000)8.4×95.0625×1,000=−97.7N\ast=-\frac{S^\ast S}{F^\ast F}=\frac{-(7.8\times10,000,000)}{8.4\times95.0625\times1,000}=-97.7N∗=−∗​F∗​S​=8.4×95.0625×1,000−(7.8×10,000,000)​=−97.7, or 98 contracts. Note ththe relevant ration for the futures is thof the CT other numbers are irrelevant. 公式里面没有正负号一般怎么判断？