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hanfei · 2023年10月08日

最后一句的duration是多余信息嘛？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2016082404000022

问题如下：

On June 2, a fund manager with USD 10 million invested in government bonds is concerned that interest rates will be highly volatile over the next three months. The manager decides to use the September Treasury bond futures contract to hedge the portfolio. The current futures price is USD 95.0625. Each contract is for the delivery of USD 100,000 face value of bonds. The duration of the manager’s bond portfolio in three months will be 7.8 years. The cheapest-to-deliver (CTD) bond in the Treasury bond futures contract is expected to have a duration of 8.4 years at maturity of the contract. At the maturity of the Treasury bond futures contract, the duration of the underlying benchmark Treasury bond is nine years. What position should the fund manager undertake to mitigate his interest rate risk exposure?

选项：

A.

  Short 94 contracts

B.

  Short 98 contracts

C.

  Short 105 contracts

D.

  Short 113 contracts

解释：

ANSWER: B

The number of contracts to short is N∗=−DS∗SDF∗F=−(7.8×10,000,000)8.4×95.0625×1,000=−97.7N\ast=-\frac{D_S^\ast S}{D_F^\ast F}=\frac{-(7.8\times10,000,000)}{8.4\times95.0625\times1,000}=-97.7, or 98 contracts. Note that the relevant duration for the futures is that of the CTD; other numbers are irrelevant.

At the maturity of the Treasury bond futures contract, the duration of the underlying benchmark Treasury bond is 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duration怎么套到公式里面

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李坏_品职助教 · 2023年10月08日

嗨，从没放弃的小努力你好：


这个意思是指的，国债期货的对应的现货——债券指数的久期是9年。这属于干扰项，因为我们用的是7.8，这个才是需要对冲的资产组合的久期。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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