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lion · 2023年03月02日

求解释。。。

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=DSSDFF=(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.

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

2 个答案

李坏_品职助教 · 2023年07月27日

嗨,爱思考的PZer你好:


等式右边的括号里应该是95.0625*1000,不是*100000。


每一张期货合约的面值是100000美元,但是这道题里面期货合约的报价F是95.0625,这个意思是每100美元对应的期货价格是95.0625

所以应该是95.0625*100000/100 = 95.0625*1000

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李坏_品职助教 · 2023年03月02日

嗨,爱思考的PZer你好:


久期乘以价格是美元久期(dollar duration):

这个对冲公式是债券的hedging ratio。因为dollar duration表示债券在利率增加1单位的情况下,债券价格的变化量,对冲的目的是让债券期货的变化正好抵消债券现货的变化,所以应该是:Ds * S =N* DF * F,这里DF是一张期货的久期,F是一张期货的总价,F = 95.0625 * 100000,N代表债券期货的数量,求出来N就行了。



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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年07月27日

助教你好:我用这个式子算Ds * S =N* DF * F,7.8*10M = N*8.4*(95.0625 * 100000),然后算出N是0.976,能把B选出来,但我想问为啥是0.976?怎么跟97.6差了100倍?这个地方我一直不明白

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