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wilsonxu · 2021年08月28日

这个题目好像没duration什么事的？

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000081

问题如下：

The trading department of Dragon Fruit Bank now has a hedging position based on the duration. They shorted the $ 500 million U.S. Treasury bond and bought the $ 473 million U.S. TIPS. The analysis department of the bank has just made a regression analysis of the nominal interest rate and real interest rate, and found that when the nominal interest rate changes by 1 basis point, the real interest rate changes by 0.992 basis points. Based on this relationship, how should the trading department adjust their existing positions?

选项：

A.

There is no need to change the position.

B.

purchase $3.8 million TIPS.

C.

Purchase $4.8 million Treasury bond

D.

Sell $3.8 million TIPS

解释：

B is correct.

考点：Empirical Approaches To Risk Metrics And Hedging

解析：因为利率变化不同，原有的duration hedge平衡被打破了，实际需要的TIPS是473/0.992=476.8 million。所以要再买3.8million的TIPS。

这个题目好像没duration什么事的？当利率变化是1:1时，不需要500和473不需要做任何调整。不用考虑duration吗？就是说duration不会变化了吗？本题两者的duration没有办法得知？感觉500*D1*1=TIPS*D2*0.992，中D1、D2多余是的？
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DD仔_品职助教 · 2021年08月28日

嗨，爱思考的PZer你好：


同学你好~

这个题跟duration是有关系的。

portfolio=short T-bond + long TIPS = TIPS - T-bond

我们为了简便，定义T-bond为1，TIPS为2

duration hedge的目标是利率变动不影响portfolio变化，

即delta portfolio= delta TIPS - delta T-bond=0

价格变动= -Duration*Price*delta y

delta portfolio=0= (-D2*P2*delta y2) - (-D1*P1*delta y1)

当利率变化为1:1时，不需要对头寸T-bond=500 TIPS=473做调整

那么0=（-D2*473*1）- (-D1*500*1)

我们可以得出T-bond与TIPS的duration的关系：D1=473/500D2

当利率变化不是1:1时，1bp的T-bond变化对应着0.992个TIPS利率的变化

delta y2=0.992 delta y1

那么头寸就需要做出变化

0=（-D2*P2*0.992）- (-D1*P1*1）

带入D1=473/500D2

0=（-D2*P2*0.992）- (-473/500D2*P1*1）

原本的头寸是short500m T-bond不变，P1=500

0=（-D2*P2*0.992）- (-473/500D2*500*1），D2可以消去

我们得出P2=476.81

当利率变动1:1时我们需要473的TIPS

当利率变动不是1：1时我们只需要476.81的TIPS

所以原本的473不够用了，还需要再购买3.81的TIPS


答案写的很简略，如果熟练了的话，遇到这种题，用答案这样做更快~

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加油吧，让我们一起遇见更好的自己！

𝒜𝒩𝒥𝒜 安雅🎃 · 2023年08月15日

为什么这个式子delta portfolio=0= (-D2*P2*delta y2) - (-D1*P1*delta y1)，两个括号之间是减号，而不是加号？老师课堂上一直写delta P= delta B + delta H = 0

DD仔_品职助教 · 2023年08月16日

嗨，从没放弃的小努力你好：


同学你好，应该是加号

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努力的时光都是限量版，加油！

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