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梦梦 · 2025年03月26日

这里的回归关系是不是反了？

  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。

老师好，虽然做对了，但是感觉和课程里讲的回归的谁是X，谁是Y不同，哪里想错了吗？



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李坏_品职助教 · 2025年03月26日

嗨，从没放弃的小努力你好：


本题只要保证△Treasury+△TIPS=0这个对冲等式成立就可以了。


不考虑利率变化不同时的对冲等式：-500*D1+473*D2=0，这个等式的前提是：假如nominal 和real interest rate变动幅度一样的话。D1和D2指的是久期。


但是两个利率的变动幅度不一样，所以：考虑了利率变化不同时的对冲等式：-500*D1*1 + Tips*D2*0.992=0


两个等式如果都要成立的话：

Tips *0.992 = 473

所以我们可以算出来 Tips = 473/0.992.

△Treasury+△TIPS=0就行了

这道题虽然给出了类似回归系数的条件，但是那只是为了让你用到第二个等式里，这道题不需要判断x和y，只要保证△Treasury+△TIPS=0就行了。


可以回看Empirical Approaches To Risk Metrics And Hedging这节课：

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梦梦 · 2025年03月26日

哦哦，好的，谢谢

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