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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年08月15日

这题涉及到了regression hedge吗？

  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。

我看见when the nominal interest rate changes by 1 basis point, the real interest rate changes by 0.992 basis points. 以为是在讲beta，能写出Yb = beta * Yh。

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李坏_品职助教 · 2023年08月16日

嗨，从没放弃的小努力你好：


这个题比较特殊，虽然是属于regression hedge，但是不需要计算beta。我们只要保证△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，这个等式意思是：假如nominal 和real interest rate变动幅度一样的话。

但是二者变动幅度不一样，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

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