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上小学 · 2023年08月08日

请问此题为何没有久期？为什么这么解答呢？

  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。

请问此题有何公式可用？为何没有久期？谢谢

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已采纳答案

李坏_品职助教 · 2023年08月08日

嗨，从没放弃的小努力你好：


这个题目是用的regression analysis，根据题目的条件不需要用久期。


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

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


原理就是：如果treasury bond和TIPS两者利率变化是1比1的话，short 500m的bond和long 473的TIPS是完美对冲的。

但是现在发现他俩的利率变化不是1比1了才需要调整。

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