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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年08月15日

这题涉及到了regression hedge吗?

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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