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程冠林 · 2023年01月11日

如果是通过计算判断，是否可以用含convexity的计算公式？

  1. CFA III
  2. Fixed Income

NO.PZ2021120102000011

问题如下：

A junior analyst considers a 10-year high-yield bond issued by EKN Corporation (EKN) position in a high-yield portfolio. The bond has a price of 91.82, a modified duration of 8.47, and a spread duration of 8.47.

The analyst speculates on the effects of an interest rate increase of 20 bps and, because of a change in its credit risk, an increase in the EKN bond’s credit spread of 20 bps.

The analyst comments that because the modified duration and the credit spread duration of the EKN bond are equal, the bond’s price will not change (all else being equal) in response to the interest rate and credit spread changes.

Is the analyst’s prediction correct that the EKN bond price will not change in response to the interest rate and credit spread changes, all else being equal?

选项：

A.

Yes.

B.

No, the bond price should decrease.

C.

No, the bond price should increase.

解释：

B is correct. An increase in interest rates results in a decrease in the bond price. An increase in the credit spread also results in a decrease in the bond price.

For the EKN bond, its modified duration shows the effect of the 20 bp increase in interest rates. The approximate percentage price change resulting from the increase in interest rates is –8.47 × 0.0020 = –1.694%.

The spread duration shows the effect of the 20 bp increase in the credit spread. The approximate percentage price change resulting from the increase in the credit spread is –8.47 × 0.0020 = –1.694%. The combined effect is a total change of –3.388%, or a price decrease of roughly 3.4%

如题，%△P=-MD*△y+0.5*conv*△y^2这个公式可以用吗？另外，想问含con的公式与%△P=-MD*△y使用上有何区别。

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已采纳答案

pzqa015 · 2023年01月12日

嗨，从没放弃的小努力你好：


收益率小幅移动时，用%△P=-MD*△y就可以，收益率大幅移动时，需要用%△P=-MD*△y+0.5*conv*△y^2这个公式，因为仅仅用duration衡量的债券价格变动不再准确了，需要考虑二阶导convexity。

具体多少算大幅，多少算小幅，并没有一个明确的门槛值。所以，在做题时，只要题目给了convexity的信息，一般都需要用%△P=-MD*△y+0.5*conv*△y^2这个公式，如果没给，那么就用%△P=-MD*△y就行了。

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