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考拉 · 2024年02月02日

关于计算债券价格受利率变动影响的公式有两个,这两个公式在应用上有什么关系

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%

关于计算债券价格变动的公式1.change in price=modified duration *change in interest rate; 2.change in price=.-(modified duration*change in yield)+1/2*convexity*the square of change in yield.请问这两个公式是不是都能计算债券价格的变动?这两个公式在应用上有什么关系

1 个答案
已采纳答案

pzqa015 · 2024年02月03日

嗨,努力学习的PZer你好:


duration是价格对利率变动的一阶导;convexity是价格对利率变动的二阶导。

在数学中,一阶导可以用来衡量小范围利率变动对价格的影响,但如果大范围利率变动,一阶导无法准确度量债券价格的变动了,此时需要用到二阶导。

所以,这两个公式区别在于适用范围不同,公式1适用于利率小范围变动;公式2适用于利率大范围变动。

但具体多少是小范围变动,多少是大范围变动,并没有明确的定量值。

所以,考试中,如果题目给了convexity和duration,那么就要用公式2来计算价格变动;如果只给了duration,那么只能用公式1了。

或者即使给了convexity,但明确只考虑duration的作用,那么也用公式1。

----------------------------------------------
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