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Christinafx · 2025年04月22日

所以这道题interest rate变动会影响modified duration是吗?

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%

modified duration难道不受spread变动影响吗?只受基准利率影响?

1 个答案

发亮_品职助教 · 2025年04月23日

modified duration受到spread改变的影响,也受基准利率改变的影响。这道题有2个算法哈。这道题就是纯考modified duration, spread duration的概念。


modified duration是指:债券的YTM改变时,引起的债券价格波动。注意,是以债券的YTM为基准衡量的duration哈。

而债券的YTM = 基准利率 + spread,所以无论是spread改变,还是基准利率改变,都会通过债券的modified duration影响债券价格波动。所以modified duration即会受到benchmark的影响,也会受到spread的影响。

但需要注意的是,基准利率的改变和spread的改变,要先影响到YTM,然后是YTM再通过modified duration影响价格。


例如,这道题的题干说,基准利率上升20bps(interest rate increase of 20 bps),债券的credit spread上升20bps(an increase in the EKN bond’s credit spread of 20 bps)。那么可以知道,债券的YTM会上升40bps。

已知债券的modified duration=8.47,则引起的债券价格改变为:

-8.47×(0.40%)

这是这道题背景带来的总影响。


这道题还有一个解法,就是他给了spread duration。可以把spread单独分开算。

已知基准利率上升20bps,那他带来的YTM改变是上升20bps。通过modified duration对债券价格的影响是:

-8.47×(0.20%),在这里只考虑了benchmark对YTM的影响,未考虑spread的影响。因为spread的影响我们打算用spread duration算。

债券的credit spread上升20bps,债券的spread duration=8.47,spread的改变通过spread duration对债券价格的影响是:

-8.47×(0.20%)


以上2个影响加总,就是spread改变与基准利率改变对债券的影响:

-8.47×(0.20%)+(-8.47)×(0.20%) = -8.47 × (0.40%)


总结下就是,spread duration只能算spread改变的影响。

而modifie duration是算YTM改变的影响,而YTM的改变会来自于benchmark与spread。


这道题有个陷阱,就是很多同学会把benchmark上升20bps和spread上升20bp加总,算出YTM上升40bps,用Modified duration算价格影响,此外,又算了spread上升20bps通过spread duration的影响,再把以上影响加总。这种就是重复计算了spread改变的影响。


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