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410140980 · 2022年10月06日

增加利率会降低DV01?

NO.PZ2018122701000061

问题如下:

A bond portfolio consists of five bonds:

Bond 1: 5%, annual-pay bond with a 10-year maturity and a yield of 4.5%.

Bond 2: 5%, semiannual-pay bond with a 10-year maturity and a yield of 4.5%.

Bond 3: A zero-coupon bond with a 10-year maturity and a yield of 4.5%.

Bond 4: 4%, semiannual-pay bond with a 10-year maturity and a yield of 4.5%.

Bond 5: 5%, annual-pay bond with a 10-year maturity and a yield of 5.5%.

Which of the following statements about these bonds is Correct?

选项:

A.

Bond 1 has a shorter duration than Bond 2.

B.

The Macaulay duration of Bond 3 is five years.

C.

Bond 4 has a shorter duration than Bond 2.

D.

The DV01 of Bond 5 is lower than the DV01 of Bond 1.

解释:

D is correct.

考点 Measures of Pricing Sensitivity Based on Parallel Yield Shifts

解析 Increasing the yield will lower the DV01. Since Bond 5 has a higher yield than Bond 1, it must have a lower DV01. Choice B is incorrect. The Macaulay duration of a zero-coupon bond will be equal to its maturity Choices A and C are incorrect. All else equal, a semiannual-pay bond will have a shorter duration than an annual-pay bond, so Bond 2 has a shorter duration than Bond 1. A premium bond will have a shorter duration than a discount bond, so Bond 2 will have a shorter duration than Bond 4.

老师解析的第一句话怎么理解?DV01不是衡量利率每变动1bp债券价格的变化百分比吗?那和市场利率如何变化好像没有关系

1 个答案

pzqa27 · 2022年10月06日

嗨,从没放弃的小努力你好:


这个有很多种方法可以推导出来,我们就选个最简单了方法好了。我们知道DV01=Modified Duration*market value*1bp。

其中Modified Duration*market value=money duration。我们可以简单画个图像

如上图,我们知道money duration 可以看作是债券价格和利率之间的敏感度,即导数,也就是切线斜率了,从图像上可以看到4.5%对应的斜率的数值是大于5.5%对应的斜率的数值。因此bond 1的money duration> bond 5。 所以推出bond 5的DV01小一些

----------------------------------------------
努力的时光都是限量版,加油!

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