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410140980 · 2022年10月06日

增加利率会降低DV01？

  1. FRM II
  2. Market Risk Measurement And Management

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

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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

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努力的时光都是限量版，加油！

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NO.PZ2018122701000061 这个是一级的结论吗0.o 求详细讲讲~ 谢谢谢谢（节日快乐btw （顺便问问你萌假期回答问题吗~

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