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滴滴姐姐~ · 2021年09月18日

求问 yield越高 为什么duration越低呢~

  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.

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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1 个答案

品职答疑小助手雍 · 2021年09月19日

嗨，努力学习的PZer你好：


同学你好，我印象这个是一级的结论哈。

主要是因为本身最后一期FV占的权重一般是最大的，但是duration是按PV的比重来算的，所以折现率越大，对FV折成PV的影响越大。相对而言coupon折现期限比FV短，影响相对小一些。

此时长期限比重变小（FV的），短期险比重变大（coupon的），所以duration下降。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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