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hillock1122 · 2021年01月16日

问一道题：NO.PZ2018122701000061 [ FRM II ]

  1. FRM II
  2. Market Risk Measurement And Management

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.

​请老师帮忙解释一下C选项？

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2 个答案

品职答疑小助手雍 · 2021年01月18日

这个也是在“All else equal”的前提下的，原理和我解释的内容是一样的。

品职答疑小助手雍 · 2021年01月16日

嗨，从没放弃的小努力你好：


麦考林久期其实就是平均还款期，如果其他条件相同的话，如果coupon越大，那意味着前期现金流的占的比重越大，但是比重大的前期现金流的对应的还款期限是更短的，所以coupon越大的话，平均的还款期就越短。duration就越小。

所以C选项里bond4的久期应该小于bond2的久期，选项错误。


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hillock1122 · 2021年01月17日

这个我懂，C的解释中说溢价发行比折价发行的债券久期短，这个没懂。

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