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I Yuan · 2021年12月24日

我知道A是对的，但是为什么C是错误的

  1. CFA III
  2. Fixed Income

NO.PZ2021120102000010

问题如下：

Which of the following statements best describes empirical duration?

选项：

A.

A common way to calculate a bond’s empirical duration is to run a regression of its price returns on changes in a benchmark interest rate.

B.

A bond’s empirical duration tends to be larger than its effective duration.

C.

The price sensitivity of high-yield bonds to interest rate changes is typically higher than that of investment-grade bonds

解释：

A is correct. A bond’s empirical duration is often estimated by running a regression of its price returns on changes in a benchmark interest rate.

助教您好。我知道A是对的，但是为什么C是错误的？不是HY bond对利率的敏感性更大？我的理解是它只有在经济趋势往上走的时候才会和investment grade bond的利差缩小。


谢谢。

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1 个答案

pzqa015 · 2021年12月24日

嗨，从没放弃的小努力你好：


公司债的折现率可以用这个公式来表示：yc=yb+spread①

C选项的interest rate changes指的是yb的change，即基准收益率的改变。

根据公式①，yb改变，会传导至yc，进而引起公司债券价格发生变化。

关于yb与spread，有个结论是：yb与spread呈负相关关系，也即，yb上升，spread通常会下降；yb下降，spread通常会上升，现实意义是：yb上升，代表经济回暖，公司债的利差spread变小；yb下降，代表经济下行，公司债的利差与spread变大，对于不同评级的债券，负相关关系的大小是不一样的，通常来说，HYB的负相关关系更大，IG的负相关关系更小，原因是相对于IG，HYB的spread更容易受经济周期的影响。

讲义对这里的描述如下图：

正式由于HYB的spread与yb的负相关关系大，所以spread对yb的抵消作用大，所以同样yb变动1bp，HYB的yc变化是小于IG的yc变化的，导致HYB的price变化小于IG的price变化，所以，C选项正确的表述应该是：the price sensitivity of high yield bonds to interest rate changes is typically lower than that of investment grade bonds




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虽然现在很辛苦，但努力过的感觉真的很好，加油！

Felix Young · 2023年01月07日

老师好，就回复继续请教下。 根据yc=yb+spread ， 打比方： 初始状态下 yb=4%, hyb的spread=5%、IG的spread=2%， 则hyb的yc=9%、 ig的yc=6%； 当 yb上升△=1%后， 假设hyb spread 下降更多 △=-2%，ig spread 下降更少 △=-1%，此时 hyb yc'=5%+3%=8%, ig yc'=5%+1%=6% 这时候 hyb 的变动依旧比 IG的变动更大，进而引起HYB的债券价格变化要大于IG的债券价格变化？ 不知道这么思考是哪里出问题了？

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