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穿行 · 2024年06月02日

C为什么不对

  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.

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


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2 个答案

发亮_品职助教 · 2024年07月22日

参考LM 4的标题empirical duration这个视频；Or讲义275页

发亮_品职助教 · 2024年06月03日

嗨，努力学习的PZer你好：


C选项说反了。


主题干讨论的是empirical duration，三个选项都是关于Empirical duration的讨论哈。

关于empirical duration正确的结论就是，high-yield bond的empirical duration要小于investment-grade bond的empirical duration


原因是empirical duration是利用债券的实际价格变动和Benchmark rate的改变做的回归。即：

y = a + bx + 残差项


其中因变量y就是债券价格的实际改变，而x自变量就是benchmark rate的改变，回归出来的系数b，其含义就是benchmark rate变动1单位时，债券的实际价格变动多少单位，所以系数b本质就是empirical duration。


对于公司债来讲，当benchmark rate改变时，债券的实际价格波动，也就是因变量y是比较小的，所以1单位x改变带来的y改变较少，于是回归出来的系数b,empirical duraiton较小。

而同样一单位的benchmark rate改变，投资级别的债券investment grade bond的价格改变y较大，所以回归出来的系数b，empirical duration较大。


原因就是high-yield bond会出现较大的benchmark rate与credit spread的反向抵消变化，这导致债券的YTM改变不大，于是导致HYB的价格波动不大。


比如，benchmark rate上升1%，而HYB的Credit spread下降0.8%，于是HYB债券的YTM只上升了0.2%，基于0.2%的YTM改变，HYB的实际价格波动比较小。


利用HYB较小的实际价格波动（因变量y）和benchmark rate的改变1%（自变量x）做回归算出来的系数empirical duration就较小。


而对于Investment grade bond来讲，benchmark rate上升1%，其credit spread只下降0.1%，于是债券的YTM上升0.9%，基于这样的YTM改变，其实际价格波动较大。

于是基于较高的实际价格变化和Benchmark rate上升1%做回归出来的empirical duration就较大。


总结下：越是垃圾债，benchmark rate与credit spread的反向变化关系就越明显，其价格对benchmark rate的敏感度就越低，因为benchmark rate的改变绝大部分被credit spread反向改变抵消了，最终引起的价格变动就小，所以HYB对benchmark rate就不敏感，即，empirical duration小，小于Investment grade bond的ED。

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努力的时光都是限量版，加油！

fanfan1989 · 2024年07月05日

每次看到是发亮老师写的回答，就放心了，肯定能讲清楚

缨水珞 · 2024年07月22日

这个知识点在哪个Module的哪个知识点下面？帮忙定位下，谢谢老师

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