开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

mino酱是个小破货 · 2025年03月02日

关于B项，effective duration和empirical duration区别？谢谢

  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.

empirical duration是观察到的债券价格对基准利率变动的敏感程度，effecive duration是理论上计算的债券价格对基准利率变动的敏感程度。empirical duration小于effective duration，尤其是HYB，二者的差异更大，这是一个实证检验观察到的一个现象。具体原因如下：

由于yc=yb+spread且yb与credit spread有负相关关系（理论基础是△yb＞0表明经济好，此时，投资者对市场未来看好，对债券credit premium要求较低，因此credit spread变小），所以△yb＞0，credit spread下降，也就是△spread＜0，进而△yc＜△yb，抵消作用就是credit spread与基准利率的负相关导致的。

假设△yb=1%，那么根据上面的分析，△yc＜1%，△yc引起的△%P＜△yb引起的△%P，前者是empirical duration，后者是effective duration，所以，empirical duration 通常要比 effective duration小。

相比于IG，因为HYB的credit spread与yb负相关关系更大，所以相对于IG，HYB的empirical duration比effective duration小的更多。


我的思路也是如此，但是发亮老师的讲解，effective duartion和emprical duration都是基于benchmark计算的，是类似概念，但不是analytical duration(假设yb和spread独立变化），所以想问下，那么B错在哪？谢谢


添加评论
1 个答案

发亮_品职助教 · 2025年03月03日

选项B的问题是他刚好说反了：

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

所有债券的empirical duration都小于其effective duration，HY bond这种现象更明显。


提问里说的理解思路没什么问题，是正确的理解。


根据上面的理解，同一个债券，他的empirical duration < effective duration。这也是正确的结论。

因为benchmark rate上升1%，对于effective duration不考虑spread的反向改变，1%的基准利率改变全部传导到债券的价格改变上，假设价格改变幅度是4%，则effective duration=4%/1%=4


对于empirial duration，因为有benchmark rate和credit spread的反向改变，benchmark rate上升1%，credit spread可能下降0.7%，最终净效果是只有0.3%的利率上升传导到了债券价格改变上，实际债券价格改变幅度更小，假设债券的价格只改变了1.5%。

但注意，在回归算empirical duration的时候，是拿债券价格实际改变幅度1.5%和benchmark rate改变1%做回归，相当于是benchmark rate上升1%，债券价格只改变了1.5%，其empirical duration = 1.5%/1% = 1.5

所以empirical duration也是基于benchmark rate的duration。


因为这种反向抵消，在empirical duration里，债券的实际价格改变幅度更小。即，benchmark rate利率改变1单位，对应更小的债券价格波动，于是empirical duration更小。


analytical duration是债券的理论duration。包含基于债券YTM的modified/macaulay duration（yield duration statistics），也包含基于benchmark rate的effective duration（curve duration）。这是都是基于公式算的理论值。


empirical duration是债券的实际价回归duration，回归的自变量是benchmark rate，衡量benchmark rate变动1单位，债券价格的实际改变幅度。这里是基于benchmark rate算的回归，只不过在考虑债券价格改变时，考虑到了benchmark rate与spread的反向抵消。

  • 1

    回答

  • 0

    关注

  • 6

    浏览
相关问题

NO.PZ2021120102000010 问题如下 Whiof the followingstatements best scribes empiricration? A.A common wto calculate a bons empiricration is to run aregression of its prireturns on changes in a benchmark interest rate. B.A bons empiricration ten to larger thits effective ration. C.The prisensitivity of high-yielbon to interest rate changes is typically higher ththof investment-gra bon Ais correct. A bons empiricration is often estimaterunning aregression of its prireturns on changes in a benchmark interest rate. 可否改为The prisensitivity of high-yielbon to interest rate changes is typically lower ththof investment-gra bon because cret sprea minate their yielcomposition.高收益债券（High-YielBon）通常对信用风险的敏感性更高，而非对利率变化的敏感性更高。相比投资级债券（Investment-Gra Bon），高收益债券的价格对利率变化的敏感性通常较低，因为其收益率中信用利差的比重较大，而利率波动的影响较小。

2024-12-08 20:35 1 · 回答

NO.PZ2021120102000010 问题如下 Whiof the followingstatements best scribes empiricration? A.A common wto calculate a bons empiricration is to run aregression of its prireturns on changes in a benchmark interest rate. B.A bons empiricration ten to larger thits effective ration. C.The prisensitivity of high-yielbon to interest rate changes is typically higher ththof investment-gra bon Ais correct. A bons empiricration is often estimaterunning aregression of its prireturns on changes in a benchmark interest rate. 拜托老师帮忙复习一下，为什么HY的sensitivity小于IG的？

2024-07-18 21:57 2 · 回答

NO.PZ2021120102000010 问题如下 Whiof the followingstatements best scribes empiricration? A.A common wto calculate a bons empiricration is to run aregression of its prireturns on changes in a benchmark interest rate. B.A bons empiricration ten to larger thits effective ration. C.The prisensitivity of high-yielbon to interest rate changes is typically higher ththof investment-gra bon Ais correct. A bons empiricration is often estimaterunning aregression of its prireturns on changes in a benchmark interest rate. C:The prisensitivity of high-yielbon to interest rate changes is typically higher ththof investment-gra bon

2024-06-02 21:31 2 · 回答

NO.PZ2021120102000010 问题如下 Whiof the followingstatements best scribes empiricration? A.A common wto calculate a bons empiricration is to run aregression of its prireturns on changes in a benchmark interest rate. B.A bons empiricration ten to larger thits effective ration. C.The prisensitivity of high-yielbon to interest rate changes is typically higher ththof investment-gra bon Ais correct. A bons empiricration is often estimaterunning aregression of its prireturns on changes in a benchmark interest rate. 问题1: 请问老师，教材原文对于empiricration 的是什么？问题2: 请问老师 empiricration 衡量的是价格对yc变化的敏感程度，还是价格对yb变化的敏感程度呢？我的理解应该是价格对于yc变化的敏感程度，只有这样，sprea变化和benchmark 的变化才能相互抵消。基于问题2里我对于empiricration的理解，我认为A不对，因为A写的是对于benmark利率的回归得出了empiricration。请老师做解读，谢谢。

2024-05-25 17:48 3 · 回答