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我爱荷包蛋 · 2024年06月07日

我的解题思路

NO.PZ2021120102000005

问题如下:

An active fixed-income manager holds a portfolio of commercial and residential mortgage-backed securities that tracks the Bloomberg Barclays US Mortgage-Backed Securities Index. Which of the following choices is the most relevant portfolio statistic for evaluating the first-order change in his portfolio’s value for a given change in benchmark yield?

选项:

A.

Effective duration

B.

Macaulay duration

C.

Modified duration

解释:

A is correct.

Effective duration is a yield duration statistic that measures interest rate risk using a parallel shift in the benchmark yield curve (ΔCurve).

Effective duration measures interest rate risk for complex bonds whose future cash flows are uncertain because they are contingent on future interest rates. Both Macaulay duration (B) and modified duration (C) are relevant statistics only for option-free bonds.

备注:本题题干说明是投资MBS与CMBS(commercial and residential mortgage-backed securities)。由于MBS、CMBS的基础资产为房贷,而房贷存在提前偿还的“期权”,所以本题的投资组合可以理解为含权债券(类似Callable bond),因此应该使用Effective duration。

老师您好,我在做这道题的时候,不是从含权债券的角度来考虑的,而是我在credit strategies这个章节中,有个印象:

基于YTM的yield curve duration包含:macaulay duration, modified duration;

基于Benchmark rate的benchmark duration包含:effective duration。

题目说了是基于Benchmark rate的duration,所以我选了effective duration。

这两个解题思路的本质是一样的吗?



1 个答案

pzqa31 · 2024年06月10日

嗨,努力学习的PZer你好:


这道题问的是当基准利率变动一单位,应该用哪个一阶导来衡量这个投资组合价值的变化,这考的就是这几个duration最基本的含义,是二级的知识。mortgage-backed securities本身是embedded call option的,类似callable bond,MBS底层房贷的借款人有提前还款的权利,类似callable发行人提前赎回的权利,所以用effective duration。


然后同学说的是duration的细分,也是没错的,不过并不是这道题要考的重点。根据利率的不同,有两种Duration概念:一种是Yield duration,就是基于债券Yield的,代表债券Yield变动1单位,债券的价格变动多少;比如说Modified duration就是这种。另外一种就是Curve duration,他是基于Benchmark rate的,就是Benchmark rate变动1单位,债券价格变动多少;比如说Effective duration。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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