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王小周 · 2025年06月22日

1+r有没有可能小于1呢

NO.PZ2016031001000114

问题如下:

Which of the following statements about duration is correct? A bond’s:

选项:

A.

effective duration is a measure of yield duration.

B.

modified duration is a measure of curve duration.

C.

modified duration cannot be larger than its Macaulay duration.

解释:

C is correct.

A bond’s modified duration cannot be larger than its Macaulay duration. The formula for modified duration is:

ModDur=MacDur1+rModDur=\frac{MacDur}{1+r}

where r is the bond’s yield-to-maturity per period. A bond’s yield-to-maturity has an effective lower bound of 0, and thus the denominator 1 + r term has a lower bound of 1. Therefore, ModDur will typically be less than MacDur.

Effective duration is a measure of curve duration. Modified duration is a measure of yield duration.

考点:duration

解析:curve duration只有effective duration,其他(Modified and Macaculay)都是yield duration。故选项A、B均不正确。区别在于yield duration是价格对债券自身YTM的敏感性,而Curve duration是价格对benchmarke yield curve的敏感性,用于含权债券。

r通常大于0,1+r通常大于1,所以Modified duration通常比Macaculay duration小,故选项C正确。

r是否会出现小于0的情况呢?

1 个答案

笛子_品职助教 · 2025年06月23日

嗨,爱思考的PZer你好:


r是否会出现小于0的情况呢?

Hello,亲爱的同学~

前几年确实出现过负利率的情况。

但在CFA考试的这个章节里,是默认为利率大于0的一般情形。

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