衡量nonparallel的是哪一种久期

问题如下：

The followings are some descriptions of different kinds of duration. Which is most accurate?

选项：

A.

Macaulay duration is used for measuring the curve duration.

B.

Effective duration measures interest rate risk in terms of a nonparallel shift in the benchmark yield curve.

C.

A bond’s Macaulay duration always larger than its modified duration.

解释：

C is correct.

A bond’s Macaulay duration always larger than its modified duration. The relationship between Macaulay duration and modified duration is presented as following:

$Modified\;duration=\frac{Macaulay\;duration}{1+r}$

Where r is yield per period which is always larger than zero. Depending on this, the denominator ( 1 + r ) is always larger than 1. So a bond’s Macaulay duration always larger than its modified duration.

A is incorrect because Macaulay duration is used for measuring the yield duration, not the curve duration.

B is incorrect because effective duration measures interest rate risk in terms of a parallel shift in the benchmark yield curve.

考点：duration

解析：effective duration而非Macaulay duration衡量的是curve duration，A选项说法不正确。

有效久期衡量利率风险的时候，假设的是benchmark利率曲线发生一个平行移动，而不是nonparallel shift。parallel shift是指收益率曲线发生平行移动，也就是曲线上的每一个点都变动相同的幅度。B选项说法不正确。

修正久期等于麦考利久期/(1+一期的市场利率)，市场利率通常情况下＞0,因此（1+市场利率）通常情况下大于1。所以，C选项说法正确，当选。