怎么判断zero coupon的Mac duration和bond的哪个大？

问题如下：

Relative to a five-year zero-coupon bond priced to yield 5%, Bond Three has a modified duration that is best described as:

选项：

A.

lower than the zero-coupon bond’s modified duration.

B.

the same as the zero-coupon bond’s modified duration.

C.

greater than the zero-coupon bond’s modified duration.

解释：

A is correct. No calculation is necessary, as we know that a five-year zero-coupon bond has a Macaulay duration of 5, which is greater than that of a coupon bond like Bond three. Since they have the same yields, the bond’s modified durations will have the same relationship as their Macaulay duration.