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HW · 2020年03月28日

问一道题:NO.PZ2019103001000026

问题如下:

Mowery informs Compton that DFC has a single $500 million liability due in nine years, and she wants SD&R to construct a bond portfolio that earns a rate of return sufficient to pay off the obligation.

Compton provides the four US dollar–denominated bond portfolios in Exhibit 1 for consideration. Compton explains that the portfolios consist of non-callable, investment-grade corporate and government bonds of various maturities because zero-coupon bonds are unavailable.

Based on Exhibit 1, which of the portfolios will best immunize SD&R’s single liability?

选项:

A.

Portfolio 1

B.

Portfolio 2

C.

Portfolio 3

解释:

B is correct.

In the case of a single liability, immunization is achieved by matching the bond portfolio’s Macaulay duration with the horizon date. DFC has a single liability of $500 million due in nine years. Portfolio 2 has a Macaulay duration of 8.9, which is closer to 9 than that of either Portfolio 1 or 3. Therefore, Portfolio 2 will best immunize the portfolio against the liability.

表格第三行数字average time of maturity 这不是麦考利久期的定义吗?如果没有第四行麦考利久期,是不是可以用这一行的数字来和liability的duration比较?

1 个答案

发亮_品职助教 · 2020年03月29日

嗨,努力学习的PZer你好:


“表格第三行数字average time of maturity 这不是麦考利久期的定义吗?”


其实并不是这样。Maturity就是指债券的到期日,债券的到期日和债券的Macaulay duration不一定相等。


债券的Macaulay duration是指债券现金流发生的平均时间,一支期限(Maturity)等于10年的付息债券,他的Macaulay duration一定小于10。

原因是Maturity只衡量债券到期的时间,也就是只衡量最后一笔本金到期的时间;

而付息债券,在债券的早期就有现金流,所以对于这支附息债券来讲,我们对债券的所有现金流时间做加权平均,算下来的平均现金流发生时间Macaulay duration一定小于他的最后一笔本金现金流的发生时间(Maturity)。

只有零息债券,因为只有一笔现金流,所以加权平均时间Macaulay duration就等于他最后一笔现金流的发生时间Maturity,附息债券的Macaulay duration一定小于他的Maturity。

所以,average time to maturity并不是债券Macaulay duration的概念。



“如果没有第四行麦考利久期,是不是可以用这一行的数字来和liability的duration比较?”


不行,单期负债匹配的时候一定要严格按照Macaulay duration。题目会给Macaulay duration的。


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