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monicaaaaa · 2025年05月28日

duration

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ201812020100000502

问题如下：

Which duration measure should be matched when implementing Strategy 2?

选项：

A.

Key rate

B.

Modified

C.

Macaulay

解释：

C is correct.

An investor having an investment horizon equal to the bond’s Macaulay duration is effectively protected, or immunized, from the first change in interest rates, because price and coupon reinvestment effects offset for either higher or lower rates.

这里我理解的是，这个公司是有multiple liability的，所以选成了modified duration。那么如果答案是mac D，是不是题眼是那一句continuously matching duration？

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1 个答案

发亮_品职助教 · 2025年05月28日

这道题比较特殊。原题是一个multiple liabilities没错。但是匹配的时候没有当成多期负债匹配，而是把多期负债里面的每笔负债拿出来，每一笔负债都是单独的，当成单期匹配。

如，负债有3笔cash flow，第一年cash outflow=10, 第三年cash outflow=30, 第5年cash outflow=80.

现在是把上面的多期负债，当成了3个单期负债。找一个债券去匹配第一个年cash outflow，再找第2个债券资产匹配第二笔cash outflow，同理，再找第3个资产债券去匹配第三笔cash outflow


注意看题目的描述: immunization of the single liabilities using coupon-bearing bonds while continuously matching duration

注意他说的是匹配多个单期负债（single liabilities），是逐个匹配单期负债，并没有说是一次性匹配multiple liabilities。

所以其实就是把多期负债打散，当成多个单期负债匹配。


单期负债匹配的duration是看macaulay duration

多期负债匹配的duration是看money duration/BPV/PVBP，只看Modified duration不行哈。


另外continuously matching duration是为了保证时刻匹配。因为随着时间的流逝，资产的duration和负债的duration会发生偏离，可能不再相等，不再相等就不能实现duration-matching。为了保证组合时刻满足免疫的条件，就需要不停地rebalancing，这样就可以保证资产的duration总是match负债的duration，实现持续的immunization。

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