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阿祥 · 2025年06月26日

负债是3年到8.5年久期的负债，为何可以使用c里面的1.5到11年的久期呢？不是应该首先去掉c债券么

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000014

问题如下：

The second project for Serena is to help Trey immunize a $20 million portfolio of liabilities. The liabilities range from 3.00 years to 8.50 years with a Macaulay duration of 5.34 years, cash flow yield of 3.25%, portfolio convexity of 33.05, and basis point value (BPV) of $10,505. Serena suggested employing a duration-matching strategy using one of the three AAA rated bond portfolios presented in Exhibit 2.


Based on Exhibit 2, the portfolio with the greatest structural risk is:

选项：

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释：

Correct Answer: C

C is correct. Structural risk arises from the design of the duration-matching portfolio. It is reduced by minimizing the dispersion of the bond positions, going from a barbell structure to more of a bullet portfolio that concentrates the component bonds’ durations around the investment horizon. With bond maturities of 1.5 and 11.5 years, Portfolio C has a definite barbell structure compared with those of Portfolios A and B, and it is thus subject to a greater degree of risk from yield curve twists and non-parallel shifts. In addition, Portfolio C has the highest level of convexity, which increases a portfolio’s structural risk.

负债是3年到8.5年久期的负债，为何可以使用c里面的1.5到11年的久期呢？不是应该首先去掉c债券么

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1 个答案

发亮_品职助教 · 2025年06月28日

有一点问题。负债不是3年到8.5年期的久期，而是负债的到期日（maturity）是3年到8.50年，然后负债整体的macaulay duration是5.34年：

The liabilities range from 3.00 years to 8.50 years with a Macaulay duration of 5.34 years

负债的Macaulay duration=5.34，意思是把负债当成一个整体看，负债现金流的发生平均时间是5.35年。


11.5 year也是组合C里面的债券期限（maturity or term），并非macaulay duration。macaulay duration的数据在表格第三列有给出。


duration-matching匹配的时候不用管负债的内部现金流发生日期是啥样，不用管负债内部的债券啥时候到期。资产同理，不用管组合内部债券的到期期限。

因为负债到期时，资产内部未到期的债券可以直接卖出变现偿还负债。而在负债到期日之前提前收到的资产现金流会进行再投资直至负债到期。duration-matching之所以成功，就是让再投资风险和变现债券价格不确定的风险抵消，即，利率风险不会影响到资产收益率。债券资产是一个确定的投资。

不管怎么样，负债到期时，总是可以用资产偿还。所以资产内部具体各个债券的到期日不重要。


匹配的时候是把负债打包当成了一个整体对待。其中Macaulay duration就是负债的整体指标，衡量整体上看负债现金流发生的平均时间。

在匹配的时候，资产也一样，只看整体指标macaulay duration。只要匹配的时候资产与负债的这个整体指标一致。那意思是，资产现金流的平均发生时间和负债现金流发生的平均时间一致，那么就是可以用资产cover住负债。


多期负债匹配也是一样，只要资产的整体指标BPV（money duration）和负债的整体指标BPV（money duration）能够匹配上即可。不用管资产、负债内部的现金流到期日是如何的。

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