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Jwang · 2024年07月18日

如题

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000031

问题如下：

Doug, the newly hired chief ­financial officer for the City of Radford, asks the deputy ­financial manager, Hui, to prepare an analysis of the current investment portfolio and the city’s current and future obligations. The city has multiple liabilities of different amounts and maturities relating to the pension fund, infrastructure repairs, and various other obligations.

Hui observes that the current ­fixed-income portfolio is structured to match the duration of each liability. Previously, this structure caused the city to access a line of credit for temporary mismatches resulting from changes in the term structure of interest rates.

Doug asks Hui for different strategies to manage the interest rate risk of the city’s ­fixed-income investment portfolio against one-time shifts in the yield curve. Hui considers two different strategies:

  • Strategy 1: Immunization of the single liabilities using zero-coupon bonds held to maturity.
  • Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.
Which duration measure should be matched when implementing Strategy 2?

选项：

A.

Key rate

B.

Modi­fied

C.

Macaulay

解释：

Correct Answer: C

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.

本题考查Single liability duration matching的条件。这个条件只能使用Macaulay duration。

因为只要当资产的Macaulay duration = 投资期时，债券的Price risk和reinvestment risk才能相互抵消，债券才能实现利率风险免疫。我们认为实现利率风险免疫后的债券是安全的，投资是可靠的。所以用该债券去匹配负债是合适的，于是再让投资期等于负债的期限，即，让免疫后的债券投资匹配上了负债。

如，单期负债的期限是5年，为了构建免疫，资产的投资期必须是5年，这样资产到期时可以偿还负债。为了让资产的投资对利率免疫，则找到macaulay duration = 投资期 = 5的债券，于是得到了Macaulay duration = 投资期 = 负债的期限，我们实现了利率免疫。

老师好，是不是strategy1和2都用MacD因为single liability，如果是multiple liability，用modifiedD或moneyD？

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pzqa31 · 2024年07月19日

嗨，从没放弃的小努力你好：


是的，Single liability和Multiple liability不一样，Single liability看Macaulay duration，Multiple liability看BPV。如果是计算BPV用到的是Modified duration（effective duration也可以，因为两者近似），咱们做题的时候BPV一般是直接给的，也不用计算。

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