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jerryhuqian · 2023年08月12日

关于 statement 1，请问single liability 为什么还会有影响?

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000025

问题如下：

Leah informs Molly 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. Leah expresses concern about the risks associated with an immunization strategy for this obligation. In response, Molly makes the following statements about liability-driven investing:

  • Statement 1: Although the amount and date of SD&R’s liability is known with certainty, measurement errors associated with key parameters relative to interest rate changes may adversely affect the bond portfolios.
  • Statement 2: A cash flow matching strategy will mitigate the risk from non-parallel shifts in the yield curve.
Which of Molly’s statements about liability-driven investing is (are) correct?

选项：

A.

Statement 1 only.

B.

Statement 2 only.

C.

Both Statement 1 and Statement 2.

解释：

Correct Answer: C

C is correct. Molly is correct that measurement error can arise even in immunization strategies for Type 1 cash flows, which have set amounts and set dates. Also, a parallel shift in yield curves is a sufficient but not a necessary condition to achieve the desired outcome. Non-parallel shifts as well as twists in the yield curve can change the cash flow yield on the immunizing portfolio; however, minimizing the dispersion of cash flows in the asset portfolio mitigates this risk. As a result, both statements are correct.

 关于 statement 1，请问single liability 为什么还会有影响?

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1 个答案

pzqa31 · 2023年08月13日

嗨，努力学习的PZer你好：


Statement 1是专门针对 Measurement errors的。

关于债券、或者债券Portfolio，我们有一些关键指标来衡量他们的特性，比如折现率（YTM/Cash flow yield），Macaulay duration、Modified duration等等。这些指标可以描述债券的特性，也是咱们在匹配负债时，着重参考的依据。

一旦这些指标不准确，就会给匹配带来风险，也就是在匹配时，由指标不准确带来的不匹配的风险，就称为Measurement errors，他属于Model risk里的细分项。


即便是Single liability，依然存在这个风险。例如，我们要匹配题目说的Maturity=9年的负债，那我们需要在市场上找到Macaulay duration=9的债券资产。

假设我们用的是债券Portfolio，那我们必须要计算出来Portfolio的Macaulay duration是多少。这时候就非常容易产生Measurement errors；

按Macaulay duration的定义，我们需要把Portfolio的现金流计算出来，然后一笔笔算Portfolio现金流的平均回流时间（Macaulay duration）；但实际操作中，这样很麻烦，很多人并不会这么算，而是简单的把Portfolio里成份债券的Macaulay duration做加权平均，用这个平均数当成组合的Mac.Duration。

显然，这个Mac.Duration衡量债券组合的特性并不精确，所以哪怕是匹配单期负债，用这样参数的组合匹配负债依然有Measurement errors。所以答案说即便对于Type 1负债的匹配，依然存在风险（measurement errors）是正确的。


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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