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蕾 · 2024年01月08日

请详细解释一下这道题谢谢

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000015

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.


Which portfolio in Exhibit 2 fails to meet the requirements to achieve immunization for multiple liabilities?

选项：

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释：

Correct Answer: A

A is correct. The two requirements to achieve immunization for multiple liabilities are for the money duration (or BPV) of the asset and liability to match and for the asset convexity to exceed the convexity of the liability. Although all three portfolios have similar BPVs, Portfolio A is the only portfolio to have a lower convexity than that of the liability portfolio (31.98, versus 33.05 for the $20 million liability portfolio), and thus, it fails to meet one of the two requirements needed for immunization.

解释A答案

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1 个答案

笛子_品职助教 · 2024年01月10日

嗨，爱思考的PZer你好：


多期负债匹配的3个条件是：


1、PV Asset ≥ PV liability

2、Asset BPV = Liability BPV

3、Asset convexity > liability convexity

以上就已经满足了多期负债匹配条件，那如果要使得匹配效果尽可能地好，我们就需要在满足以上3个条件的基础上，尽可能的降低Asset convexity。


匹配这里的条件，可以取近似，只要偏离的不是太离谱就都可以。一般这种题目就是在一堆组合里面，找到一个相对最优的匹配组合。选的时候，就是用匹配的条件一项项排除。


例如，这道题里面，负债的BPV=35211，三个资产的BPV分别是：35219；35213；35214；

整体来看，3个资产的BPV和负债的BPV基本差不多，有偏差也不大，所以从BPV的角度看，3个组合都满足匹配条件。3个组合都进入备选。


接下来，我们换另外一个匹配条件来筛选，用Convexity来排除：

负债的Convexity=42，那直接排除Portfolio A，他的Convexity=40过小，不满足Asset convexity > liability convexity。


剩下Portfolio B与Portfolio C，均满足本题的多期负债匹配的要求，如果要选最优的，就是Portfolio B。因为他的Convexity在大于负债Convexity的基础上，又足够的小。


这道题要求选择： fails to meet the requirements to achieve immunization 

A不能满足，因此选A。


碰到匹配选择Portfolio的题目，就按以上方法，一个标准一个标准进行筛选，有偏差也不要紧，只要偏差不是很大即可，直至选出最优组合。另外需要注意单期负债匹配，多期负债匹配，在匹配时需要的条件不同，有时候题目会有干扰信息。

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