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wangyihan · 2023年12月28日

这一题A选项的convexity比负债的小，为什么还选A呢

  1. CFA III
  2. Fixed Income

NO.PZ2023032703000032

问题如下：

Serena Soto is a risk management specialist with Liability Protection Advisors. Trey Hudgens, CFO of Kiest Manufacturing, enlists Soto’s help with three projects.

The second project for Soto is to help Hudgens 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. Soto 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：

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.

谢谢！这一题A选项的convexity比负债的小，为什么还选A呢

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1 个答案

pzqa31 · 2023年12月29日

嗨，从没放弃的小努力你好：


题目问的是哪个选项 fails to meet the requirements，选一个不符合免疫条件的，只有Portfolio A的convexity是小于liability的convexity，所以选A。


多期负债匹配，需要满足的3个条件：

1、PV Asset ≥ PV Liabilities

2、Asset BPV = Liability BPV

3、Asset convexity ＞ Liability Convexity，并且在此基础上，Asset的Convexity越小越好。

满足以上3个条件，就可以实现多期负债的Immunization（Duration-matching）。

因为这道题，以及绝大多数情况，题目没有资产PV与负债PV的数据，所以我们默认三个Portfolio都满足PV的要求。

所以如果要满足匹配的条件，剩下就需要满足两个条件：资产BPV=负债BPV，资产Convexity大于负债Convexity。

资产负债的BPV相等，代表利率变动时，资产、负债的变动金额一致，这样就实现了利率变动时，资产负债的变动同步，资产Cover负债；

资产的Convexiy大于负债的Convexity，是因为我们要确保资产的现金流更加分散、能够包裹住负债的现金流，这样负债到期时，资产的现金流会提前出现，这样能保证足额偿还负债。

因为现金流的分散程度与Convexity数据成正比，现金流越分散代表Convexity数据越大，所以要保证资产的现金流比负债的现金流更分散，就是要求资产的Convexity比负债的Convexity更大。

所以在多期负债的要求里：就是资产的Convexity大于负债的Convexity

但同时资产的Convexity不能太大，否则会引入其他风险：资产不匹配负债的风险（Structural risk），所以我们的要求就是Asset convexity ＞ Liability Convexity，并且在此基础上，Asset的Convexity越小越好。不过这道题没有涉及到这点，其他题目可以注意下这种情况。

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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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