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sincex · 2023年04月29日

为什么asset convexity要大于liability convexity才能免疫成功呢?

NO.PZ2018120301000015

问题如下:

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


Whichportfolio in Exhibit 2 fails to meet the requirements to achieveimmunization 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.

如题,为什么asset 凸度要大于负债凸度才可以呢?

1 个答案
已采纳答案

pzqa31 · 2023年04月29日

嗨,努力学习的PZer你好:


convexity可以代表现金流的离散程度,convexity越大,则现金流越离散。

如果资产的convexity大于负债的convexity,说明资产现金流比负债更离散,或者可以理解为资产的现金流可以包住负债的现金流。

比如负债有3、5年期,资产有1、3、5、7年期,那么这样的资产现金流是比负债现金流离散的,可以包住负债现金流。

这样做是为了避免最后一期负债没有对应的资产现金流可以cover,如果资产现金流比负债更分散,那么负债的最后一笔现金流,肯定可以通过资产的coupon或者sale price来覆盖的,这样免疫策略才会成功。

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