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Sophiener · 2020年01月23日

问一道题:NO.PZ2019103001000015

问题如下:

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.

答案是不是错了,应该选B吧?

1 个答案
已采纳答案

发亮_品职助教 · 2020年02月03日

嗨,爱思考的PZer你好:


“答案是不是错了,应该选B吧?”


注意题干说的是:Fails to meet,也就是不能实现Duration-matching的组合是哪个。

对于多期负债的Duration-matching,我们的要求为:

1、Asset PV 大于等于 Liability PV

2、Asset BPV = Liability BPV(Money duration相等)

3、Asset Convexity大于Liability Convexity

满足以上条件的组合,都可以实现多期负债的匹配。因为大多数题目不会给PV的条件,所以如果题目没给,就默认备选Portfolio的PV已经满足匹配的要求了,所以我们只需比较剩下两个条件即可。


表格里的三个备选Portfolio,他们的BPV都差不多在负债的BPV(10,505)的附近,所以三个Portfolio的BPV满足匹配的条件。

因为负债的Convexity=33.05, 所以备选Portfolio的Convexity要大于这个数才能满足多期负债匹配的要求。因为Portfolio A的Convexity小于这个数,所以被排除,Fails to meet the requirements to achieve immunization for multiple liabilities.

因为Portfolio B/C,他俩的BPV满足条件,Convexity都大于负债的Convexity数据,所以他俩都能做多期负债的Duration-matching。

如果要在他俩里挑一个最优的,我们要选择Portfolio B,因为Portfolio B的Convexity在大于负债Convexity 33.05的基础上,又尽可能的小,所以Portfolio B的Structural risk小于Portfolio C,于是Portfolio B/C都能满足多期负债匹配,但是Portfolio B又是最优的。


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