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格蕾絲 · 2020年01月06日

问一道题:NO.PZ2019103001000026 [ CFA III ]

问题如下图:

选项:

A.

B.

C.

解释:

为啥考虑Mac Duration优先于Comvexity

1 个答案

发亮_品职助教 · 2020年01月06日

嗨,爱思考的PZer你好:


"为啥考虑Mac Duration优先于Comvexity"


在这道题里,对于Portfolio 1/3,他们的Macaulay duration无法满足单期负债匹配的要求,所以直接排除。

Portfolio 1/2/3里只有Portfolio 2的Macaulay duration符合要求,所以选择Portfolio 2。

 


在做单期负债匹配时,我们的要求是:

1. Asset Macaulay duration = Investment horizon = Liability's due date (Macaulay duration)

2. Asset PV 大于等于 Liability PV

3. Minimize Asset Convexity

一般碰到几个Portfolio,让选出最优的匹配组合,我们就逐项分析,把不满足要求的先排除掉。

因为负债的期限=9年,所以负债的Macaulay duration = 9,匹配时需要找资产的Macaulay duration=9的。

发现4个Portfolio里只有Portfolio 2与Portfolio 4的Macaulay duration接近9,所以只有这两个组合进入备选项。其他两个被排除掉了。

然后PV没有告诉,本题就默认大家PV都满足条件。

下来就是看Convexity数据了,Portfolio 2和Portfolio 4比较,发现Portfolio 4的Convexity更小,所以最优的匹配组合应该是Portfolio 4


但是因为答案是让在Portfolio 1/2/3里面选,Portfolio 1/3因为Macaulay duration条件都被排除掉了,所以只剩Potfolio 2满足条件。

如果这道题是让在Portfolio 1/2/3/4里面选,那最优的就是Portfolio 4。



总结下:

选匹配的组合时,因为Convexity这个数据,并没有说要达到啥标准才行,给定的要求是尽可能地小,所以一定要把其他能满足的条件先满足了,然后对于Convexity的要求是尽可能地小、越小越好。(多期负债是资产的Convexity在大于负债Convexity的基础上越小越好)。

 


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