问题如下图：
选项：
A. 
B. 
C. 
解释：
为啥考虑Mac Duration优先于Comvexity
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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