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荷间心素 · 2019年05月02日

问一道题:NO.PZ201812020100000202 第2小题 [ CFA III ]

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问题如下图:

选项:

A.

B.

C.

解释:

此题为何不选c?策略2和策略1相比,确实相关系数低了呀(看绝对值)。另外何老师课后题讲解上说策略2相关性比1高,好像不对吧,相关性不是比较绝对值吗?

1 个答案

发亮_品职助教 · 2019年05月04日

“相关性不是比较绝对值吗?”

带上符号比,越小提供的分散化效果越好。

两个资产间的Correlation只要小于+1就可以提供分散化的效果越小越能提供更好的分散化效果

+1表现出来的特征是:两个资产的收益率是perfectly positively correlated;两个资产收益变动是总是同向的。所以当Correlation=1时,组合的风险就是组合内部各资产风险的直接加权平均。

当把两个资产间的Correlation调小,只要小于+1,那么整个组合的风险一定是小于上面+1相关系数的组合。即组合表现出来的风险小于组合内各资产风险的直接加权平均,如下面这段话截自原版书一级组合部分:

Portfolio risk falls, however, when the two assets are not perfectly correlated (ρ12 < +1).

当Correlation等于-1时,两个资产的收益率是perfectly negatively correlated;两个资产收益变动是总是反向的。这种情况下,组合能够实现最大的Risk reduction。


假设组合有2个资产组合,Fixed-income和Equity,那么组合的风险计算如下公式:

其中W代表权重,发现根号里面其实是一个完全平方公式,当p12取到1时,组合的Standard deviation最大,小于1时即可使得组合的Standard deviation变小,等于-1时,使得组合的Standard deviation最小。

所以Correlation是带上符号比,越小分散化效果越好。

Strategy 1的Correlation是-0.15小于Strategy 2的-0.10,所以Strategy 1提供更好的diversification效果。

弓 · 2021年10月16日

厉害!话都被你说完了。

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