相关系数为什么不能是-1

问题如下：

A portfolio has two assets （which returns are normally distributed） with equal amount investment. Which of the following is correct regarding portfolio VaR?

选项：

A.

when correlation=0, we can derive the upper bound of portfolio VaR.

B.

when correlation=1, we can derive the lower bound of portfolio VaR.

C.

when correlation=1, we can derive the upper bound of portfolio VaR.

D.

portfolio VaR can be higher than the sum of the individual VaRs.

解释：

C is correct.

考点：Portfolio VaR

解析：首先选项D肯定错误，组合的分散化效应，portfolio VaR无论如何不会高于individual VaR的总和。

correlation=0, portfolio VaR=sqr(VaR1²+VaR2²) , lower bound. correlation=1，portfolio VaR= VaR1 + VaR2 , upper bound. 因此，选项C正确。