老师，为什么cov等于110？看解释没看明白，请老师详细解释下，谢谢。

问题如下：

An analyst develops the following covariance matrix of returns:

The correlation of returns between the hedge fund and the market index is closest to:

选项：

A.

0.005.

B.

0.073.

C.

0.764.

解释：

C is correct.

The correlation between two random variables Ri and Rj is defined as ρ(Ri,Rj) = Cov(Ri,Rj)/σ(Ri)σ(Rj). Using the subscript i to represent hedge funds and the subscript j to represent the market index, the standard deviations are σ(Ri) = 256^1/2 = 16 and σ(Rj) = 81^1/2 = 9. Thus, ρ(Ri,Rj) = Cov(Ri,Rj)/σ(Ri) σ(Rj) = 110/(16 × 9) = 0.764

hedge fund的return的方差就是256，标准差即为16；

Market index的return的方差就是81，标准差就是9。

右上角的110是market index和hedge fund的covariance，所以都相同均为110。

然后就正常代入ρ的公式：

ρ=cov/（σ hedge fund * σ market index）=110/（16*9）=0.764。