题目
An analyst develops the following covariance matrix of returns:「huixue_img/importSubject/1564548691447123968.png」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.
答案
C
解析
： 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) = 2561/2 = 16 and σ(Rj) = 811/2 = 9. Thus, ρ(Ri,Rj) = Cov(Ri,Rj)/[σ(Ri) σ(Rj)] = 110/(16 × 9) = 0.764. ： C正确。 两个随机变量之间的相关性Ri和Rj被定义为ρ(Ri, Rj) = Cov (Ri, Rj) /(σ(Ri)σ(Rj)]。使用下标代表对冲基金和下标j代表市场指数,标准偏差是σ(Ri) = 256^(1/2) = 16和σ(Rj) = 81^(1/2) = 9。因此,ρ(Ri, Rj) = Cov (Ri, Rj) /(σ(Ri)σ(Rj)] = 110 / (16×9) = 0.764。