NO.PZ2017092702000086
问题如下:
The total number of parameters that fully characterizes a multivariate normal distribution for the returns on two stocks is:
选项:
A.3.
B.4.
C.5.
解释:
C is correct.
A bivariate normal distribution (two stocks) will have two means, two variances and one correlation. A multivariate normal distribution for the returns on n stocks will have n means, n variances and n(n – 1)/2 distinct correlations.
这道题目问衡量两只同时服从正态分布的的股票,需要几个参数。可以从如下的角度出发分析:一个正态分布有两个参数,均值和方差。所以从两只股票各自都服从正态分布的角度出发,就各自有一个均值和一个方差,一共是四个参数。从两只股票还要同时都服从正态分布的角度出发,还需要有一个correlation的参数,一共就是5个。
为什么还要考虑correlations?