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陆佳莹 · 2021年08月21日

这道题中mean这个条件有什么作用？

  1. CFA I
  2. Quantitative

NO.PZ2021061603000034

问题如下：

Consider two variables, A and B. If variable A has a mean of-0.56, variable B has a mean of 0.23, and the covariance between the two variables is positive, the correlation between these two variables is:

选项：

A.negative. B.zero. C.positive.

解释：

C is correct. The correlation coefficient is positive because the covariance is Dositive. The fact that one or both variables have a negative mean does not affect the sign of the correlation coefficient.

这道题中mean这个条件有什么作用？还有一个不理解的就是，covariance大于0推出correlation也大于0是如何得到的呢？correlation不是由covariance除以两个变量的标准差得到的么？这道题的逻辑怎么给他理顺？求助一下，谢谢

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星星_品职助教 · 2021年08月21日

同学你好，

①mean是干扰条件，可以忽略。或者说题目想用负的mean来干扰判断选择出正的correlation，总之没有用。

②covariance＞0可以等价于correlation＞0，这是因为标准差都是正值，所以直接关联covariance和correlation的符号就可以了。

18816562889 · 2022年06月08日

老师，请问标准差都是正值，是肯定的对吗？因为每个数与平均数的距离的平方开根号肯定是大于等于0的？然后有没有可能会等于0？

星星_品职助教 · 2022年06月10日

@18816562889

当资产收益率为常数时，标准差为0

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