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刘茜娅 · 2023年01月03日

我有点迷糊CV和COV的区别

NO.PZ2021062201000003

问题如下：

A two-stock portfolio includes stocks with the following characteristics:

What is the standard deviation of portfolio returns？

选项：

A.

14.91%

B.

18.56%

C.

21.10%

解释：

B is correct. The covariance between the returns for the two stocks is

Cov (R1,R2) = ρ (R1,R2) σ (R1) σ(R2) = 0.20 (12) (25) = 60.

The portfolio variance is：

${\sigma ^2}{R_p} = w_1^2{\sigma ^2}({R_1}) + w_2^2{\sigma ^2}({R_2}) + 2{w_1}{w_2}Cov({R_1},{R_2})$

=(0.30)2(12)2+(0.7)2(25)2+2(0.30)(0.70)(60)

=12.96 +306.25 +25.2

=344.41

The portfolio standard deviation is：

${\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%$

知识点：Probability Concepts

我有点迷糊CV和COV的区别，可以麻烦解释下吗？

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星星_品职助教 · 2023年01月04日

@刘茜娅

1）这一组公式针对的样本的情况，即样本协方差和样本相关系数。

2）这一组公式和抽样无关。

Cov中的E为根据概率做加权平均。correlation中，上面的r为样本相关系数，这里的ρ为总体相关系数。

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星星_品职助教 · 2023年01月03日

同学你好，

CV是描述单个变量的离散程度的指标，和方差/标准差，range，MAD这些是一类的，衡量的是变量自身的风险；

Covariance / correlation是描述两个变量共同变化的指标，所以使用的范围多数都是资产组合，衡量变量之间组合在一起如何实现分散化，改善组合的风险。

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刘茜娅 · 2023年01月03日

是因为一个是Sxy和rxy采样的，而cov和p的表达是总体吗？

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