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欢欢 · 2021年11月04日

Cov (R1,R2)和σ2（Rp）不是一个概念么？有点搞混了

  1. CFA I
  2. Quantitative

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：

σ2Rp=w12σ2(R1)+w22σ2(R2)+2w1w2Cov(R1,R2){\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：

σ2(RP)=344.411/2=18.56%{\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%

知识点：Probability Concepts

根据公式能看出来不是一个概念，但是从理解的角度，怎么觉得组合的方差不就是这个组合内部的协方差吗？谢谢老师

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已采纳答案

星星_品职助教 · 2021年11月05日

同学你好，

协方差反应的是资产1和资产2的return同时发生变动的情况。例如同增同减，协方差为正。

组合方差反应的是整个组合自身的波动和风险。

通过两资产组合的公式可以清晰的看出cov只是组合方差的一部分。组合方差除了取决于协方差外，还有两个资产自身的方差以及权重。

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