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Anny Yang · 2022年05月02日

为什么不能直接将196、225和400作为标准差代入公式？

  1. CFA I
  2. Quantitative

NO.PZ2021062201000004

问题如下：

Lena Hunziger has designed the three-asset portfolio summarized below：


Hunziger estimated the portfolio return to be 6.3%. What is the portfolio standard deviation?

选项：

A.

13.07%

B.

13.88%

C.

14.62%

解释：

C is correct. For a three-asset portfolio, the portfolio variance is：

σ2Rp=w12σ2(R1)+w22σ2(R2)+w32σ2(R3)+2w1w2Cov(R1,R2)+2w1w2Cov(R1,R3)+2w1w2Cov(R2,R3){\sigma ^2}{R_p} = w_1^2{\sigma ^2}({R_1}) + w_2^2{\sigma ^2}({R_2}) + w_3^2{\sigma ^2}({R_3}) + 2{w_1}{w_2}Cov({R_1},{R_2}) + 2{w_1}{w_2}Cov({R_1},{R_3}) + 2{w_1}{w_2}Cov({R_2},{R_3})

=(0.20)2(196) + (0.30)2(225) + (0.50)2(400) + 2(0.20)(0.30)(105) + (2)(0.20(0.50)(140) + (2)(0.30)(0.50)(150)

=7.84 + 20.25 + 100 + 12.6+ 28 +45

=213.69

知识点：Probability Concepts

请问为什么给A,B,C三只股票的covariance开根号，即196，225，400开根号后作为A、B、C标准差代进公式后，结果不一样？

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1 个答案

星星_品职助教 · 2022年05月02日

同学你好，

本题题干给出的表格是协方差矩阵。

这个矩阵中，196,225,400这条对角线表示的是自己和自己的协方差，也就是方差，而不是标准差。

所以需要开一次根号才能得到标准差。

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