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🌊Yuri🌊 · 2022年11月30日

问

  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

这道题我一点都没看懂。。。 题干中不是已经给出了各个标准差的占比，问题就是两个组合之前的标准差是多少，为什么不能直接两个相加呢？

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1 个答案

星星_品职助教 · 2022年12月01日

同学你好，

题目中给出的是Stock1和2对应的标准差数值。也就是σ1=12%，σ2=25%。

通常而言，标准差不能直接相加，也不能和return一样直接用加权平均进行计算。需要根据如下的两资产组合的方差公式，逐项代入数值求得。

将求出来的组合方差开方，就得到了“ standard deviation of portfolio returns”

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