开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

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

添加评论
1 个答案
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。

  • 1

    回答

  • 1

    关注

  • 791

    浏览
相关问题

NO.PZ2021062201000003 问题如下 A two-stoportfolio inclus stocks with the following characteristics: Whis the stanrviation of portfolio returns？ A.14.91% B.18.56% C.21.10% B is correct. The covarianbetween the returns for the two stocks isCov (R1,R2) = ρ (R1,R2) σ (R1) σ(R2) = 0.20 (12) (25) = 60. The portfolio varianisσ2Rp=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})σ2Rp​=w12​σ2(R1​)+w22​σ2(R2​)+2w1​w2​Cov(R1​,R2​)=(0.30)2(12)2+(0.7)2(25)2+2(0.30)(0.70)(60)=12.96 +306.25 +25.2=344.41The portfolio stanrviation isσ2(RP)=344.411/2=18.56%{\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%σ2(RP​)=344.411/2=18.56% 知识点Probability Concepts 还是在portfolio里如果有AB两个产品的情况下，AB的covaraince就是portfolio的variance

2023-07-28 17:35 1 · 回答

NO.PZ2021062201000003 问题如下 A two-stoportfolio inclus stocks with the following characteristics: Whis the stanrviation of portfolio returns？ A.14.91% B.18.56% C.21.10% B is correct. The covarianbetween the returns for the two stocks isCov (R1,R2) = ρ (R1,R2) σ (R1) σ(R2) = 0.20 (12) (25) = 60. The portfolio varianisσ2Rp=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})σ2Rp​=w12​σ2(R1​)+w22​σ2(R2​)+2w1​w2​Cov(R1​,R2​)=(0.30)2(12)2+(0.7)2(25)2+2(0.30)(0.70)(60)=12.96 +306.25 +25.2=344.41The portfolio stanrviation isσ2(RP)=344.411/2=18.56%{\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%σ2(RP​)=344.411/2=18.56% 知识点Probability Concepts 如上

2023-07-28 17:30 1 · 回答

NO.PZ2021062201000003 问题如下 A two-stoportfolio inclus stocks with the following characteristics: Whis the stanrviation of portfolio returns？ A.14.91% B.18.56% C.21.10% B is correct. The covarianbetween the returns for the two stocks isCov (R1,R2) = ρ (R1,R2) σ (R1) σ(R2) = 0.20 (12) (25) = 60. The portfolio varianisσ2Rp=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})σ2Rp​=w12​σ2(R1​)+w22​σ2(R2​)+2w1​w2​Cov(R1​,R2​)=(0.30)2(12)2+(0.7)2(25)2+2(0.30)(0.70)(60)=12.96 +306.25 +25.2=344.41The portfolio stanrviation isσ2(RP)=344.411/2=18.56%{\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%σ2(RP​)=344.411/2=18.56% 知识点Probability Concepts 麻烦详细讲讲COV（R1，R2）的计算过程，谢谢

2023-03-12 22:24 1 · 回答

NO.PZ2021062201000003 问题如下 A two-stoportfolio inclus stocks with the following characteristics: Whis the stanrviation of portfolio returns？ A.14.91% B.18.56% C.21.10% B is correct. The covarianbetween the returns for the two stocks isCov (R1,R2) = ρ (R1,R2) σ (R1) σ(R2) = 0.20 (12) (25) = 60. The portfolio varianisσ2Rp=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})σ2Rp​=w12​σ2(R1​)+w22​σ2(R2​)+2w1​w2​Cov(R1​,R2​)=(0.30)2(12)2+(0.7)2(25)2+2(0.30)(0.70)(60)=12.96 +306.25 +25.2=344.41The portfolio stanrviation isσ2(RP)=344.411/2=18.56%{\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%σ2(RP​)=344.411/2=18.56% 知识点Probability Concepts 我有点迷糊CV和COV的区别，可以麻烦下吗？

2023-01-03 00:24 2 · 回答

NO.PZ2021062201000003 问题如下 A two-stoportfolio inclus stocks with the following characteristics: Whis the stanrviation of portfolio returns？ A.14.91% B.18.56% C.21.10% B is correct. The covarianbetween the returns for the two stocks isCov (R1,R2) = ρ (R1,R2) σ (R1) σ(R2) = 0.20 (12) (25) = 60. The portfolio varianisσ2Rp=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})σ2Rp​=w12​σ2(R1​)+w22​σ2(R2​)+2w1​w2​Cov(R1​,R2​)=(0.30)2(12)2+(0.7)2(25)2+2(0.30)(0.70)(60)=12.96 +306.25 +25.2=344.41The portfolio stanrviation isσ2(RP)=344.411/2=18.56%{\sigma ^2}({R_P}) = {344.41^{1/2}} = 18.56\%σ2(RP​)=344.411/2=18.56% 知识点Probability Concepts COV为什么是这样算的？跟视频里老师讲的不一样啊

2022-11-30 07:20 1 · 回答