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chuziyang · 2022年04月10日

請問如何看出來選C

  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

請問得到答案213.69，如何確定選C？

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星星_品职助教 · 2022年04月10日

同学你好，

213.69为三资产组合的方差，单位为百分号的平方。

开方后即可得到 14.6181，单位为百分号（%）

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NO.PZ2021062201000004 问题如下 Lena Hunziger hsignethe three-asset portfolio summarizebelowHunziger estimatethe portfolio return to 6.3%. Whis the portfolio stanrviation? A.13.07% B.13.88% C.14.62% C is correct. For a three-asset portfolio, the portfolio varianisσ2Rp=w12σ2(R1)+w22σ2(R2)+w32σ2(R3)+2w1w2Cov(R1,R2)+2w1w3Cov(R1,R3)+2w2w3Cov(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_3}Cov({R_1},{R_3}) + 2{w_2}{w_3}Cov({R_2},{R_3})σ2Rp​=w12​σ2(R1​)+w22​σ2(R2​)+w32​σ2(R3​)+2w1​w2​Cov(R1​,R2​)+2w1​w3​Cov(R1​,R3​)+2w2​w3​Cov(R2​,R3​)=(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 所以variance-covarianmatrix的意思就是两两协方差/方差的值吗

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