Linda · 2022年12月20日
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：
=(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
看解答还是不是很清晰
星星_品职助教 · 2022年12月20日
同学你好，
提问需要具体写明是哪里不明白。
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本题考察三资产组合标准差的公式，如下：
题目表格中给出了协方差矩阵（variance-covariance matrix）。这个矩阵里每个数字都是两两之间的协方差。例如矩阵中第一列中间的105就说明资产1和资产2的协方差 Covariance 1,2=105。同理，Cov1,3=140，Cov2,3=150
其中自己和自己的协方差就是方差。由此可知资产1方差为196，σ1=16；同理，资产2方差为225，σ2=15；σ3=20
以上逐个代入公式即可得到三资产组合方差，由于题目要求的是标准差，再开方即可
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=w12σ2(R1)+w22σ2(R2)+w32σ2(R3)+2w1w2Cov(R1,R2)+2w1w3Cov(R1,R3)+2w2w3Cov(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
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=w12σ2(R1)+w22σ2(R2)+w32σ2(R3)+2w1w2Cov(R1,R2)+2w1w3Cov(R1,R3)+2w2w3Cov(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 我好像沒有學過這條公式的感覺
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=w12σ2(R1)+w22σ2(R2)+w32σ2(R3)+2w1w2Cov(R1,R2)+2w1w3Cov(R1,R3)+2w2w3Cov(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 6.3%在计算中是不是没用到
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)+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})σ2Rp=w12σ2(R1)+w22σ2(R2)+w32σ2(R3)+2w1w2Cov(R1,R2)+2w1w2Cov(R1,R3)+2w1w2Cov(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 为什么这里没有平方？
