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Linda · 2022年12月20日

这题可以具体讲解一下吗?

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)+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})

=(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

1 个答案

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。

--------

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

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