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Lee13 · 2022年02月16日

您好，请问是在哪一小节学的这个内容呢？完整的公式是什么呀？矩阵是怎么看的呢？

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：

${\sigma ^2}{R_p} = w_1^2{\sigma ^2}({R_1}) + w_2^2{\sigma ^2}({R_2}) + w_3^2{\sigma ^2}({R_3}) + 2{w_1}{w_2}Cov({R_1},{R_2}) + 2{w_1}{w_2}Cov({R_1},{R_3}) + 2{w_1}{w_2}Cov({R_2},{R_3})$

=(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

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?

您的回答B, 正确答案是: C

A

13.07%

B

不正确13.88%

C

14.62%

数据统计(全部)

做对次数: 180

做错次数: 141

正确率: 56.07%

数据统计(个人)

做对次数: 0

做错次数: 1

正确率: 0.00%

解析

C is correct. For a three-asset portfolio, the portfolio variance is：

σ

2

R

p

=

w

1

2

σ

2

(

R

1

)

+

w

2

2

σ

2

(

R

2

)

+

w

3

2

σ

2

(

R

3

)

+

2

w

1

w

2

C

o

v

(

R

1

,

R

2

)

+

2

w

1

w

2

C

o

v

(

R

1

,

R

3

)

+

2

w

1

w

2

C

o

v

(

R

2

,

R

3

)

σ2

Rp

=w1

2

σ2

(R1

)+w2

2

σ2

(R2

)+w3

2

σ2

(R3

)+2w1

w2

Cov(R1

,R2

)+2w1

w2

Cov(R1

,R3

)+2w1

w2

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

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1 个答案

星星_品职助教 · 2022年02月17日

同学你好，

本题考察三资产组合标准差的公式。公式是上课老师板书的内容，直接看下面即可。

1）公式

2）协方差矩阵

这个矩阵里每个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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