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陈Shelly · 2022年05月17日

请问这里为什么后面不用乘以2呢?

* 问题详情,请 查看题干

NO.PZ201809170400000504

问题如下:

Based on Exhibit 2, the portion of total portfolio risk that is explained by the market factor in Fund 1’s existing portfolio is closest to:

选项:

A.

3%.

B.

81%.

C.

87%.

解释:

C is correct.

The portion of total portfolio risk explained by the market factor is calculated in two steps. The first step is to calculate the contribution of the market factor to total portfolio variance as follows:

CVmarket  factor=j=1nXmarket  factorXjCmf,jCV_{market\;factor}={\textstyle\sum_{j=1}^n}X_{market\;factor}X_jC_{mf,j}

=Xmarket  factorj=1nXjCmf,j=X_{market\;factor}{\textstyle\sum_{j=1}^n}X_jC_{mf,j}

Where

CVmarket factor = contribution of the market factor to total portfolio variance

xmarket factor = weight of the market factor in the portfolio

xj = weight of factor j in the portfolio

Cmf,j = covariance between the market factor and factor j

The variance attributed to the market factor is as follows:

CVmarket factor = (1.080 × 0.00109 × 1.080) + (1.080 × 0.00053 × 0.098) + (1.080 × 0.00022 × –0.401) + (1.080 × –0.00025 × 0.034)

CVmarket factor = 0.001223

The second step is to divide the resulting variance attributed to the market factor by the portfolio variance of returns, which is the square of the standard deviation of returns:

Portion of total portfolio risk explained by the market factor = 0.001223/(0.0374)^2

Portion of total portfolio risk explained by the market factor = 87%

根据我们画的表格  σp 中有factor market应该是横一列 纵一列 所以应该是 (1.080 × 0.00109 × 1.080) +2*【 (1.080 × 0.00053 × 0.098) + (1.080 × 0.00022 × –0.401) + (1.080 × –0.00025 × 0.034)】

请问这里为什么后面不用乘以2呢?

1 个答案
已采纳答案

笛子_品职助教 · 2022年05月17日

嗨,爱思考的PZer你好:


求portfolio的总方差才需要乘以2。

计算某个因子对组合方差的贡献,不需要乘以2。


见以下笔记展示的单一因子的风险贡献,以及组合方差的计算过程。


----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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