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常晓磊 · 2024年06月03日

计算

NO.PZ2019012201000065

问题如下:

Based on Exhibit 2, theportion of total portfolio risk that is explained by the market factor in Fund1’s existing portfolio is closest to:

选项:

A.

3%

B.

81%

C.

87%

解释:

The portion oftotal 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 totalportfolio variance as follows:


Where

CVmarket factor = contribution of the market factor to totalportfolio variance

xmarket factor = weight of the market factor in theportfolio

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 isto divide the resulting variance attributed to the market factor by theportfolio variance of returns, which is the square of the standard deviation ofreturns:

Portion of totalportfolio risk explained by the market factor = 0.001223/(0.0374)2

Portion of totalportfolio risk explained by the market factor = 87%

协方差里不是已经包含了相关系数了么,为什么还要再乘一遍

1 个答案

笛子_品职助教 · 2024年06月04日

嗨,从没放弃的小努力你好:


协方差里不是已经包含了相关系数了么,为什么还要再乘一遍

Hello,亲爱的同学~

协方差里确实已经包含相关系数了,同学理解正确。

但本题的coefficient,并不是相关系数。

coefficient是回归系数,可以理解为因子权重。

在计算风险贡献的时候,我们需要使用到权重这个数据,也就是coefficient。

回归系数(coefficient)与相关系数(correlation),这两者是不同的。

同学记忆一下这里的相关英文描述哦。

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努力的时光都是限量版,加油!

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