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vvvv03 · 2022年12月16日

为什么相关系数可以当权重使用

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%

如题,为什么相关系数当权重使用,这个相关系数是谁和谁的相关系数

2 个答案

笛子_品职助教 · 2022年12月24日

嗨,从没放弃的小努力你好:


我感觉回答还是没有说明白。因为基于课上的例题,asset XYZ的权重加起来是100%,而这里用factor的分析return,虽然看起来类似,但是前面的系数或者叫return对factor的敏感程度加起来显然是不等于100%的。难道只是形式相似就可以直接用系数类比weight去计算吗?我不太认同,请问有更清楚的解释吗?


asset XYZ的权重加起来是100%这个不一定的。

因为可以做空,还可以使用杠杆。

如果我们使用10倍杠杆,那么asset XYZ是可以1000%的。

如果我们做空,那么asset XYZ的权重加起来是可以小于100%的。

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努力的时光都是限量版,加油!

笛子_品职助教 · 2022年12月17日

嗨,爱思考的PZer你好:


如题,为什么相关系数当权重使用,这个相关系数是谁和谁的相关系数

相关系数不能用于权重。

这里的coefficient是因子系数,并不是相关系数。

因子的相关系数等同于股票的权重。


股票的权重是W,股票用S表示:

则portfolio return = w1*S1 + w2*S2 +...+wn*Sn + residual


因子的系数是C,因子用F表示:

则portfolio return = C1*F1 + C2*F2 + ...Cn*Fn + residual


我们看到,基于权重和股票的表达式,与基于系数和因子的表达式,形式上是相同的。


所以我们计算S1的方差对portfolio 方差的贡献时,与计算F1的方差对portfolio方差的贡献时,所用的计算方法也是相同的。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

Jane Z · 2022年12月24日

我感觉回答还是没有说明白。因为基于课上的例题,asset XYZ的权重加起来是100%,而这里用factor的分析return,虽然看起来类似,但是前面的系数或者叫return对factor的敏感程度加起来显然是不等于100%的。难道只是形式相似就可以直接用系数类比weight去计算吗?我不太认同,请问有更清楚的解释吗?

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