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Yang 于洋🌻 · 2022年12月27日

各个风险因子的权重为啥是用Coefficient代替?

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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%

coefficient 不是β吗?β=covariance(i,M)/variance(i) ?  那 coefficent 也不是权重啊

1 个答案

笛子_品职助教 · 2022年12月27日

嗨,爱思考的PZer你好:


各个风险因子的权重为啥是用Coefficient代替?


如果是权重,我们写出表达式:

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

w表示去权重,S表示某只股票的收益。


如果是系数,我们写出表达式:

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

C表示系数,F表示因子。


从上述两个公式看出,因子系数C和股票权重w,是同样的含义。因此系数也就是回归系数,它也就是这个因子的权重。

因为表达式是一样的,则某个因子对portfolio 方差贡献,和某个股票对portfolio 方差贡献,计算方法也就一样了。

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