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luojy · 2024年05月21日

两个疑问点

NO.PZ2023010903000072

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:

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:

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%

两个问题:

1.为什么coefficient可以直接作为权重weight, coefficient在统计学中应该是beta, 而beta=cov/(σm^2), 和weight还是有区别的,所以这里我不理解

2.最终结果算risk的占比或者说risk的贡献,什么情况下用方差相除,什么情况下用标准差相除?

1 个答案
已采纳答案

笛子_品职助教 · 2024年05月22日

嗨,爱思考的PZer你好:


为什么coefficient可以直接作为权重weight, coefficient在统计学中应该是beta, 而beta=cov/(σm^2), 和weight还是有区别的,所以这里我不理解

coefficient还有一个名称:因子权重。


我们看股票权重的回归式:w为权重,S为股票收益

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


我们看因子的回归式:C为因子系数,因子权重。F为因子收益。

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


从回归式子可以看出,cofficient和weight,因子收益和股票收益,在回归式里的位置,都是相同的。


最终结果算risk的占比或者说risk的贡献,什么情况下用方差相除,什么情况下用标准差相除?

同学注意:这个知识点来自书本例题。

在书本例题里,使用的是方差相除。

因此CFA如果出到这里的题目,也只能有方差相除。

这个知识点不可以使用标准差相除。

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