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凉茶325 · 2022年12月13日

完全看不懂

NO.PZ2019012201000065

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:


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%

coefficients 是weights吗 为什么和w1这种对应 这个题目看到应该怎么做


1 个答案

笛子_品职助教 · 2022年12月13日

嗨,爱思考的PZer你好:


coefficients 是weights吗


系数就是权重。

如果是系数的话,我们写成:

portfolio Return = W1*S1+W2*S2 + W3*S3+...+ Wn*Sn + 截距项 + 残差

W是股票权重,S是股票系数


如果是因子的话,我们写成:

portfolio Return = C1*F1+C2*F2 + C3*F3+...+ Cn*Fn + 截距项 + 残差

C是因子系数,F是因子。


所以系数就是权重。


为什么和w1这种对应 这个题目看到应该怎么做

这道题就是书上的例题,例题是权重,碰到这道因子的,照样套用就好。



不过这道例题看起来比较复杂一些,李老师在视频中讲到了一个方便记忆的九宫格方法,同学可以看以下基础视频。


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005 · 2023年08月22日

请问这里的模型和CME里的multifactor model是一样的吗?CME里方差公式中带有残差项的方差,这里没有吗?

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