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dognmnm · 2022年05月12日

系数以及权重

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%

我想下这边把系数当做权重是有时么逻辑吗? 我计算可以掌握, 就是这个系数一下子很难想到就是权重的关系

1 个答案

伯恩_品职助教 · 2022年05月12日

嗨,从没放弃的小努力你好:


关于权重这里和我们上课讲过的例子稍稍有些不同,我们上课讲的例子是以资产来看的,所以计算的是资产的weighting,方差和相关系数,而这个题目是从risk factor的角度来看的,是把收益回归成以risk factor为变量的方程,方程可以表达为y=a+1.08*market factor+0.098*size factor-0.401*Value factor+0.034*Momentum factor+E,coefficient系数就是这个因子的变动程度,也可以理解为是这个因子的weight.


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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