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Zhao Yidai · 2020年09月26日

问一道题: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%

coefficient系数为什么可以理解为是这个因子的weight?所有的答疑答案都只是说了这一句。并没有深入解释。

2 个答案

maggie_品职助教 · 2021年02月22日

TO: 过程


你说的没错,因为这道题比较贴近实务,请看表格的标题,它只是FUND1截取的数据,所以权重加总可能不等于1(还有其他因子但是题目为了简化,所以没有全部列出)。此外,我们只需要根据题干给出的信息来计算就可以啦。

maggie_品职助教 · 2020年09月27日

嗨,努力学习的PZer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(因为回归系数加总要等于1,哪个系数高就说明哪个因子对组合收益的解释力度大,即影响大因此可以看作是每个因子的权重). 


-------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!


过程 · 2021年02月21日

关于您说得“因为回归系数加总要等于1”,我看这四个回归系数(1.08、0.098、-0.401、0.034)加总不等于1啊。还是我理解错了,请指教。

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