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shelly0205 · 2020年11月13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%

不好意思老师我真的是完全没看懂这个题的解法,为什么两个coefficient要相乘呢

2 个答案
已采纳答案

maggie_品职助教 · 2020年11月14日

嗨,从没放弃的小努力你好:


同学这道题除了权重给我们的方式不同,其它都和咱们讲义245页的例题是一样的。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. 所以你就按照咱们上课的思路去解题就好,这道题咱们课后题、经典题、基础班例题都有讲解,如果忘了怎么做赶紧去听下课。


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努力的时光都是限量版,加油!


菱秋秋 · 2021年04月10日

为什么这道题可以把coefficient当portpolio weight类比来看呢?它们之间有什么共性吗?

maggie_品职助教 · 2021年04月10日

回复菱秋秋:我们的回归方程就是想看下组合的总收益在多大程度上(百分之多少)来源于各个因子。因此回归系数coefficient可以当作portpolio w权重来看。

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