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小米 · 2020年02月24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%

李老师例题我听的非常明白。但是这道题看不懂。关键问题是:

1⃣️,第三行数据是啥,前面那么长的一堆咋翻译,我真的没理解到第三行数据的意义。??

2⃣️,答案中的计算为啥每一项都乘以1.08????

1 个答案

maggie_品职助教 · 2020年02月25日

嗨,爱思考的PZer你好:


1、第三行就是为了简化把方差和协方差数据写在一行了,因为这道题只针对市场因子,那以第一数据是市场因子自己和自己的方差,第二数据是size和市场因子之间的协方差。。。以此类推。

2、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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