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Normy · 2022年01月11日

这里的coefficient怎么理解?理解为权重?

* 问题详情,请 查看题干

NO.PZ201809170400000504

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:

C is correct.

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:

CVmarket  factor=j=1nXmarket  factorXjCmf,jCV_{market\;factor}={\textstyle\sum_{j=1}^n}X_{market\;factor}X_jC_{mf,j}

=Xmarket  factorj=1nXjCmf,j=X_{market\;factor}{\textstyle\sum_{j=1}^n}X_jC_{mf,j}

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%

谢谢

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伯恩_品职助教 · 2022年01月11日

嗨,从没放弃的小努力你好:


同学你好,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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