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Arnie · 2022年10月13日

针对variance of the market factor return and covariances with the market factor return 的理解

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%


covariance 就是代表了 market factor与其他factor的covariance了吗?为什么前面还要写variance of the market factor return?

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笛子_品职助教 · 2022年10月14日

嗨,从没放弃的小努力你好:


covariance 就是代表了 market factor与其他factor的covariance了吗?为什么前面还要写variance of the market factor return?


Hello,亲爱的同学!

因子X与因子X自己的协方差,也称为X的variance。

因子X与因子Y的协方差,才是covariance。

这里是为了表述准确,也写了variance of the market factor return。意思是,market因子与market因子自己的协方差,也就是market 因子的方差。


同学大致理解一下这个含义哈。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

笛子_品职助教 · 2022年12月03日

嗨,从没放弃的小努力你好:


请问下这个公式在讲义的具体哪里一页呢?


知识点章节是allocating the risk budget。同学可以从基础讲义245页看起。如果不想翻讲义,也可以看下面老师的截图。


这个题目就是书上的一道例题。是个固定算法。所有这类题目都是一个解题套路。

1.08可以看成是 market factor的权重。然后遵循以下基础讲义例题的解题套路。





这道题总结成如下笔记。





可以先看基础讲义截图,看不明白再看笔记,然后再看看对应视频。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

笛子_品职助教 · 2022年10月14日

嗨,从没放弃的小努力你好:


老师补充一个图,同学结合图形来看:


绿色方框,是market factor与market factor的协方差,也就是market factor的方差。

后面才是协方差,例如size这列,是market factor和size的协方差

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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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