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Jingwen · 2023年07月15日

关于公式的理解和代入

NO.PZ2019012201000066

问题如下:

Selected data on Manager C’s portfolio, which contains three assets, is presentedin Exhibit 1.

Based on Exhibit 1, the proportion of Manager C’s total portfolio variance con tributed by Asset 2 is closest to:

选项:

A.

0.0025

B.

0.0056

C.

0.0088

解释:

B is correct. The contribution of an asset to total portfolio variance equals the summation of the multiplication between the weight of the asset whose contribution is being measured, the weight of each asset (xj), and the covariance between the asset being measured and each asset (Cij), as follows:

The contribution of Asset 2 to portfolio variance is computed as the sum of the following products:

老师,在做这道题的时候,发现和Allocation the risk budget这个经典题里代入的公式不一样?

就看到公式是:xixjCij的加总,但是我不是很理解每个的意思。(唉,我真的是数量差,看不懂这些符号)


这道题里面,是用的weight1*weight2*covariance12

然后在经典题里,代入的是,variance(market)*variance2*coefficient(market),(虽然好像解答里套用的公式写的是weight of the market factor in the portfolio,但是在表格里,它写的就是variance of the market factor return and covariances with the maket factor return,我就不懂了,就感觉是两个不同的表达呢?为啥这俩就是同一个东西了呀?)

然后老师上课的时候讲的是w1w2r1r2ρ12,这里为什么又和r,(就是李老师写的像r的东西,我也不认识怎么读,难道是r1r2ρ12=covariance吗?这是怎么解释呀?)

为啥每次都不一样呢?


portfolio variance,指的是,这个portfolio整体的方差,方差的意思,是它的波动率吗?

然后这题目里又说到了standard deviation,这个东西又有啥用呢?是不是只有求占比的时候才有用?

3 个答案
已采纳答案

笛子_品职助教 · 2023年07月16日

嗨,从没放弃的小努力你好:


谢谢老师,您回答的第一和第三部分我明白了。 但是第二部分,我其实对于这个解答还是有点疑惑,就这个东西到底在求的是什么呀?就是你说的归因是吗?但是这个归因,到底是怎么求呢? 比如,为啥要两个weight乘一起呢?为啥要两个variance乘一起呢?我一般能够想到的就是比如一个占比,就是weight/总量,但这里两个weight,两个variance好奇怪哦。


Hello,亲爱的同学~

这是一道仿照基础讲义例题的习题,我们可以先把基础讲义例题看一看。


这个东西到底在求的是什么呀?就是你说的归因是吗?

这就是基础讲义247页的红框内的内容:每个资产对portfolio方差的贡献度。这个术语要记忆一下。看到这个词,就要想起这个知识点。


但是这个归因,到底是怎么求呢? 比如,为啥要两个weight乘一起呢?为啥要两个variance乘一起呢?我一般能够想到的就是比如一个占比,就是weight/总量,但这里两个weight,两个variance好奇怪哦。


我们看248页和249页的基础班讲义:



具体怎么求解仿照这个例题的讲解。李老师在基础讲义视频里,讲了一个记忆方法,九宫格法。


具体来说,就是X和X协方差与权重、X和Y协方差与权重、X和Z的协方差与权重,就是X对portfolio贡献的方差

统计学里,X与X的协方差就是X的方差


同学可以先看一看这部分基础讲义对应的视频讲解。如果看完后还有问题,欢迎随时提问,祝学习顺利~




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努力的时光都是限量版,加油!

Jingwen · 2023年07月16日

呜呜呜,笛子老师我好爱你!!!谢谢!!!Equity如果还有什么不清楚的再问你!!!我再去把原版书题目看一看,应该当时听的时候也挺懵的。

笛子_品职助教 · 2023年07月17日

嗨,爱思考的PZer你好:


呜呜呜,笛子老师我好爱你!!!谢谢!!!Equity如果还有什么不清楚的再问你!!!我再去把原版书题目看一看,应该当时听的时候也挺懵的。


得到同学的认可老师很开心,一起加油哦~

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努力的时光都是限量版,加油!

笛子_品职助教 · 2023年07月16日

嗨,努力学习的PZer你好:


老师,在做这道题的时候,发现和Allocation the risk budget这个经典题里代入的公式不一样?

就看到公式是:xixjCij的加总,但是我不是很理解每个的意思。(唉,我真的是数量差,看不懂这些符号)


忽略这些符号。equity这里不建议记忆教材上的公式,直接记忆例题的解法即可。

equity里的风险归因只有一种算法:对Asset2进行风险贡献归因


这道题里面,是用的weight1*weight2*covariance12

然后在经典题里,代入的是,variance(market)*variance2*coefficient(market),(虽然好像解答里套用的公式写的是weight of the market factor in the portfolio,但是在表格里,它写的就是variance of the market factor return and covariances with the maket factor return,我就不懂了,就感觉是两个不同的表达呢?为啥这俩就是同一个东西了呀?)

然后老师上课的时候讲的是w1w2r1r2ρ12,这里为什么又和r,(就是李老师写的像r的东西,我也不认识怎么读,难道是r1r2ρ12=covariance吗?这是怎么解释呀?)

为啥每次都不一样呢?


可以对应上的。

经典题里的coefficient就是这里的weight。

market和market的协方差就是variance(market)


例题和习题的回归形式是一致的

例题:R = w1*S1+ ...+ wn*Sn

习题:R = C1*F1+.....+ Cn*Fn

股票1收益S1就对应因子1的收益F1

股票1权重W1就对应因子1的权重C1。


portfolio variance,指的是,这个portfolio整体的方差,方差的意思,是它的波动率吗?

然后这题目里又说到了standard deviation,这个东西又有啥用呢?是不是只有求占比的时候才有用?

波动率可以用多个指标来衡量。

portfolio variance是方差,是衡量波动率的一个指标。

standard deviation是标准差,也是衡量波动率的一个指标。









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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!

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