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Zunniyaki · 2021年04月09日

围绕skewness再问两个问题

NO.PZ2019012201000073

问题如下:

In Fund 3’s latest quarterly report, Ap reads that Fund 3 implemented a new formal risk control for its forecasting model that constrains the predicted return distribution so that no more than 60% of the deviations from the mean are negative.

Which risk measure does Fund 3’s new risk control explicitly constrain?

选项:

A.

Volatility

B.

Skewness

C.

Drawdown

解释:

Skewness measures the degree to which return expectations are non-normally distributed. If a distribution is positively skewed, the mean of the distribution is greater than its median—more than half of the deviations from the mean are negative and less than half are positive—and the average magnitude of positive deviations is larger than the average magnitude of negative deviations. Negative skew indicates that that the mean of the distribution lies below its median, and the average magnitude of negative deviations is larger than the average magnitude of positive deviations. Fund 3’s new risk control constrains its model’s predicted return distribution so that no more than 60% of the deviations from the mean are negative. This is an explicit constraint on skewness.

  1. 题目中no more than 60% of the deviations from the mean are negative为什么能判断出来是positive skewness正偏?我理解题干这句话相当于more than 60% of the deviations from the mean are positive,通过图形难道不应该是负偏么?

  1. 答案中说如果是正偏,the average magnitude of positive deviations is larger than the average magnitude of negative deviations这句话怎么理解?谢谢!
2 个答案
已采纳答案

maggie_品职助教 · 2021年04月10日

嗨,从没放弃的小努力你好:


首先如果是正态分布,相当于均值左右两边正负收益的分布的对称的,即偏度等于0,均值等于中位数等于众数。

而正偏,说的是右边有一条长长的尾巴,即极端数据在右边,而大部分的数据都落在左边(众数在左边),才会出现众数小于中位数小于平均数的情况。

而负偏正好相反,频数分布的高峰向右偏移,长尾向左延伸成为负偏态分布,还是以MEAN来划分左右分布,即极端数据在左边,而大部分的数据都落在右边(众数在右边)。先理解这个,然后我们再说一下你提问中的这两句话。


more than half of the deviations from the mean are negative and less than half are positive和the average magnitude of positive deviations is larger than the average magnitude of negative deviations,这两句话咋一看怎么说的是反的,其实是从两个角度阐述表明的是同一个意思,一个角度是个数,一个角度是距离。

这两句话都说的是正偏,因为正偏指的是右边有一条长长的尾巴,即极端数据在右边,而大部分的数据都落在左边(众数在左边)。这里解释的是第一句话more than half of the deviations from the mean are negative and less than half are positive。均值左侧的个数大于50%,右侧的个数小于50%。极端数据虽然把均值拉向右边,但是极端数据的个数少。

而第二句话是从数据距离均值远近的角度来说的,the average magnitude of positive deviations is larger than the average magnitude of negative deviations,虽然左边的个数多,但距离均值近,而右边极端数据少,但在右侧拖了一条长长的尾巴,即距离均值远。


负偏也是一个意思,我就不重复赘述了。偏度是一级数量的知识点,不是三级权益的重点,这里只需要通过题目表述了解他说的是Sknewness即可,这个点考察几率非常低。


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maggie_品职助教 · 2021年04月11日

嗨,爱思考的PZer你好:


不一定哈,而且这道题也并没有让你选正偏还是负偏,从这句话“no more than 60% of the deviations from the mean are negative” 我们能get到的就是它在陈述“Skewness”。但如果一定要从这半句里判断是正偏还是负偏,我更倾向于正偏,因为我理解它的目的在于限制正偏的幅度不要过大,因为只要存在左侧大于50%,他就是正偏。但这里考察的不是我们是否能分辨正偏还是负偏,所以完全不需要纠结啦。

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