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小雨 · 2024年07月26日

答案对skewness的解释没读懂

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.

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. 


如果是positively skewed,不是右边正的部分面积大吗?那为什么说more than half of the deviations from the mean are negative and less than half are positive?不应该是大部分偏离均值的都是positive吗?

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笛子_品职助教 · 2024年07月26日

嗨,从没放弃的小努力你好:


Hello,亲爱的同学~

同学这里首先了解右偏的定义。

右偏是指极端值,在概率分布的右边。

极端值不是面积。

画图:这个图右边的极端数值(横坐标)会非常大,远远大于左边的极端值,所以是右偏。


要想极端值在分布的右边,就要使均值大于中位数。

即: the mean of the distribution is greater than its median。


中位数左边是一半的个数,右边是一半的个数。

中位数小于均值,意味着均值左边的个数,大于均值右边的个数。

符合这个特征的,是右偏。


本题说,no more than 60% of the deviations from the mean are negative。均值左边有60%的数,均值右边有40%的数。这符合中位数小于均值,曲线极端值在右边的特点,因此是右偏。

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