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圣灵霜子 · 2020年10月23日

问一道题:NO.PZ2019012201000073 [ CFA III ]

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.

为什么不是理解为正态分布里面,偏离mean的部分中小于零的部分不能超过60%?
3 个答案

maggie_品职助教 · 2020年10月26日

请看下我给你的截图(一级讲义),如果是正太分布,那么就是均值两边就是50%和50%,如果一边大一边小这就是有偏的分布。此外,这里的问哪个风险衡量指标会受到限制,Drawdown 是 跌幅、回撤的概念,而Volatility是波动性,只有skewnes是衡量的偏度的。

这是一个很偏的知识点,考到几率很低,不需要在此花太多时间。

maggie_品职助教 · 2020年10月25日

没说不能啊,这道题的表述说明收益率的分布是非对称性的,所以衡量有偏度的分布我们要用skewnes.这是一级数量的内容。可以参考下如下截图:

圣灵霜子 · 2020年10月25日

您说“这里题干描述的是“deviations from the mean”偏离均值的程度不超过60%”,所以有偏;但题目原文是“no more than 60% of the deviations from the mean are negative”,直译:不超过60%的偏离为负。我不明白的是,原文这句话怎么能看出是非对称/有偏呢?

maggie_品职助教 · 2020年10月24日

嗨,努力学习的PZer你好:


注意正太分布是对称性的分布,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。而这里题干描述的是“deviations from the mean”偏离均值的程度不超过60%,说明这不是对称分布啊。在衡量非对称分布的偏度的时候用的是skewness。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!


圣灵霜子 · 2020年10月24日

题目里说的是no more than 60% of the deviations from the mean are negative,不超过60%的偏离为负,而不是不能有偏离不能超过60%的偏离呀

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