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12345678wdv · 2024年11月13日

这一题可以用下面公式 求解吗，如果可以，如何求解

  1. FRM II
  2. Risk Management And Investment Management

NO.PZ2023101902000011

问题如下：

An analyst regresses the returns of 100 stocks against the returns of a major market index. The resulting pool of 100 alphas has a residual risk of 18% and an information coefficient of 9%. If the alphas are normally distributed with a mean of 0%, roughly how many stocks have an alpha greater than 4% or less than -4%?

选项：

A.5 B.10 C.20 D.25

解释：

The standard deviation (std) of the alphas = Residual Risk (volatility) x Information Coefficient (IC) = 0.20 * 0.10 = 0.02. So, 4% is twice the standard deviation of the alphas. The alphas follow normal distribution with mean 0, so about 5% of the alphas are out of the interval [-4%, 4%]. The total number of stocks is 100, so roughly there are 5 alphas that are out of the range.



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pzqa27 · 2024年11月13日

嗨，从没放弃的小努力你好：


跟上面这个公式关系不是很大

题目最后给了α的区间范围是正负4%，也就是[0 - Z * σ, 0 + Z*σ] = [-4%, 4%]。

置信区间是和置信度（95%或者99%或者90%）相关。首先要确定标准正态分布Z值是多少，就可以倒推出置信度。


由于α的σ = 0.2 * 0.1 = 0.02，所以α的区间范围可以写成[0 - Z * 0.02, 0 + Z * 0.02] = [-4%, 4%]，

当Z = 2时，等式成立。而2这个Z值，可以近似看做是1.96，而1.96对应的双尾置信度是95%，所以有5%的数据是极端值。


本题最后问的就是有多少个极端值，那就100 * 5% = 5个。

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