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海胆君 · 2021年03月20日

为什么用N（0.995）？？不是99%CI吗？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021205000060

问题如下：

A stock has an expected return of 15% and a volatility of 20%. The current price of the stock is USD 50. Estimate a 99% confidence interval for the price at the end of one day.

选项：

解释：

Here, we are dealing with a short time period, and so it is reasonable to assume that the return is normally distributed. The return has a mean of 15% X (1 /252) = 0.0595%, and a standard deviation of 20% X 1/252\sqrt{1/252} = 1.2599%. The 99% confidence interval for the percentage return is between:

0.0595 - 1.2599 X N−1N^{-1}(0.995) = -3.186%

and

0.0595 + 1.2599 X N−1N^{-1}(0.995)= +3.305%

The confidence interval for the stock price is therefore between 50 X 0.96814 = 48.4 and

50 X 1.03305 = 51.7.

计算中，是采用Return~N来算的，return不是可正可负吗那为什么要把99%置信区间换成99.5%？这是双尾变单尾？？？不是可正可负吗

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品职答疑小助手雍 · 2021年03月21日

嗨，爱思考的PZer你好：


这个N负一次方的公式代表的是正态分布累计概率的反函数，现在你要求的是一个中间区间占了99%的区间，也就是区间两边各剩下0.5%的概率。

那你用的分位点应该是累计了0.5%和99.5%概率的两个点。这题是要双尾查表，但是N负一次方那个函数是一直累计的那种函数（换言之它是单尾的）。


如果前面你还是看不懂，那就只能记住，正态分布里单尾0.995和双尾的0.99是一样的，N那个公式里面对应的都是单尾数值。

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海胆君 · 2021年03月21日

理解了 谢谢！

品职答疑小助手雍 · 2021年03月20日

嗨，从没放弃的小努力你好：


用的是单边99.5%分位点，两边各0.5%，中间部分就是99%了。

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努力的时光都是限量版，加油！

海胆君 · 2021年03月20日

没听懂……不是说先判断单双边再查表吗？ 那这个就应该是找的N(0.99）啊

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