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粗眉毛辣椒油 · 2024年01月15日

这道题的考点是什么?

NO.PZ2020010303000011

问题如下:

If the return on a stock, R, is normally distributed with a daily mean of 8%/252 and a daily variance of (20%)2/252(20\%)^2/252, find the values where

a. Pr(R < r) = .001

b. Pr(R < r) = .01

c. Pr(R < r) = .05

选项:

解释:

a. The mean is 0.031% per day and the variance is 1.58 per day (so that the standard deviation is 1.26% per day). To find these values, we transform the variable to be standard normal, so that

Pr(R<r)=.001=Pr(Z<rμσ)=.001 Pr(R < r) = .001 = Pr(Z<\frac{r-\mu}{\sigma})= .001

The value for the standard normal is -3.09

(NORM.S.INV(0.001) in Excel) so that 3.09σ+μ=3.86%-3.09 * \sigma + \mu = -3.86\%.

b. The same idea an be used here where z = -2.33 so that Pr(Z < z) = .01. Transforming this value, r=2.33σ+μ=2.89%r = -2.33 * \sigma + \mu = -2.89\%.

c. Here the value of z is -1.645 so that r=1.645σ+μ=2.04%r = -1.645 * \sigma + \mu = -2.04\%.

These are all common VaR quan-tiles and suggest that there is a 5% chance that the return would be less than -2.04% on any given day, a 1% change that it would be less than -2.89%, and a one in 1,000 chance that the return would be less than -3.86%, if returns were normally distributed.

请问这是已知概率,反求z的取值吗?查表方式可以计算?

4 个答案

品职答疑小助手雍 · 2024年01月17日

计算器的计算程序设计逻辑其实和小学时候学的运算符号一样的,一定要符合运算逻辑,减号和乘号时不能连着写的。

计算器里想要把3.09变成负数,需要摁2nd 再摁右下角等号左边那个+竖杠-那个按钮。如果对计算器太陌生,建议看一下计算器的使用课程,在早读课里可以找到。

品职答疑小助手雍 · 2024年01月17日

2.第一小问的0.001需要查表的意思是,这个不是常见的分位点,不需要专门记忆,如果要解这道题的话需要查正态分布对应的分位点那个表格。

不是说表里没这个数。

品职答疑小助手雍 · 2024年01月17日

1.是跟置信区间一样的知识点,就是正态分布95%,99%这种对应的分位点。哪里讲的不重要,一定要记牢分位点对应Z值。

品职答疑小助手雍 · 2024年01月15日

同学你好,给的0.01和0.05这两个对应99%和95%分位点的值是需要记忆的,不用查表。第一小问的0.001那个不属于常见范围,需要查表。

不过Z值是标准正态分布里的,题目给的正态分布不是标准正态

所以算出Z值之后再根据题目给的均值和标准差计算具体分布里的值即可。

粗眉毛辣椒油 · 2024年01月17日

1.给的0.01和0.05这两个对应99%和95%分位点的值是需要记忆的,不用查表。请问这是哪个知识点讲的?这与置信区间知识点一样吗? 2.第一小问的0.001那个不属于常见范围,需要查表。请问这个意思是不是当概率为0.001时,对应的z为多少,课件中的标准正态分布表中是不是没有这个数。 3.第一问求r的计算公式r=-3.09*1.26%+0.031%,我自己使用计算器的算法:3.09,-,*1.26,%,+,0.031,%,=。请问这个输入过程哪里不对?

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NO.PZ2020010303000011问题如下 If the return on a stock, R, is normally stributewith a ily meof 8%/252 ana ily varianof (20%)2/252(20\%)^2/252(20%)2/252, finthe values where Pr(R r) = .001Pr(R r) = .01Pr(R r) = .05 The meis 0.031% per y anthe varianis 1.58 per y (so ththe stanrviation is 1.26% per y). To finthese values, we transform the variable to stanrnormal, so thatPr(R r)=.001=Pr(Z r−μσ)=.001 Pr(R r) = .001 = Pr(Z \frac{r-\mu}{\sigma})= .001 Pr(R r)=.001=Pr(Z σr−μ​)=.001The value for the stanrnormis -3.09(NORM.S.INV(0.001) in Excel) so th−3.09∗σ+μ=−3.86%-3.09 * \sigma + \mu = -3.86\%−3.09∗σ+μ=−3.86%.The same ia usehere where z = -2.33 so thPr(Z z) = .01. Transforming this value, r=−2.33∗σ+μ=−2.89%r = -2.33 * \sigma + \mu = -2.89\%r=−2.33∗σ+μ=−2.89%.Here the value of z is -1.645 so thr=−1.645∗σ+μ=−2.04%r = -1.645 * \sigma + \mu = -2.04\%r=−1.645∗σ+μ=−2.04%.These are all common Vquan-tiles ansuggest ththere is a 5% chanththe return woulless th-2.04% on any given y, a 1% change thit woulless th-2.89%, ana one in 1,000 chanththe return woulless th-3.86%, if returns were normally stribute 老师好,方差是用20%^2/252吗?这样算,得出的是方差是0.0158%,而不是1.58%。另外,20%^2大于252,能直接用20%^2除以252吗?

2024-05-27 14:22 2 · 回答

NO.PZ2020010303000011 问题如下 If the return on a stock, R, is normally stributewith a ily meof 8%/252 ana ily varianof (20%)2/252(20\%)^2/252(20%)2/252, finthe values where Pr(R r) = .001Pr(R r) = .01Pr(R r) = .05 The meis 0.031% per y anthe varianis 1.58 per y (so ththe stanrviation is 1.26% per y). To finthese values, we transform the variable to stanrnormal, so thatPr(R r)=.001=Pr(Z r−μσ)=.001 Pr(R r) = .001 = Pr(Z \frac{r-\mu}{\sigma})= .001 Pr(R r)=.001=Pr(Z σr−μ​)=.001The value for the stanrnormis -3.09(NORM.S.INV(0.001) in Excel) so th−3.09∗σ+μ=−3.86%-3.09 * \sigma + \mu = -3.86\%−3.09∗σ+μ=−3.86%.The same ia usehere where z = -2.32 so thPr(Z z) = .01. Transforming this value, r=−2.32∗σ+μ=−2.89%r = -2.32 * \sigma + \mu = -2.89\%r=−2.32∗σ+μ=−2.89%.Here the value of z is -1.645 so thr=−1.645∗σ+μ=−2.04%r = -1.645 * \sigma + \mu = -2.04\%r=−1.645∗σ+μ=−2.04%.These are all common Vquan-tiles ansuggest ththere is a 5% chanththe return woulless th-2.04% on any given y, a 1% change thit woulless th-2.89%, ana one in 1,000 chanththe return woulless th-3.86%, if returns were normally stribute

2022-05-17 21:52 2 · 回答

老师,这道题你了,但是我没有理解,请详细下这套题的分析过程。

2020-02-22 18:13 1 · 回答

a ily varianof (20%)²>252 怎么推出“the varianis 1.58 per y (so ththe stanrviation is 1.26% per y)”?

2020-02-15 20:01 1 · 回答