开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

CFApipa · 2022年07月19日

请问老师类似的题是不是如果没说'if the return of the portfolio are normal'就应该assume不是标准化所以要用到z公式

  1. CFA I
  2. Quantitative

NO.PZ2021062201000011

问题如下：

A portfolio has an expected mean return of 8% and standard deviation of 14%. The probability that its return falls between 8% and 11% is closest to:

选项：

A.

8.5%

B.

14.8%

C.

58.3%

解释：

A is correct.

P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponding to 11%) – N(Z corresponding to 8%).

For the first term, NORM.S.DIST(11% – 8%)/14% = 58.48%. To get the second term immediately, note that 8% is the mean, and for the normal distribution, 50% of the probability lies on either side of the mean.

Therefore, N(Z corresponding to 8%) must equal 50%, So, P(8% ≤ Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848, or approximately 8.5%.


基于下列总公式：

P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponding to 11%) – N(Z corresponding to 8%).

本公式第一部分：利用excel中NORM.S.DIST这个公式，我们解得：58.48%

本公式第二部分，8%为均值，且为正态分布，则50%的概率落在均值两侧，所以，N(Z corresponding to 8%)=50%，

带入总公式：P(8% ≤ Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848 = 8.5%

讲义给的例子是说了相反的情况即标准化的情况，所以不需要查表，对吗？



添加评论
1 个答案

星星_品职助教 · 2022年07月19日

同学你好，

这道题目不是很严谨，应该在题干里附加说明一下return服从正态分布。然后按照正态分布标准化的公式去解就可以了。

原版书课后题也有的没有专门说服从正态分布，但如果是类似本题的形式，都是在考察标准化公式的计算。

截图的例题考察的是置信区间，此时给出服从正态分布的目的是提示查表需要查z表，即关键值为1.96。


  • 1

    回答

  • 0

    关注

  • 446

    浏览
相关问题

NO.PZ2021062201000011问题如下 A portfolio hexpectemereturn of 8% anstanrviation of 14%. The probability thits return falls between 8% an11% is closest to: A.8.5%B.14.8%C.58.3% A is correct.P(8%≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponngto 8%). For the firstterm, NORM.S.ST(11% – 8%)/14% = 58.48%. To get the secontermimmeately, note th8% is the mean, anfor the normstribution, 50% ofthe probability lies on either si of the mean.Therefore, N(Z corresponng to 8%) must equ50%, So, P(8% ≤Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848, or approximately 8.5%.基于下列总公式 P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponng to 8%). 本公式第一部分利用excel中NORM.S.ST这个公式，我们解得58.48%本公式第二部分，8%为均值，且为正态分布，则50%的概率落在均值两侧，所以，N(Z corresponng to 8%)=50%，带入总公式P(8% ≤ Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848 = 8.5% 老师以后在出这种用到Criticvalue(不是常见的1，1.65，1.98，和2.58时？） 值的时候，可不可以附上对应的概率呢？

2023-08-06 22:50 1 · 回答

NO.PZ2021062201000011 问题如下 A portfolio hexpectemereturn of 8% anstanrviation of 14%. The probability thits return falls between 8% an11% is closest to: A.8.5% B.14.8% C.58.3% A is correct.P(8%≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponngto 8%). For the firstterm, NORM.S.ST(11% – 8%)/14% = 58.48%. To get the secontermimmeately, note th8% is the mean, anfor the normstribution, 50% ofthe probability lies on either si of the mean.Therefore, N(Z corresponng to 8%) must equ50%, So, P(8% ≤Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848, or approximately 8.5%.基于下列总公式 P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponng to 8%). 本公式第一部分利用excel中NORM.S.ST这个公式，我们解得58.48%本公式第二部分，8%为均值，且为正态分布，则50%的概率落在均值两侧，所以，N(Z corresponng to 8%)=50%，带入总公式P(8% ≤ Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848 = 8.5% 考察的哪部分的知识点

2023-03-20 18:06 1 · 回答

NO.PZ2021062201000011 问题如下 A portfolio hexpectemereturn of 8% anstanrviation of 14%. The probability thits return falls between 8% an11% is closest to: A.8.5% B.14.8% C.58.3% A is correct.P(8%≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponngto 8%). For the firstterm, NORM.S.ST(11% – 8%)/14% = 58.48%. To get the secontermimmeately, note th8% is the mean, anfor the normstribution, 50% ofthe probability lies on either si of the mean.Therefore, N(Z corresponng to 8%) must equ50%, So, P(8% ≤Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848, or approximately 8.5%.基于下列总公式 P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponng to 8%). 本公式第一部分利用excel中NORM.S.ST这个公式，我们解得58.48%本公式第二部分，8%为均值，且为正态分布，则50%的概率落在均值两侧，所以，N(Z corresponng to 8%)=50%，带入总公式P(8% ≤ Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848 = 8.5% 我的确算出来了p（o z 0.214）， 但是对应的那个表在哪里可以看到啊？

2022-11-21 07:11 1 · 回答

NO.PZ2021062201000011问题如下 A portfolio hexpectemereturn of 8% anstanrviation of 14%. The probability thits return falls between 8% an11% is closest to: A.8.5%B.14.8%C.58.3% A is correct.P(8%≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponngto 8%). For the firstterm, NORM.S.ST(11% – 8%)/14% = 58.48%. To get the secontermimmeately, note th8% is the mean, anfor the normstribution, 50% ofthe probability lies on either si of the mean.Therefore, N(Z corresponng to 8%) must equ50%, So, P(8% ≤Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848, or approximately 8.5%.基于下列总公式 P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) – N(Z corresponng to 8%). 本公式第一部分利用excel中NORM.S.ST这个公式，我们解得58.48%本公式第二部分，8%为均值，且为正态分布，则50%的概率落在均值两侧，所以，N(Z corresponng to 8%)=50%，带入总公式P(8% ≤ Portfolio return ≤ 11%) = 0.5848 - 0.50 = 0.0848 = 8.5% 我算出来的结果是0.0832，选择了一个接近的数值。① 标准化，是要求0＜Z＜0.21的概率。0.21是通过（11-8）/14得来的。然后查0.21的正态分布数等于0.5832，减去0.5，得到的0.0832。请问，问题出在哪里呢？

2022-07-07 14:30 1 · 回答