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

Yuki119808 · 2023年03月20日

完全没有懂，可以仔细讲下步骤吗

  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%

考察的哪部分的知识点

添加评论
1 个答案
已采纳答案

星星_品职助教 · 2023年03月20日

同学你好，

本题考察正态分布标准化。

题目要计算收益率落在8%和11%之间的概率。由于普通正态分布不能查表，所以需要将8%和11%这两个数字标准化后，通过查表来得到概率。

1）对11%的处理，代入标准化的公式 （X-μ）/σ，可得(11% – 8%)/14%=0.2143。根据0.2143查Z表。由于z表只能精确到两位小数，所以可以得到Z(0.2143)的值在0.5832（对应Z=0.21）和0.5871（对应Z=0.22）之间


2）对于8%的处理比较简单，由于8%正好是均值，所以处于分布的一半，即50%。

3）最后用11%对应的概率（约为58.32%），去减掉8%对应的概率50%，即可得到答案近似为8.32%，选择最靠近的8.5%即可。

  • 1

    回答

  • 0

    关注

  • 485

    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% 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% 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？

2022-07-19 08:47 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