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Coral · 2020年03月29日

问一道题:NO.PZ2017092702000087 [ CFA I ]

问题如下:

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

选项:

A.

8.3%

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, Z = (11% – 8%)/14% = 0.21 approximately, and using the table of cumulative normal distribution given in the problem, N(0.21) = 0.5832. To get the second term immediately, note that 8 percent is the mean, and for the normal distribution 50 percent of the probability lies on either side of the mean. Therefore, N(Z corresponding to 8%) must equal 50 percent. So P(8% ≤ Portfolio return ≤ 11%) = 0.5832 – 0.50 = 0.0832 or approximately 8.3 percent.

老师, 请问一下 x≦8的概率具体求法不是应该也标准化吗?那x-8/14应该等于零啊?答案的50%怎样用公式算呢?
1 个答案

星星_品职助教 · 2020年03月29日

同学你好,

x≦8的概率需要标准化,标准化后的结果是N(0),也就是标准正态分布中“0”左侧的所有面积,如果查表,会发现j就是表格左上角的0.5000。或者不用查表,由于标准正态分布的均值就是0,所以左侧的面积直接就是总面积的一半,也就是50%。

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NO.PZ2017092702000087问题如下A portfolio hexpectemereturn of 8 percent anstanrviation of 14 percent. The probability thits return falls between 8 an11 percent is closest to:A.8.3% B.14.8%.C.58.3%. A is correct. P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) - N(Z corresponng to 8%). For the first term, Z = (11% – 8%)/14% = 0.21 approximately, anusing the table of cumulative normstribution given in the problem, N(0.21) = 0.5832. To get the seconterm immeately, note th8 percent is the mean, anfor the normstribution 50 percent of the probability lies on either si of the mean. Therefore, N(Z corresponng to 8%) must equ50 percent. So P(8% ≤ Portfolio return ≤ 11%) = 0.5832 – 0.50 = 0.0832 or approximately 8.3 percent. 1.(11%-8%)/14%是对正态分布标准化的过程,直接套用标注化公式(X-均值)/标准差, 即可。2. 标准化后得到的关键值就是Z值,之后可以通过查表求得对应的概率。比如N(0.5832)3. 题目要求的P(8%<X<11%),我们可以求得P(X<11%)以及P(X<8%),再用前者减去后者 横轴纵轴都什么意思呢

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NO.PZ2017092702000087 问题如下 A portfolio hexpectemereturn of 8 percent anstanrviation of 14 percent. The probability thits return falls between 8 an11 percent is closest to: A.8.3% B.14.8%. C.58.3%. A is correct. P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponng to 11%) - N(Z corresponng to 8%). For the first term, Z = (11% – 8%)/14% = 0.21 approximately, anusing the table of cumulative normstribution given in the problem, N(0.21) = 0.5832. To get the seconterm immeately, note th8 percent is the mean, anfor the normstribution 50 percent of the probability lies on either si of the mean. Therefore, N(Z corresponng to 8%) must equ50 percent. So P(8% ≤ Portfolio return ≤ 11%) = 0.5832 – 0.50 = 0.0832 or approximately 8.3 percent. 1.(11%-8%)/14%是对正态分布标准化的过程,直接套用标注化公式(X-均值)/标准差, 即可。2. 标准化后得到的关键值就是Z值,之后可以通过查表求得对应的概率。比如N(0.5832)3. 题目要求的P(8%<X<11%),我们可以求得P(X<11%)以及P(X<8%),再用前者减去后者 这是MOLE4 基础视频里第几个视频有知识点讲解?我重新看一遍,谢谢。

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