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勇往直前 · 2021年12月12日

请问是Z发布吗

  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%

老师,不知道从何入手，这是哪个知识点.考试中无法用Excel，怎么解答呢？ 请问可以详细列一下解题步骤吗？谢谢
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星星_品职助教 · 2021年12月13日

同学你好，

做题并不需要用Excel公式，考试也不会给。

这道题要求11%和8%之间的概率，即P（X=11%）-P（X=8%）。非正态分布不能查表，所以要做标准化转化。

利用下图正态分布标准化的公式，对于P（X=11%）进行标准化后得到Z（0.2143），查表得到对应面积在58.32%和58.71%之间；对P（X=8%）标准化后得到Z（0）。对应面积即为50%。

所以最终结果在 58.71%-50%=8.71%，和58.32%-50%=8.32%之间，即选择A选项对应的8.5%。

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