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Nicole Xiang · 2023年08月06日

一个小小的建议

  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 correspondingto 8%).

For the firstterm, NORM.S.DIST(11% – 8%)/14% = 58.48%. To get the second termimmediately, note that 8% is the mean, and for the normal distribution, 50% ofthe 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%

老师以后在出这种用到Critical value(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？ 

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星星_品职助教 · 2023年08月07日

同学你好，

“学员资料下载处”有基于原版书的z/t表可下载，可下载后直接查询。

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