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𝘼𝙣𝙩𝙝𝙤𝙣𝙮 · 2022年07月06日

我查表是0.5832

  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%

.。。 我做对了，但是是猜的。

因为 （11-8）/14 = 0.21428 查表只能查0.21 0.21对应的概率是 0.5832 -0.5 = 8.32% 我选了个离8.32%最近的8.5%。。。不知道是我的问题还是这个表的问题

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1 个答案

星星_品职助教 · 2022年07月06日

同学你好，

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，

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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