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胖婷肥周 · 2022年07月07日

请老师帮忙看一下问题出在哪里？

  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%

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？

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1 个答案

星星_品职助教 · 2022年07月08日

同学你好，

标准化后的结果为Z（0.2143），查表得到的结果是在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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