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%
利用excel中NORM.S.DIST这个公式,我们解得:58.48%。这个能否写一下详细的计算过程?