题目
A portfolio has an expected mean return of 8 percent and standard deviation of 14 percent. The probability that its return falls between 8 and 11 percent is closest to:
选项
A.8.3%
B.14.8%.
C.58.3%.
答案
A
解析
A is correct. P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponding to 11%) –N(Z corresponding to 8%). For the first term, Z = (11% – 8%)/14% = 0.21 approximately, and using the table of cumulative normal distribution given in the problem, N(0.21) = 0.5832. To get the second term immediately, note that 8 percent is the mean, and for the normal distribution 50 percent of the probability lies on either side of the mean. Therefore, N(Z corresponding to 8%) must equal 50 percent. So P(8% ≤ Portfolio return ≤ 11%) = 0.5832 – 0.50 = 0.0832 or approximately 8.3 percent. A正确。 P(8%≤投资组合收益率≤11%)= N(11%对应的Z值) -N(8%对应的Z值)。 对于上面公式中的第一项11%对应的Z值，Z =(11% - 8%)/14%约等于0.21，利用累积正态分布表，N(0.21) = 0.5832。 8%是均值，正态分布中，50%的观测值落在均值左侧，另外50%落在均值右侧，因此，N(8%均值对应的Z值)一定等于50%。 因此，P(8%≤投资组合收益率≤11%)= 0.5832 - 0.50 = 0.0832或大约8.3%。