题目
A portfolio has a mean value of $75 million and a daily standard deviation of $4.27 million. Assuming that the portfolio values are normally distributed, the probability of the portfolio value falling below $40 million within the next seven days is closest to:
选项
A.0.10%
B.1.00%
C.5.00%
D.15.87%
答案
A
解析
Given that the daily standard deviation is $4.27 million,「huixue_img/importSubject/1564169387395649536.png」Using this standard deviation, the level of $40 million is (40-75)/11.29 = -3.1 standard deviations from the mean value. Given that the returns are normally distributed the probability of value falling more than -3.1 standard deviations from the mean value is 0.1% (since 100% of the probability falls between ±3.1 standard deviations of the mean).