Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%. If the returns are normally distributed, the approximate probability of receiving a return greater than 72%, or less than -48% is:
A) greater than 99%
B) greater than 95%
C) less than 5%
D) less than 1%

Question

Quizplus · Accepted Answer

Given the returns are normally distributed, we can use the empirical rule or z-scores to estimate probabilities. A return greater than 72% or less than -48% is 3 standard deviations away from the mean (since 3*20% = 60%, and 12% ± 60% gives us -48% and 72%). According to the empirical rule, approximately 99.7% of observations fall within 3 standard deviations of the mean in a normal distribution, leaving less than 0.3% (or less than 1%) of observations outside this range. Therefore, the probability of receiving a return greater than 72% or less than -48% is less than 1%.

Suppose You Own a Risky Asset with an Expected Return