Question

: If stock ABC has a mean return of 10 percent with a standard deviation of 5 percent, then the probability of earning a negative return is approximately ___ percent.

a) 2.5%
b) 5%
c) 10%
d) 15%

Answer 1

Using the empirical rule for the normal distribution, approximately 2.5% of the data would fall more than 2 standard deviations below the mean, which for stock ABC, indicates a 2.5% chance of a negative return.

Step-by-step explanation:

If stock ABC has a mean return of 10 percent with a standard deviation of 5 percent, we can use the properties of the normal distribution to estimate the probability of earning a negative return. In this context, a negative return would be any return below 0 percent (mean return - mean return) which is 2 standard deviations below the mean (10% - 2*5% = 0). According to the empirical rule, approximately 2.5% of data lies more than 2 standard deviations below the mean in a normal distribution. Hence, the probability of a negative return is approximately 2.5% percent.