Suppose you own a risky asset with an expected return of 12.6 percent and a standard deviation of 18.2 percent.If the returns are normally distributed,the most accurate probability that the stock will return more than 50 percent in any one given year is best described as less than:
A).025 percent.
B).05 percent.
C)2.5 percent.
D).01 percent.
E)1.25 percent.

Question

Quizplus · Accepted Answer

Given the returns are normally distributed, we can use the Z-score formula to find the probability of a return greater than 50%. The Z-score is calculated as (X - μ) / σ, where X is the value we're interested in (50% return), μ is the mean (12.6%), and σ is the standard deviation (18.2%). The calculated Z-score will then correspond to a probability in the standard normal distribution table. Since the Z-score for a return of 50% would be significantly higher than the mean, the probability of achieving more than a 50% return would be very low, falling into the tail of the distribution. Among the given options, "less than 2.5 percent" is the most accurate description of this low probability, indicating that it's a rare event.

Suppose You Own a Risky Asset with an Expected Return