A stock has an expected rate of return of 7.9% and a standard deviation of 6.2%. Which one of the following best describes the probability that this stock will lose more than 4.5% in any one given
Year?

Question

Quizplus · Accepted Answer

To calculate the probability of the stock losing more than 4.5%, we need to use the formula:

Z = (X - μ) / σ

where:
Z = the number of standard deviations from the mean
X = the rate of return we want to calculate the probability for (-4.5% in this case)
μ = the expected rate of return (7.9%)
σ = the standard deviation (6.2%)

Plugging in the values, we get:

Z = (-4.5 - 7.9) / 6.2 = -1.58

Looking at a standard normal distribution table, we can find that the probability of a value being less than -1.58 standard deviations from the mean is approximately 0.05 or 5%. However, we are interested in the probability of the stock losing MORE than 4.5%, which is the probability of being more than -1.58 standard deviations from the mean. Since the normal distribution is symmetric around the mean, this probability is also approximately 5%. Therefore, the correct answer is D, less than 2.5%.

A Stock Has an Expected Rate of Return of 7