A stock has an expected rate of return of 8.3 percent and a standard deviation of 6.4 percent.Which one of the following best describes the probability that this stock will lose more than 4.50 percent in any one given year?
A)Less than 2.5 percent
B)Less than 1.0 percent
C)Less than 1.5 percent
D)Less than .5 percent
E)Less than 5 percent

Question

Quizplus · Accepted Answer

To determine the probability of a stock losing more than 4.50 percent in any given year, we can use the concept of standard deviation in relation to the expected rate of return. The expected rate of return is 8.3 percent, and the standard deviation is 6.4 percent. A loss of more than 4.50 percent means the return would be below -4.50 percent. This scenario is significantly below the expected return, falling more than one standard deviation away from the mean (since 8.3% - 4.5% > 6.4%). In a normal distribution, about 68% of outcomes lie within one standard deviation of the mean, about 95% within two, and over 99% within three. Given this, the probability of a return falling more than one standard deviation below the mean (thus into the loss of more than 4.5%) would be in the tail, which is less than 16% (100% - 84%). However, since the loss of more than 4.5% is significantly below the mean, it would likely fall into the far tail, making the probability even lower, aligning with the option stating "Less than 2.5 percent". This is a rough estimation, as exact calculations would require Z-score or similar statistical analysis, but it gives a general idea of the probability's range.

A Stock Has an Expected Rate of Return of 8