Stock A has an expected return of 12% with a standard deviation of 8%.If returns are normally distributed,then approximately two-thirds of the time the return on stock A will be
A) between 12% and 20%.
B) between 8% and 12%.
C) between -4% and 28%.
D) between 4% and 20%.

Question

Quizplus · Accepted Answer

To find the range of returns that approximately two-thirds of the time fall within, we use the empirical rule, also known as the 68-95-99.7 rule for normally distributed data. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

In this case, we know that the expected return is 12%, and the standard deviation is 8%. Therefore:

- One standard deviation above the mean is 12% + 8% = 20%
- One standard deviation below the mean is 12% - 8% = 4%

Since we're looking for the range of returns that approximately two-thirds of the time fall within, we're interested in the range between one standard deviation above the mean and one standard deviation below the mean. Based on the above calculations, this range is between 4% and 20%.

Therefore, the best choice is D, between 4% and 20%.

Stock a Has an Expected Return of 12% with a Standard