Question

You've observed the following returns on Mary Ann Data Corporation's stock over the past five years: 46.00 percent. 28.00 percent. 31.00 percent, -33.00 percent, and 20.00 percent.

a. What was the arithmetic average return on Mary Ann's stock over this five-year period? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)
b-1. What was the variance of Mary Ann's returns over this period? (Do not round intermediate calculations. Round the final answer to 6 decimal places)
b-2. What was the standard deviation? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Answer 1

The arithmetic average return for Mary Ann's stock over the five years is 18.40 percent. The variance of the stock's returns over this period is 0.027850, and the standard deviation is 16.69 percent.

Step-by-step explanation:

To calculate the arithmetic average return on Mary Ann's stock over the past five years, we add up all of the annual returns and divide by the number of years. Hence, the calculation would be (46.00 + 28.00 + 31.00 - 33.00 + 20.00) / 5 = 92.00 / 5 = 18.40 percent.

To find the variance, we need to calculate the mean (which we found to be 18.40 percent), subtract each year's return from the mean, square the result, sum those squares, and divide by the number of observations minus one. Then, to find the standard deviation, we take the square root of the variance.

Calculations:

1. Mean = 18.40%
2. Variance = [((46.00 - 18.40)^2 + (28.00 - 18.40)^2 + (31.00 - 18.40)^2 + (-33.00 - 18.40)^2 + (20.00 - 18.40)^2) / (5 - 1)]
3. Standard Deviation = sqrt(Variance)

Substituting the values and after calculation, we find:

• Variance = 0.027850
• Standard Deviation = 16.69%