Question

You’ve observed the following returns on Mary Ann Data Corporation’s stock over the past five years: 38.00 percent, 20.00 percent, 23.00 percent, −25.00 percent, and 12.00 percent.

a. What was the arithmetic average return on Mary Ann’s stock over this five-year period?
b.What was the variance of Mary Ann’s returns over this period? What was the standard deviation?

Answer 1

The arithmetic average return on Mary Ann's stock for the five-year period is 13.6%. The variance of the returns is 555.75, and the standard deviation is approximately 23.57%.

Step-by-step explanation:

Calculating the Arithmetic Average Return and Variance

To calculate the arithmetic average return on Mary Ann's stock over the five-year period, we simply sum up the annual returns and divide by the number of years. The returns are: 38.00%, 20.00%, 23.00%, -25.00%, and 12.00%. The arithmetic average return, therefore, is (38 + 20 + 23 - 25 + 12) / 5 = 13.6%.

Calculating Variance and Standard Deviation

To find the variance of Mary Ann's returns, we first calculate the deviation of each year's return from the average return, square each deviation, sum up these squares, and then divide by the number of observations minus one (N - 1) for a sample variance. Thus, the calculations for each year's squared deviation are as follows:

• (38 - 13.6)^2 = 593.76
• (20 - 13.6)^2 = 41.16
• (23 - 13.6)^2 = 88.36
• (-25 - 13.6)^2 = 1497.16
• (12 - 13.6)^2 = 2.56

The sum of these squared deviations is 2223.00. Thus, variance = 2223.00 / (5 - 1) = 555.75.

To find the standard deviation, we take the square root of the variance: sqrt(555.75) ≈ 23.57%.

These calculations help in understanding the volatility and the expected return of an investment in the stock market.