You’ve observed the following returns on Doyscher Corporation’s stock over the p
ID: 2750245 • Letter: Y
Question
You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –25.5 percent, 14.0 percent, 31.0 percent, 2.5 percent, and 21.5 percent.
What was the arithmetic average return on the stock over this five-year period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
What was the variance of the returns over this period? (Do not round intermediate calculations. Round your answer to 6 decimal places (e.g., 32.161616).)
What was the standard deviation of the returns over this period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –25.5 percent, 14.0 percent, 31.0 percent, 2.5 percent, and 21.5 percent.
Explanation / Answer
Arithmetic mean = -25.5 + 14.0 + 31.0 +2.5 + 21.5 / 5
Arithmetic mean = 43.5 / 5
Arithmetic mean = 8.7%
8.7% is the Arithmetic average return on stock over 5 years
Years
Returns
Deviation from arithmetic mean(8.7)
Square of deviation
1
-25.5
-34.2
1169.64
2
14.0
5.3
28.09
3
31.0
22.3
497.29
4
2.5
-6.2
38.44
5
21.5
12.8
163.84
Variance = 1169.64 + 28.09 + 497.29 +38.44 +163.84 / n-1
Variance = 1897.3 / 4
Variance = 474.325
Standard deviation is square root of variance = (474.325)1/2
Standard devaiaiton = 21.78
Years
Returns
Deviation from arithmetic mean(8.7)
Square of deviation
1
-25.5
-34.2
1169.64
2
14.0
5.3
28.09
3
31.0
22.3
497.29
4
2.5
-6.2
38.44
5
21.5
12.8
163.84
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