Youve observed the following returns on Doyscher Corporation

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).)

Solution

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