Youve observed the following returns on Barnett Corporations

You’ve observed the following returns on Barnett Corporation’s stock over the past five years: –27.3 percent, 15.2 percent, 33.4 percent, 3.1 percent, and 22.1 percent.

What was the arithmetic average return on the stock over this five-year period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Arithmetic average return % =

What was the variance of the returns over this period? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.)

Variance =

What was the standard deviation of the returns over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation % =

Solution

1)

Arithmetic average return = ( -0.273 + 0.152 + 0.334 + 0.031 + 0.221) / 5

Arithmetic average return = 0.465 / 5

Arithmetic average return = 0.093 or 9.3%

2)

Variance = [( -0.273 - 0.093)² + ( 0.152 - 0.093)² + ( 0.334 - 0.093)² + ( 0.031 - 0.093)² + ( 0.221 - 0.093)²] 5 - 1

Variance = [ 0.133956 + 0.003481 + 0.058081 + 0.003844 + 0.016384 ] / 4

Variance = 0.215746 / 4

Variance = 0.053937

3)

Standard deviation = ( 0.053937 )^1/2

Standard deviation = 0.2322 or 23.22%