You’ve observed the following returns on Doyscher Corporation’s stock over the p

Question

You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –24.9 percent, 13.6 percent, 30.2 percent, 2.3 percent, and 21.3 percent.

What was the arithmetic average return on the stock over this five-year period?

What was the variance of the returns over this period?

What was the standard deviation of the returns over this period?

You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –24.9 percent, 13.6 percent, 30.2 percent, 2.3 percent, and 21.3 percent.

Explanation / Answer

Arithmetic Average of returns = 8.5

Variance of returns = 362.95

Standard Deviation of returns = 19.05

Returns during the five year period = -24.9%, 13.6%, 30.2%, 2.3%, 21.3%

Arithmetic Average of returns = (-24.9 + 13.6+30.2+2.3+21.3)/5 = 42.5 / 5 = 8.5%

Variance of returns = [(-24.9-8.5)^2 + (13.6-8.5)^2+(30.2-8.5)^2+(2.3-8.5)^2+(21.3-8.5)^2]/5

                                    = [(-33.4)^2 + (5.1)^2+(21.7)^2+(-6.2)^2+(12.8)^2]/5

                                    = [1115.56+26.01+470.89+38.44+163.84]/5

                                     = 1814.74/5 = 362.948 or 362.95 (rounded off)

Standard Deviation of Returns = Square Root of (362.948) = (362.948)^1/2 = 19.0512 or 19.05%

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