Question

You observe monthly returns on stock A of -2.23%, 3.24%, 1.24%, and -0.64%. What is the sample annualized standard deviations of these returns? Hint: To annualize the standard deviation of subperiod returns, multiply your answer by the square root of the number of those subperiods in one year.

Answer 1

mean return = sum of all return / number of returns

= -2.23% + 3.24% + 1.24% - 0.64% / 4

= 1.61% / 4

= 0.4025%

Standard deviation = √ sum of all (Return - mean)^2 / n - 1

= √ (-0.0223 - 0.004025)^2 + (0.0324 - 0.004025)^2 + (0.0124 - 0.004025)^2 + (-0.0064 - 0.004025)^2 / 4 - 1

= √ (-0.026325)^2 + (0.028375)^2 + (0.008375)^2 + (0.010425)^2 / 3

= √ (0.000693) + (0.000805) + (0.000070) + (0.00011) / 3

= √ 0.001678 / 3

= √ 0.000559

= 2.36%

Annual standard deviation = 2.36% × √12

= 2.36% × 3.464

= 8.175%