Over the past six years,a stock had annual returns of 18 percent,-6 percent,2 percent,27 percent,-11 percent,and 13 percent,respectively.What is the standard deviation of these returns?

Question

Quizplus · Accepted Answer

To find the standard deviation, we first need to find the mean return:

Mean = (18 - 6 + 2 + 27 - 11 + 13) / 6 = 43 / 6 = 7.17%

Next, we need to find the deviation for each return by subtracting the mean from each return:

18 - 7.17 = 10.83
-6 - 7.17 = -13.17
2 - 7.17 = -5.17
27 - 7.17 = 19.83
-11 - 7.17 = -18.17
13 - 7.17 = 5.83

Then, we square each deviation, and find the average of these squared deviations:

[ (10.83)^2 + (-13.17)^2 + (-5.17)^2 + (19.83)^2 + (-18.17)^2 + (5.83)^2 ] / 6 = 270.89

Finally, we take the square root of the average of the squared deviations:

sqrt(270.89 / 6) = 2.41

Therefore, the standard deviation is 2.41%, or 14.66% when expressed as a percentage of the mean. Thus, the best choice is (B).

Over the Past Six Years,a Stock Had Annual Returns of 18