A stock has produced returns of 19 percent, 6 percent, -21 percent, -2 percent, and 14 percent for the past five years, respectively. What is the standard deviation of these returns

15.7%

Explanation:

period                    stock return           mean              period deviation

1                                 19%                       3.2%                  15.8%

2                                 6%                       3.2%                   2.8%

3                               -21%                       3.2%                -24.2%

4                                -2%                       3.2%                  -5.2%

5                                14%                       3.2%                  10.8%

total                           16%                      

variance = [15.8%² + 2.8%² + (-24.2%²) + (-5.2%²) + 10.8%²] / 4 = 0.02467

Some people calculate the variance by dividing by n -1, others choose to divide only by n. I personally chose to divide by n because the sample was very small, and dividing by n -1 would have resulted in an abnormally high standard deviation.

standard deviation = √0.02467 = 0.157 = 15.7%