Question

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

Answer 1

15.7%

Step-by-step 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%