Question

A stock had returns of 18.78 percent, 22.30 percent, −15.62 percent, 9.26 percent, and 28.33 percent for the past five years. What is the standard deviation of the returns?

Answer 1

To calculate the standard deviation of the returns, we first need to find the average (mean) return:

Mean return = (18.78% + 22.30% - 15.62% + 9.26% + 28.33%) / 5
Mean return = 12.41%

Next, we calculate the variance of the returns. To do this, we first calculate the difference between each return and the mean return, then square each of these differences, and finally take the average of the squared differences:

Variance = [(18.78% - 12.41%)^2 + (22.30% - 12.41%)^2 + (-15.62% - 12.41%)^2 + (9.26% - 12.41%)^2 + (28.33% - 12.41%)^2] / 5
Variance = [38.79 + 99.16 + 688.83 + 9.01 + 244.08] / 5
Variance = 215.57

Finally, we take the square root of the variance to find the standard deviation:

Standard deviation = sqrt(Variance)
Standard deviation = sqrt(215.57)
Standard deviation = 14.68%

Therefore, the standard deviation of the returns is approximately 14.68%.