Question

A stock had returns of 16.75 percent, -6.55 percent, and 23.60 percent for the past three years. What is the standard deviation of the returns?

Answer 1

The standard deviation is 9.16 percent.

Step-by-step explanation:

To find the standard deviation of the returns, you first need to calculate the mean return. Add up the returns for the past three years and divide by the number of years (3 in this case). The mean return is (16.75 - 6.55 + 23.60) ÷ 3 = 11.93 percent.

Next, calculate the variance by finding the squared difference between each return and the mean return, and then summing up those squared differences. The squared differences are
`(16.75 - 11.93)^2`,
`(-6.55 - 11.93)^2`, and
`(23.60 - 11.93)^2`, which result in 20.45, 369.92, and 136.89, respectively. The sum of these squared differences is 20.45 + 369.92 + 136.89 = 527.26.

Finally, divide the variance by the number of years and take the square root to find the standard deviation. The standard deviation is the square root of (527.26 ÷ 3) = 9.16 percent.