A stock had annual returns of 6 percent, 13 percent, 11 percent, - 8 percent, and 3 percent for the past five years, respectively. What is the standard deviation of returns for this stock?

8.27%

Explanation:

Given:

Annual returns = 6 percent, 13 percent, 11 percent, - 8 percent, and 3 percent

The average rate of return = (Sum of all the values) / Number of values

= (0.06 + 0.13 + 0.11 - 0.08 + 0.03) / 5

= 0.05

Now,

the variance

= { (0.06 - 0.05) ² + (0.13 - 0.05) ² + (0.11 - 0.05) ² + (-0.08 - 0.05) ² + (0.03 - 0.05) ²} / (5 - 1)

= (0.0001 + 0.0064 + 0.0036 + 0.0169 + 0.0004) / 4

= 0.00685

Now

the standard deviation, σ = √ (Variance)

σ = √0.00685

or

σ = 0.0827

or

σ = 0.0827 * 100% = 8.27%