Question

Returns for the Alcoff Company over the last 3 years are shown below. What's the standard deviation of the firm's returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.)Year Return2010 21.00%2009 −12.50%2008 25.00%a. 20.08%b. 20.59%c. 21.11%d. 21.64%e. 22.18%

Answer 1

Answer:

the standard deviation for the sample is 6.83%

Explanation:

∑ ( (x1-X)^2 ) / N-1

whre X is the mean of the sample and N is the number of samples.

Year Return

2010  21.00%

2009 12.50%

2008 25.00%

Average: (0.21 + 0.125 + 0.25 )/3 = 0.195

Difference between average and actual result squared:

(0.21-0.195)^2+(0.125 -0.195)^2+(0.25 -195)^2 =

(0.015)^2+(-0.07)^2+(0.055)^2 = 0.00815

1/(N-1) = 1/(3-1) = 1/2

standard deviation = √(0.00815/2) = 0.06837397166 = 6.83%