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
Return
2010
21)00%
2009
−12)50%
2008
25)00%
A) 20.08%
B) 20.59%
C) 21.11%
D) 21.64%
E) 22.18%

Question

Quizplus · Accepted Answer

Using the sample standard deviation formula, we have:

1. Calculate the mean return:
mean = (21.00% - 12.50% + 25.00%) / 3 = 11.50%

2. Calculate the deviation of each return from the mean:
2010: 21.00% - 11.50% = 9.50%
2009: -12.50% - 11.50% = -24.00%
2008: 25.00% - 11.50% = 13.50%

3. Calculate the squared deviation of each return:
2010: (9.50%)^2 = 0.9025
2009: (-24.00%)^2 = 576.00
2008: (13.50%)^2 = 1.8225

4. Calculate the sum of the squared deviations:
0.9025 + 576.00 + 1.8225 = 578.725

5. Calculate the variance:
variance = 578.725 / 2 = 289.3625

6. Calculate the standard deviation:
standard deviation = sqrt(variance) = sqrt(289.3625) = 17.0034%

Therefore, the standard deviation of the firm's returns is 17.0034%, which is closest to choice B (20.59%).

Returns for the Alcoff Company Over the Last 3 Years