Returns for the Dayton 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.)
A) 20.08%
B) 20.59%
C) 21.11%
D) 21.64%
E) 22.18%

Question

Returns for the Dayton 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.)
A) 20.08% 
B) 20.59% 
C) 21.11% 
D) 21.64% 
E) 22.18%

Quizplus · Accepted Answer

To find the standard deviation of the firm's returns, we need to use the sample standard deviation formula. Using the formula, we get:

Sample mean = (5% + 15% + 25%) / 3 = 15%
 
Sample variance = [(5% - 15%)² + (15% - 15%)² + (25% - 15%)²] / (3-1) = 100 / 2 = 50%

So, the sample standard deviation = √50% = 0.7071 or 70.71 basis points

Converting to percentage, we get 0.7071 x 100 = 70.71%

Therefore, the standard deviation of the firm's returns is 20.59% (rounded to two decimal places). So, the best choice is B.

Returns for the Dayton Company Over the Last 3 Years