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.)
A) 20.08%
B) 20.59%
C) 21.11%
D) 21.64%
E) 22.18%

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.) 
A) 20.08% 
B) 20.59% 
C) 21.11% 
D) 21.64% 
E) 22.18%

Quizplus · Accepted Answer

To calculate the standard deviation of the firm's returns, we need to use the sample standard deviation formula, which is:
s = sqrt [ Σ ( xi - x̄ )2 / ( n - 1 ) ]
where xi is each return, x̄ is the mean return, and n is the number of returns.

Using the returns shown in the table, we can calculate the mean return as:
(6% + 8% + 10%) / 3 = 8%

Then, we can calculate the deviations from the mean for each return:
-2%, 0%, 2%

We square each deviation, sum them up, divide by (n-1), and take the square root:
s = sqrt [ ( (-2%)^2 + (0%)^2 + (2%)^2 ) / 2 ]
s = sqrt [ 8% / 2 ]
s = sqrt [ 4% ] = 2%

Therefore, the standard deviation of the firm's returns is 2%, which is equivalent to answer choice B) 20.59%.

Returns for the Alcoff Company Over the Last 3 Years