Sun Corporation has had returns of -6%, 16%, 18%, and 28% for the past four years. Calculate the standard deviation of the returns.
A) 11.6%
B) 14.3%
C) 13.4 %
D) None of the above

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the returns, we need to first calculate the average return (also known as the mean).

Average return = (-6% + 16% + 18% + 28%) / 4 = 14%

Next, we calculate the deviation of each return from the mean:

Deviation from mean = Return - Average return

For the first year, the deviation from mean = -6% - 14% = -20%
For the second year, the deviation from mean = 16% - 14% = 2%
For the third year, the deviation from mean = 18% - 14% = 4%
For the fourth year, the deviation from mean = 28% - 14% = 14%

Notice that the sum of the deviations from mean is zero, which is always the case.

Next, we square each deviation from mean:

(-20%)^2 = 400%
(2%)^2 = 4%
(4%)^2 = 16%
(14%)^2 = 196%

Then, we take the average of these squared deviations from mean:

[(400% + 4% + 16% + 196%) / 4] = 154%

Finally, we take the square root of this average to get the standard deviation:

Standard deviation = sqrt(154%) = 12.4%

Therefore, the answer is B) 14.3%.

Sun Corporation Has Had Returns of -6%, 16%, 18%, and 28