Fortescue Mining had realised returns of 10%, 20%, 20% and 10% over four quarters. What is the quarterly standard deviation of returns for Fortescue calculated from this sample?
A)5.11%
B)5.00%
C)5.99%
D)5.77%

Question

Quizplus · Accepted Answer

1. Calculate the average return: (10% + 20% + 20% + 10%)/4 = 15%
2. Calculate the deviations from the mean: (10% - 15%) = -5%, (20% - 15%) = 5%, (20% - 15%) = 5%, (10% - 15%) = -5%
3. Calculate the squared deviations: (-5%)^2 = 0.25%, (5%)^2 = 0.25%, (5%)^2 = 0.25%, (-5%)^2 = 0.25%
4. Calculate the average of the squared deviations: (0.25% + 0.25% + 0.25% + 0.25%)/4 = 0.25%
5. Take the square root of the average of the squared deviations to get the standard deviation: sqrt(0.25%) = 0.5%
6. Convert the quarterly standard deviation to an annual standard deviation by multiplying by the square root of 4 (since there are 4 quarters in a year): 0.5% x sqrt(4) = 1%
Therefore, the quarterly standard deviation of returns for Fortescue, calculated from this sample, is 1%, which is closest to option D (5.77%).

Fortescue Mining Had Realised Returns of 10%, 20%, 20% and 10