Fortescue had realised returns of 10%, 25%, -20%, and -15% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

Question

Quizplus · Accepted Answer

To find the quarterly standard deviation, we need to first calculate the average (or mean) return and then calculate the deviations from the mean for each quarter.

The average return is:
(10% + 25% - 20% - 15%) / 4 = 0%

Now we calculate the deviations from the mean for each quarter:

Quarter 1: 10% - 0% = 10% 
Quarter 2: 25% - 0% = 25%
Quarter 3: -20% - 0% = -20%
Quarter 4: -15% - 0% = -15%

Next, we square these deviations:

Quarter 1: (10% - 0%)^2 = 100%
Quarter 2: (25% - 0%)^2 = 625%
Quarter 3: (-20% - 0%)^2 = 400%
Quarter 4: (-15% - 0%)^2 = 225%

We then find the average of these squared deviations:

(100% + 625% + 400% + 225%) / 4 = 337.5%

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

sqrt(337.5%) = 18.37%

Therefore, the quarterly standard deviation of returns for Fortescue is 18.37%, which is closest to option B (21.21%).

Fortescue Had Realised Returns of 10%, 25%, -20%, and -15