Calculate the standard deviation of an investment with ﬁve year returns of 10%, 6%, 4%, 2% and (10%).

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we need to first calculate the mean return. 
Mean return = (10% + 6% + 4% + 2% + 10%)/5 = 6.4%
Next, we calculate the deviation of each return from the mean:
- 10% - 6.4% = -3.6%
- 6% - 6.4% = -0.4%
- 4% - 6.4% = -2.4%
- 2% - 6.4% = -4.4%
- 10% - 6.4% = -3.6%
Then, we square each deviation:
- (-3.6%)^2 = 0.13%
- (-0.4%)^2 = 0.00%
- (-2.4%)^2 = 0.06%
- (-4.4%)^2 = 0.19%
- (-3.6%)^2 = 0.13%
Next, we calculate the average of the squared deviations:
(0.13% + 0.00% + 0.06% + 0.19% + 0.13%)/5 = 0.10%
Finally, we take the square root of the average squared deviations to get the standard deviation:
√(0.10%) = 0.754%
Therefore, the answer is B) 7.54%.

Calculate the Standard Deviation of an Investment with ﬁVe Year