NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return
A stock's returns over five years were 10%, 20%, -10%, 30% and 0%. What is the sample standard deviation of these returns?
The sample standard deviation is 15.81%. The mean return is 10%, the sum of squared deviations is 1000, dividing by n-1 (4) gives variance of 250, and its square root is about 15.81%. Dividing by 5 would give the population value of 14.14%.
- A14.14%
- B15.81%Correct
- C12.65%
- D20.00%
Explanation
Mean = (10+20-10+30+0)/5 = 10%. Deviations: 0, 10, -20, 20, -10; squares: 0, 100, 400, 400, 100 = 1000. Sample variance = 1000/4 = 250, SD = 15.81%. Dividing by 5 gives 200 and 14.14%, which is the population figure and is wrong for a sample.
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