FRM Part I · FRM Exam Part I · Random Variables
A portfolio's returns have a variance of 9 (in squared percentage points) and a third central moment of -54. What is the skewness of the returns?
Skewness is -2.0. It equals the third central moment of -54 divided by the standard deviation cubed. The standard deviation is 3, so its cube is 27. The negative sign indicates a longer left tail.
- A-2.0Correct
- B-6.0
- C2.0
- D-18.0
Explanation
Skewness = third central moment / sigma^3. Sigma = 3, so sigma^3 = 27, and -54/27 = -2.0. Dividing by the variance gives -6, which uses the wrong scaling. Dividing by sigma gives -18, which is also wrong. The sign is negative, indicating a longer left tail.
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