FRM Part I · FRM Exam Part I · Sample Moments
Two assets have return standard deviations of 10% and 20% and a correlation of 0.30. A trader holds a long position of one unit in the first asset and a short position of one unit in the second, so the position return is X - Y. What is the standard deviation of the position return?
The standard deviation is about 19.49%. The variance of a long-short position is 0.01 plus 0.04 minus twice 0.30 times 0.10 times 0.20, which equals 0.038. Its square root is 19.49%. Adding the covariance term instead would give 24.90%.
- A19.49%Correct
- B24.90%
- C22.36%
- D10.00%
Explanation
Var(X-Y) = 0.01 + 0.04 - 2(0.30)(0.10)(0.20) = 0.05 - 0.012 = 0.038. The square root is 19.49%. Using +2ρσσ gives 0.062 and 24.90%, which is the long-long case. Ignoring correlation gives sqrt(0.05)=22.36%.
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