FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
A risk manager decomposes a portfolio's tracking error of 4% into a systematic (factor) component and a stock-specific component. The factor-driven active variance is 12 (%²). What is the specific (idiosyncratic) tracking error, assuming factor and specific risks are uncorrelated?
Specific tracking error is 2.0%. Total active variance is 16 (4% squared); removing the 12 from factors leaves 4, whose square root is 2%. Variances add under zero correlation, whereas standard deviations do not.
- A2.0%Correct
- B2.31%
- C1.0%
- D4.0%
Explanation
Total active variance = 4^2 = 16. Specific variance = 16 - 12 = 4, so specific TE = sqrt(4) = 2.0%. Subtracting standard deviations (4 - sqrt12 = 0.54) is wrong; variances, not volatilities, add.
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