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FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management

A portfolio has annual volatility of 12% and its benchmark has annual volatility of 10%. The correlation between portfolio and benchmark returns is 0.90. What is the portfolio's annual tracking error (nearest value)?

Tracking error is about 5.3%. The variance of active return is 144 plus 100 minus 2 times 0.9 times 12 times 10, which equals 28, and its square root is roughly 5.29%. Simply subtracting volatilities gives 2%, which is wrong.

  1. A2.0%
  2. B5.3%Correct
  3. C2.8%
  4. D5.8%

Explanation

Variance of the difference = 12² + 10² − 2(0.9)(12)(10) = 144 + 100 − 216 = 28. The square root is 5.29%, about 5.3%. Using 12 − 10 = 2% ignores the imperfect correlation; 2.8 treats the variance 28 as if it were in percent terms divided incorrectly (28/10).

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