FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management
A fund holds two managers with standalone active risk (tracking error) of 3% for Manager A and 4% for Manager B. Their active returns are uncorrelated and each receives 50% of assets. What is the total fund tracking error?
Total tracking error is 2.50%. With zero correlation, variance is 0.25 times 9 plus 0.25 times 16, which equals 6.25, and its square root is 2.5%. The simple weighted average of 3.5% ignores diversification benefits between the managers' active returns.
- A1.75%
- B2.50%Correct
- C3.50%
- D5.00%
Explanation
Variance = 0.5^2*9 + 0.5^2*16 = 2.25 + 4 = 6.25, so TE = 2.5%. Weighted average of 3.5% ignores diversification from zero correlation. 1.75% would be wrongly using 0.25 weights on volatilities.
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