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

A fund has two managers. Manager A has a tracking error of 3% and Manager B has a tracking error of 4%. Their active returns are uncorrelated, and the sponsor allocates 50% of capital to each. What is the approximate total tracking error of the combined active portfolio?

The combined tracking error is 2.5%. With uncorrelated active returns and 50% weights, variance is 2.25 plus 4, or 6.25, and its square root is 2.5%. Averaging the two tracking errors to 3.5% wrongly ignores the diversification benefit.

  1. A2.50%Correct
  2. B3.50%
  3. C1.75%
  4. D5.00%

Explanation

Weighted variance = (0.5×3)² + (0.5×4)² = 2.25 + 4 = 6.25, so TE = 2.5%. A simple weighted average gives 3.5%, which ignores diversification from zero correlation. The sum of 7% scaled wrongly or 5% from the root of 9+16 ignores the weights.

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