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

A plan sponsor has two managers with standalone active (tracking-error) risks of 4% and 3% of plan assets. The correlation between their active returns is 0.5. Both have equal weights in the sponsor's total active risk calculation, with the figures already expressed as contributions to plan assets. What is the total plan active risk?

Total active risk is the square root of 16 plus 9 plus 12, which is the square root of 37, about 6.1%. The managers' correlation of 0.5 adds covariance, so the result lies between the 5% zero-correlation figure and the 7% perfect-correlation sum.

  1. A3.5%
  2. B7.0%
  3. C5.0%
  4. D6.1%Correct

Explanation

Variance = 4^2 + 3^2 + 2(0.5)(4)(3) = 16 + 9 + 12 = 37. The square root is 6.08%, about 6.1%. Adding the risks (7%) assumes correlation of 1; 5% assumes zero correlation (sqrt 25); 3.5% is a simple average.

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