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

A sponsor uses the standalone tracking error of each manager to allocate risk budgets, but the managers' active returns are positively correlated. Compared with the sponsor's total active risk, the sum of the managers' stand-alone tracking errors is:

The sum of standalone tracking errors exceeds total active risk whenever correlation is below 1, because it ignores diversification. Positive correlation reduces the gap compared with zero correlation, but the sum still overstates total risk unless correlation is exactly 1.

  1. ALower, because correlation reduces each manager's risk
  2. BEqual, provided the managers have identical benchmarks
  3. CHigher only if correlations are negative
  4. DHigher, because the sum ignores diversification, though the gap is smaller than with zero correlationCorrect

Explanation

Total risk equals the sum of standalone risks only when correlation is 1. With any correlation below 1, including positive ones like 0.5, the total is less than the sum. The diversification benefit shrinks as correlation rises, so the gap is smaller than under zero correlation.

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