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

A sponsor's total fund has a portfolio standard deviation of 10%. Managers X and Y have weights of 60% and 40%. Their marginal contributions to risk (beta of each manager to the total fund times its stand-alone volatility, expressed as weight × beta × total volatility) are such that X has beta 0.90 and Y has beta 1.15 relative to the total fund. What percentage of total fund risk is contributed by Y?

Manager Y contributes 46% of total fund risk. Its risk share equals its weight times its beta to the total fund, 0.4 times 1.15. Because the beta exceeds one, Y's risk contribution is larger than its 40% capital weight. The 54% figure belongs to manager X.

  1. A46%Correct
  2. B40%
  3. C54%
  4. D115%

Explanation

Contribution share = weight × beta. X: 0.6×0.90 = 0.54; Y: 0.4×1.15 = 0.46. The sum is 1.00, confirming consistency. Y contributes 46% of risk, more than its 40% capital weight because its beta is above 1. Choosing 40% ignores beta; 54% is X's share.

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