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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A portfolio has a 99% VaR of USD 10 million. Its two sub-portfolios A and B have standalone VaRs of USD 8 million and USD 6 million. Component VaRs are USD 7 million for A and USD 3 million for B. Which statement is correct?

Component VaRs add up to the total VaR (7 plus 3 equals 10 million), so B contributes 30% of portfolio risk. Standalone VaRs sum to 14 million, which overstates risk because it ignores diversification.

  1. AComponent VaRs sum to total VaR, and B's contribution is 30% of portfolio riskCorrect
  2. BComponent VaRs should sum to USD 14 million, the sum of standalone VaRs
  3. CB's contribution is 50% because it has the smaller standalone VaR
  4. DComponent VaRs are not additive, so percentage contributions cannot be computed

Explanation

Component VaRs (weight x marginal VaR) sum by Euler decomposition to total VaR: 7 + 3 = 10. B's share is 3/10 = 30%. Standalone VaRs sum to 14, exceeding 10 because of diversification, so they are not the decomposition.

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