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FRM Part II · FRM Exam Part II · The Financial Stability Implications of Artificial Intelligence

Two funds each hold USD 100 million. Both use AI-driven strategies with a 1-day 99% VaR of USD 2.0 million for each fund (the same model family, so standalone VaRs are equal). A risk analyst estimates the return correlation between the funds at 0.9 and uses the variance-covariance approach. What is the combined 1-day 99% VaR of the two funds?

The combined VaR is about USD 3.90 million. With equal standalone VaRs of 2 million and correlation 0.9, portfolio VaR is the square root of 4 plus 4 plus 7.2, which is 15.2, giving 3.90 million. High correlation leaves almost no diversification benefit.

  1. AUSD 3.90 millionCorrect
  2. BUSD 3.82 million
  3. CUSD 4.00 million
  4. DUSD 2.00 million

Explanation

Combined VaR = sqrt(2^2 + 2^2 + 2*0.9*2*2) = sqrt(4 + 4 + 7.2) = sqrt(15.2) = 3.899, about 3.90 million. Using a sum of 4.00 assumes correlation of 1 and ignores the small diversification benefit. The 3.82 option comes from mistakenly using sqrt(14.6) via a wrong covariance term.

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