FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
A portfolio has two positions with standalone one-day 99% VaRs of USD 3 million and USD 4 million. Returns are jointly normal with correlation 0.5 (zero means). What is the portfolio VaR?
Portfolio VaR is about USD 6.08 million. With normal returns, VaRs combine like standard deviations: the square root of 9 plus 16 plus 2 times 0.5 times 3 times 4, which is the square root of 37, reflecting diversification below the simple sum of 7.
- AUSD 5.00 million
- BUSD 7.00 million
- CUSD 6.08 millionCorrect
- DUSD 4.58 million
Explanation
VaR = sqrt(3^2 + 4^2 + 2 x 0.5 x 3 x 4) = sqrt(9 + 16 + 12) = sqrt(37) = USD 6.08m. USD 5.00m ignores correlation (rho = 0), USD 7.00m assumes rho = 1, and USD 4.58m uses a negative correlation of -0.5 (sqrt(13) is 3.61, so it is not that either, but sqrt(21) = 4.58 comes from dropping the cross-term's sign mistakenly).
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