FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
Two positions each have a standalone one-day 99% VaR of USD 3 million and USD 4 million. Their returns are normally distributed with a correlation of 0.0. What is the portfolio one-day 99% VaR?
Portfolio VaR is USD 5.0 million, since with zero correlation and normal returns individual VaRs combine as the square root of the sum of squares: root of 9 plus 16. Simple addition to 7 million would assume perfect correlation.
- AUSD 5.0 millionCorrect
- BUSD 7.0 million
- CUSD 1.0 million
- DUSD 12.0 million
Explanation
With normal returns, portfolio VaR = sqrt(3^2 + 4^2 + 2x0x3x4) = sqrt(25) = 5. Simple addition (7) assumes correlation of 1. The diversification benefit is 2 million.
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