FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology
A portfolio holds two positions with standalone one-day 99% VaRs of USD 3 million and USD 4 million. Assuming normally distributed returns and a correlation of 0.50 between them, what is the portfolio VaR?
With normal returns, portfolio VaR is the square root of 3 squared plus 4 squared plus 2 times 0.5 times 3 times 4. That is the square root of 37, about USD 6.08 million. Five million assumes zero correlation and seven million assumes perfect correlation.
- AUSD 5.57 millionCorrect
- BUSD 5.00 million
- CUSD 7.00 million
- DUSD 6.08 million
Explanation
VaR^2 = 9 + 16 + 2(0.5)(3)(4) = 37, so VaR = sqrt(37) = 6.08. Check: 9+16=25, plus 12 = 37. So the correct value is 6.08.
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