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FRM Part I · FRM Exam Part I · Measures of Financial Risk

Two assets each have a one-day 99% VaR, computed with a normal distribution, of USD 3 million and USD 4 million. Their return correlation is 0.5. What is the one-day 99% VaR of the combined portfolio?

The combined VaR is about USD 6.08 million. For normally distributed returns, VaR combines like volatility: the square root of 3 squared plus 4 squared plus twice 0.5 times 3 times 4, which is the square root of 37.

  1. AUSD 5.00 million
  2. BUSD 6.08 millionCorrect
  3. CUSD 7.00 million
  4. DUSD 4.58 million

Explanation

Portfolio VaR = sqrt(3² + 4² + 2×0.5×3×4) = sqrt(9 + 16 + 12) = sqrt(37) = 6.08 million. USD 5.00 million assumes zero correlation, while USD 7.00 million assumes perfect correlation.

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