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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

Two assets each have a one-day 99% normal VaR (zero mean): Asset A USD 4 million and Asset B USD 3 million. The return correlation is 0.5. What is the one-day 99% VaR of the combined portfolio, and how does it compare with the sum of stand-alone VaRs?

With normal returns, VaRs combine like volatilities: the square root of 16 plus 9 plus 2 times 0.5 times 4 times 3 equals the square root of 37, about USD 6.08 million. This is below the USD 7 million sum because correlation is less than one, reflecting diversification.

  1. AAbout USD 6.08 million, below the USD 7 million sumCorrect
  2. BAbout USD 5.00 million, below the USD 7 million sum
  3. CAbout USD 7.00 million, equal to the sum
  4. DAbout USD 6.08 million, above the USD 7 million sum

Explanation

Portfolio VaR = sqrt(4^2 + 3^2 + 2*0.5*4*3) = sqrt(16+9+12) = sqrt(37) = 6.08 million. Check: that is below 7, showing diversification benefit. 5.00 corresponds to zero correlation. 7.00 corresponds to perfect correlation.

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