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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A desk holds two positions with stand-alone 99% parametric VaRs of $6 million and $8 million. Returns are normally distributed and the correlation between the positions is zero. What is the diversified portfolio VaR?

Diversified VaR is $10 million. With zero correlation and normal returns, the stand-alone VaRs combine as the square root of the sum of squares: the square root of 36 plus 64. The simple sum of $14 million assumes perfect correlation and overstates risk.

  1. A$14 million
  2. B$10 millionCorrect
  3. C$2 million
  4. D$7 million

Explanation

With normal returns, diversified VaR = sqrt(6² + 8² + 2ρ(6)(8)). With ρ = 0 this is sqrt(36 + 64) = sqrt(100) = $10 million. The $14 million figure is the undiversified sum, which assumes perfect correlation, and the diversification benefit is $4 million.

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