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FRM Part I · FRM Exam Part I · Enterprise Risk Management and Future Trends

A bank aggregates two risks with stand-alone economic capital of 60 and 80. Which correlation assumption makes the square-root aggregation formula give exactly 100?

A correlation of zero gives exactly 100, because the square root of 3,600 plus 6,400 is 100. Perfect correlation would give the simple sum of 140, and correlation of -1 would give 20, so only zero fits.

  1. ACorrelation of zeroCorrect
  2. BCorrelation of 1
  3. CCorrelation of 0.5
  4. DCorrelation of -1

Explanation

With correlation 0, aggregate = sqrt(60^2 + 80^2) = sqrt(3600 + 6400) = sqrt(10000) = 100. Correlation 1 gives the simple sum of 140, and -1 gives 20. Correlation 0.5 gives sqrt(3600+6400+4800) = about 121.7.

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