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

A firm has stand-alone economic capital of USD 60 million for market risk and USD 80 million for credit risk. Assuming total capital aggregates as the square root of the sum of squares plus the correlation term, with a correlation of 0.50 between the two risks, what is the total economic capital?

Total capital equals the square root of 3,600 plus 6,400 plus 4,800, which is the square root of 14,800, about USD 121.7 million. This lies between the zero-correlation figure of 100 and the perfect-correlation sum of 140, so the closest option is USD 122.1 million.

  1. AUSD 100.0 million
  2. BUSD 122.1 millionCorrect
  3. CUSD 140.0 million
  4. DUSD 111.4 million

Explanation

Total = sqrt(60^2 + 80^2 + 2*0.5*60*80) = sqrt(3600 + 6400 + 4800) = sqrt(14800) = 121.7 approx. Check: 121.66^2 = 14800. So the value is about USD 121.7 million, closest to USD 122.1 million. Option 100 assumes zero correlation; 140 assumes perfect correlation.

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