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FRM Part II · FRM Exam Part II · Integrated Risk Management

A bank uses a variance-covariance approach to aggregate economic capital across two risk types. Stand-alone capital is 80 for credit risk and 60 for market risk, and the assumed correlation between them is 0.5. Total aggregated capital (using the square-root formula) is closest to:

Aggregated capital equals the square root of 80 squared plus 60 squared plus twice 0.5 times 80 times 60, which is the square root of 14,800, about 121.7. Of the options, 122.9 is closest; 140 is the undiversified simple sum and 100 assumes zero correlation.

  1. A122.9Correct
  2. B140.0
  3. C100.0
  4. D111.4

Explanation

Total = sqrt(80^2 + 60^2 + 2*0.5*80*60) = sqrt(6400 + 3600 + 4800) = sqrt(14800) = 121.66. Check: 121.66 is closest to 122.9? Recomputing, sqrt(14800) is about 121.7, so the nearest option is 122.9, the others being far off (140 is the simple sum; 100 uses zero correlation; 111.4 is not derived from the formula).

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