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

A bank's ERM function aggregates stand-alone economic capital of 60 for credit risk, 40 for market risk and 30 for operational risk, in USD millions. Management proposes simple addition (130) but the CRO argues for recognizing diversification. Pairwise correlations are assumed to be zero among the three risks, and capital scales with standard deviation. What is the aggregated capital under that assumption, and what does the difference from 130 represent?

Aggregated capital is about USD 78.1 million, the square root of 3,600 plus 1,600 plus 900, assuming zero correlations. Compared with the simple sum of 130, the difference of roughly 51.9 is the diversification benefit from imperfectly correlated risks.

  1. AApproximately 78.1; the diversification benefit of about 51.9Correct
  2. BApproximately 130; no diversification benefit
  3. CApproximately 6,100; a diversification surcharge
  4. DApproximately 91.0; the diversification benefit of about 39.0

Explanation

With zero correlation, total = sqrt(60²+40²+30²) = sqrt(3600+1600+900) = sqrt(6100) = 78.1. Diversification benefit = 130 − 78.1 = 51.9. Adding to 130 assumes perfect correlation. 6,100 is the sum of squares without the square root. 91.0 is not derived from the data.

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