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

A firm's ERM team aggregates stand-alone economic capital of 60 for market risk, 80 for credit risk and 40 for operational risk, in USD millions. The three risk types are assumed to have pairwise correlations of 0.5, and aggregation uses the square-root (variance-covariance) formula. What is the firm-wide economic capital, to the nearest USD million?

Firm-wide economic capital is about USD 148 million. Variance equals the sum of squared stand-alone figures (11,600) plus 2 times 0.5 times the cross products (10,400), giving 22,000, whose square root is 148. Simple addition of 180 ignores diversification, and 134 ignores correlation.

  1. A180
  2. B148Correct
  3. C134
  4. D120

Explanation

Variance = 60²+80²+40² + 2×0.5×(60×80 + 60×40 + 80×40) = 3600+6400+1600 + (4800+2400+3200) = 11600+10400 = 22000. The square root is 148.3, so 148. Simple summation (180) assumes perfect correlation, and 134 (√(sum of squares)) wrongly assumes zero correlation.

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