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FRM Part II · FRM Exam Part II · Risk Capital Attribution and Risk-Adjusted Performance Measurement

A bank has two business units with stand-alone economic capital of USD 120 million (Unit A) and USD 80 million (Unit B). The correlation between their losses is 0.5, and economic capital is proportional to loss standard deviation. A manager wants to know the total diversified economic capital. Which is closest?

Diversified economic capital is about USD 174 million. Using the square-root formula with correlation 0.5, total equals the square root of 14,400 plus 6,400 plus 9,600, which is 30,400. Simple addition to USD 200 million would overstate capital by assuming perfect correlation.

  1. AUSD 140 million
  2. BUSD 174 millionCorrect
  3. CUSD 200 million
  4. DUSD 264 million

Explanation

Total = sqrt(120^2 + 80^2 + 2*0.5*120*80) = sqrt(14,400 + 6,400 + 9,600) = sqrt(30,400) = about 174.4. Simple summing (200) assumes perfect correlation. 140 wrongly uses a correlation-free calculation sqrt only of part terms; 264 would be an arithmetic error.

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