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

A bank's stand-alone economic capital is USD 90 million for credit risk and USD 120 million for market risk. The correlation between the two is 0.20. Which is the diversification benefit, measured as the sum of stand-alone capital minus aggregate capital?

Aggregate capital is the square root of 26,820, about USD 163.8 million, so the diversification benefit is about USD 46.2 million against the simple sum of USD 210 million.

  1. AUSD 210.0 million minus USD 150.0 million, i.e. USD 60.0 million
  2. BUSD 210.0 million minus USD 178.4 million, i.e. USD 31.6 millionCorrect
  3. CUSD 210.0 million minus USD 200.0 million, i.e. USD 10.0 million
  4. DUSD 210.0 million minus USD 156.2 million, i.e. USD 53.8 million

Explanation

Aggregate = sqrt(90^2 + 120^2 + 2*0.2*90*120) = sqrt(8100 + 14400 + 4320) = sqrt(26820) = 163.8. Diversification benefit = 210 - 163.8 = 46.2. None of the listed numbers matches exactly, so the closest is not valid; this question is flawed.

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