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

A bank has stand-alone economic capital of 90 for credit risk and 40 for market risk. Using the square-root formula with correlation 0.5 between them, what is the diversification benefit relative to the simple sum of stand-alone capital?

Aggregate capital is the square root of 13,300, about 115.3. The simple sum is 130, so the diversification benefit is about 14.7. None of the listed figures matches this exactly.

  1. AAbout 130 less 118.3, so 11.7Correct
  2. BAbout 9.0
  3. CAbout 21.3
  4. DAbout 130

Explanation

Aggregate = sqrt(8100 + 1600 + 2*0.5*90*40) = sqrt(8100+1600+3600) = sqrt(13300) = 115.3. Simple sum is 130, so the benefit is 130 - 115.3 = 14.7. The option stating 11.7 is therefore not exact; the true benefit is 14.7.

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