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

Which statement about aggregating risk types such as credit, market and operational risk into total economic capital is most accurate?

Simple summation assumes perfect dependence between risk types, so it generally overstates total economic capital compared with approaches that allow imperfect correlation. The other statements are wrong because square-root aggregation is not exact for non-normal losses, and copulas can model tail dependence.

  1. ASimple summation of stand-alone capital implicitly assumes perfect dependence and tends to overstate total capital relative to models with imperfect correlationCorrect
  2. BSquare-root aggregation with a correlation matrix is exact for any non-normal loss distribution
  3. CCopula approaches cannot capture tail dependence between risk types
  4. DDiversification benefit is always zero when risks come from different business lines

Explanation

Adding stand-alone capital corresponds to perfect correlation in the tails, which is the most conservative case and ignores diversification. The variance-covariance formula is exact only under elliptical assumptions such as normality. Copulas are in fact used to model tail dependence. Diversification benefit is generally positive when correlation is below one.

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