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FRM Part II · FRM Exam Part II · Range of Practices and Issues in Economic Capital Frameworks

A bank aggregates economic capital for two business lines using a Gaussian copula calibrated to a correlation of 0.30 in normal times. During a crisis, losses in the two lines rise together far more than the copula implies. Which limitation of the aggregation approach does this best illustrate?

This illustrates that the Gaussian copula lacks tail dependence. It matches ordinary correlation but understates how often extreme losses occur together, so diversification benefits are overstated in crises. The problem is the dependence structure, not stand-alone capital levels or the confidence level.

  1. AThe Gaussian copula has no tail dependence, so it understates joint extreme lossesCorrect
  2. BThe copula overstates the stand-alone capital for each business line
  3. CThe confidence level chosen for the copula is too high relative to the target rating
  4. DThe linear correlation is too high for the copula to be calibrated

Explanation

A Gaussian copula has asymptotically zero tail dependence, so joint extreme losses are underestimated even when the central correlation is matched. This leads to overstated diversification benefit in stress. The issue is about dependence structure, not stand-alone capital.

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