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

A bank has stand-alone economic capital of 600 million for credit risk, 300 million for market risk and 100 million for operational risk. It simply sums these to 1,000 million. A new model uses a Gaussian copula and gives total capital of 820 million. A risk committee member objects that the model may understate capital in a crisis. Which concern is most valid?

The most valid concern is that correlations estimated in normal times may rise in stress and the Gaussian copula lacks tail dependence, so the 180 million diversification benefit could be overstated. Additivity is not mandatory, and cross-risk diversification is accepted in practice if modeled prudently.

  1. ACorrelations estimated in normal times may rise in stress and tail dependence may exceed what the Gaussian copula implies, so diversification benefit of 180 million may be overstatedCorrect
  2. BThe 180 million benefit is invalid because capital must always be additive
  3. CDiversification can only occur within a risk type, never across types
  4. DThe copula approach overstates capital because it ignores correlation

Explanation

Diversification benefit is 1,000 − 820 = 180 million. The key practical issue is that correlations are unstable and tend to rise in stress, and the Gaussian copula has no tail dependence, so the benefit may be overstated. Simple addition assumes perfect correlation and is conservative but not required. Cross-risk diversification is recognized, and the copula does use correlation.

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