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FRM Part II · FRM Exam Part II · Integrated Risk Management

A bank computes aggregate capital of 134 from stand-alone amounts of credit 90, market 60 and operational 30 (sum 180). Using the standard variance-covariance contribution method, the credit risk contribution is 90 x (90 + 0.5 x 60) / 134 = 80.6. Which statement about this result is correct?

The 80.6 is credit risk's diversified Euler-type contribution to aggregate capital. Contributions computed this way are additive, so those of credit, market and operational risk sum to the aggregate 134, which makes the method suitable for allocating capital to business lines.

  1. AIt is the stand-alone capital of credit risk adjusted by the portfolio-wide average correlation
  2. BIt is the marginal contribution, and the contributions of all risk types need not sum to 134
  3. CIt is the diversified (Euler-type) contribution, and contributions across risk types sum to the aggregate 134Correct
  4. DIt shows credit risk generates a diversification benefit of 80.6

Explanation

Contribution_i = EC_i x (covariance of i with total)/total variance times total... equivalently EC_i x sum_j rho_ij EC_j / aggregate. Credit: 90 x 120 / 134 = 80.6. Market: 60 x (60+45)/134 = 47.0; operational: 30 x 30/134 = 6.7. Sum = 134.3, approximately 134 (rounding). So contributions are additive, unlike marginal capital figures.

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