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Outline the comprehensive risk (CR) capital charge that applies to portfolios of positions exposed to default correlation.

FRM® Part II · Operational Risk and Resilience · Solvency, Liquidity, and Other Regulation After the Global Financial Crisis · FRM2.ORR.22.c

The idea

The comprehensive risk measure (CRM) is the Basel 2.5 charge for the correlation trading portfolio. It holds securitization tranches and nth-to-default credit derivatives whose reference names are single-name instruments or indices with liquid two-way markets, together with their hedges. Resecuritizations and options on tranches are excluded. Because these positions depend on default correlation, the bank models at 99.9 percent over one year the defaults and migrations, credit spread and correlation changes, recovery rate variability and basis risk between index and single-name hedges. The model charge has a floor, set at 8 percent of the charge from the standardized securitization approach for the same positions: Capital = max(model CRM, 0.08 × standardized charge). A bank without an approved model simply uses the standardized charge. Other trading book securitizations are outside the CRM and take the standardized charge too.

Formulas

Comprehensive risk measure with its floor

CRM = max(CRMmodel, 0.08 × SSA)

CRMmodel
the charge from the bank's approved CRM model
SSA
the standardised securitization charge for the same positions

Applies only with an approved model; without one the full standardised charge applies.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which risk factors does the CRM model have to cover that the IRC does not?

  1. Only interest rate risk, since the CRM covers government bond hedges of the tranchesWhy not: Interest rate risk sits in the general VaR; CRM is about credit and correlation risk in tranched products.
  2. Only default risk, since the CRM leaves out rating migration risk altogetherWhy not: CRM includes migration as well as default; it does not drop a component.
  3. Only liquidity risk, since the CRM measures the cost of unwinding tranchesWhy not: Liquidity is handled through liquidity horizons; the CRM is broader than a single risk factor and is price-risk based.
  4. Spread, correlation and recovery rate changes and basis risk, as well as default and migration - correct

Because tranche prices respond to spreads, implied correlation, recovery rates and index versus single-name basis, the CRM model has to capture those in addition to the default and migration risks of the IRC.

A harder one

A bank's approved CRM model gives a charge of USD 36 million for its correlation trading portfolio. The standardized securitization approach would give a capital charge of USD 600 million for the same positions. The CRM capital charge the bank must hold is:

  1. USD 48 million - correct
  2. USD 36 millionWhy not: Ignores the floor; the charge cannot fall below 8% of the standardized charge.
  3. USD 84 millionWhy not: Adds the floor to the model charge rather than taking the larger of the two.
  4. USD 600 millionWhy not: Uses the full standardized charge, forgetting that only 8% of it acts as the floor.

Floor = 0.08 x 600 = 48. CRM charge = max(36, 48) = 48. The floor binds because the model figure is below it.

The hardest tier

A bank's approved CRM model gives USD 45 million for its correlation trading portfolio, for which the standardized securitization approach gives USD 800 million. Other trading book securitization positions outside the portfolio carry a standardized charge of USD 120 million. The total capital charge for all these positions under Basel 2.5 is closest to:

  1. USD 165 millionWhy not: Ignores the 8% floor on the CRM charge.
  2. USD 64 millionWhy not: Applies the floor correctly but leaves out the standardized charge on the other securitizations.
  3. USD 184 million - correct
  4. USD 73.6 millionWhy not: Applies the 8% floor to the other securitizations as well; those positions take the full standardized charge.

CRM = max(45, 0.08 x 800 = 64) = 64. Other securitizations: standardized 120 in full. Total = 64 + 120 = 184.

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