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Outline the revised output floor brought in by the Basel III reforms and the approaches available for computing it.

FRM® Part II · Operational Risk and Resilience · High-level summary of Basel III reforms · FRM2.ORR.23.c

The idea

The output floor stops a bank's internally modelled RWA from falling too far below what the standardised approaches would give. U-TRWA is the bank's RWA using its approved internal models plus standardised approaches elsewhere. S-TRWA is the RWA for the whole portfolio computed with the standardised approaches only. Those are the standardised approach for credit risk, the revised standardised approach for market risk, and the standardised approach for operational risk. The floor sets the bank's total RWA at the higher of the modelled figure and a fixed share of the standardised figure. RWA = max(U-TRWA, 72.5% × S-TRWA). The test is applied to total RWA, not risk type by risk type. The floor is permanent and is phased in, starting at 50% and rising in steps to 72.5%. It replaces the Basel II floor, which was set against Basel I. A common error is applying 72.5% to the bank's own RWA instead of to the standardised figure.

Formulas

Revised output floor

RWA = max(U-TRWA, 0.725 × S-TRWA)

U-TRWA
total RWA using approved internal models and standardised approaches elsewhere
S-TRWA
total RWA using the standardised approaches only

Tested on the total, not by risk type. Applying 72.5 percent to the modelled figure is the usual error. Phased in from 50 percent.

A practice question

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

Which expression describes the revised output floor?

  1. Total RWA = max(U-TRWA, 72.5 percent x S-TRWA), where S-TRWA is computed using the standardised approaches. - correct
  2. Total RWA = min(U-TRWA, 72.5 percent x S-TRWA), where S-TRWA is computed using the standardised approaches.Why not: A floor sets a minimum, so it is a maximum of the two figures; min would be a cap.
  3. Total RWA = U-TRWA + 72.5 percent x S-TRWA.Why not: Adds the two figures; the floor replaces modelled RWA when it is lower, it does not add to it.
  4. Total RWA = max(U-TRWA, 72.5 percent x U-TRWA).Why not: Applies 72.5 percent to the bank's own modelled RWA, which can never bind; the floor is set against standardised RWA.

The floor sets total RWA at the higher of modelled RWA and 72.5 percent of the RWA from the standardised approaches.

A harder one

A bank has U-TRWA of EUR 620 billion, S-TRWA of EUR 900 billion and CET1 capital of EUR 70 billion. After applying the 72.5 percent output floor, its CET1 ratio is closest to:

  1. 11.29 percentWhy not: Divides by U-TRWA, ignoring that the floor binds.
  2. 7.78 percentWhy not: Divides by the full S-TRWA instead of 72.5 percent of it.
  3. 15.57 percentWhy not: Applies 72.5 percent to the modelled RWA instead of the standardised RWA: 70 / (0.725 x 620).
  4. 10.73 percent - correct

Floor = 0.725 x 900 = 652.5, which exceeds U-TRWA of 620, so RWA = 652.5. CET1 ratio = 70 / 652.5 = 10.73 percent.

The hardest tier

A bank reports modelled and standardised RWA in EUR million: credit risk 300 modelled and 500 standardised; market risk 100 modelled and 180 standardised; operational risk 90 under the standardised approach in both. Using a 72.5 percent floor on the total, the bank's RWA is closest to:

  1. EUR 490 millionWhy not: Ignores the floor and sums the modelled figures.
  2. EUR 583 millionWhy not: Applies the floor to each risk type separately, instead of to the total.
  3. EUR 552.5 millionWhy not: Applies the floor to credit risk only and leaves market risk modelled.
  4. EUR 558.25 million - correct

U-TRWA = 300 + 100 + 90 = 490; S-TRWA = 500 + 180 + 90 = 770; floor = 0.725 x 770 = 558.25, which is above 490, so RWA = 558.25. The floor is tested on the total.

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