The output floor · RiskAtoms Academy

By the end you will be able to

1Calculate the output floor: 72.5% of standardised RWA, the approaches allowed in its base, and the add-on.
2Find which portfolios drive the floor on an IRB bank, its break-even factor, and the marginal risk weight while it binds.
3Apply the phase-in in the Basel Framework, the EU and the UK, and the UK's OF-ADJ.
4Explain why the Basel Committee agreed the floor: the variability of IRB RWA.

Why it matters

RiskAtoms Bank plc's mortgage model says its £30.2bn of home loans need RWA of £3,526.3m. The standardised approach says £8,949.6m. Which one counts? Since Basel III was finalised, partly both: total RWA can never be less than 72.5% of the standardised figure. On this book that rule, the output floor, adds £1,249.6m of RWA and takes 0.77 percentage points off the CET1 ratio. It also changes what each new loan costs.

Core explanation

A floor under the models

L4.1.04: Risk-weighted assets introduced the output floor in outline, and L4.1.08: Basel 3.1 from 2027: UK, EU and US its timetable in each jurisdiction. This lesson opens it up: how the floor is calculated, what it does to a bank on the IRB approach of L4.2.04: The IRB approach, and why it exists.

Illustrative dataRiskAtoms Bank plc's capital book

The same made-up UK bank as Level 3: £67bn of assets and £4bn of equity at 31 December 2025, in £ millions. Module 4.1 adds its regulatory layer: own funds, deductions, risk-weighted assets by risk type, buffers, the leverage exposure and MREL, computed from the Level 3 credit, trading, derivatives and operational risk books. Every figure is illustrative, not any bank's data.

Pro forma. The book applies Basel 3.1, the 2017 finalisation of Basel III, to the 31 December 2025 balance sheet. On that date the bank still reported under the old UK CRR. The UK applies Basel 3.1 from 1 January 2027, and the internal model approach for market risk from 1 January 2028 (PRA PS1/26, paras 1.23 and 1.24). So the book shows the bank as it would look under the new rules.

Two totals and a max

The bank calculates its RWA twice. U-TREA uses the approaches it is approved for: F-IRB for corporates, retail IRB for mortgages, the standardised approaches for the rest. S-TREA replaces every model with the standardised approach for that risk. RWA are the higher of U-TREA and 72.5% of S-TREA (RBC20.4). Only standardised approaches may feed S-TREA (RBC20.11): IRB, the securitisation IRB approach (SEC-IRBA), the internal model approach for market risk and the internal models method for counterparty risk are all barred, directly or by cross-reference (RBC20.12).

Sort itWhat goes into S-TREA?

For the floor's standardised total, what does the bank use for each exposure?

Corporate loans on F-IRB
Mortgages on retail IRB
A senior securitisation tranche on SEC-IRBA
Consumer loans already on the standardised approach
Derivatives exposures under SA-CCR
Operational risk

Which portfolios drive it

The floor is a test on the total, not portfolio by portfolio. But the total splits exactly. The floor exceeds U-TREA by the sum, over portfolios, of x × SA RWA less RWA as used. A portfolio whose models give less than x of its SA RWA pushes the floor up; one already on the SA holds it down, by (1 − x) of its RWA. On the book, at x = 72.5%:

Portfolio	RWA as used	SA RWA	Used ÷ SA	x × SA − used
Corporates (F-IRB)	8,934.7	13,412.2	66.6%	789.2
Mortgages (retail IRB)	3,526.3	8,949.6	39.4%	2,962.1
Credit on the SA	5,277.0	5,277.0	100.0%	−1,451.2
Counterparty, CVA, market and operational	3,820.1	3,820.1	100.0%	−1,050.5
Total	21,558.1	31,459.0	68.5%	1,249.6

Mortgages are the driver: their model gives 39.4% of the SA figure, far below 72.5%, and they alone push the floor £2,962.1m above their modelled RWA. Corporates add £789.2m. The standardised portfolios and the other risks hold it back by £2,501.7m, leaving the add-on of £1,249.6m. A bank with more standardised business, or less mortgage lending, would sit below its floor.

The break-even factor is U-TREA ÷ S-TREA = 68.53%. Above it the floor binds. RBC90.1 phased x in from 50% in 2023 to 72.5% from 1 January 2028, and supervisors may cap the floor's increase at 25% of RWA before the floor during the phase-in (RBC90.2, transitional cap). On the book that cap would sit at £26,947.7m, well above the floor, so it would not bite.

Output floor factor by year; the EU and the UK reach 72.5% in 2030
Year	Basel (RBC90.1)	EU (Art 465(1))	UK (Art 92(5))	Book, UK with OF-ADJ
2023	50.0%	none	none	no floor
2024	55.0%	none	none	no floor
2025	60.0%	50.0%	none	no floor
2026	65.0%	55.0%	none	no floor
2027	70.0%	60.0%	60.0%	21,558.1 (does not bind)
2028	72.5%	65.0%	65.0%	21,558.1 (does not bind)
2029	72.5%	70.0%	70.0%	22,955.8 (binds)
2030	72.5%	72.5%	72.5%	23,742.3 (binds)

What a binding floor does to each loan

While the floor binds, a new loan adds x times its standardised risk weight to RWA, whatever its model says: its marginal risk weight. For the book's mortgages that is 72.5% × 29.6% = 21.5% against a modelled 11.7%; for its corporates, 63.1% against 58.0%. A floor-bound bank finds low-risk mortgages much dearer than its models suggest, which is why the EU gave them a transitional treatment (L4.2.11: Credit risk capital: what changes from 2027). The reverse also holds: a better model saves nothing until U-TREA rises above the floor again.

Why it was agreed

After 2008, investors stopped trusting risk-weighted ratios: two banks with similar assets could report very different RWA. The Basel Committee tested it. In its 2013 study of banking book credit risk, 32 banks rated the same borrowers in a benchmarking exercise, and the reported capital ratios of outlier banks could differ by as much as 2 percentage points from a 10% benchmark. Most of the variation in RWA came from what banks held, but a material part came from bank and supervisory practice (BCBS press release, 5 July 2013). The December 2017 reforms set out to reduce this excessive variability of RWA: input floors and limits on IRB (L4.2.04: The IRB approach), and a floor on the output. The floor exists “to reduce excessive variability of RWA and to enhance the comparability of risk-based capital ratios” (RBC20.11).

TimelineFrom the variability studies to the full floor

1 / 6

Jul 2013

RCAP banking book study

Same borrowers, different RWA: up to 2 percentage points of capital ratio either way.

The formal version

With U the RWA as used, S the standardised RWA, x the floor factor (M-A11: Min, max, floors and caps) and i the portfolios (RBC20.4; RBC90.1; PRA Rulebook Article 92(2A)):

\begin{aligned} \text{RWA} &= \max\big(U,\ x\,S\big), \qquad x = 72.5\% \\ x\,S - U &= \sum_i \big(x\,S_i - U_i\big) \qquad \text{(the add-on when positive)} \\ x^{*} &= \frac{U}{S} \qquad \text{(the floor binds when } x > x^{*}) \\ \frac{\partial\,\text{RWA}}{\partial\,\text{EAD}_j} &= x \cdot \text{RW}^{\text{SA}}_j \qquad \text{(while the floor binds)} \\ \text{RWA}^{\text{UK}} &= \max\big(U,\ x\,S + \text{OF-ADJ}\big), \quad \text{OF-ADJ} = 12.5\,\big(T2_{\text{IRB}} - \text{CET1}_{\text{IRB}} - \text{GCRA} + T2_{\text{SA}}\big) \end{aligned}

$T2_{\text{IRB}}$ : excess IRB provisions counted in Tier 2; $\text{CET1}_{\text{IRB}}$ : the IRB expected-loss shortfall deducted from CET1; GCRA: general credit risk adjustments, capped at 1.25% of S; $T2_{\text{SA}}$ : SA general provisions counted in Tier 2. The EU and Basel have no OF-ADJ.

Try it

Halve what the IRB models give: does the bank's RWA fall? Now lower the factor to 60%, the UK's 2027 value, and try again. Then set the models back to × 1.00 and switch to the UK rules: the break-even falls to 65.6%, as in the regulatory lens.

Try itWhat drives the floor

Floor factor x72.5%

IRB models' RWA× 1.00

Rules

RWA as used (U-TREA)

£21,558m

72.5% × S-TREA

£22,808m

RWA (the higher)

£22,808m

Floor bindsyes

Floor add-on£1,250m

Break-even factor68.53%

CET1 ratio13.24% (no floor 14.01%)

Each portfolio's pull on the floor: x × SA RWA − RWA as used

Corporates (F-IRB)

Mortgages (retail IRB)

Credit on the SA

Counterparty, CVA, market and operational

left: holds the floor down · right: pushes it up

The gaps add up to the floor less RWA as used; the floor binds when the total is positive
Portfolio	RWA as used	SA RWA	Used ÷ SA	x × SA − used
Corporates (F-IRB)	8,934.7	13,412.2	66.6%	789.2
Mortgages (retail IRB)	3,526.3	8,949.6	39.4%	2,962.1
Credit on the SA	5,277.0	5,277.0	100.0%	−1,451.2
Counterparty, CVA, market and operational	3,820.1	3,820.1	100.0%	−1,050.5
Total	21,558.1	31,459.0	68.5%	1,249.6

The model slider scales only the two IRB portfolios; everything else is on the standardised approaches already, so its RWA as used equal its SA RWA. Pro forma book, illustrative data, £ millions.

Worked example

RiskAtoms Bank plc's floor, step by step

£ millions, from the book. Basel rules, fully phased in.

From two totals to one RWA

Step 1 of 6

1
U-TREA
$U = \underbrace{17{,}738.1}_{\text{credit as used}} + \underbrace{3{,}820.1}_{\text{CCR, CVA, market, op}} = 21{,}558.1$

Regulatory lens

Basel: RBC20.4, RBC20.11–20.13 and RBC90.1–90.2. Status as at 3 November 2026 as at 3 Nov 2026.

In the UK

From 1 January 2027, TREA = max{U-TREA; x · S-TREA + OF-ADJ}, with OF-ADJ = 12.5 × (IRB T2 − IRB CET1 − GCRA + SA T2) and x phased in at 60%, 65% and 70% in 2027 to 2029, then 72.5% (PRA Rulebook, Required Level of Own Funds (CRR) Part, Article 92(2A) and (5)). The floor applies to a stand-alone UK bank, to a ring-fenced bank (on its sub-consolidated basis if it has one) and to a UK group on its consolidated basis, unless the group is an international subsidiary with the PRA's permission. Other group entities use their un-floored RWA (Article 92(2A)).

OF-ADJ exists because IRB and the SA treat provisions differently: an IRB bank counts excess provisions in Tier 2 and deducts a shortfall, while the SA counts general provisions in Tier 2. On the book IRB T2 is the £74.8m of excess provisions (L4.2.07: Expected loss, provisions and the shortfall), and the other terms are 0, so OF-ADJ = 12.5 × 74.8 = £934.6m. The UK floor is £23,742.3m, an add-on of £2,184.2m, and its break-even falls to 65.6%. CET1, Tier 1 and total capital ratios are 12.72%, 14.40% and 16.83%. These use the book's S-TREA, which weights mortgages by the Basel whole-loan table; with the UK's loan-splitting the floor is higher (L4.2.11: Credit risk capital: what changes from 2027). In effect 8% of the extra RWA, £74.8m, cancels the Tier 2 credit for the excess provisions. Year by year, the UK floor does not bind in 2027 and is £21,382.9m in 2028, £175m short; it binds from 2029, adding £1,397.7m against £463.1m without OF-ADJ. The rest of this module uses the Basel figure, £22,807.7m.

In the EU

TREA = max(U-TREA, x · S-TREA) with x = 72.5% and no OF-ADJ (CRR Article 92(3), as amended by Regulation (EU) 2024/1623). Article 465(1) phases x in from 50% in 2025 to 70% in 2029, and Article 465 also gives transitional weights for unrated corporates and low-risk mortgages in S-TREA until 2032. They are worked on the book in L4.2.11: Credit risk capital: what changes from 2027.

In the US

The largest banks already run two stacks: their capital ratios are the lower of those on standardised RWA and on advanced approaches RWA (12 CFR 217.10(d)), which works like a floor at 100% of a standardised total. The agencies' proposals of 19 March 2026 would replace it for Category I and II firms (L4.1.08: Basel 3.1 from 2027: UK, EU and US).

Spark Atoms

Spark AtomTwo percentage points from one portfolio

In the Basel Committee's 2013 benchmarking exercise, 32 banks rated the same borrowers. For a bank at a 10% capital ratio, the outliers' models moved the ratio by as much as 2 percentage points either way: the gap between comfortably above and close to the minimum, from modelling choices alone.

Spark AtomThe floor reprices mortgages

On RiskAtoms Bank plc's book the floor nearly doubles the marginal risk weight of a mortgage, from 11.7% to 21.5%, but lifts that of a corporate loan only from 58.0% to 63.1%. A floor-bound lender that competes on mortgages with standardised lenders loses much of its modelling advantage, and a bank whose floor binds may find corporate lending relatively cheaper.

Key takeaways

RWA = max(U-TREA, 72.5% × S-TREA), where S-TREA replaces every model with the standardised approach (RBC20.4, 20.11–20.12).
The add-on splits by portfolio as x × SA − used. On the book mortgages push it up by £2,962m, corporates by £789m, and standardised business holds it down: add-on £1,249.6m.
The floor binds above the break-even U ÷ S = 68.53%. While it binds a new loan costs x times its SA weight, and model improvements save nothing.
Basel phased it in from 50% in 2023 to 72.5% in 2028; the EU runs from 50% in 2025 and the UK from 60% in 2027, both reaching 72.5% in 2030.
The UK adds OF-ADJ for provisions: on the book £934.6m, so the UK floor is £23,742.3m.
The floor answers the variability of IRB RWA that the Basel Committee found in its own tests.

Reaction

Check what stuck

Question 1 · objective 1

A bank's RWA as used are £40,000m and its standardised RWA £60,000m. With the full Basel output floor, what are its RWA, in £m?

£m

Question 2 · objective 2

The same bank's floor binds. It lends £1m more on a mortgage that its model weights at 10% and the standardised approach at 30%. What risk weight does the loan effectively add to RWA, in %?

%

Question 3 · objective 1

Which approach can a bank NOT use when it calculates the standardised RWA behind the floor?

AThe securitisation internal ratings-based approach (SEC-IRBA)BThe standardised approach for counterparty credit risk (SA-CCR)CThe securitisation standardised approach (SEC-SA)DThe standardised approach for operational risk

Question 4 · objective 3

A UK bank on IRB counts £40m of excess provisions in Tier 2. It has no expected-loss shortfall and no standardised provisions. What is its OF-ADJ, in £m?

£m

Question 5 · objective 4

What was the main reason the Basel Committee agreed the output floor?

AIts own studies found that banks' models gave materially different RWA for the same risks, which hurt confidence in risk-weighted ratiosBStandardised approaches had proved too low in the 2008 crisisCTo raise every bank's capital requirement by 27.5%DTo replace the leverage ratio

Glossary

Output floor: Output floor: a bank's RWA may not fall below 72.5% of the RWA it would have with every risk on the standardised approaches (RBC20.4).
U-TREA: U-TREA: the un-floored total risk exposure amount, the RWA under the approaches the bank is approved to use, models included. The UK and EU term for RWA as used.
S-TREA: S-TREA: the standardised total risk exposure amount, the same RWA with every model replaced by the standardised approach for that risk (RBC20.11–20.12).
Floor add-on: Floor add-on: the RWA the floor adds when it binds, x × S-TREA less U-TREA.
Break-even factor: Break-even factor: U-TREA ÷ S-TREA. The floor binds whenever the floor factor is above it.
Marginal risk weight: Marginal risk weight: what one more £1 of an exposure adds to total RWA. While the floor binds it is x times the standardised risk weight, whatever the model says.
RWA variability: RWA variability: different banks' models giving different RWA for the same risk. The Basel Committee's tests found part of it came from bank and supervisory practice, not from risk.
OF-ADJ: OF-ADJ: the UK output floor adjustment, 12.5 × (IRB T2 − IRB CET1 − GCRA + SA T2), added to x × S-TREA. It evens out the different treatment of provisions under IRB and the SA (PRA Rulebook, Art 92(2A)).
Transitional cap: Transitional cap: during the phase-in a supervisor may limit the floor's increase in RWA to 25% of RWA before the floor (RBC90.2).

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, Regulatory Consistency Assessment Programme (RCAP): Analysis of risk-weighted assets for credit risk in the banking book, July 2013: the evidence behind the floor. Advanced.
Basel Committee on Banking Supervision, High-level summary of Basel III reforms, December 2017: why the floor, input floors and IRB limits were agreed together. Intermediate.

Origins

Basel Committee on Banking Supervision, RBC20, paras 20.4 and 20.10–20.13, and RBC90, paras 90.1–90.2, bis.org.
Basel Committee on Banking Supervision, press release on the regulatory consistency of risk-weighted assets in the banking book, 5 July 2013.
Basel Committee on Banking Supervision, High-level summary of Basel III reforms, 7 December 2017.
Prudential Regulation Authority, PRA Rulebook: Required Level of Own Funds (CRR) Part, Article 92(2A) and (5), version in force from 1 January 2027.
Regulation (EU) No 575/2013 (CRR), Articles 92(3) and 465(1), as amended by Regulation (EU) 2024/1623.
12 CFR 217.10(d), eCFR.

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