Output Floor Specification¶

Basel 3.1 output floor mechanism limiting the benefit of internal models relative to the Standardised Approach.

Regulatory Reference: PRA PS1/26 Art. 92(2A)–(2D), Rules 3.1–3.3 Test Group: B31-F

Requirements Status¶

Overview¶

The output floor prevents IRB firms from reducing their total RWA below a specified percentage of what the Standardised Approach would produce. This addresses the concern that internal models can produce unjustifiably low capital requirements.

Floor Calculation¶

The full TREA formula from PRA PS1/26 Art. 92(2A) is:

TREA = max{U-TREA; x × S-TREA + OF-ADJ}

Where:

• U-TREA = un-floored total risk exposure amount (Art. 92(3))
• S-TREA = standardised total risk exposure amount (Art. 92(3A)) — calculated without IRB, SFT VaR, SEC-IRBA, IAA, IMM, or IMA
• x = 72.5% fully phased (or transitional rate per Art. 92(5))
• OF-ADJ = own-funds adjustment reconciling IRB vs SA provisions treatment — see below

At the RWA level (ignoring OF-ADJ for simplicity):

RWA_floored = max(RWA_IRB, floor_percentage × RWA_SA)
floor_impact = max(0, floor_percentage × RWA_SA - RWA_IRB)

The floor applies at the portfolio level (per entity/basis combination — see Entity-Type Applicability), not to individual exposures. The floor impact is allocated pro-rata to IRB exposures by their share of S-TREA.

PRA Transitional Schedule¶

Art. 92(5), Rules 3.1–3.3

The transitional percentages are permissive ("may apply"), not mandatory. An institution may elect to apply the full 72.5% floor from day one. If the transitional is elected, the following schedule applies:

OF-ADJ Capital Adjustment¶

Art. 92(2A)

The TREA formula includes an OF-ADJ term that reconciles the different treatment of provisions under IRB and SA, ensuring the floor comparison is on a like-for-like own-funds basis:

OF-ADJ = 12.5 x (IRB_T2 - IRB_CET1 - GCRA + SA_T2)

The 12.5 multiplier converts own-funds amounts to risk-weighted equivalents (the inverse of the 8% minimum capital ratio). Under IRB, EL shortfall adds to capital requirements (via CET1 deduction) while excess provisions provide T2 relief. Under SA, general credit risk adjustments provide T2 relief directly. Without OF-ADJ, switching from IRB to SA in the floor comparison would change the own-funds base, making the TREA comparison inconsistent.

Art. 40 — no deferred-tax grossing-up of the EL-shortfall deduction¶

PRA PS1/26 Art. 92(2A) defines the IRB CET1 input to OF-ADJ as "amounts calculated in accordance with point (d) of paragraph 1 of Article 36 and Article 40 of Own Funds (CRR) Part" (PS1/26 App 1, p. 13). Art. 40 is not a separate prudential filter or supervisory deduction — it is a one-line technical clarifier that ring-fences how the Art. 36(1)(d) EL- shortfall deduction is measured.

In practical terms, Art. 40 forbids the firm from netting a hypothetical deferred-tax benefit against the EL-shortfall CET1 deduction. The deduction is the gross EL-minus-provisions amount; the firm cannot argue that "if we had topped provisions up to EL, we would have recognised a DTA, so the net CET1 hit is smaller" — that DTA does not exist and Art. 40 prevents it from being imputed.

Effect on the OF-ADJ denominator¶

The PS1/26 Art. 92(2A) cross-reference to Art. 40 ensures the IRB CET1 term in OF-ADJ is the same gross figure that would be deducted from CET1 under the Own Funds Part:

IRB CET1 (in OF-ADJ) = Art. 36(1)(d) EL-shortfall deduction (gross of imputed DTA per Art. 40)
                     = max(0, EL - eligible provisions)        # Art. 159 Pool A/B/C/D outcome

Because OF-ADJ enters the floor formula as 12.5 × (IRB T2 − IRB CET1 − GCRA + SA T2), any under-statement of IRB CET1 (for example, by netting a hypothetical DTA) would understate the CET1 add-back and inflate the floored TREA. Art. 40 closes that arbitrage: the same gross EL-shortfall figure that hits CET1 under Art. 36(1)(d) is the figure that flows into the OF-ADJ denominator.

T2 Component Caps — Art. 62(c) and Art. 62(d)¶

IRB T2, SA T2, and GCRA are each capped relative to a different RWA base. The three caps interact but never reduce a positive OF-ADJ below itself by a single combined ceiling — each input is capped independently before the formula is evaluated:

Distinguishing GCRA from SA T2¶

GCRA and SA T2 both capture general credit risk adjustments, but they enter OF-ADJ at different points and under different caps:

• SA T2 is the Art. 62(c) Tier 2 credit — GCRAs that the firm admits to Tier 2 capital, capped at 1.25% of SA credit-risk RWA. It enters OF-ADJ with a positive sign (adding to the Tier 2 base on the SA side of the reconciliation).
• GCRA is the same population of general credit risk adjustments measured gross of tax effects and capped at 1.25% of S-TREA — the output-floor reference base. It enters OF-ADJ with a negative sign (subtracting the GCRA element that would otherwise be double-counted on the SA side).

The two caps reference different RWA bases (SA credit-risk RWA vs S-TREA), so the input figures sa_t2_credit and gcra_amount will not in general be equal even when they describe the same provisions.

Worked illustration¶

Inputs (post Art. 62 caps applied upstream):
  irb_t2_credit       = £20m   (already capped at 0.6% of IRB RWA per Art. 62(d))
  irb_cet1_deduction  = £15m
  gcra_amount         = £40m   (uncapped — engine applies 1.25% of S-TREA)
  sa_t2_credit        = £30m   (already capped at 1.25% of SA RWA per Art. 62(c))
  s_trea              = £2,400m

Engine GCRA cap (Art. 92(2A)):
  gcra_cap     = 1.25% × £2,400m = £30m
  gcra_capped  = min(£40m, £30m) = £30m

OF-ADJ:
  = 12.5 × (irb_t2_credit − irb_cet1_deduction − gcra_capped + sa_t2_credit)
  = 12.5 × (20 − 15 − 30 + 30)
  = 12.5 × 5
  = £62.5m

If the firm passed an irb_t2_credit or sa_t2_credit that exceeded the Art. 62(d) / Art. 62(c) caps, the engine would not detect or correct it — the post-cap discipline is institution-side. Reconciliation between the OF-ADJ inputs and the Tier 2 line items in the firm's COREP own funds template is the audit gate; see the output reporting spec for the OF 02.00 / OF 02.01 mapping that consumes these post-cap values.

General Credit Risk Adjustments (GCRA) — Qualifying Criteria¶

Art. 110(1)–(3A), Art. 62(c), Commission Delegated Regulation (EU) No 183/2014

The OF-ADJ GCRA term (capped at 1.25% of S-TREA) and the SA_T2 term both aggregate general credit risk adjustments only — specific credit risk adjustments (SCRAs) follow a different capital path via exposure-value reduction (SA) or Pool D of Art. 159 (IRB defaulted). Incorrectly classifying an SCRA as GCRA (or vice versa) produces a mis-stated OF-ADJ, so the GCRA/SCRA boundary and its IFRS 9 mapping must be established upstream of the engine.

GCRA vs SCRA Definition¶

The general/specific CRA split is fixed by Commission Delegated Regulation (EU) No 183/2014 — the "RTS on credit risk adjustments", onshored under UK law and cross-referenced by Art. 110 and Art. 159(1). Reg (EU) 183/2014 superseded EBA GL 2013/04, which had set the same framework prior to CRR2.

Framework Treatment by Approach¶

Art. 110 routes each CRA category to a different capital path depending on whether the underlying exposure is measured under SA or IRB:

See the Provisions Specification for full Art. 159 Pool A / B / C / D mechanics.

Mixed-Approach Allocation (Art. 110(3), (3A))¶

Institutions that apply IRB to some exposures and SA to others must split GCRA between the two capital paths before OF-ADJ is computed. The allocation is prescriptive:

• Art. 110(3)(a) — GCRA of a subsidiary that exclusively applies IRB → IRB treatment (Art. 159 + Art. 62(d)).
• Art. 110(3)(b) — GCRA of a subsidiary that exclusively applies SA → SA treatment (Art. 62(c)).
• Art. 110(3)(c) — The remainder (unallocated parent-level GCRA) is pro-rated across IRB and SA by the share of risk-weighted exposure amounts subject to each approach.
• Art. 110(3A) — Where the IRB firm uses the Risk-Weight Substitution Method (Art. 235), the covered portion of an exposure is treated as if it were under SA for the purposes of the GCRA allocation. The substituted RW drives the classification, not the original obligor's approach.

Double-Count Avoidance¶

The GCRA / SCRA framework is designed to recognise each loss allowance exactly once. The key invariants are:

1. SCRAs reduce EAD at the exposure level under SA (Art. 111(1)(a)). They do not additionally flow into SA_T2 or the GCRA term in OF-ADJ. The same amount cannot be used twice.
2. GCRAs never reduce EAD under either approach. They are a capital-side item only, feeding SA_T2 for SA exposures (Art. 62(c)) and Pool B of Art. 159 for IRB exposures.
3. Under IRB, neither GCRA nor SCRA reduces EAD. Both feed Pool B (non-defaulted) or Pool D (defaulted SCRA only) in the Art. 159 comparison — see Art. 159(1) Pool B items (i) general CRAs, (ii) specific CRAs for non-defaulted exposures.
4. Securitisation exclusion (Art. 159(2)(b)) — general and specific CRAs that relate to securitised exposures are excluded from both B and D; the securitisation framework handles those provisions separately.
5. Risk-Weight Substitution exclusion (Art. 159(2)(c)) — CRAs on the portion of an exposure covered by Art. 235 substitution are excluded from B and D because the covered portion is already reflected via the guarantor's risk weight.

Input Source and Validation¶

from rwa_calc.contracts.config import CalculationConfig

cfg = CalculationConfig.basel_3_1(
    gcra_amount=50_000_000.0,   # £50m Reg 183/2014-qualifying GCRA
    sa_t2_credit=50_000_000.0,  # same amount if fully SA-allocated
)

Entity-Type Applicability¶

Art. 92(2A)(a)–(d)

The output floor formula applies only to specific entity/basis combinations. All other combinations use U-TREA (the un-floored amount) directly.

Floor Applies To¶

Floor Does NOT Apply To¶

Unrated Corporate Election (Art. 122(8))¶

Art. 122(7)–(8)

Art. 122(8) governs how IRB firms treat unrated non-SME corporate exposures (Art. 112(1)(g)) in the S-TREA leg of the output floor. The election is output-floor-specific — it does not alter how the same exposures are risk-weighted for U-TREA (IRB) or for SA firms' regular SA capital.

Two Branches¶

Art. 122(11) SME corporates (turnover ≤ GBP 44m) retain the 85% weight under both branches — the (a)/(b) election only governs the unrated non-SME population.

Notification Obligation¶

Art. 122(8)(b)'s final sentence requires a notification to the PRA whenever the firm starts or stops applying the IG/non-IG split in S-TREA. This is in addition to the Art. 122(6) prior-permission requirement and the Art. 122(7) sound-processes obligation. Because the notification is symmetric, the firm must keep a record of every branch switch — for example, a firm that elects branch (b) for 2027 and reverts to branch (a) for 2028 owes the PRA two notifications (one at adoption, one at cessation). This is a firm-governance step upstream of the calculator; the engine does not emit or record the notification.

Consistency — Portfolio-wide¶

Both Art. 122(8)(a) and (b) apply to "all exposures for which a credit assessment by a nominated ECAI is not available". The election is portfolio-wide within the output-floor corporate population. A firm that has Art. 122(6) permission but assesses no obligor as IG still applies 135% to every unrated non-SME corporate under branch (b) — it cannot cherry-pick branch (a) for non-IG obligors while using branch (b) for IG obligors.

Why This Matters for Floor-Binding IRB Firms¶

The S-TREA leg determines the minimum RWA when the output floor binds. Branch (a) fixes every unrated non-SME corporate at 100%, which is conservative relative to an IG-heavy portfolio. Branch (b) lets the firm recognise its internal IG assessment (65%) in S-TREA — typically reducing floor impact materially — at the cost of the 135% penalty on any obligor assessed as non-IG. Firms that expect the floor to bind should compare the portfolio-weighted 100% against the portfolio-weighted w_IG × 65% + w_nonIG × 135% before electing.

SA Specialised Lending in S-TREA (Art. 122A–122B, Art. 139(2B))¶

Art. 122A, Art. 122B, Art. 139(2B)

When an IRB firm computes the S-TREA leg of the output floor, exposures that the firm risk-weights via SL slotting under IRB (Art. 153(5)) must be re-mapped to the SA specialised-lending regime in Art. 122A–122B, because S-TREA is the SA-equivalent quantity (Art. 92(3A) excludes the IRB approach). This subsection records the rule that determines whether a given SL exposure picks up an ECAI-driven weight or the unrated SL ladder when it crosses into S-TREA.

Mechanic¶

Art. 122B(1) routes a rated SA SL exposure to the rated corporate ECAI table in Art. 122(2): "Where a relevant issue-specific credit assessment by a nominated ECAI is available for a specialised lending exposure, an institution shall apply the risk weight treatment set out in Article 122(2)" (PS1/26 App 1 p. 46). Under the general ECAI rules, Art. 139(2) and Art. 139(2A) would let the firm fall back to an issuer-level rating (or a rating on a different issue) where no directly applicable issue-specific rating exists. Art. 139(2B) switches both fallbacks off for the purposes of Art. 122B(1):

• Art. 139(2) — issuer-level rating, or rating from a different issue, where the exposure ranks pari passu / senior — disapplied for SA SL.
• Art. 139(2A) — issuer-level rating that applies only to a limited class of liabilities — disapplied for SA SL.
• Art. 122B(1) therefore requires a directly issue-specific credit assessment on the SL exposure itself before the rated corporate table is used; otherwise the exposure falls to the unrated SL ladder in Art. 122B(2).

Numerical effect on S-TREA¶

The practical consequence for IRB firms computing S-TREA is that more SL exposures end up on the unrated SL ladder than they would under the general ECAI rules:

Because Art. 122B(2) weights cluster at 100% (object/commodities finance and operational PF) and 130% (pre-operational PF), Art. 139(2B) is generally conservative — it prevents firms from using a low-CQS issuer rating to weight an unrated PF tranche at 20%–50% in S-TREA. The 80% high-quality operational PF weight under Art. 122B(4) remains available where the Art. 122B(5) criteria are met, but it is not an ECAI fallback — it is a structural-quality test on the unrated path.

The rule applies to both branches of the floor formula via S-TREA: it shapes the SA-equivalent input to x × S-TREA + OF-ADJ and is unaffected by the transitional x in Art. 92(5). U-TREA is computed using IRB SL slotting (Art. 153(5)) and is not touched by Art. 139(2B).

Engine status¶

The engine's S-TREA path runs the SA calculator over the IRB-permissioned population, so SL exposures classified under Art. 122A automatically pick up the Art. 122B(2)/(4) ladder when no rated SA path applies. The Art. 139(2B) constraint on the rated-SL fallback is not currently encoded as a dedicated rating-eligibility check — the engine treats the firm-supplied external_cqs as already reflecting Art. 138 / Art. 139 routing (consistent with how Art. 139(6) implicit-support handling is treated upstream — see Art. 138(1)(g) / Art. 139(6) treatment in the SA spec).

Firms must therefore either (i) pre-adjust external_cqs for SL exposures so that issuer-level / cross-issue ratings are suppressed before the S-TREA run, or (ii) model the SL population as unrated and rely on Art. 122B(2)/(4). This is a documentation gap in IMPLEMENTATION_PLAN.md (no dedicated code item filed at the time of writing) and should be tracked there as a follow-up if firms in scope of the output floor are observed to rely on Art. 139(2)/(2A) fallbacks for SL.

Structural Invariants¶

The output floor has two structural invariants verified by acceptance tests:

1. Non-reduction invariant — The floor can only increase total RWA, never decrease it: RWA_floored >= RWA_IRB
2. Non-negative impact — The floor impact is always ≥ 0: floor_impact >= 0

These invariants hold regardless of portfolio composition or floor percentage.

Per-exposure vs portfolio-level reporting¶

Key Scenarios¶

Acceptance Tests¶