IRB for retail and specialised lending · RiskAtoms Academy

Know these first

L3.3.03: Analysing a household's credit
L3.3.14: Retail credit portfolios
L3.3.15: Wholesale and specialised lending

Math Atoms

By the end you will be able to

1State the retail correlations (mortgages, qualifying revolving, other retail) and explain why retail has no maturity adjustment.
2Compute a mortgage risk weight, and compare the bank's mortgages with the standardised approach and the PRA's 10% average.
3Apply the PD, LGD and EAD floors, and say when each binds.
4Weight specialised lending by slotting and compare it with F-IRB.

Why it matters

RiskAtoms Bank plc holds £30,240m of UK mortgages. Under the standardised approach they would carry £8,950m of RWA. Under the bank's retail IRB permission they carry £3,526m, an average risk weight of 11.7%. The difference, £5,423m, is 24% of the bank's total RWA of £22,808m. That is why mortgage lenders want IRB, and why supervisors put floors under it.

Core explanation

Pools, floors and slots

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.

The credit figures are the Level 3 credit book (Module 3.3): its twelve corporate borrowers and three mortgage segments, each scaled up to stand for a slice of the bank's £12bn corporate and £30bn mortgage books. Grades, PDs and LGDs are unchanged.

Retail: the same formula, three correlations

L3.3.14: Retail credit portfolios showed that retail lenders score borrowers and manage them in pools. Retail IRB follows: the bank estimates PD, LGD and EAD for each pool, not for each person (CRE30.19 to 30.22, for the definition of retail). The risk-weight formula is the one from L4.2.05: The IRB risk-weight formula with two differences. The correlation is set by the class of exposure, and there is no maturity adjustment (CRE31.14 to 31.16).

Retail class	Correlation R	Example in this bank
Residential mortgages	15%	Owner-occupied mortgages by LTV band
Qualifying revolving retail	4%	Credit cards: transactors and revolvers
Other retail	From 16% at low PDs to 3% at high PDs (15.6% at PD 0.1%, 3.4% at 10%)	Personal loans by score band

The correlation still feeds the conditional PD, N of a shifted G(PD) (M-C06: The normal distribution). A high R means the pool's bad year is much worse than its average year. The rule gives mortgages a high fixed figure and cards a low one. The BCBS explanatory note gives two reasons: mortgage losses are strongly linked to the value of the house, and mortgages usually run for many years; both effects are weaker for revolving cards (section 5.3). At the same PD and LGD of 45%, the curves sit in the order of their correlations:

Corporate, M 2.5Mortgage (R 15%)Other retail (R 16% to 3%)QRRE (R 4%)

The bank's mortgages by LTV band

The bank segments its mortgages by loan-to-value, as L3.3.14: Retail credit portfolios did. Lower LTV means a lower PD (more equity to lose before walking away) and a much lower LGD (more house to sell). The standardised column uses the whole-loan LTV table of L4.2.02: The standardised approach: retail and real estate.

Segment	PD	LGD	Cond. PD	IRB RW	EAD	IRB RWA	SA RW	SA RWA
LTV up to 60%	0.3%	5%at the floor	4.63%	2.7%	11,544.5	312.1	22.5%	2,597.5
LTV 60–80%	0.6%	12%	7.68%	10.6%	13,119.6	1,394.1	30.0%	3,935.9
LTV 80–95%	1.5%	20%	14.56%	32.6%	5,575.9	1,820.1	43.3%	2,416.2
All mortgages				11.7%	30,240.0	3,526.3	29.6%	8,949.6

The PRA's 10% average

From 1 January 2022 the PRA has expected UK IRB banks to hold an exposure-weighted average risk weight of at least 10% on their UK residential mortgages, excluding defaulted loans (PS16/21, July 2021). This bank's 11.7% clears it; at exactly 10% its mortgage RWA would be £3,024m. The PRA consulted on making it a rule with Basel 3.1 (CP16/22, paras 4.152 to 4.153).

The consumer book on retail IRB: an illustration

The bank keeps its personal loans and cards on the standardised approach. Had it built retail IRB models for them, with the pools of L3.3.14: Retail credit portfolios, the result would be:

Pool	Class	PD	LGD	R	EAD	RW	RWA
Score band A	Other retail	1.2%	65%	11.5%	1,283.8	71.2%	914.1
Score band B	Other retail	3.5%	70%	6.8%	878.4	99.7%	875.6
Score band C	Other retail	9.0%	75%	3.6%	337.8	122.0%	412.1
Transactors	QRRE	0.8%	80%	4.0%	429.9	25.8%	110.9
Revolvers	QRRE	4.5%	85%	4.0%	965.4	96.4%	931.0
Consumer book							3,243.7

Product	Retail IRB RWA	SA RWA
Personal loans (other retail)	2,201.8	1,875.0
Cards, transactors (QRRE)	110.9	193.5
Cards, revolvers (QRRE)	931.0	577.6
Total	3,243.7	2,646.0

IRB is not always cheaper. The transactors fall from 193.5 to 110.9, but the revolvers, with PD 4.5% and LGD 85%, rise from 577.6 to 931.0, and the whole book costs £598m more. The standardised 75% for regulatory retail is a flat average; a high-risk pool pays for its risk under IRB.

The floors: the larger of the estimate and the minimum

Basel 3.1 puts a minimum under each input a bank estimates. The formula takes the larger of the two, $\max(\text{estimate},\ \text{floor})$ (M-A11: Min, max, floors and caps). A floor binds only when the estimate is below it.

Exposure	PD floor	LGD floor	Rule
Corporate A-IRB unsecured (PD floor also for banks)	0.05%	25%	CRE32.4, 32.16
Corporate, A-IRB secured by real estate	0.05%	10% on the secured part	CRE32.17
Residential mortgage	0.05%	5%	CRE32.58
QRRE transactor	0.05%	50%	CRE32.58
QRRE revolver	0.10%	50%	CRE32.58
Other retail, unsecured	0.05%	30%	CRE32.58

PD. The 0.05% floor is the one the slider stopped at in L4.2.05: The IRB risk-weight formula. No pool in this bank sits below it.
LGD on mortgages. The up-to-60% band is already at the 5% floor. If the bank's model said 2.5%, the formula would still use 5%: risk weight 2.70% instead of 1.35%.
LGD on secured corporates. Under A-IRB the floor for a partly secured loan blends 25% on the unsecured part with the collateral's floor on the secured part (CRE32.17). For Pellcourt Properties Ltd, with £2,731.3m of its £3,034.8m secured on property at 10%, the floor is 11.50%. A model LGD of 10.88%, before any downturn add-on, would be lifted to the floor, and RWA from £640.4m to £677.2m.
EAD and CCF. An A-IRB or retail IRB EAD must be at least the drawn balance plus 50% of the undrawn line at the standardised CCF (CRE32.36, CRE32.64). For Quorrel Systems BV the bank's own EAD is £1,034.5m against a floor of £565.5m; it binds on none of the bank's loans.

Specialised lending: slotting

L3.3.15: Wholesale and specialised lending described specialised lending: project, object and commodities finance, and income-producing real estate, where the loan is repaid from the asset it finances. A bank that cannot estimate PD for these uses supervisory slotting: it grades each loan on the CRE33 criteria into one of five categories, each with a fixed risk weight (CRE30.39 to 30.41, CRE33.2).

Category	Broadly like	Risk weight	HVCRE	EL risk weight
Strong	BBB− or better	70%	95%	5%
Good	BB+ or BB	90%	120%	10%
Satisfactory	BB− or B+	115%	140%	35%
Weak	B to C−	250%	250%	100%
Default	In default	0%	0%	625%

The bank's two property lenders, slotted by their master-scale grades (an assumption: real slotting scores the CRE33 criteria, such as the property's cash flow and the sponsor's strength):

Borrower	Category	EAD	Slotting RWA	Slotting EL	F-IRB RWA	F-IRB EL
Pellcourt Properties Ltd	Strong	3,034.8	2,124.3	12.14	1,043.2	3.81
Vellacourt Hôtels SAS	Satisfactory	992.3	1,141.1	27.78	679.4	5.82

Slotting costs both far more than F-IRB: the five weights are coarse and set to cover the whole category. A Strong or Good loan with less than 2.5 years to run may get a preferential 50% or 70% where the supervisor allows it (CRE33.4). Pellcourt would then need £1,517.4m with no expected loss, but its loan has 4 years to run. Land and construction lending classed as high-volatility commercial real estate gets 95% to 250% (CRE33.5).

Sort itWhich treatment?

For each exposure at an IRB bank, pick the risk-weight function or approach it falls under.

A 25-year owner-occupied mortgage at 75% LTV
A credit card with a £6,000 limit, repaid in full every month for a year
A five-year £15,000 car loan to a household
An office building loan repaid from the tenants' rents, where the bank has no PD model
A revolving credit line of €150,000 to an individual
A loan to buy land for a housing development, before building starts

The formal version

For a non-defaulted retail exposure (CRE31.14 to 31.16), with the floors of CRE32.58 applied first:

\begin{aligned} \text{PD} &= \max(\widehat{\text{PD}},\ \text{PD}_{\min}), \qquad \text{LGD} = \max(\widehat{\text{LGD}},\ \text{LGD}_{\min}) \\ R &= 0.15 \ \text{(mortgages)}, \qquad R = 0.04 \ \text{(QRRE)} \\ R &= 0.03 \cdot \frac{1-e^{-35\,\text{PD}}}{1-e^{-35}} + 0.16 \cdot \left(1-\frac{1-e^{-35\,\text{PD}}}{1-e^{-35}}\right) \ \text{(other retail)} \\ K &= \text{LGD}\cdot N\!\left(\frac{G(\text{PD}) + \sqrt{R}\cdot G(0.999)}{\sqrt{1-R}}\right) - \text{PD}\cdot\text{LGD} \\ \text{RW} &= 12.5 \cdot K \end{aligned}

For specialised lending under slotting (CRE33.2, CRE33.8):

\text{RWA} = \text{RW}_{\text{slot}} \cdot \text{EAD}, \qquad \text{EL} = 8\% \cdot \text{RW}^{\text{EL}}_{\text{slot}} \cdot \text{EAD}

$\widehat{\text{PD}}, \widehat{\text{LGD}}$ : the bank's own estimates for the pool. $\text{PD}_{\min}$ , $\text{LGD}_{\min}$ : the floors in the table above.
$N$ and $G$ : the standard normal distribution function and its inverse, as in L4.2.05: The IRB risk-weight formula; $G(0.999) = 3.0902$ .
$\text{RW}_{\text{slot}}$ , $\text{RW}^{\text{EL}}_{\text{slot}}$ : the category's risk weight and EL risk weight from the slotting table. EL feeds the comparison with provisions in L4.2.07: Expected loss, provisions and the shortfall.

Try it

Start at the 80% to 95% mortgages. Push the LGD down to 1% and watch the 5% floor take over. Raise the LTV and see the standardised weight step up. Then switch to a card revolver and set a low PD: the 0.1% floor binds before the 0.05% one would.

Try itRetail IRB with its floors

Exposure

The bank's PD estimate1.50%

The bank's LGD estimate20%

Loan-to-value (for the SA weight)90%

PD used = max(1.500%, 0.05%)1.500%

LGD used = max(20%, 5%)20%

Correlation R15.00%

Conditional PD at 99.9%14.56%

K (no maturity factor)2.611%

EL = PD × LGD0.300%

IRB risk weight32.64%

SA risk weight (CRE20.82 by LTV)40%

IRB needs 18% less than the SA here.

Starts at the bank's 80% to 95% LTV mortgages. Floors from CRE32.58: PD 0.05% (0.1% for QRRE revolvers); LGD 5% mortgages, 50% QRRE, 30% other unsecured retail. Illustrative.

Worked example

A mortgage band, then a hotel loan

The 80% to 95% LTV mortgages: PD 1.5%, LGD 20%, EAD £5,575.9m. Then Vellacourt Hôtels SAS, a hotel group, slotted. £ millions.

Retail IRB and slotting

Step 1 of 6

1
Floors
PD 1.5% is above 0.05% and LGD 20% is above 5%, so neither floor binds: the formula uses the bank's own estimates.

Regulatory lens

Retail definitions are in CRE30, the functions in CRE31, the floors in CRE32 and slotting in CRE33. Statements on jurisdictions are as at 3 November 2026 as at 3 Nov 2026.

In the UK

The PRA's 10% average risk weight on UK IRB mortgages has applied as an expectation since 1 January 2022 (PS16/21). The Basel 3.1 rules, from 1 January 2027 (PS1/26, para 1.23), bring in the input floors, with a PD floor of 0.1% rather than 0.05% for UK residential mortgages (as the PRA's DP1/25, para 4.7, describes the near-final rules of PS9/24). PS1/26 corrected the retail LGD floor for the unsecured part of a partly secured exposure from 25% to 30% (para 2.8). Supervisory statement SS4/24 expects firms to apply all the parameter and risk-weight floors (para 2.5(g)).

In the EU

CRR3 applies from 1 January 2025. It raises the PD floor from 0.03% to 0.05% for corporates, institutions and retail, and to 0.1% for QRRE revolvers, and brings in LGD floors such as 50% for QRRE, 30% for unsecured other retail and 5% to 10% for exposures secured by property (CRR Articles 160, 163 and 164 as amended; KPMG summary of CRR3, 2024).

In the US

The US advanced approaches apply to the largest banks, the US G-SIBs and Category II firms (12 CFR 217.100), and the agencies proposed removing them on 19 March 2026 (Federal Reserve fact sheet). As far as we could find, no final rule had been published by 3 November 2026.

Spark Atoms

Spark AtomTwo-fifths of the standardised weight

The bank's mortgages average 11.7% under IRB against 29.6% under the standardised approach. The output floor of L4.2.09: The output floor exists because gaps like this, multiplied across a book, can be large.

Spark AtomWhy “slotting”?

The bank does not compute a risk weight; it slots the loan into one of five pre-cut categories, much as a rating agency slots an issuer into a rating band. CRE33.3 says the categories broadly correspond to external ratings from BBB− or better down to C−.

Key takeaways

Retail IRB rates pools, not names, with the corporate formula less the maturity adjustment.
Correlations are fixed by class: 15% for mortgages, 4% for QRRE, and 16% falling to 3% for other retail.
The bank's mortgages need £3,526.3m of RWA under IRB (11.7%) against £8,949.6m under the SA, above the PRA's 10% average.
Floors take the larger of estimate and minimum: PD 0.05% (0.1% for QRRE revolvers); LGD 5% mortgages, 50% QRRE, 30% other unsecured; EAD at least drawn plus half the SA CCF.
Slotting gives five fixed weights. Vellacourt at Satisfactory needs £1,141.1m against £679.4m under F-IRB.

Reaction

Check what stuck

Question 1 · objective 1

Why does the retail risk-weight function have no maturity adjustment?

AThe Basel formula for retail sets the maturity factor aside: retail K is LGD × (conditional PD − PD) and nothing moreBRetail loans are always shorter than one yearCRetail PDs are too high for maturity to matterDThe bank chooses whether to apply it

Question 2 · objective 3

A credit-card revolver pool has the bank's own PD of 0.06% and LGD of 40%. After the floors, what is its IRB risk weight, in %?

Question 3 · objective 4

A project finance loan of £200m is slotted as Good. What are its RWA, in £m?

£m

Question 4 · objective 2

What is the IRB risk weight of a mortgage pool with PD 1% and LGD 15%, in %?

Question 5 · objective 2

On the illustration, retail IRB on the card revolvers gives £931m of RWA against £578m under the standardised approach. Why?

ATheir PD of 4.5% and LGD of 85% are high, while the SA gives every regulatory retail exposure the same 75%BIRB adds 1.06 to retail exposuresCQRRE has the highest correlation of all retail classesDThe LGD floor of 50% binds on them

Glossary

Retail pool: Retail pool (segment): a group of similar retail exposures that the bank rates together, with one PD, LGD and EAD for the pool rather than for each borrower.
QRRE: Qualifying revolving retail exposure (QRRE): revolving, unsecured and uncommitted lines to individuals of up to €100,000, such as credit cards (CRE30.24).
Transactor: Transactor: a QRRE customer who has repaid the balance in full at each scheduled date for the past 12 months, or an overdraft not drawn in that time (CRE30.25).
Input floor: Input floor: a minimum value for a bank's own PD, LGD or EAD estimate. The formula uses the larger of the estimate and the floor.
RWA density: RWA density: RWA divided by exposure, the book's average risk weight. Used to compare books and approaches.
Supervisory slotting: Supervisory slotting: for specialised lending where the bank cannot estimate PD, the loan is graded into one of five categories, each with a fixed risk weight (CRE33).
Income-producing real estate: Income-producing real estate (IPRE): lending on property where repayment comes mainly from the rents or sale of that property, such as offices or hotels (CRE30.14).
HVCRE: High-volatility commercial real estate (HVCRE): commercial property lending with higher loss rate volatility, such as land acquisition and construction finance (CRE30.15).

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, An Explanatory Note on the Basel II IRB Risk Weight Functions, July 2005: the formulas, their constants and the reasons for them. Intermediate.
Prudential Regulation Authority, PS16/21, July 2021: the reasons for the 10% mortgage average. Intermediate.

Origins

Basel Committee on Banking Supervision, CRE30: IRB approach: overview and asset class definitions, paras 30.14–30.15, 30.19–30.25 and 30.39–30.41, bis.org.
Basel Committee on Banking Supervision, CRE31: IRB approach: risk weight functions, paras 31.14–31.16; CRE32: IRB approach: risk components, paras 32.4, 32.16–32.17, 32.36, 32.58 and 32.64; CRE33: IRB approach: supervisory slotting approach for specialised lending, paras 33.2–33.10, bis.org.
Prudential Regulation Authority, PS16/21, July 2021; CP16/22, paras 4.152–4.153, November 2022; PS1/26, paras 1.23 and 2.8, January 2026; SS4/24, para 2.5(g), January 2026; DP1/25 on residential mortgage LGD and PD estimation, para 4.7, July 2025.
Basel Committee on Banking Supervision, An Explanatory Note on the Basel II IRB Risk Weight Functions, July 2005, section 5.3.
Regulation (EU) No 575/2013 as amended by Regulation (EU) 2024/1623, Articles 160, 163 and 164.
KPMG AG Wirtschaftsprüfungsgesellschaft, EU-Bankenpaket und CRR III: Diese regulatorischen Neuerungen erwarten Institute im IRB-Ansatz, 2024.
12 CFR 217.100; Board of Governors of the Federal Reserve System, Fact sheet on the capital proposals, 19 March 2026.

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The IRB risk-weight formula

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Expected loss, provisions and the shortfall