Risk-weighted assets · RiskAtoms Academy

By the end you will be able to

1List the parts of RWA (credit, counterparty credit, CVA, market and operational risk) and the size of each on RiskAtoms Bank plc's book.
2Explain the 12.5 factor and turn a capital charge into RWA and back.
3Outline the output floor: the 72.5% of standardised RWA, its phase-in, and when it binds.
4Say what drives each part of RWA, and read RWA density across a book and across banks.

Why it matters

Every capital ratio in L4.1.01: Capital ratios and the capital stack divides by the same number. For RiskAtoms Bank plc it is £22,807.7m, against £67,000m of assets. The capital is the easy half: it is in the accounts. RWA are built line by line from models, tables and formulas, and the same £100 of mortgage counts as £12 under the bank's models and £30 under the standardised approach. Which one wins is decided by the output floor.

Core explanation

Five risks, one denominator

The parts

Basel III's total risk-weighted assets are the sum of credit risk (counterparty credit included), CVA, market and operational risk, floored at 72.5% of the standardised total (RBC20.4). Credit risk is weighted exposure: a risk weight times an exposure at default. The others are measured as a capital charge and multiplied by 12.5. On the book:

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.

Part	Approach	RWA as used	Share	Capital at 8%	Standardised RWA
Credit: corporatesCRE31, CRE32	Foundation IRB	8,934.7	41.4%	714.8	13,412.2
Credit: mortgagesCRE31, CRE32	Retail IRB	3,526.3	16.4%	282.1	8,949.6
Credit: other portfoliosCRE20, CRE22	Standardised	5,277.0	24.5%	422.2	5,277.0
Counterparty creditCRE52	SA-CCR	31.2	0.1%	2.5	31.2
CVAMAR50	Reduced BA-CVA	48.6	0.2%	3.9	48.6
MarketMAR20–21	FRTB SA (simplified)	417.7	1.9%	33.4	417.7
OperationalOPE25	Standardised (ILM = 1)	3,322.7	15.4%	265.8	3,322.7
Sum		21,558.1	100%	1,724.7	31,459.0
Output floor add-on	72.5% × 31,459.0	1,249.6		100.0
Total RWA		22,807.7		1,824.6

Credit risk is 82% of RWA as used. Operational risk is the next largest; the bank's small trading desk and handful of derivatives add little. Only the two IRB portfolios differ between the columns: everything else is standardised already.

The 12.5 factor

L2.7.03: Basel II: three pillars introduced it: 12.5 is 1 ÷ 8%. A capital charge K becomes RWA of 12.5K, whose 8% minimum is K again. Basel III writes it into each standard: market risk RWA are found by “multiplying the capital requirements” by 12.5 (MAR20.1), CVA likewise (MAR50.1), and “RWA for operational risk are equal to 12.5 times” the operational risk capital (OPE25.2). It hides inside the IRB formula too: an IRB risk weight is 12.5 times the capital K per £1 of exposure that L3.3.11: Unexpected loss and default correlation derived. On the book:

Charge	Capital K (£m)	× 12.5 = RWA (£m)
CVA (reduced BA-CVA)	3.89	48.6
Market (FRTB SA, high-correlation scenario)	33.41	417.7
Operational (BIC, ILM = 1)	265.81	3,322.7

With Basel's internal loss multiplier of 1.093 the operational figure would be £3,631.1m. The book follows the UK, where the ILM is 1 (L3.7.07: Measuring frequency and severity).

What drives each part

Part	What moves it	In detail
Credit, standardised	Exposure, external rating, loan-to-value, exposure class, credit conversion factors for undrawn lines	L4.2.01: The standardised approach: corporates, banks and sovereigns, L4.2.02: The standardised approach: retail and real estate, L4.2.03: Off-balance sheet items and other exposures
Credit, IRB	PD, LGD, maturity and the asset correlation in the formula; EAD	L4.2.04: The IRB approach, L4.2.05: The IRB risk-weight formula, L4.2.06: IRB for retail and specialised lending
Counterparty credit	Replacement cost and potential future exposure under SA-CCR: netting, margin, the trades' maturity and volatility	L4.4.01: SA-CCR: replacement cost and the multiplier, L4.4.02: SA-CCR: the add-ons
CVA	The counterparties' sector and rating, the netting sets' maturity and EAD (here £36.9m)	L4.3.09: CVA capital: the basic approach
Market	Sensitivities to each risk factor times regulatory risk weights, aggregated with correlations under three scenarios	L4.3.02: The sensitivities-based method: delta and vega, L4.3.08: Total market risk capital
Operational	The business indicator, a measure of size from the income statement (here £1,948.1m), and in Basel the loss history through the ILM	L4.4.05: Operational risk: the standardised approach

Sort itWhich part moves?

Each change raises the bank's RWA. Which part of RWA does it land in?

House prices fall, so mortgage loan-to-values rise
A corporate borrower is downgraded from A to BBB
An interest rate swap counterparty stops posting margin
The trading desk doubles its FTSE 100 futures position
Net interest income rises by a quarter
The bank sells a large unhedged FX forward to a hedge fund

The output floor, in outline

Internal models give lower RWA than the standardised approaches for the same book: that is why banks use them. Basel III limits the gap. Total RWA are the higher of RWA as used and 72.5% of the standardised RWA (RBC20.4, RBC20.11). RBC20.13's own example: RWA as used of 76 against standardised RWA of 140 give 72.5% × 140 = 101.5. On the book the floor binds: 72.5% × £31,459.0m = £22,807.7m, above the £21,558.1m as used, so the add-on is £1,249.6m. The floor would just bind at a factor of 68.53%.

Year	Basel (RBC90.1)	UK (Art 92(5))	The book's RWA, UK factor
2023	50.0%	None	21,558.1 (no floor)
2024	55.0%	None	21,558.1 (no floor)
2025	60.0%	None	21,558.1 (no floor)
2026	65.0%	None	21,558.1 (no floor)
2027	70.0%	60.0%	21,558.1
2028	72.5%	65.0%	21,558.1
2029	72.5%	70.0%	22,021.3 (binds)
2030	72.5%	72.5%	22,807.7 (binds)

Under the UK's phase-in the book's floor would first bind in 2029, at 70%. How the floor is calculated, its UK and EU adjustments, and what it does to IRB banks are in L4.2.09: The output floor.

RWA density

RWA density compares RWA with the balance sheet. The book's is 34.0%: 32.2% on RWA as used and 47.0% if everything were standardised. By portfolio, per £1 of exposure:

Portfolio	As used	Standardised	Ratio
Central bank reserves, gilts	0%	0%
Mortgages (retail IRB)	11.7%	29.6%	0.39
Corporate loans (F-IRB)	58.0%	87.1%	0.67
Whole bank, RWA ÷ total assets	32.2%	47.0%	0.69

Density reflects both the assets and the approach. Two banks with the same mortgages can show different densities because one uses models and the other does not, and a low density can mean safe assets or optimistic models. That gap is what the output floor narrows and what the leverage ratio of L4.1.06: The leverage ratio ignores altogether.

The formal version

Summing over every banking book exposure i (M-A08: Summation notation), with x the output floor factor:

\text{RWA} = \max\!\Big(\underbrace{\sum_{i} \text{RW}_i\,\text{EAD}_i + \text{RWA}_{\text{CCR}} + 12.5\,\big(K_{\text{CVA}} + K_{\text{mkt}} + K_{\text{op}}\big)}_{\text{RWA as used}},\ x \cdot \text{RWA}_{\text{SA}}\Big)

For an IRB exposure, with K the capital per £1 of EAD from the IRB formula:

\text{RW}_i = 12.5 \times K_i, \qquad \text{RWA}_i = 12.5 \times K_i \times \text{EAD}_i

And the floor binds when $x > \text{RWA}_{\text{used}} / \text{RWA}_{\text{SA}}$ , here 68.53%.

Try it

Push the IRB slider down with the floor at 72.5%: does total RWA move? Now set the floor to None. Then raise the market or operational charge and watch both bars grow.

Try itBuild the RWA

IRB credit RWA, % of today's100%

Market risk capital, % of today's100%: £33.4m

Operational risk capital, % of today's100%: £265.8m

Output floor

As used (modelled): £21,558.1m

All standardised: £31,459.0m

Credit
CCR and CVA
Market
Operational
Floor add-on
Dashed: the floor

Total RWA£22,807.7m

CET1 ratio13.24%

Floor binds?Yes

Floor add-on£1,249.6m

Market RWA = 12.5 × capital£417.7m

Operational RWA = 12.5 × capital£3,322.7m

Break-even floor factor68.53%

Pillar 1 total capital, 8% of RWA£1,824.6m

The floor binds: moving the IRB slider changes nothing until modelled RWA climb back above the floor. Market and operational risk still count, because they are in both totals.

CET1 held at the book's figure. The UK floor adds an adjustment for provisions (OF-ADJ) that this sketch leaves out (L4.2.09). Illustrative data, £ millions.

Worked example

RiskAtoms Bank plc's RWA, part by part

£ millions, from the book above.

From exposures to total RWA

Step 1 of 6

1
Credit risk
$\underbrace{8{,}934.7}_{\text{corporates, F-IRB}} + \underbrace{3{,}526.3}_{\text{mortgages, IRB}} + \underbrace{5{,}277.0}_{\text{standardised}} = 17{,}738.1$

Regulatory lens

RBC20 sets out how the parts combine and the floor; each risk has its own standard (CRE for credit, MAR for market and CVA, OPE for operational risk). Modules 4.2 to 4.4 take them in turn.

In the UK

From 1 January 2027 the PRA Rulebook sets total risk exposure as the higher of the un-floored amount and x times the standardised amount plus an adjustment, OF-ADJ, that reflects differences in how provisions are treated under IRB and the standardised approach: it is built from the provision amounts that count in, or are deducted from, own funds (Required Level of Own Funds (CRR) Part, Article 92(2A)). The factor x is 60% in 2027, 65% in 2028, 70% in 2029 and 72.5% after (Article 92(5) and (2A)). Article 92(4)(b) uses the same factor of 12.5. The book applies the full 72.5% and leaves OF-ADJ out; L4.2.09: The output floor and L4.1.08: Basel 3.1 from 2027: UK, EU and US come back to both.

Spark Atoms

Spark AtomWhen models stop mattering

With the floor binding, a model that cut the bank's IRB RWA by £500m would leave total RWA at £22,807.7m: the add-on would simply grow to £1,749.6m. A saving counts in full only if modelled RWA stay above the floor after it, and each saving lowers the break-even: 68.53% today, 66.94% after this cut. Only with a floor factor below 66.94% would all £500m count.

Spark AtomMortgages at a fraction

The bank's IRB mortgages carry 11.7% of RWA per £1, against 29.6% standardised, 0.39 of it; its corporates carry 0.67. On this book mortgages are where the models save the most, so they are where the floor takes most of the saving back.

Key takeaways

RWA add up credit (weighted exposure, counterparty credit included), CVA, market and operational risk. On the book: £21,558.1m as used, 82% of it credit.
Capital charges become RWA by multiplying by 12.5 = 1 ÷ 8%; an IRB risk weight is 12.5 × K too.
The output floor sets RWA at no less than 72.5% of standardised RWA: £22,807.7m on the book, an add-on of £1,249.6m. The UK phases it in from 60% in 2027.
Each part has its own drivers: ratings, LTVs, PD and LGD for credit; netting and margin for CCR; sensitivities for market risk; the business indicator for operational risk.
RWA density, RWA over assets, is 34.0% for the book. It mixes the riskiness of the assets with the approach used to measure them.

Reaction

Check what stuck

Question 1 · objective 2

A bank's market risk capital charge is £40m. What does it add to RWA, in £m?

£m

Question 2 · objective 3

A bank's RWA as used are £30,000m. With every risk on the standardised approaches they would be £45,000m. With the full output floor, what are its RWA, in £m?

£m

Question 3 · objective 2

Why are the market, CVA and operational risk capital charges multiplied by 12.5?

A12.5 is 1 ÷ 8%, so the 8% minimum on the resulting RWA equals the charge, and every risk sits in one denominatorBTo add a safety margin of 12.5% to the chargesCBecause those risks are 12.5 times riskier than credit riskDTo convert annual losses into a ten-day horizon

Question 4 · objective 3

A bank's RWA as used are £21,000m and its standardised RWA £30,000m. Above what floor factor, in %, does the output floor bind?

%

Question 5 · objective 4

RiskAtoms Bank plc's floor binds. A better mortgage model would cut its IRB credit RWA by £500m. What happens to its total RWA?

ANothing: total RWA are set by the floor, which depends only on the standardised figuresBThey fall by £500mCThey fall by 72.5% of £500mDThey rise, because the floor add-on grows by more than the saving

Glossary

Risk-weighted assets (RWA): Risk-weighted assets: exposures weighted by their riskiness, plus 12.5 times the capital charges for CVA, market and operational risk. The denominator of every capital ratio.
Risk weight: Risk weight: the share of an exposure that counts towards RWA. Set by the standardised tables, or by the IRB formula as 12.5 × K.
Exposure at default (EAD): Exposure at default: what the bank expects to be owed if the borrower defaults, including drawn amounts and a share of undrawn commitments.
Capital charge: Capital charge K: an amount of capital the rules ask for directly, as for market, CVA and operational risk. RWA = 12.5 × K.
12.5 factor: 12.5 = 1 ÷ 8%. It turns a capital charge into the RWA whose 8% minimum is exactly that charge, so all risks share one denominator.
RWA as used: RWA as used: the sum of the parts under the approaches the bank is approved to use, internal models included. Sometimes called un-floored RWA.
Standardised RWA: Standardised RWA: the same sum with every risk on the standardised approaches. The output floor's base (RBC20.11).
Output floor: Output floor: total RWA may not fall below 72.5% of the RWA the bank would have with every risk on the standardised approaches (RBC20.4).
Floor add-on: Floor add-on: the RWA the output floor adds when it binds, the floor less the RWA as used.
RWA density: RWA density: RWA divided by total assets (or by an exposure). A rough measure of how risky, or how modelled, a book is.

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, RBC20: Calculation of minimum risk-based capital requirements: two pages that hold the whole structure of this lesson, with the floor example. Intermediate.

Origins

Basel Committee on Banking Supervision, RBC20, paras 20.4, 20.9–20.13 (version effective 1 January 2023), and RBC90, para 90.1, bis.org.
Basel Committee on Banking Supervision, MAR20, para 20.1, MAR50, para 50.1, and OPE25, para 25.2, bis.org.
Prudential Regulation Authority, PRA Rulebook: Required Level of Own Funds (CRR) Part, Article 92(2A), (4) and (5), version in force from 1 January 2027.
Prudential Regulation Authority, PS1/26, 20 January 2026, paras 1.23–1.24.

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