The floor is one comparison per year, made on the whole bank. The year it binds is a result of two ladders, and after it binds lower internal weights buy nothing.
The output floor sets a bank's risk-weighted assets at the higher of its internal-model figure and a floor rate times the fully standardised figure. Northbank runs 29,908.9 million of internal-model risk-weighted assets against 44,825.1 million standardised, a ratio of 66.72 per cent, so the floor first binds in 2029 when the EU rate reaches 70 per cent, and in 2030 at 72.5 per cent it adds 2,589.3 million and takes 108.2 basis points off the CET1 ratio.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Northbank plc is the fictional European bank of Financial Regulation, with 80,240 million of assets and 4,060 million of common equity tier 1. Every exposure is weighted twice: once on the standardised ladder, with the mortgage book split at 55 per cent of property value, and once with internal models. Figures in millions of euros.
| Block | Standardised | Internal models |
|---|---|---|
| Credit risk, on balance sheet | 35,620.1 | 22,949.4 |
| Credit risk, off balance sheet | 2,935.0 | 1,629.5 |
| Market risk | 1,950.0 | 1,240.0 |
| Operational risk | 3,680.0 | 3,680.0 |
| Credit valuation adjustment | 640.0 | 410.0 |
| Total risk-weighted assets | 44,825.1 | 29,908.9 |
Operational risk carries the same figure on both ladders, because there is now one approach and no internal option. The floor compares totals, so all four blocks are in it.
RWA = max(internal-model RWA, x × standardised RWA)
The floor binds when x > internal / standardised = 29,908.9 / 44,825.1 = 66.72 per cent
Excel, year in A, rate in B: =MAX(RWA_IRB,B8*RWA_SA) and the first binding year =INDEX(A8:A13,MATCH(TRUE,INDEX(B8:B13*RWA_SA>RWA_IRB,0),0))
The comparison is made once, on the whole bank. In the EU, CRR3 also adds an adjustment for the difference in how the two approaches treat provisions, which is nil here, and allows until the end of 2029 a cap that limits the floored figure to 125 per cent of the unfloored one, 37,386.1 million for Northbank. The floored amounts below stay under it, so it changes nothing. CRR3 also offers, until the end of 2032, two optional reliefs inside the standardised figure used for the floor: a 65 per cent weight for unrated corporates with an internal PD of 0.5 per cent or less, and a reduced weight, 10 per cent at first and rising in steps, on the secured part of qualifying residential mortgages. Northbank's case applies neither, so the standardised ladder here is the full one; with the mortgage relief the floor would bind later.
| Year | Floor rate | Floor | RWA used | Added by floor | CET1 ratio |
|---|---|---|---|---|---|
| 2025 | 50.0% | 22,412.6 | 29,908.9 | 0.0 | 13.57% |
| 2026 | 55.0% | 24,653.8 | 29,908.9 | 0.0 | 13.57% |
| 2027 | 60.0% | 26,895.1 | 29,908.9 | 0.0 | 13.57% |
| 2028 | 65.0% | 29,136.3 | 29,908.9 | 0.0 | 13.57% |
| 2029 | 70.0% | 31,377.6 | 31,377.6 | 1,468.7 | 12.94% |
| 2030 | 72.5% | 32,498.2 | 32,498.2 | 2,589.3 | 12.49% |
At today's capital the common equity ratio falls from 13.5746 per cent to 12.9392 in 2029 and 12.4930 in 2030: 63.5 and then 108.2 basis points. Holding the ratio at 13.5746 would take 351.5 million of additional common equity by 2030. Even at the distribution trigger of 10.595 per cent, the extra 2,589.3 million of risk-weighted assets consumes 274.3 million of capital.
The date is a result, not a fact about the calendar. It comes from the ratio of the two ladders, and anything that moves either ladder moves it.
| Variant | Internal RWA | Ratio to standardised | First binding year | CET1 today | CET1 2030 |
|---|---|---|---|---|---|
| As reported | 29,908.9 | 66.72% | 2029 | 13.57% | 12.49% |
| Large corporates 40% to 55% | 32,083.9 | 71.58% | 2030 | 12.65% | 12.49% |
| Mortgages 13.5% to 10% | 29,173.9 | 65.08% | 2029 | 13.92% | 12.49% |
| Large corporates 40% to 30% | 28,458.9 | 63.49% | 2028 | 14.27% | 12.49% |
| All internal credit weights 10% lower | 27,451.0 | 61.24% | 2028 | 14.79% | 12.49% |
Read the last column. Once the floor binds, every variant ends at the same 12.49 per cent, because the bank's risk-weighted assets are then 72.5 per cent of the standardised ladder whatever the models say. A model change that lowers internal weights raises today's ratio and brings the binding year forward; it buys nothing in 2030. From the year the floor binds, the standardised ladder is the one to manage, and the mortgage loan split, worked in how loan splitting sets a mortgage risk weight, becomes a line in the bank's real capital requirement.
The error is applying the floor portfolio by portfolio, as if each book had to carry 72.5 per cent of its own standardised figure. Northbank's mortgages carry 2,835.0 million on internal models against 5,827.1 million standardised, 48.7 per cent; floored alone they would add 1,389.7 million. Large corporates, at 53.3 per cent, would add 2,084.4 million. Summed line by line, the 2030 figure becomes 35,060.1 million, 2,561.8 million too high, and the CET1 ratio reads 11.58 per cent instead of 12.49.
The rule is aggregate: books whose models land above the floor rate, such as defaulted exposures and equities on the same weight on both ladders, offset those well below it. The line-by-line view is still useful, as a map of where the floor's cost comes from, and some banks price new lending on the higher of the two weights. It is not the requirement.
Internal-model weights for corporate loans come from the IRB formula; how one is computed from PD, LGD and maturity is in the IRB risk weight of a corporate loan.
Both ladders, line by line, with the floor across all six years and the binding year read by lookup, are in the free workbook for this case.
When the floor rate exceeds the ratio of internal-model to standardised risk-weighted assets. Northbank's ratio is 66.72 per cent, so the EU schedule's 65 per cent in 2028 does not bind and its 70 per cent in 2029 does, adding 1,468.7 million of risk-weighted assets. Lower the internal weights and the ratio falls, bringing the binding year forward.
To the whole bank: one comparison of total internal-model against total standardised risk-weighted assets, across credit, market, operational and CVA risk. Applied line by line it would overstate the 2030 figure here by 2,561.8 million, because portfolios where models give low weights, such as mortgages at 48.7 per cent of standardised, would be floored without credit for those above the rate.
Under CRR3 the floor rate is 50 per cent in 2025, 55 in 2026, 60 in 2027, 65 in 2028, 70 in 2029 and 72.5 from 2030. The Basel text ran the same steps from 2023 to 2028. For Northbank the 2030 rate takes risk-weighted assets to 32,498.2 million and needs 351.5 million more common equity to keep a 13.5746 per cent ratio.
The output floor is dated across all six years of its schedule, with the binding year looked up rather than typed, in the workbook for chapters 2 to 6 of Financial Regulation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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