A bank's lending capacity is not its capital ratio but its surplus over the ratio it intends to hold, divided by what each loan consumes, and below a certain risk weight the leverage ratio takes over.
A bank's additional lending capacity is its CET1 surplus over the ratio it intends to hold, divided by that target ratio times the risk weight of the new loans. For an illustrative bank with 2,400 million of CET1 against 20,000 million of RWA and a 10.5 per cent target, the 300 million surplus supports 2,857.1 million of unrated corporate loans, or 14,285.7 million of mortgages weighted 20 per cent. Below a risk weight of 10.53 per cent the leverage ratio binds first.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The question is asked in every budget round and answered badly in most of them, usually from the reported CET1 ratio. A 12 per cent ratio says how strong the bank is. It does not say how much it can grow, because growth consumes only the part of capital above the level the bank has committed to hold, and each loan type consumes it at a different rate.
| Item | Value |
|---|---|
| CET1 capital | 2,400 |
| Additional tier 1 | 300 |
| Risk-weighted assets, all risks | 20,000 |
| Leverage exposure measure | 50,000 |
| CET1 requirement including Pillar 2 and the combined buffer | 9.0% |
| Management buffer above it | 1.5% |
| CET1 target | 10.5% |
| Leverage ratio minimum plus management buffer | 3.0% + 0.5% = 3.5% |
The CET1 ratio is 12.00 per cent and the leverage ratio 5.40 per cent. Tier 1 and total capital requirements are assumed met by the AT1 and tier 2 the bank holds; where they are not, the gap is filled with CET1 and the surplus shrinks, as shown in the AT1 shortfall example.
Lending capacity = min( (CET1 − target × RWA) ÷ (target × RW), tier 1 ÷ leverage target − leverage exposure )
In Excel, with CET1 in B1, RWA in B2, target in B3, tier 1 in B4, leverage exposure in B5, leverage target in B6 and the loan's risk weight in B7: =MIN((B1-B3*B2)/(B3*B7),B4/B6-B5).
Step 1: the surplus. The target needs 10.5% × 20,000 = 2,100 of CET1. The surplus is 2,400 − 2,100 = 300 million. That is the only capital available for growth.
Step 2: the RWA it supports. 300 ÷ 10.5% = 2,857.1 million of new RWA. Every euro of surplus supports 9.52 euros of RWA.
Step 3: convert RWA to loans. Divide by the risk weight. Unrated corporates at 100 per cent: 2,857.1 of loans. Check: RWA become 22,857.1 and the CET1 ratio 2,400 ÷ 22,857.1 = 10.50 per cent, exactly the target.
Step 4: the leverage room. Tier 1 of 2,700 at a 3.5 per cent target allows exposure of 77,142.9, so 27,142.9 million more than today. Lending 2,857.1 of corporates takes the leverage ratio only to 5.11 per cent, so CET1 binds.
| New assets | Risk weight | Risk-based capacity | Leverage room | Capacity | Per euro of surplus |
|---|---|---|---|---|---|
| Unrated corporate loans | 100% | 2,857.1 | 27,142.9 | 2,857.1 | 9.52 |
| Corporates rated BBB, or regulatory retail | 75% | 3,809.5 | 27,142.9 | 3,809.5 | 12.70 |
| Residential mortgages, LTV 60% | 24.58% | 11,623.9 | 27,142.9 | 11,623.9 | 38.75 |
| Residential mortgages, LTV 50% | 20% | 14,285.7 | 27,142.9 | 14,285.7 | 47.62 |
| Covered bonds rated AAA | 10% | 28,571.4 | 27,142.9 | 27,142.9 | 90.48 |
The mortgage weights follow the EU loan-splitting approach: 20 per cent on the part of the loan up to 55 per cent of the property value and 75 per cent on the rest, so a loan at 60 per cent LTV weighs 24.58 per cent and one at 50 per cent weighs 20 per cent.
The leverage ratio binds when the risk-based capacity exceeds the leverage room: 300 ÷ (10.5% × 27,142.9) = 10.53 per cent. Above that weight, the CET1 surplus is the constraint; below it, tier 1 against the leverage target is. For this bank only very low-weighted assets reach the switch, which is why its growth question is a CET1 question. The structural version of the same test, for the whole balance sheet, is in when the leverage ratio binds.
| Change | CET1 surplus | Capacity |
|---|---|---|
| Base case, target 10.5% | 300 | 2,857.1 |
| Countercyclical buffer up 1 point, target 11.5% | 100 | 869.6 |
| RWA 5% higher, at 21,000, before any new lending | 195 | 1,857.1 |
| A year's retained profit of 200 | 500 | 4,761.9 |
| No management buffer, target 9.0% | 600 | 6,666.7 |
Capacity is a small difference between two large numbers, so it is far more volatile than the ratio. One point of countercyclical buffer takes the CET1 target from 10.5 to 11.5 per cent, a small move next to a 12.00 per cent ratio, and cuts corporate lending capacity by more than two-thirds. A 5 per cent inflation of RWA, from a model change or a rising output floor, removes a third of it before a single loan is written.
All figures are illustrative. Requirements, buffers and weights are bank and jurisdiction specific, and lending capacity is also limited by funding, large exposure limits and risk appetite.
The book's bank, with its capital stack, buffers and the constraint that actually binds, is in the free workbooks for this case.
One divided by the target ratio times the risk weight. At a 10.5 per cent CET1 target, one euro of surplus supports 9.52 euros of loans weighted 100 per cent, 12.70 at 75 per cent and 47.62 at 20 per cent. The multiplier is set by the target the bank holds, not by the 4.5 per cent minimum.
Because the buffers above the minimum are where distribution restrictions begin. Measured against 4.5 per cent, this bank's surplus is 1,500 million and its corporate lending capacity 33,333.3 million, 11.7 times the real figure, and lending it would take the CET1 ratio to 4.50 per cent, deep inside the combined buffer.
When the asset's risk weight is low enough that the risk-based capacity exceeds the room under the leverage target. Here tier 1 of 2,700 million at a 3.5 per cent target allows 27,142.9 million more exposure, so the leverage ratio binds for assets weighted below 10.53 per cent, such as AAA covered bonds at 10 per cent.
This article is one calculation from 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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