The ratio is one division. The useful number is the density of risk-weighted assets below which the backstop, not the risk-based trigger, becomes the constraint.
A bank's leverage ratio is tier 1 capital divided by its exposure measure: on-balance-sheet exposures, derivatives and securities financing at exposure value, and off-balance-sheet commitments after credit conversion factors. Northbank holds 4,580 million of tier 1 against 83,970 million of exposure, a leverage ratio of 5.4543 per cent against a 3 per cent minimum. It binds before the risk-based distribution trigger only if risk-weighted assets fall below 25.10 per cent of exposure; Northbank runs at 35.62.
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, a domestic systemically important institution, so the 3 per cent minimum applies without the buffer reserved for global systemic banks. Figures are in millions of euros at the model date.
| Item | Value |
|---|---|
| Common equity tier 1 | 4,060.0 |
| Additional tier 1 | 520.0 |
| Tier 1 | 4,580.0 |
| Total assets | 80,240.0 |
| Risk-weighted assets | 29,908.9 |
| Leverage ratio requirement | 3% |
| CET1 distribution trigger | 10.595% |
The measure starts from the balance sheet, without risk weights and without netting of most collateral. Northbank's 80,240.0 million of assets already carries its derivatives at the SA-CCR exposure value, 1,480.0 million, which includes the 1.4 multiplier, and its securities financing at 2,360.0 million. Off-balance-sheet items are added after conversion factors, which turn an undrawn commitment into the share expected to be drawn.
| Line | Nominal | Conversion factor | Exposure |
|---|---|---|---|
| On-balance-sheet exposures, derivatives and SFTs | 80,240.0 | ||
| Committed credit lines to corporates | 7,200 | 40% | 2,880.0 |
| Guarantees and sureties given | 1,100 | 50% | 550.0 |
| Unconditionally cancellable lines | 3,000 | 10% | 300.0 |
| Exposure measure | 11,300 | 83,970.0 |
A full regulatory return goes further on two lines: securities financing transactions are measured gross with a counterparty add-on, and amounts deducted from tier 1, such as intangibles, are also deducted from the exposure so the numerator and denominator stay consistent. The structure is the same.
Leverage ratio = tier 1 / exposure measure
= 4,580.0 / 83,970.0 = 5.4543 per cent
Required tier 1 = 3% × 83,970.0 = 2,519.1; surplus = 2,060.9 million, or 2.4543 points
Excel: =(CET1+AT1)/(OnBS+SUMPRODUCT(OffNominal,CCF))
Read as capacity, the leverage ratio would allow the exposure measure to reach 4,580.0 / 3% = 152,666.7 million, 68,696.7 million more than today, or 1.82 times the current balance sheet.
A leverage ratio of 5.45 per cent tells you little until it is set against the risk-based constraint. On the risk-based side, Northbank's CET1 of 4,060.0 million supports risk-weighted assets up to the distribution trigger: 4,060.0 / 10.595% = 38,320.0 million. On the leverage side, tier 1 supports an exposure measure of 152,666.7 million. The ratio of the two is the density of risk-weighted assets at which both run out together.
Switching density = (CET1 / trigger) / (tier 1 / 3%)
= 38,320.0 / 152,666.7 = 25.10 per cent
Northbank's density = 29,908.9 / 83,970.0 = 35.62 per cent, 1,051.8 basis points above the switch
Above the switch, the risk-based trigger binds first. Growing at today's density, Northbank reaches the distribution trigger after 23,614.3 million of new exposure, while the leverage ratio would allow 68,696.7 million, 2.9 times as much. Below the switch, the order reverses and the leverage ratio becomes the requirement that decides the balance sheet.
Two things lower the density: lower internal-model risk weights, and growth in exposures that carry no risk weight, such as central bank reserves. The first is limited by the output floor: in the model year the floor holds risk-weighted assets at no less than 24,653.8 million, a density of 29.36 per cent, still above the switch, so lower internal weights alone cannot make leverage bind. The second has no such limit.
| Reserves added | Exposure measure | Leverage ratio | RWA density |
|---|---|---|---|
| 0.0 | 83,970.0 | 5.45% | 35.62% |
| 10,000.0 | 93,970.0 | 4.87% | 31.83% |
| 20,000.0 | 103,970.0 | 4.41% | 28.77% |
| 35,186.9 | 119,156.9 | 3.84% | 25.10% |
The CET1 ratio does not move in any row, because reserves carry a zero risk weight. The leverage ratio falls by more than a point and a half. At 35,186.9 million of additional reserves, the kind of inflow a bank receives when deposits arrive faster than it can lend, the two constraints meet. This is exactly the situation the leverage ratio was designed for: a balance sheet that grows without its risk-weighted assets noticing.
The table follows the Basel text and the EU rule, under which central bank reserves count in the exposure measure. The EU allows a temporary exclusion only when the supervisor declares exceptional circumstances, with the 3 per cent requirement recalibrated upwards to offset it; the UK leverage framework excludes qualifying central bank claims altogether, which would leave this bank's ratio unchanged as reserves grow.
Three slips recur. Using CET1 instead of tier 1 gives 4.84 per cent and understates the ratio. Using total assets alone, without the off-balance-sheet lines, gives 5.71 and overstates it. Adding the off-balance-sheet lines at their full nominal of 11,300 gives an exposure of 91,540.0 and 5.00 per cent, understating it again, because the conversion factors belong in the measure. A fourth mistake is conceptual: reporting the leverage ratio as a level, when the decision-relevant figure is its distance from the switching density. The capital stack it sits beside, including the additional tier 1 that counts here and not in the CET1 ratio, is in whether an additional tier 1 shortfall cuts headroom.
The measure, the switching density and the floor's effect on it are live in the free workbook for this case; the floor itself is worked in how to calculate the output floor.
Three per cent of tier 1 capital over the exposure measure, with an additional buffer for global systemically important banks equal to half their G-SIB capital buffer. Northbank, a domestic systemic bank, needs 2,519.1 million of tier 1 against its 83,970 million exposure and holds 4,580 million, a ratio of 5.4543 per cent and a surplus of 2,060.9 million.
Tier 1, which is common equity tier 1 plus additional tier 1. Using CET1 alone understates the ratio: for Northbank 4,060 / 83,970 gives 4.84 per cent instead of 5.45. This is one reason banks close to the leverage minimum issue additional tier 1 instruments, which count in the leverage numerator but not in the CET1 ratio.
Because its assets carry low risk weights. If risk-weighted assets are a small share of the exposure measure, the risk-based ratio looks strong while tier 1 is thin against the balance sheet. For Northbank the leverage ratio becomes the binding constraint only below a density of 25.10 per cent; adding 35,186.9 million of zero-weighted reserves would bring it there.
The exposure measure, the ratio and the switching density are computed in the workbook for chapters 7 to 10 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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