The CRR3 loan-splitting rule on one loan and on a 21.0 billion book, band by band and on the average loan, and why the two disagree by 248.5 basis points.
Under the EU's loan-splitting approach, the part of a residential mortgage up to 55 per cent of the property value is weighted at 20 per cent and the rest is weighted as an unsecured loan to the borrower, 75 per cent for a retail individual. A loan at 80 per cent loan-to-value therefore weighs 37.19 per cent. Applied to a whole book, the weight has to be computed loan by loan or band by band: on an illustrative 21.0 billion book that gives 27.75 per cent, against 25.26 per cent on the average loan, a difference of 521.9 million of risk-weighted assets.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Since 1 January 2025 the Capital Requirements Regulation, as amended by CRR3, no longer applies 35 per cent to the part of a residential mortgage up to 80 per cent of the property value under the standardised approach. Article 125 splits each eligible exposure at 55 per cent of the property value (after any prior-ranking charges). The part below carries 20 per cent. The part above is treated as an unsecured exposure to the counterparty, which for a qualifying retail individual means 75 per cent. Transitional arrangements for the output floor aside, that is the whole calculation.
Weight = 20% × min(1, 55% / LTV) + 75% × max(0, 1 − 55% / LTV)
Excel: =0.2*MIN(1,0.55/LTV)+0.75*MAX(0,1-0.55/LTV)
A loan of 400,000 against a property worth 500,000 is at 80 per cent LTV. The first 275,000, which is 55 per cent of the property value and 68.75 per cent of the loan, carries 20 per cent: 55,000 of risk-weighted assets. The remaining 125,000, or 31.25 per cent of the loan, carries 75 per cent: 93,750. Together 148,750, which is 37.19 per cent of the loan.
| LTV | Share at 20% | Share at 75% | Risk weight |
|---|---|---|---|
| 40% | 100.00% | 0.00% | 20.00% |
| 55% | 100.00% | 0.00% | 20.00% |
| 60% | 91.67% | 8.33% | 24.58% |
| 70% | 78.57% | 21.43% | 31.79% |
| 80% | 68.75% | 31.25% | 37.19% |
| 90% | 61.11% | 38.89% | 41.39% |
| 100% | 55.00% | 45.00% | 44.75% |
The curve has a shape that matters. It is flat at 20 per cent up to 55 per cent, kinks sharply there, and then rises ever more slowly: the first five points above the threshold add 4.58 points of weight, the last ten points to 100 per cent add 3.36.
Northbank plc, an illustrative European bank, has 21.0 billion of residential mortgages in five loan-to-value bands. Each band is weighted with the formula above and the results are averaged by balance.
| Band | Share of book | Average LTV | Band weight | Contribution | RWA |
|---|---|---|---|---|---|
| 1 | 38% | 42% | 20.00% | 7.60% | 1,596.0 |
| 2 | 27% | 63% | 26.98% | 7.29% | 1,530.0 |
| 3 | 22% | 75% | 34.67% | 7.63% | 1,601.6 |
| 4 | 10% | 85% | 39.41% | 3.94% | 827.6 |
| 5 | 3% | 95% | 43.16% | 1.29% | 271.9 |
| Book | 100% | 60.82% | 27.75% | 5,827.1 |
The book weighs 27.75 per cent (27.7483 to four places), or 5,827.1 million of risk-weighted assets.
The tempting shortcut is to take the book's average loan-to-value, 60.82 per cent, and put it through the formula once. That gives a secured share of 90.43 per cent and a weight of 25.26 per cent, or 5,305.2 million. The shortcut is 248.5 basis points light, which is 521.9 million of risk-weighted assets and, at Northbank's distribution trigger of 10.60 per cent, 55.3 million of common equity the plan does not hold.
The reason is the kink. Band 1 sits entirely below 55 per cent and cannot benefit from being averaged with anything; the average pulls the riskier bands down towards the flat part of the curve, where their unsecured slice shrinks. On this book that flatters.
It does not always flatter. Above the threshold the curve is concave, so averaging overstates. Take only the 62 per cent of the book above 55 per cent LTV: band by band it weighs 32.50 per cent, while its average loan at 72.35 per cent weighs 33.19. There the shortcut is 69.5 basis points too heavy. The sign depends on how much of the book sits below the kink, which is why neither direction can be assumed.
The old flat weight has not disappeared from the rulebook. The net stable funding ratio gives a 65 per cent required funding factor to residential mortgages of a year or more carrying a risk weight of 35 per cent or less, and 85 per cent to those above. Under the split, a loan crosses 35 per cent at an LTV of 75.63 per cent. The test reads each loan's own weight, not the portfolio's. Northbank's book averages 27.75 per cent, yet bands 4 and 5, 13 per cent of the book, sit above 35 per cent on their own weights and take the 85 per cent factor.
The mistake is computing the weight on aggregated data: an average LTV, or LTV buckets so wide that a single bucket straddles 55 per cent. Both feed the formula numbers that no loan actually has. The fix is to compute at the lowest level the data allows, ideally loan by loan with current property values, and to report the average-loan figure only as a check whose sign you can explain.
The split, both ladders and the output floor are rebuilt in the free workbook for this case, and the capital the extra weight consumes is followed through in whether an additional tier 1 shortfall cuts headroom.
Under the loan-splitting approach the part of the exposure up to 55 per cent of the property value takes 20 per cent and the remainder is weighted as unsecured exposure to the borrower, 75 per cent for a qualifying retail individual. A loan at 55 per cent LTV or below weighs 20 per cent; at 80 per cent it weighs 37.19; at 100 per cent, 44.75. The property must meet the eligibility conditions of the regulation.
Not reliably. The weight is flat at 20 per cent up to 55 per cent LTV and curves above it, so averaging the loans first gives a different answer from weighting each loan. On the worked book the average-loan shortcut gives 25.26 per cent against 27.75 band by band; on the part of the book above 55 per cent it overstates by 69.5 basis points instead.
With a 20 per cent weight up to 55 per cent of value and 75 per cent on the remainder, the weight reaches 35 per cent at an LTV of 75.63 per cent. That matters beyond capital: the net stable funding ratio gives the 65 per cent funding factor only to mortgages at or below a 35 per cent weight, so in the example 13 per cent of the book funds at 85 per cent.
The band-by-band split and the average-loan shortcut are discussed in chapter 4 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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