The large exposures test worked on one group of connected clients, with the conversion factors, the collateral, and the capital base that turns a breach into false headroom.
A bank's large exposure limit is 25 per cent of its tier 1 capital, measured against everything it is owed by a group of connected clients after conversion factors and eligible collateral. With tier 1 of 4,580 million the limit is 1,145.0 million, and a connected group carrying 1,284.0 million of exposure is 139.0 million over the limit, at 28.03 per cent of tier 1. Measured on total own funds, as is sometimes done by habit, the same exposure would look 88.5 million inside it.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The Basel large exposures framework, and Article 395 of the CRR in the EU since CRR2, caps a bank's exposure to a single client or group of connected clients at 25 per cent of tier 1 capital. Any exposure of 10 per cent of tier 1 or more is a large exposure and must be reported. Exposures between global systemically important banks are capped at 15 per cent. Clients are connected when one controls the others, or when they are so economically interdependent that the failure of one would probably bring down the rest.
The bank is Northbank, the fictional bank of the book's companion workbooks: common equity tier 1 of 4,060 million, additional tier 1 of 520 and tier 2 of 910, so tier 1 of 4,580 and total own funds of 5,490. Its largest connected counterparty totals 1,284 million; the split of that exposure across the group below is illustrative.
| Entity | Item | Nominal | CCF | Exposure |
|---|---|---|---|---|
| Parent | Term loan | 700 | 100% | 700.0 |
| Subsidiary A | Revolving facility, drawn | 200 | 100% | 200.0 |
| Subsidiary A | Revolving facility, undrawn | 450 | 40% | 180.0 |
| Subsidiary B | Bonds held | 150 | 100% | 150.0 |
| Subsidiary B | Derivatives, SA-CCR exposure value | 104 | 100% | 104.0 |
| Subsidiary B | Performance guarantee issued | 200 | 50% | 100.0 |
| Gross exposure | 1,434.0 | |||
| Less cash collateral on the parent loan | -150.0 | |||
| Exposure after credit risk mitigation | 1,284.0 | |||
Exposure value = Σ on-balance-sheet amounts + Σ (off-balance-sheet nominal × CCF) + derivative exposure values − eligible credit risk mitigation
Limit = 25% × tier 1 = 25% × 4,580 = 1,145.0
Test: exposure / tier 1 = 1,284.0 / 4,580 = 28.03% > 25%
Excel, with the table in B:F: =SUMPRODUCT(D2:D7,E2:E7)-150 for the exposure in F10, =F10/(4060+520) for the ratio.
Before CRR2, the EU measured large exposures against eligible capital that could include a slice of tier 2. Spreadsheets and habits built on that definition survive. On total own funds of 5,490 the limit is 1,372.5, the exposure is 23.39 per cent and the bank appears to have 88.5 million of headroom. Nothing about the exposure has changed; the base has manufactured 227.5 million of room that does not exist. Tier 2 absorbs losses only once the bank is failing, and the large exposure limit is meant to keep a single default from getting it there.
Additional tier 1 does count. Without its 520 of AT1, the bank's limit would be 1,015.0 and the excess 269.0, which is one reason an AT1 call that is not replaced reaches well beyond the capital ratios.
| Scenario | Exposure | Limit | Headroom | Share of base |
|---|---|---|---|---|
| As measured | 1,284.0 | 1,145.0 | -139.0 | 28.03% |
| Cancel 347.5 of the undrawn line | 1,145.0 | 1,145.0 | 0.0 | 25.00% |
| Take 139.0 more cash collateral | 1,145.0 | 1,145.0 | 0.0 | 25.00% |
| Sell the 150 of bonds | 1,134.0 | 1,145.0 | 11.0 | 24.76% |
| Issue 556 of AT1 | 1,284.0 | 1,284.0 | 0.0 | 25.00% |
| Measured on total own funds (wrong base) | 1,284.0 | 1,372.5 | 88.5 | 23.39% |
The conversion factor makes undrawn commitments the cheapest lever and the hardest to pull: every euro of commitment cancelled frees only 40 cents of exposure, so the bank must cancel 347.5 of the client's 450 line to cure a 139.0 excess. Selling the bonds is the only option on the list that leaves real room. Raising 556 of tier 1 to accommodate one client is a measure of how large the breach is, not a remedy anyone would choose.
The same tier 1 figure is the numerator of the leverage ratio; see how to calculate a bank's leverage ratio. The CET1 inside it is built in how to calculate the CET1 ratio.
The limit on both bases, with the exposure as an input you can move, is in the free workbooks for this book.
25 per cent of tier 1 capital for exposure to one client or a group of connected clients, after credit conversion factors and eligible credit risk mitigation, under the Basel framework and Article 395 of the CRR. Between global systemically important banks it is 15 per cent. A bank with tier 1 of 4,580 million may hold up to 1,145.0 million against one group.
When it reaches 10 per cent of tier 1 capital, after conversion factors and mitigation. It must then be reported, even if it is far below the 25 per cent limit. For a bank with tier 1 of 4,580 million that threshold is 458.0 million; in the worked case the parent company alone, at 550.0, is a large exposure.
Yes, at the standardised credit conversion factor, 40 per cent for most commitments under the final Basel III rules. An undrawn 450 million revolver counts as 180.0. Taking it at nominal overstates the exposure by 270.0, and ignoring it can turn a breach into an apparent pass.
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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