The IRB expected loss versus provisions comparison, worked on performing and defaulted books, with the 0.6 per cent Tier 2 cap on any surplus.
An IRB bank compares its regulatory expected loss with its eligible provisions; where expected loss is higher, the shortfall is deducted from CET1 in full. The comparison is not one netted total: provisions on defaulted loans cannot cover expected loss on performing ones. On an illustrative book with a 60.1 shortfall on performing exposures and a 75.0 surplus on defaulted ones, the deduction is 60.1, not zero, and the CET1 ratio falls from 12.00 to 11.60 per cent, 40 basis points.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Under the standardised approach, provisions simply reduce the exposure value. Under the internal ratings-based approach they do something different: the bank's risk-weighted assets cover unexpected loss only, and expected loss is meant to be covered by provisions. The rule that enforces this is the EL-provision comparison. A shortfall comes straight off CET1; a surplus can be added to Tier 2 capital, but only up to 0.6 per cent of IRB credit risk-weighted assets. The asymmetry is what makes the calculation worth doing line by line.
EL = PD × LGD × EAD, summed across exposures, with the bank's IRB parameters
Excel: =SUMPRODUCT(EAD,PD,LGD)
| Segment | EAD | PD | LGD | EL |
|---|---|---|---|---|
| Large corporates | 15,000 | 1.0% | 40% | 60.0 |
| SME corporates | 5,000 | 3.0% | 35% | 52.5 |
| Residential mortgages | 18,000 | 0.8% | 15% | 21.6 |
| Consumer loans | 2,000 | 4.0% | 70% | 56.0 |
| Performing book | 40,000 | 190.1 |
The method is the one in expected loss as PD x LGD x EAD, with one difference that matters here: these are regulatory parameters, through-the-cycle PDs and, for many portfolios, downturn LGDs. They are not the point-in-time inputs behind the accounting provisions, which is why the two numbers rarely agree.
For defaulted exposures PD is 100 per cent and EL is the bank's best estimate of loss (ELBE) times EAD
EL defaulted = 600 × 45% = 270.0; specific provisions = 345.0; surplus = 75.0
| Book | Expected loss | Eligible provisions | Shortfall (−) / surplus |
|---|---|---|---|
| Performing | 190.1 | 130.0 | −60.1 |
| Defaulted | 270.0 | 345.0 | 75.0 |
| Netted total (not allowed) | 460.1 | 475.0 | 14.9 |
CET1 deduction = performing shortfall = 60.1
CET1 = 1,800 − 60.1 = 1,739.9; CET1 ratio = 1,739.9 ÷ 15,000 = 11.60%, down from 12.00%
Under the Basel framework and the EU Capital Requirements Regulation, specific provisions on defaulted exposures may not be used to cover expected loss on other exposures (CRR Article 159). The negative amount is deducted from CET1 under Article 36(1)(d); a positive amount goes to Tier 2 under Article 62(d), within the 0.6 per cent cap. The 75.0 of surplus on the defaulted book does not rescue the performing book. The deduction is not risk-weighted and does not reduce RWA, so every 10 of shortfall costs 6.7 basis points of CET1 ratio on this bank. The full ladder of deductions it sits in is set out in how to calculate a bank's CET1 ratio.
Here performing provisions cover 68 per cent of regulatory EL. That is the ordinary result of comparing IFRS 9 provisions, which for stage 1 loans hold only twelve months of point-in-time expected credit loss, with a regulatory EL built on long-run PDs and conservative LGDs. In a benign year, point-in-time PDs are low and the gap widens; after a downturn, stage 2 transfers and lifetime ECL can push provisions above EL. The shortfall is therefore partly a cycle indicator, and it moves CET1 in a direction that cushions the provision charge: when provisions rise in a downturn, part of the hit to profit is offset by a smaller shortfall deduction.
| Performing provisions | CET1 deduction | Surplus | Added to Tier 2 | CET1 ratio |
|---|---|---|---|---|
| 130.0 | 60.1 | 0.0 | 0.0 | 11.60% |
| 160.0 | 30.1 | 0.0 | 0.0 | 11.80% |
| 190.1 | 0.0 | 0.0 | 0.0 | 12.00% |
| 220.0 | 0.0 | 29.9 | 29.9 | 12.00% |
| 300.0 | 0.0 | 109.9 | 66.0 | 12.00% |
The asymmetry is plain in the table. Each unit of shortfall costs a full unit of CET1. Each unit of surplus is worth at most a unit of Tier 2, the weaker layer, and only up to the cap: at 300.0 of provisions, 43.9 of the surplus earns no capital credit at all. Surplus never reaches CET1: holding CET1 before the comparison at 1,800, the ratio cannot rise above the 12.00 per cent it shows with no shortfall, and in practice the extra provisions that create a surplus have already been charged against profit and CET1.
Netting the two books. Total EL of 460.1 against total provisions of 475.0 shows a surplus of 14.9, which suggests no deduction and a small Tier 2 add-on. The correct answer is a 60.1 deduction from CET1. On a bank running 40 basis points above a management buffer, that is the whole buffer. A second mistake is to include provisions that are not eligible, such as provisions on exposures under the standardised approach, in the IRB comparison; check the bank's own definition before trusting any reported shortfall.
The rules for which provisions are eligible, how general and specific provisions are allocated between IRB and standardised exposures, and whether any surplus on the defaulted book is recognised vary by jurisdiction. The calculation above follows the structure of the Basel standard; local rules decide the inputs.
Compute EL on performing and defaulted exposures separately, compare each with its own eligible provisions, deduct any performing shortfall from CET1 in full, and cap any recognised surplus at 0.6 per cent of IRB credit RWA in Tier 2. Here that is a 60.1 deduction and a 40 basis point lower CET1 ratio, on a book whose netted figures say there is nothing to deduct. The capital stack, the risk weight engine and the constraint that binds are worked through in the free workbook for this case.
Where eligible provisions exceed expected loss, the surplus can be added to Tier 2 capital, capped at 0.6 per cent of IRB credit risk-weighted assets. On 11,000 of IRB credit RWA the cap is 66. A bank with 109.9 of surplus counts only 66.0, and none of it ever reaches CET1.
No. Specific provisions on defaulted exposures may not cover expected loss on other exposures. In the illustrative case the defaulted book has a 75.0 surplus and the performing book a 60.1 shortfall; the deduction from CET1 is the full 60.1, not the netted surplus of 14.9.
Stage 1 holds twelve months of point-in-time expected credit loss, while regulatory EL uses through-the-cycle PDs and, often, downturn LGDs. In a benign year point-in-time PDs are lower. In the example performing provisions cover 68 per cent of EL, leaving a 60.1 shortfall worth 40 basis points of CET1 ratio.
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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