Bucket by bucket from PD, LGD and maturity to the one number that anchors every SEC-IRBA tranche weight, worked on a fictional seven-grade corporate portfolio.
KIRB is the capital the regulation would require on the securitised pool if it had never been securitised, expected loss included, expressed as a share of the pool: KIRB = (IRB RWA × 8% + expected loss) ÷ exposure. On the fictional Northwall 2026-1 portfolio, 4,000 million of corporate loans carry 3,077.08 million of risk-weighted assets and 14.03 million of expected loss, so KIRB is 6.51 per cent. Every SEC-IRBA tranche weight is then measured against that number.
Worked in full in Significant Risk Transfer by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Northwall Bank, from Significant Risk Transfer, buys protection on a junior tranche of a 4,000 million portfolio of corporate and mid-market loans and keeps the senior. Before any tranche can be weighted, the bank needs KIRB, and KIRB needs the pool's own IRB capital, computed loan by loan or, as here, by rating bucket. The figures are illustrative and follow the IRB corporate formula of CRR Article 153, with the SME size adjustment of Article 153(4).
| Grade | EAD | PD | LGD | M, years | Risk weight | RWA | Expected loss |
|---|---|---|---|---|---|---|---|
| 1 (AA/A) | 520 | 0.09% | 35% | 3.4 | 26.62% | 138.4 | 0.16 |
| 2 (BBB+) | 720 | 0.21% | 38% | 3.8 | 48.36% | 348.2 | 0.57 |
| 3 (BBB) | 880 | 0.38% | 40% | 4.1 | 70.01% | 616.1 | 1.34 |
| 4 (BBB-) | 780 | 0.67% | 42% | 4.3 | 94.28% | 735.3 | 2.19 |
| 5 (BB+), sales 38 | 560 | 1.21% | 44% | 4.0 | 108.35% | 606.7 | 2.98 |
| 6 (BB), sales 24 | 380 | 2.24% | 45% | 3.7 | 115.68% | 439.6 | 3.83 |
| 7 (BB-), sales 15 | 160 | 4.10% | 45% | 3.2 | 120.42% | 192.7 | 2.95 |
| Total | 4,000 | 76.93% | 3,077.1 | 14.03 |
Step 1: the IRB risk weight of each bucket. The corporate formula takes PD, LGD and maturity M, derives an asset correlation R from PD (reduced for borrowers with sales between 5 and 50 million), takes the loss at the 99.9th percentile, deducts expected loss and scales by a maturity adjustment. The single-loan version is worked in how to calculate the IRB risk weight of a corporate loan; here it runs seven times.
K = [LGD × N((G(PD) + √R × G(0.999)) ÷ √(1 − R)) − PD × LGD] × MA
Grade 4: R = 20.58%, MA = 1.662, K = 7.54%, risk weight = 12.5 × K = 94.28%, RWA = 780 × 94.28% = 735.3
Expected loss, grade 4 = 0.67% × 42% × 780 = 2.19
Excel, per row: =(LGD*NORMSDIST((NORMSINV(PD)+SQRT(R)*NORMSINV(0.999))/SQRT(1-R))-PD*LGD)*MA*12.5
Step 2: add up. The seven buckets carry 3,077.08 of RWA, a density of 76.93 per cent, and 14.03 of expected loss.
Step 3: convert to capital at the 8 per cent minimum and add expected loss.
Capital = 3,077.08 × 8% = 246.17, or 6.15% of the pool
Expected loss = 14.03, or 0.351% of the pool
KIRB = (246.17 + 14.03) ÷ 4,000 = 6.51%, an amount of 260.2
Excel: =(SUM(RWA)*0.08+SUM(EL))/SUM(EAD)
Two other pool inputs come out of the same table, because SEC-IRBA's p-factor needs them: the effective number of exposures, 166.27 on the name counts per bucket, and the exposure-weighted LGD, 40.6 per cent.
KIRB of 6.51 per cent is the line in the capital structure below which the regulation expects losses to be consumed by capital that already exists. A tranche attaching below it is weighted at 1250 per cent for the part under the line. Northwall's senior attaches at 7.00 per cent, 0.49 points above KIRB, so with a p-factor of 0.47 it weighs 35.34 per cent, the result derived in how to calculate the SEC-IRBA risk weight.
The buckets do not contribute in proportion to their size. Grade 4 is 19.5 per cent of exposure but 23.9 per cent of RWA; grade 6 is 9.5 per cent of exposure and 27.3 per cent of expected loss. The investment-grade top of the book, grade 1, is 13.0 per cent of exposure and 4.5 per cent of RWA.
Hold the structure fixed, the senior attaching at 7.00 per cent, and move one input across the whole pool.
| Case | RWA | EL | KIRB | Attachment less KIRB, pts | Senior risk weight |
|---|---|---|---|---|---|
| Base | 3,077.1 | 14.03 | 6.51% | +0.49 | 35.34% |
| Every PD × 1.25 | 3,324.2 | 17.54 | 7.09% | −0.09 | 45.34% |
| Every PD × 1.5 | 3,532.4 | 21.05 | 7.59% | −0.59 | 54.30% |
| LGD + 5 points | 3,446.4 | 15.65 | 7.28% | −0.28 | 51.55% |
| Maturity 1 year shorter | 2,693.6 | 14.03 | 5.74% | +1.26 | 24.03% |
| No SME size adjustment | 3,229.8 | 14.03 | 6.81% | +0.19 | 40.44% |
A quarter more default probability across the book pushes KIRB through the 7.00 per cent attachment; the senior then straddles KIRB and picks up a 1250 per cent slice. That is why KIRB is recomputed on every rating migration and on every replenishment: the tranche boundaries are fixed in the contract, KIRB is not. Maturity is the quiet lever. One year off every loan cuts RWA by 383.4 and drops the senior to 24.03 per cent, without changing expected loss at all.
KIRB applies only where the bank has IRB permission for the underlying exposures and can compute it for the pool. Where it cannot, the hierarchy sends the bank to SEC-SA, which uses a standardised KA instead.
The usual error is to measure KIRB at the bank's own capital target rather than at 8 per cent. Northwall manages to 13.50 per cent CET1, and that is the right ratio for measuring the capital an SRT releases. It is the wrong ratio for KIRB. At 13.50 per cent the pool's ratio becomes 10.74 per cent, above the attachment, and the senior would weigh 107.38 per cent. The opposite error, dropping expected loss, gives 6.15 per cent and a senior of 29.89 per cent, which looks like more capital relief than the bank is entitled to. KIRB is a regulatory constant of the pool: 8 per cent of RWA, plus expected loss, over exposure.
The bucket table, the SME adjustment and the clearance above KIRB are all live formulas in the free workbook for Northwall 2026-1, where you can overwrite the seven grades with your own portfolio.
The 8 per cent minimum. KIRB is defined as the IRB capital requirement of the pool as if it had not been securitised, which is 8 per cent of risk-weighted assets plus expected loss. On an illustrative 4,000 million pool that gives 6.51 per cent. Using a 13.50 per cent target instead would produce 10.74 per cent, a KIRB above the 7.00 per cent attachment, and a senior weight of 107.38 per cent instead of 35.34.
Because the IRB risk weight covers only unexpected loss; expected loss is meant to be absorbed by provisions and pricing. A securitisation tranche has to absorb both. On an illustrative corporate pool the capital part is 6.15 per cent and expected loss adds 0.351 points, for a KIRB of 6.51 per cent. Leaving it out understates KIRB and flatters every senior risk weight above it.
Maturity, LGD and default probability, in that order for plausible moves. On an illustrative 4,000 million corporate pool, cutting the average maturity by one year lowers KIRB from 6.51 to 5.74 per cent, five extra points of LGD take it to 7.28, and scaling every PD by 1.25 raises it to 7.09 per cent. Across those three moves the senior risk weight at a fixed 7.00 per cent attachment ranges from 24.03 to 51.55 per cent.
This article is one calculation from Significant Risk Transfer. 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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