The clearance between KIRB and the attachment point is not a buffer that holds the relief steady until it is crossed. The senior gets heavier with every notch of migration.
The relief erodes from the first downgrade, not when KIRB crosses the attachment point. On the fictional Northwall 2026-1 trade, a rise in KIRB of 50 basis points, from 6.51 to 7.01 per cent, takes the retained senior's weight from 35.34 to 43.87 per cent and cuts the capital released from 223.9 million to 209.8 million. Of the 42.8 million of extra capital the bank then holds, only 0.3 million comes from the thin slice now weighted at 1250 per cent.
Worked in full in Significant Risk Transfer by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Structurers leave a clearance between KIRB and the detachment of the protected tranche as "a margin for migration". The usual reading is that the relief is safe until the clearance is used up and falls off a cliff after it. The calculation says otherwise, and it matters because ratings migrate exactly when the bank most needs the capital.
Northwall Bank buys protection on the 0 to 7.00 per cent tranche of a 4,000 million corporate pool, sells 95 per cent of it to a credit fund and deducts the 5 per cent it retains. The tape has seven rating buckets; the migration is modelled as a single multiple applied to every PD, with LGD, exposure, maturity and the number of names unchanged. All figures are illustrative.
| Input | Value |
|---|---|
| Reference pool / senior notional | 4,000 / 3,720 |
| Protected tranche, 0 to 7.00% / retained and deducted | 280 / 14 |
| IRB RWA / expected loss, today | 3,077.08 / 14.03 |
| KIRB today / clearance to the detachment | 6.51% / 0.49 pts |
| Weighted average PD today | 0.81% |
| Effective number of names / tranche maturity | 166 / 5 years |
| CET1 target / cost of equity / tax | 13.50% / 11.5% / 25% |
| Margin paid on the 266 sold | 10.50% |
1. Migrate the tape and recompute KIRB. Multiply each bucket's PD, rerun the IRB formula bucket by bucket (correlation, conditional PD, maturity adjustment) and rebuild KIRB from the new RWA and expected loss.
KIRB = (IRB RWA × 8% + expected loss) ÷ exposure
Clearance gone when KIRB = 7.00%: every PD × 1.210, weighted PD 0.98%
KIRB + 50 bp, 7.01%: every PD × 1.212
A uniform PD increase of 21.0 per cent is enough to use up the whole 0.49 point clearance. That is a mild, book-wide migration, not a crisis.
2. Reweight the senior under SEC-IRBA. KIRB enters the formula twice: in the exponent, through the attachment's distance from KIRB, and in the p-factor, which for this senior is 3.56 ÷ N − 1.85 × KIRB + 0.55 × LGD + 0.07 × maturity. At the higher KIRB the senior straddles it, so the slice between 7.00 and 7.01 per cent is weighted at 1250 per cent and the rest by the formula.
3. Measure the relief against the same book unprotected. The bank's capital without the trade rises too, from 415.4 to 444.1 million, because the pool's own RWA goes up. Relief is the difference between the two, at the 13.50 per cent target:
Capital after = senior × senior RW × 13.50% + 14 deducted
Today: 3,720 × 35.34% × 13.50% + 14 = 191.5; relief 415.4 − 191.5 = 223.9
KIRB + 50 bp: 3,720 × 43.87% × 13.50% + 14 = 234.3; relief 444.1 − 234.3 = 209.8
Excel: =CapBefore-(Senior*SeniorRW*Target+Retained)
4. Split the extra capital. Price the senior again as if none of it sat below KIRB: its weight would be 43.80 per cent. The gap to 43.87 per cent is everything the 1250 per cent slice costs, 0.3 million of the 42.8 million increase, or 0.8 per cent of it. The slice is only 0.005 points of the pool. The other 99 per cent of the damage is the formula steepening as KIRB approaches the attachment.
With KIRB 50 basis points higher, Northwall's relief falls by 14.1 million, 6.3 per cent. Return on equity with the trade falls from 17.25 to 13.14 per cent, against 11.65 without it, so the trade still earns its keep. The bank's margin ceiling, the most it could pay for the protection, falls from 12.91 to 12.10 per cent, still above the 10.50 per cent agreed.
| PD multiple | Weighted PD | KIRB | Senior RW | Relief | Ceiling | ROE with | ROE without |
|---|---|---|---|---|---|---|---|
| 1.00 (today) | 0.81% | 6.51% | 35.34% | 223.9 | 12.91% | 17.25% | 12.99% |
| 1.10 | 0.89% | 6.75% | 39.39% | 217.7 | 12.55% | 15.10% | 12.32% |
| 1.20 | 0.97% | 6.98% | 43.38% | 210.7 | 12.15% | 13.34% | 11.72% |
| 1.30 | 1.05% | 7.19% | 47.23% | 203.5 | 11.40% | 11.89% | 11.17% |
| 1.40 | 1.13% | 7.40% | 50.87% | 196.7 | 10.53% | 10.69% | 10.68% |
| 1.50 | 1.21% | 7.59% | 54.30% | 190.2 | 9.74% | 9.68% | 10.21% |
| 2.00 | 1.62% | 8.45% | 69.28% | 161.0 | 6.71% | 6.22% | 8.31% |
The relief falls in almost even steps: 6.2 million for the first tenth of migration, about 7 million for each tenth after that, up to 1.50. There is no kink at a multiple of 1.210, where the clearance runs out. The line the structurer watched is not the line the capital follows.
The economic threshold comes later. At a multiple of 1.403, a weighted PD of 1.14 per cent and KIRB of 7.40 per cent, the ceiling falls to the 10.50 per cent the bank pays and its room is gone. By then the binding test has changed: value creation would still allow 11.33 per cent, but the book's own return without the trade, 10.66 per cent, is now below the 11.5 per cent cost of equity, and above a 10.50 per cent margin the bank would earn less on equity with the trade than without it.
Treating the clearance as a buffer that keeps the relief constant until KIRB crosses the detachment. A model built that way shows 223.9 million of relief right up to a multiple of 1.210 and a sudden drop after it. In fact the relief is already down to 210.0 million at that point, 14.0 million lower, and the 1250 per cent slice has not yet cost a euro. Monitoring only the clearance, quarter by quarter, tells the bank nothing until most of the erosion has happened.
The relief is also measured against a moving base. Comparing the migrated capital after the trade with today's 415.4 million before it would overstate the damage, because the unprotected book has become more expensive too.
The migration grid, the thresholds and the full tape are in the free workbook for this case. The formula behind step 2 is worked in how to calculate the SEC-IRBA risk weight, and the ceiling in the most a bank can pay for SRT protection.
Not abruptly. The relief erodes continuously, because KIRB sits inside the SEC-IRBA exponent and the p-factor. On Northwall 2026-1 relief falls from 223.9m to 210.0m by the time KIRB reaches the 7.00 per cent attachment, and the slice weighted at 1250 per cent above that point costs only 0.3m once KIRB is 50 basis points higher.
On this portfolio, about a fifth of PD drift. Multiplying every PD by 1.210, a weighted PD of 0.98 per cent against 0.81, takes KIRB from 6.51 to 7.00 per cent and uses up the whole clearance. Each tenth of a point of clearance buys roughly four points of uniform PD increase.
When the bank's margin ceiling falls to the margin it pays. Here that happens with every PD up by a factor of 1.403, KIRB at 7.40 per cent: the ceiling, now set by return on equity rather than value creation, drops to the 10.50 per cent agreed, and the 2.41 points of room at closing are gone.
The clearance above KIRB is set in chapter 4 of Significant Risk Transfer; the companion workbook's first case takes the migration to a number. 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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