Each point of protection makes the senior lighter and the bill larger. The best detachment is where the risk-weight floor binds, and not one point further.
Thick enough for the senior tranche to reach its risk-weight floor, and no thicker. On the fictional Northwall 2026-1 portfolio, the retained senior hits the 15 per cent floor when the protected tranche detaches at 9.74 per cent of the pool. Priced at the margin the investor needs at each thickness, that structure lifts the bank's return on equity to 37.73 per cent, against 20.26 per cent for the executed 7.00 per cent thickness priced the same way.
Worked in full in Significant Risk Transfer by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Thickness is the one term of a synthetic securitisation that the structurer controls outright. Every extra point of first-loss protection makes the retained senior lighter under SEC-IRBA, but it also adds notional the bank must pay a margin on. The question is where the capital stops falling faster than the cost rises. It has an exact answer, and it is not "as thin as KIRB allows".
| Input | Value |
|---|---|
| Reference portfolio / RWA before the trade | 4,000m / 3,077.08m |
| KIRB / senior p-factor (non-STS) | 6.51% / 0.4745 |
| Junior tranche: retained vertically, deducted from CET1 | 5% |
| CET1 target / cost of equity / tax rate | 13.50% / 11.5% / 25% |
| Profit before protection, pre-tax / return on equity before | 71.97m / 12.99% |
| Best-estimate pool loss rate, a year | 0.1822% |
| Reference rate earned on the collateral / fund hurdle | 2.50% / 7.5% |
For each detachment point D, three numbers have to be computed: the capital the structure releases, the margin the investor will accept, and the bank's return on equity at that margin.
1. Senior risk weight: SEC-IRBA on the senior from D to 100 per cent, floored at 15%. Below KIRB the senior straddles it and the slice under KIRB is weighted at 12.5 times.
2. Capital released = capital before − [(1 − D) × 4,000 × senior RW × 13.50% + retained slice deducted]
3. Investor floor margin = (notional sold − PV of principal at the hurdle) ÷ PV of the outstanding balances − reference rate
4. Return on equity after = (71.97 − margin × notional sold) × (1 − 25%) ÷ capital after. In Excel, with the grid in rows: =(Profit-Margin*Sold)*(1-Tax)/CapAfter, then =INDEX(D:D,MATCH(MAX(H:H),H:H,0)) to read off the best detachment.
Step 3 needs no goal seek. The losses charged to the fund each year depend on the pool, not on the tranche, so the balances and the repayments do not depend on the margin, and the value at the hurdle is a straight line in it. At 7.00 per cent the fund buys 266.0m; its balances discount to 985.06m and its principal to 166.41m at 7.5 per cent, which gives a floor of (266.0 − 166.41) ÷ 985.06 − 2.50% = 7.61 per cent. A thicker tranche spreads the same euro losses over more notional, so its floor falls.
| Detachment | Sold | Senior RW | Capital released | Floor margin | Bank ROE |
|---|---|---|---|---|---|
| 6.00% | 228.0 | 47.76% | 161.0 | 8.07% | 15.79% |
| 7.00% (executed) | 266.0 | 35.34% | 223.9 | 7.61% | 20.26% |
| 8.00% | 304.0 | 25.83% | 271.1 | 7.27% | 25.91% |
| 9.00% | 342.0 | 18.89% | 304.6 | 7.01% | 32.48% |
| 9.75% (floor binds) | 370.5 | 15.00% | 322.8 | 6.85% | 37.73% |
| 11.00% | 418.0 | 15.00% | 321.3 | 6.63% | 35.26% |
| 12.00% | 456.0 | 15.00% | 320.1 | 6.49% | 33.34% |
| 14.00% | 532.0 | 15.00% | 317.7 | 6.27% | 29.63% |
Moving from 7.00 to 9.75 per cent sells 104.5m more protection and costs the bank 5.13m more a year, but it releases 98.9m more capital. Return on equity rises by 17.47 points. Solved exactly rather than on a quarter-point grid, the senior reaches the floor at a detachment of 9.74 per cent.
Past the floor the arithmetic turns. Each extra quarter point is a 10.0m slice: 9.5m sold and 0.5m retained and deducted at par. The senior shrinks, but it is already at 15 per cent, so the capital it saves is smaller than the retained slice adds. From 9.75 to 10.00 per cent the release actually falls by 0.30m while the bank pays a margin on 9.5m more. Thicker than the floor is strictly worse.
The opposite threshold matters too. Detach below KIRB and the senior picks up a slice weighted at 12.5 times, so the release falls fast: 161.0m at 6.00 per cent. But it only reaches zero at a detachment of 3.54 per cent, well under the 6.51 per cent KIRB. "Below KIRB destroys capital" is a slogan, not a calculation.
The table assumes the investor is paid its floor at every thickness. If the bank instead pays the agreed 10.50 per cent whatever the size, a thicker tranche costs more per euro and the answer moves.
| Detachment | Bank ROE | Value created a year |
|---|---|---|
| 7.00% | 17.25% | 4.81 |
| 8.00% | 20.81% | 7.23 |
| 9.00% | 24.40% | 8.09 |
| 9.25% | 25.26% | 8.12 |
| 9.75% | 26.78% | 7.95 |
| 12.00% | 18.96% | 0.90 |
Value created is the cost of equity on the capital released less the after-tax cost of protection: 11.5% × 223.9 − 75% × 27.93 = 4.81m at 7.00 per cent. On value, a fixed margin pulls the optimum below the floor, to about 9.25 per cent, and the curve is flat between 9.00 and 9.75; on return on equity it still sits at the floor. The floor is the upper bound of the search, not always the answer, and which metric the bank manages to decides which.
Sizing the tranche to clear KIRB by a comfortable margin and stopping there. At 7.00 per cent, 0.49 points above KIRB, Northwall's senior still weighs 35.34 per cent, more than twice its floor. The deal works, but it leaves 98.9m of capital in the bank that a 9.75 per cent structure would have released for 5.13m a year. The second mistake is the reverse: assuming that more protection always means more relief. Above 9.74 per cent the bank buys protection that releases nothing.
The SEC-IRBA arithmetic behind each row is in how to calculate the SEC-IRBA risk weight of an SRT tranche, and the bank's ceiling on the margin in the most a bank can pay for SRT protection.
The detachment grid from 3 to 14 per cent, both thresholds and the floor margin at every thickness are live formulas in the free workbooks for this case.
The point of the pool's losses at which the protected tranche is exhausted and the senior begins. A first-loss tranche detaching at 7.00 per cent of a 4,000 million pool covers the first 280 million of losses. The higher the detachment, the lighter the retained senior under SEC-IRBA, until it reaches its 15 per cent floor at 9.74 per cent on this pool.
Because the euro losses expected from the pool do not grow with the tranche, so each euro of notional bears less of them. On the Northwall pool the investor's floor margin at a 7.5 per cent hurdle is 7.61 per cent for a 7.00 per cent tranche and 6.85 per cent for a 9.75 per cent tranche.
Yes, but the senior then straddles KIRB and the slice below it is weighted at 12.5 times, so relief falls quickly. On the Northwall pool, with KIRB at 6.51 per cent, a 6.00 per cent detachment still releases 161.0 million, and the release only reaches zero at 3.54 per cent.
The capital released by detachment point is tabulated in chapter 23 of 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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