The investor's return is not the coupon. It is the coupon on a balance that losses shrink and amortisation repays, and the losses are levered about fourteen times through a thin first-loss tranche.
The return on a significant risk transfer tranche is the internal rate of return of its cash flows: the coupon, reference rate plus margin, paid on an outstanding balance that losses write down and amortisation repays, plus the principal returned at the end. On an illustrative 266 million first-loss tranche paying 13.00 per cent, best-estimate losses cut the IRR to 10.39 per cent, and 1.5 times fund leverage lifts it to 16.60. Losses at 4.17 times the estimate take the return to zero.
Worked in full in Significant Risk Transfer by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The coupon is the easy part. The return depends on three schedules that run underneath it: the reference pool, which replenishes and then amortises; the losses, which hit the tranche first; and the principal, which is repaid pro rata as the pool shrinks. Build them year by year and the IRR follows.
Northwall 2026-1 is the fictional synthetic securitisation of the case. A bank buys protection on the 0 to 7.00 per cent tranche of a 4,000 million corporate loan portfolio, keeps 5 per cent of it, and sells the rest to a credit fund as a funded credit-linked note. The fund's cash sits as collateral and earns the reference rate; the bank pays the margin on top.
| Input | Value |
|---|---|
| Reference portfolio | 4,000 |
| Tranche, 0 to 7.00% | 280 |
| Sold to the fund (95%) | 266 |
| Margin, over the reference rate | 10.50% |
| Reference rate earned on the collateral | 2.50% |
| Best-estimate loss, per year, of the pool | 0.1822% |
| Replenishment, then amortisation | 2 years, then 8% a year |
| Holding period | 5 years |
| Fund leverage, cost | 1.50x at 6.25% |
Coupont = (reference rate + margin) × opening balancet
Losst = loss rate × multiple × poolt × share sold, capped at the balance
Principalt = (opening − loss) × (1 − poolt / poolt−1), all of it at the end
Cash flowt = coupon + principal; IRR on −266 at year 0
In Excel, with the cash flows in a column: =IRR(H22:H27). Losses are not a cash flow: they reduce the balance on which the coupon is paid and the principal that comes back.
| Year | Pool | Opening | Coupon | Written down | Principal | Cash flow |
|---|---|---|---|---|---|---|
| 1 | 4,000.00 | 266.00 | 34.58 | 6.93 | 0.00 | 34.58 |
| 2 | 4,000.00 | 259.07 | 33.68 | 6.93 | 0.00 | 33.68 |
| 3 | 3,680.00 | 252.15 | 32.78 | 6.37 | 19.66 | 52.44 |
| 4 | 3,385.60 | 226.12 | 29.40 | 5.86 | 17.62 | 47.02 |
| 5 | 3,114.75 | 202.63 | 26.34 | 5.39 | 197.24 | 223.58 |
| Total | 156.78 | 31.48 | 234.52 |
Two checks before reading the IRR. Principal repaid plus losses must equal the notional: 234.52 + 31.48 = 266.00. And with no losses the IRR must equal the coupon, 13.00 per cent, which it does.
The IRR of −266 followed by the five cash flows is 10.39 per cent. Losses consumed 11.83 per cent of the tranche over five years, and cost 2.61 points of return against the 13.00 coupon. Fund leverage, on the simple formula the case uses, return + leverage × (return − cost of leverage), gives 10.39 + 1.5 × (10.39 − 6.25) = 16.60 per cent.
The tranche is thin, so the pool's losses are concentrated on it. A loss of 1 per cent of the pool is 14.29 per cent of a 7.00 per cent tranche, for the fund's 95 per cent and the bank's retained slice alike, because both take losses pro rata. That ratio is what the margin pays for.
| Loss multiple | Pool loss a year | Share of tranche lost | IRR | Levered, 1.5x |
|---|---|---|---|---|
| 0.00x | 0.00% | 0.0% | 13.00% | 23.12% |
| 1.00x | 0.18% | 11.8% | 10.39% | 16.60% |
| 2.00x | 0.36% | 23.7% | 7.52% | 9.43% |
| 3.00x | 0.55% | 35.5% | 4.32% | 1.42% |
| 3.51x | 0.64% | 41.5% | 2.54% | −3.02% |
| 4.17x | 0.76% | 49.3% | 0.00% | −9.38% |
Two break-evens matter. At 3.51 times expected losses the margin is exactly used up and the fund earns roughly what its collateral earns, 2.54 per cent. At 4.17 times, losses absorb the whole coupon and the return is zero. Because coupons less losses are a straight line in the loss multiple, both can be solved exactly rather than by goal seek. Leverage turns negative earlier: at 3.51 times the levered fund already loses 3.02 per cent a year.
| Margin | IRR | Levered, 1.5x |
|---|---|---|
| 7.61% | 7.50% | 9.37% |
| 8.00% | 7.89% | 10.35% |
| 9.00% | 8.89% | 12.85% |
| 10.50% | 10.39% | 16.60% |
| 12.00% | 11.89% | 20.35% |
The first row is the investor's floor: the margin at which the tranche just earns a 7.5 per cent hurdle. Because the balances and repayments do not depend on the margin, it solves in closed form: the notional less the present value of principal at the hurdle, 266 − 166.41, over the present value of the balances, 985.06, less the reference rate, gives 7.61 per cent. The bank's side of the same trade, the most it can pay, is worked in the maximum coupon a bank can pay for SRT protection.
Charging the loss twice. A model that subtracts each year's write-down from the cash flow and also returns only the surviving principal counts every loss two times: once as a cash outflow and once as principal not repaid. On this tranche it shows 7.78 per cent instead of 10.39, understating the return by 2.61 points and making a fairly priced trade look uneconomic. A written-down euro stops earning a coupon and does not come back. It is not also paid out.
Schedule the pool, the losses and the principal year by year, pay the coupon on the opening balance, and take the IRR: 10.39 per cent on a 13.00 per cent coupon, zero at 4.17 times the losses. Significant Risk Transfer prices the same tranche from the bank's side and the fund's side, and the free workbook for this case builds these cash flows with the six stress scenarios, the break-even multiples and the investor's floor. The capital the bank releases on the senior is set by the SEC-IRBA risk weight.
It depends on the tranche's thickness, the pool and the margin, so compute it rather than quote it. On an illustrative first-loss tranche at a 10.50 per cent margin over a 2.50 per cent reference rate, the unlevered IRR is 10.39 per cent at expected losses and 16.60 per cent with 1.5x fund leverage at 6.25 per cent. The margin at which it just earns a 7.5 per cent hurdle is 7.61 per cent.
On an illustrative first-loss tranche detaching at 7.00 per cent with a 13.00 per cent coupon, the IRR falls to zero when losses run at 4.17 times the best estimate, 0.76 per cent of the pool a year, and to 2.54 per cent, roughly the cash rate, at 3.51 times. Because the tranche is thin, each further multiple of the best estimate consumes about 11.8 per cent of it over five years.
Because the levered return is the asset return plus leverage times the gap over the borrowing cost. At 1.5x leverage costing 6.25 per cent, an unlevered 10.39 per cent becomes 16.60; at twice the expected losses the 7.52 per cent becomes 9.43, and at three times, 4.32 becomes 1.42. Leverage widens the outcomes in both directions.
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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