A funded SRT investor lends to the bank as well as insuring its loans. In expectation the second exposure is small; in the scenario where both go wrong it is the larger loss.
In expectation, very little; in the scenario that matters, a great deal. On an illustrative 200.0 million SRT tranche sold as a credit-linked note issued directly by a bank with a 0.10 per cent annual default probability and 60.0 per cent loss given default, issuer risk costs the investor 6.0 basis points a year, 0.435 million in present value, less than the 25 basis points an SPV structure costs. But if the bank fails after the pool has eaten 40 per cent of the tranche, the investor loses 76.0 per cent of its balance instead of 40.0.
Worked in full in Significant Risk Transfer by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A funded SRT investor hands its cash over at closing. Where that cash goes decides a second credit exposure that sits on top of the reference portfolio. If the bank issues the note itself, or holds the collateral as a deposit on its own balance sheet, the investor is a creditor of the bank: when the bank pays back the note, it pays from its own resources. If an SPV issues the note and invests the proceeds in high-quality collateral held away from the bank, that exposure largely disappears, at a running cost. The question is which is cheaper once the issuer risk is priced.
| Input | Value |
|---|---|
| Tranche notional sold to the investor | 200.0 |
| Replenishment, then pro rata amortisation | 2 years, then 10.0% a year |
| Expected life to the time call | 5 years |
| Issuer's annual probability of default | 0.10% |
| Investor's loss given issuer default | 60.0% |
| Issuer's senior unsecured credit spread | 80 bp |
| SPV running costs / negative carry on collateral | 15 bp / 10 bp |
| Discount rate | 7.5% |
| Tranche margin | 9.50% |
The issuer's default probability and recovery are illustrative, set for a solidly investment-grade bank. The balance profile ignores reference losses, which makes it a slight overstatement of the exposure in normal years and the right base for a first pass.
Marginal PDt = survival to t − 1 × annual PD
Expected issuer losst = opening balancet × marginal PDt × LGD
Cost in bp a year = PV of expected losses ÷ PV of balances
In Excel, with balances in B2:B6, marginal PDs in C2:C6 and discount factors in D2:D6: =SUMPRODUCT(B2:B6,C2:C6,D2:D6)*0.6/SUMPRODUCT(B2:B6,D2:D6)*10000.
| Year | Opening balance | Marginal PD | Expected loss | Present value |
|---|---|---|---|---|
| 1 | 200.00 | 0.1000% | 0.1200 | 0.1116 |
| 2 | 200.00 | 0.0999% | 0.1199 | 0.1037 |
| 3 | 180.00 | 0.0998% | 0.1078 | 0.0868 |
| 4 | 162.00 | 0.0997% | 0.0969 | 0.0726 |
| 5 | 145.80 | 0.0996% | 0.0871 | 0.0607 |
| Total | 0.50% | 0.435 |
The present value of the balances is 726.87, so the expected loss of 0.435 is 6.0 basis points a year, which is simply the annual PD times the LGD. The SPV's 25 basis points a year on the same balances cost 1.817 in present value, 4.2 times the expected loss. Priced at the issuer's own 80 basis point senior spread, which is what the market charges for lending to that bank, the exposure is priced at 5.815, 13.4 times the expected loss.
Three answers, depending on the view the investor takes. On expected loss, the direct note wins: 6.0 against 25 basis points. At market spread, the SPV wins easily. And a buy-and-hold credit fund pricing the tranche at a hurdle rate has to decide which of the two it is: a holder of expected losses, or a lender to the bank that should be paid like one.
The decisive number is not the average. Suppose the bank fails at the end of year 3, when the balance is 162.00 and a stressed pool has written the tranche down by 40 per cent. The SPV investor has lost 64.80. The direct-note investor has lost the same 64.80 to the pool and a further 58.32 on the 97.20 the bank owes it: 123.12, or 76.0 per cent. That second loss is more than three years of the tranche's margin income of 19.00 a year on the original notional, and it arrives in exactly the state of the world in which the bank's own loans are going bad.
| Annual PD | LGD 40% | 60% | 80% |
|---|---|---|---|
| 0.05% | 2.0 | 3.0 | 4.0 |
| 0.10% | 4.0 | 6.0 | 8.0 |
| 0.25% | 10.0 | 14.9 | 19.9 |
| 0.50% | 19.8 | 29.7 | 39.7 |
At 60.0 per cent LGD the SPV only pays for itself on expected loss once the issuer's annual PD exceeds 0.42 per cent, more than four times the PD assumed here. That is the arithmetic behind direct issuance by strong banks, and the reason the case for an SPV rests on the correlation between the bank's failure and the reference pool's losses rather than on the average.
Pricing the reference portfolio carefully and the issuer not at all, or adding the issuer's expected loss as a few basis points and moving on. The two risks are not independent: the reference portfolio is the bank's own loan book, and a bank that defaults is likely to be one whose loans are defaulting. A stress test that writes the tranche down without also asking who repays the remainder misses the larger part of the loss. The tranche-side return is worked in how to calculate the return on an SRT tranche, and the capital the bank obtains under each form of protection in funded vs unfunded SRT protection.
Expected issuer loss on a strong bank is about PD times LGD, 6.0 basis points a year here, below the 25 basis point cost of an SPV. The case for the SPV is the joint scenario, where issuer risk turns a 40.0 per cent write-down into 76.0. Significant Risk Transfer prices the same tranche from both the bank's and the fund's side; the free workbooks for this case carry the investor's cash flows and the six stress scenarios.
The risk that the bank which issued the note, or holds the collateral, cannot repay it. The investor then loses on the note even if the reference loans perform. On an illustrative 200.0 million tranche with a 0.10 per cent annual issuer PD and 60.0 per cent LGD, the expected cost is 6.0 basis points a year.
Because the SPV holds the proceeds as collateral away from the bank, so a bank failure does not add a second loss. In the illustrative stress, a bank default after the pool has written the tranche down by 40 per cent costs a direct-note investor a further 58.32 million, 76.0 per cent in all; the SPV investor loses 40.0 per cent.
On expected loss alone, only when the issuer is weak: at 60.0 per cent LGD the 25 basis points of SPV and carry costs exceed the expected issuer loss only above a 0.42 per cent annual PD. Priced at the bank's 80 basis point senior spread, or weighted for the correlation with the pool, the SPV is cheaper well before that.
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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