Credit: auto ABS with a step-down and a turbo

The note classes of a sub-prime auto ABS that builds its own overcollateralization: a 22-step waterfall where excess cash accelerates principal toward a target and principal beyond it is retained rather than paid.

Every number below is checked against an independent reference implementation on every commit — period by period, and on each metric, inside a declared tolerance. See benchmark methodology.

The case

A sub-prime auto lender sold $1.01bn of car loans into a trust and issued $930m of notes against them in six public classes. The gap between the two is the noteholders' protection, and on day one it is only 5.75%. The deal's job over its first half-year is to widen it to 14.75%, out of the difference between what the borrowers pay — around 12.6% a year — and what the notes cost, which is 0.95% to 3.23%.

That makes the pay-down of any class a question about cash rather than about collateral. Principal arriving from the loans is not the only thing repaying the notes, and once the target is reached it stops being enough of an answer either: principal that would carry enhancement past target is held back and released to the certificateholder, so the notes amortize alongside the pool instead of ahead of it.

The reference

The Rule 424(b)(5) prospectus dated 21 February 2017 states the priority of payments in twenty-two numbered clauses and publishes, on pp. 59-62, the percent of each class outstanding at all 62 distribution dates under four prepayment speeds — 0.50%, 1.00%, 1.50% and 2.00% ABS — with a weighted average life to call and to maturity beneath each table. 1,512 cells, of which 195 are informative: the rest are exactly 0 or 100 and assert only "retired by then" and "not started yet".

An independent implementation of the deal, written from the fourteen assumptions the tables state, shares no code with the model. The class sizes and coupons those assumptions carry are not the deal as priced — the tables were prepared before pricing — and reproducing them means using what they assume. See SOURCE.md.

What it exercises

auto_abs_tranches takes the sequential-pay axis of a deal that assumes no losses and therefore never has to build anything. This case is the other half of the same pack's job, and the mechanism is the Step-Down Amount: the Noteholders' Principal Distributable Amount is principal collected less whatever would take the notes below the Required Pro Forma Note Balance.

Written the way the prospectus writes it, that is a step-down subtracted from a distributable amount and then an accelerated principal amount capped by both available cash and the distance to target. It collapses to one statement about where the notes end the period:

min(pool - floor, max(required, notes - principal - max(excess, 0.0)))

The notes finish at the required balance; cash may stop them getting there; and overcollateralization may not fall below 0.50% of the initial pool. Clause 18 is then min(total, principal) and clause 20 is max(total - principal, 0), which is what those clauses mean. The two formulations agree to $0.0000 at all four speeds.

The reserve account is the other thing the target depends on. Clause 19 funds it at closing to 2.0% of the initial pool, and the Required Pro Forma Note Balance is 14.75% of the pool less the amount on deposit in it — so the reserve sets how far the turbo runs, and through that every class's retirement date. It is a declared account here, funded by its own inflow at closing rather than out of the waterfall, which allocates collections and never touched it. Clause 19 is then the top-up it is: whatever the balance is short of the required amount. On this deal, with no losses assumed, that is zero at every period — because the balance is at target, which is what the clause says.

All twenty-two clauses are written out. Ten of them — the parity steps and the final-maturity steps — pay nothing at every period and every speed, because the pool always covers the notes and every class retires years early. They are there because the deal has them.

The result

The model agrees with the reference to 5 cents, across all seven classes, every clause of the waterfall and all 63 periods — 32 asserted series, not the balances alone. Against the published grid, the reference reproduces:

The published grid rounds to whole percentages, so a model that is exactly right has errors uniform on [0, 0.5]. The mean and the maximum both sit where that distribution puts them, which is stronger evidence than either cell count: a model that is subtly wrong shows a biased distribution even when every individual cell passes.

Five conventions had to be recovered, none of them stated in the document: a January-cutoff pool pays twice before the first distribution, and pays two months of servicing fee with it; ABS runs from origination, which retires four seasoned pools outright at 2.00%; the step-down floor is 0.50% of the initial pool; and weighted average life runs 30E/360 from closing to the 18th, with a 25-day stub. NOTES.md records each, with the readings tested and rejected against it.

The delta

Three cells sit outside the floor, by 0.60 to 0.68 of a point: Class A-1 at its second or third distribution date, at three of the four speeds. That is about $1.1m of principal in one month on a $182m class, and it is left open rather than fitted. The stub first interest period — 25 days on a 30/360 basis or 23 actual days from closing to the first payment — was tested and is worse, which is the arithmetic consequence of the assumption that every month has 30 days.

Every published weighted average life is reproduced, to call and to maturity.

What the case does not assert

• One speed. The model runs at 1.50% ABS. The other three published speeds are the same model with abs_speed changed, and docs/20 §2.3 is the reason they are not four directories.
• The weighted average lives. All 48 are reproduced by the reference and none is asserted by the case: docs/20 §3.1 — a published life still has no series or metric to check it against.
• Anything after the clean-up call. The call retires the notes at period 47 and there is no trust left to distribute from, so the cash columns end there. The loans are repurchased at the next period — the servicer's clean-up call, an option written on the trust and exercised when the balance the trust carries in falls to 10% of the cutoff balance — and produce nothing more inside the model.
• Mutation testing. docs/20 §3.3 asks for it and it has not been run. The hole docs/20 §3.2 warns about is present by construction here: the certificateholder's step-down release absorbs whatever the notes are not paid, so a residual assertion is one-sided.

What the expectations are, and are not

expected.csv is the reference implementation's, not the prospectus's. It holds every class balance and every clause of the distribution, so the waterfall is pinned as well as the grid — without the cash columns the model's twenty-two steps would be unchecked, since the balances come from the recurrence rather than from the waterfall.

The two implementations are independent in their arithmetic and not in their inputs: the model was generated from the same twelve-pool table and the same class terms the reference carries, so a transcription error would appear in both. What guards the inputs is the published grid itself — 195 informative cells at four speeds is not something a mistyped balance or coupon survives.

model.total is a regression anchor from this model, not an external figure. Every external assertion is the independent reference against the published grid; expected.csv holds that reference's per-period class balances.

Run configuration

{"deterministic":{"annual_discount_rate":0.03}}

Verified results

Checked period by period: 31 series across 64 periods — 1576 values in all, each within ±1.00 of the reference.

• container.trust.bal_a1
• container.trust.bal_a2
• container.trust.bal_a3
• container.trust.bal_b
• container.trust.bal_c
• container.trust.bal_d
• container.trust.bal_e
• notes.distribution.servicing
• notes.distribution.trustee_fees
• notes.distribution.a1_interest
• notes.distribution.a2_interest
• notes.distribution.a3_interest
• notes.distribution.b_interest
• notes.distribution.c_interest
• notes.distribution.d_interest
• notes.distribution.e_interest
• notes.distribution.a1_principal
• notes.distribution.a2_principal
• notes.distribution.a3_principal
• notes.distribution.b_principal
• notes.distribution.c_principal
• notes.distribution.d_principal
• notes.distribution.e_principal
• notes.distribution.a1_accelerated
• notes.distribution.a2_accelerated
• notes.distribution.a3_accelerated
• notes.distribution.b_accelerated
• notes.distribution.c_accelerated
• notes.distribution.d_accelerated
• notes.distribution.e_accelerated
• notes.distribution.residual

Summary metrics for the base run: