Module 32 · Computing credit risk
Structured credit risk — losses through a waterfall
For a corporate bond, credit risk is a spread question. For a tranche of a CLO, ABS or CMBS deal, it's a distribution question, computed in two stages: first model how much the collateral pool loses, then push that loss through the waterfall to see how much reaches your tranche.
Stage one is a handful of collateral assumptions: CDR (the annual default rate), severity(loss per defaulted dollar), and how long the pool is outstanding. Together they give a cumulative collateral loss — defaults × severity.
Stage two is pure structure. Your tranche has an attachment point(the subordination beneath you — losses up to here are someone else's problem) and a detachment point(past here, you're wiped out). The payoff is a hockey stick: 0% written down below attach, 100% above detach, and a violently steep ramp in between. Three numbers summarize your position on it:
- Credit enhancement / cushion — the distance between current collateral losses and your attachment point. This is the state variable to track deal by deal, month by month.
- Break-even CDR — the constant default rate at which losses just reach your attachment. The margin of safety expressed in the collateral's own units.
- Structural leverage — inside the loss window, each 1% of extra collateral loss destroys 1/thickness of your tranche. A 3%-thick mezz bond loses 33% of face per point of collateral loss.
That leverage is why tranche risk is non-monotonic and non-linear in ways single-name credit never is: one large obligor default can wipe a thin mezzanine tranche while barely denting the senior above it, and equity and mezzanine tranches take opposite sides of default correlation (covered in Module 29).
🎛 Tranche credit lab
Tranche
10–15%
attach – detach
Cum. defaults 5y
14.1%
1 − (1 − CDR)^T
Collateral loss
5.7%
defaults × severity
Loss cushion
4.3%
attach − collateral loss
Tranche writedown
0%
of tranche face
Break-even CDR
5.59%
first dollar of loss
Wipe-out CDR
8.97%
tranche fully written down
The tranche payoff is the hockey stick above: nothing until collateral losses reach the attachment (amber line), then total destruction by the detachment (red line). Tranche credit risk is a question about the collateral loss distribution relative to those two lines — not a spread-duration number. Educational tool — not investment advice.
How the lab computes it
cum defaults = 1 − (1 − CDR)^T collateral loss = cum defaults × severity tranche loss = clamp( (col.loss − attach) / thickness, 0, 1 ) break-even CDR : solve collateral loss(CDR) = attach leverage = 1 / thickness (inside the loss window)
Real deal engines (Intex-style) run full cashflow waterfalls — coverage tests, excess spread, sequential vs pro-rata paydown — and desks run whole vectors of CDR/CPR/severity scenarios rather than single points. But every one of those scenarios lands back on this picture: where did collateral losses end up relative to attach and detach?
The portfolio trap: obligor overlap
The credit enhancement math above is per-deal. The risk that actually bites a structured-credit portfolio is that the same borrowers appear in many deals — a leveraged-loan issuer might sit in dozens of CLOs at once. Deal-level aggregation makes ten CLO positions look diversified when they share most of their collateral. Proper risk requires look-through to the obligor: map every underlying borrower across every deal, aggregate the exposure, and net it against any single-name or index hedges. (And on capital: securitizations get standardized regulatory treatment — SEC-ERBA/SEC-SA under FRTB — no matter how good your internal model is.)
Things to try
- • Pick the Mezzanine preset and raise CDR slowly — nothing, nothing, nothing, then the tranche shreds over a ~1% CDR range. That cliff is the defining feature of mezz risk.
- • Compare break-even CDR across the three presets at 40% severity — senior survives default rates that vaporize the equity several times over. Same pool, different bonds.
- • Halve the thickness of the mezz tranche — break-even CDR barely moves, but the leverage inside the loss window doubles. Thin tranches don't drift; they gap.
- • Drop severity from 40% to 20% (senior-secured loans vs subordinated collateral) — every break-even doubles. Recovery assumptions matter as much as default assumptions.