Outline how tranching works and how credit losses are spread across tranches in a securitization.
The idea
Tranching slices a pool into claims of different seniority. Each claim is defined by an attachment point A, the pool loss at which it starts to lose, and a detachment point D, the pool loss at which it is wiped out. Pool losses are absorbed from the bottom: equity first, then mezzanine, then senior. Let L be the pool loss as a percentage of the pool. Putting these together, the loss on one tranche as a percentage of the pool is Loss = max(0, min(L, D) − A). Dividing by the thickness D − A gives the loss as a percentage of tranche notional. The tranche losses always add up to the pool loss. The common mistake is to quote the loss against the pool instead of against the tranche, which hides the leverage of thin junior tranches. Exam point: a thin tranche can lose most of its notional while the pool loses only a small fraction.
Formulas
Loss on a securitisation tranche
tranche loss rate = min[max(L − A, 0) ÷ (D − A), 1]
- L
- the loss on the underlying pool, as a share of the pool
- A
- the tranche's attachment point
- D
- the tranche's detachment point; D − A is its width
Losses climb from the bottom of the structure. Divide by the tranche's thickness to state the loss against its own notional; quoting it against the pool hides the leverage.
A practice question
In a securitization, the attachment point of a tranche is:
- the pool loss at which the tranche is completely wiped out.Why not: That is the detachment point, not the attachment point.
- the pool loss at which the tranche begins to lose. - correct
- the tranche's notional as a percentage of the pool.Why not: That is the tranche's thickness, which is detachment minus attachment.
- the coupon at which the tranche is issued.Why not: The coupon is the price of the tranche, not a loss threshold.
A tranche loses nothing until pool losses reach its attachment point and loses everything at its detachment point; between the two it loses in proportion. Thickness is detachment minus attachment.
A harder one
A pool has notional USD 800 million. The tranches are equity (0 to 4 percent of the pool), mezzanine (4 to 12 percent) and senior (12 to 100 percent). Pool losses reach 7 percent. What fraction of the mezzanine tranche's notional is lost?
- 7.0 percentWhy not: Reports the pool loss rate instead of the loss on the tranche.
- 3.0 percentWhy not: Computes the loss as a percentage of the pool (7% - 4%) and does not divide by the 8% thickness.
- 58.3 percentWhy not: Treats mezzanine as absorbing the pool loss from zero (7% / 12%) instead of only the part above 4%.
- 37.5 percent - correct
The mezzanine absorbs the loss above its 4 percent attachment: 7% - 4% = 3% of the pool, which is USD 24 million. Its notional is 8% of USD 800 million = USD 64 million, so the loss is 24 / 64 = 37.5 percent.
The hardest tier
A pool of USD 1,000 million contains 100 loans of equal size, each with loss given default of 60 percent. Twelve loans default. The tranches are equity (0 to 5 percent), mezzanine (5 to 15 percent) and senior (15 to 100 percent). What loss does the mezzanine tranche suffer, as a percentage of its notional?
- 72 percentWhy not: Reports the pool loss in USD million (72) as a percentage of the mezzanine; it forgets that pool loss is 7.2% and the mezzanine absorbs only the part above 5%.
- 22 percent - correct
- 100 percentWhy not: Assumes the mezzanine is wiped out because the equity tranche is.
- 12 percentWhy not: Uses the 12 percent default rate as the pool loss, ignoring loss given default of 60 percent.
Pool loss = 12 x USD 10 million x 60% = USD 72 million = 7.2% of the pool. Equity absorbs the first 5%, leaving 2.2% of the pool = USD 22 million for the mezzanine, whose notional is 10% of USD 1,000 million = USD 100 million. The loss is 22 percent.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Structured Credit Risk
- Outline the usual kinds of structured products.
- Describe how a securitization's waterfall is organised.
- Name the chief parties taking part in securitizing assets, and spell out where their interests may clash.
- Work through and evaluate the first iteration or two of interim cashflows for a securitization split into three tiers.
- Spell out how excess spread is dealt with in a securitization structure, and work out the overcollateralization account's value as each year ends.
- Account for the tests a custodian runs on excess spread at each year end to decide what cash flows to the overcollateralization account and to equity noteholders.
- Spell out a simulation-based way of arriving at credit losses for each tranche of a securitization.
- Show why a securitization's credit risk depends on the default probabilities and default correlations of its collateral.
- Account for how tranche default sensitivities are gauged.
- Spell out the factors of risk to which structured products are subject.
- Show what is meant by implied correlation and the way it can be gauged.
- Name the motives behind the use of structured credit products.