Attachment, detachment, loss given default and the annualised default rate, worked tranche by tranche on one illustrative CLO, with the loss grid and a recovery stress.
A CLO tranche starts to lose principal when cumulative pool losses reach its attachment point, so its break-even cumulative default rate is the attachment divided by the loss given default. On an illustrative CLO whose loans lose 35 per cent in default, the BB tranche attaching at 9 per cent breaks even at a cumulative default rate of 25.71 per cent, about 5.77 per cent a year over five years, and the BBB at 37.14 per cent. The AAA, attaching at 36 per cent, would need defaults above 100 per cent of the pool.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A CLO buys a pool of senior secured loans and finances it with a stack of tranches. Losses are absorbed from the bottom: the equity first, then BB, then BBB and upwards. Each tranche is defined by two points expressed as a share of the pool. The attachment is the pool loss at which it starts to lose; the detachment is the loss at which it is wiped out. Everything below the attachment is the tranche's subordination.
The calculation therefore needs only one translation: from defaults to losses. A defaulted loan does not lose its whole face value; the pool loses the default rate times the loss given default. The grid below is the generic CLO in the companion workbook of The Credit Investor; it is illustrative, not a description of any real deal.
| Tranche | Attachment | Detachment | Thickness | Spread over SOFR |
|---|---|---|---|---|
| AAA | 36% | 100% | 64% | 1.30% |
| AA | 25% | 36% | 11% | 1.80% |
| A | 19% | 25% | 6% | 2.30% |
| BBB | 13% | 19% | 6% | 3.50% |
| BB | 9% | 13% | 4% | 6.50% |
| Equity | 0% | 9% | 9% | residual |
Loss given default on the loans is 35 per cent, a 65 per cent recovery.
Step 1: pool loss from a cumulative default rate (CDR).
Pool loss = CDR × LGD
Tranche loss, as a share of the tranche = min(max(pool loss − attachment, 0), thickness) / thickness
Excel: =MIN(MAX(CDR*LGD-Att,0),Det-Att)/(Det-Att)
Step 2: invert it. The tranche takes its first loss when CDR × LGD equals the attachment, and is wiped out when it equals the detachment.
Break-even CDR = attachment / LGD; wipe-out CDR = detachment / LGD
BB: 9 / 35 = 25.71%; wiped out at 13 / 35 = 37.14%
BBB: 13 / 35 = 37.14%; wiped out at 19 / 35 = 54.29%
Step 3: annualise, because default forecasts are quoted per year. A cumulative rate C over n years corresponds to an annual rate of 1 − (1 − C)1/n. Over five years, the BB's 25.71 per cent is 5.77 per cent a year.
| Tranche | First loss at CDR | Wiped out at CDR | First loss, a year | Wiped out, a year |
|---|---|---|---|---|
| AAA | 102.86% | never | never | never |
| AA | 71.43% | never | 22.16% | never |
| A | 54.29% | 71.43% | 14.49% | 22.16% |
| BBB | 37.14% | 54.29% | 8.87% | 14.49% |
| BB | 25.71% | 37.14% | 5.77% | 8.87% |
| Equity | 0.00% | 25.71% | 0.00% | 5.77% |
Run forward instead, the same arithmetic gives the loss grid. At a 30 per cent CDR the pool loses 10.5 per cent; the equity is gone and the BB loses (10.5 − 9) / 4 = 37.5 per cent of its face.
| CDR | Pool loss | AAA | AA | A | BBB | BB | Equity |
|---|---|---|---|---|---|---|---|
| 10% | 3.5% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 38.9% |
| 20% | 7.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 77.8% |
| 30% | 10.5% | 0.0% | 0.0% | 0.0% | 0.0% | 37.5% | 100.0% |
| 40% | 14.0% | 0.0% | 0.0% | 0.0% | 16.7% | 100.0% | 100.0% |
| 50% | 17.5% | 0.0% | 0.0% | 0.0% | 75.0% | 100.0% | 100.0% |
Set against the book's own assumption for leveraged loans, 3.00 per cent of the pool defaulting each year, five years give a cumulative rate of 14.13 per cent and a pool loss of 4.94 per cent. The equity loses 54.9 per cent of its par; the BB keeps 4.06 points of cushion and can absorb 1.92 times the assumed annual default rate before it loses anything, the BBB 2.96 times.
LGD sits in the denominator, so the break-evens are as sensitive to recoveries as to defaults.
| LGD | AA | A | BBB | BB | BBB, a year | BB, a year |
|---|---|---|---|---|---|---|
| 25% | 100.0% | 76.0% | 52.0% | 36.0% | 13.65% | 8.54% |
| 35% | 71.4% | 54.3% | 37.1% | 25.7% | 8.87% | 5.77% |
| 45% | 55.6% | 42.2% | 28.9% | 20.0% | 6.59% | 4.36% |
| 60% | 41.7% | 31.7% | 21.7% | 15.0% | 4.77% | 3.20% |
Moving recoveries from 65 to 40 per cent takes the BB's annual break-even from 5.77 to 3.20 per cent, barely above the 3.00 per cent base case. A tranche that looks safe on default rates can be thin on recoveries, so the recovery assumption deserves its own stress, not a footnote.
The common mistake is to compare a cumulative break-even with an annual default rate: reading 25.71 per cent against a 3 per cent default forecast suggests more than eight times cover, when the like-for-like figure is 1.92 times. The second is to treat this grid as a cash flow model. It ignores excess spread, which pays down losses each year, the overcollateralisation tests that divert cash from equity to the senior notes, reinvestment, and timing, all of which make real CLO debt tranches more resilient than the static grid and make the equity's return path-dependent. Use the static break-even as a floor for the debt and a first screen, not a price.
The tranche grid, the loan fund's expected loss and the rest of Part I's yield and loss figures are live formulas in the free workbook for this case. The same subordination arithmetic applied to a bank's synthetic tranche is in how to calculate the return on an SRT tranche.
The equity is wiped out when pool losses reach its detachment point, the BB attachment. With equity from 0 to 9 per cent and a 35 per cent loss given default, that is a cumulative default rate of 9 / 35 = 25.71 per cent, or 5.77 per cent a year over five years, ignoring excess spread. At 3.00 per cent annual defaults for five years the equity loses 54.9 per cent of its par.
In this static grid only if pool losses exceed its 36 per cent attachment. At a 35 per cent loss given default that needs a cumulative default rate of 102.86 per cent, more than the whole pool, so the AAA cannot lose principal. At a 60 per cent loss given default the threshold falls to 60.0 per cent of the pool defaulting, still far beyond historical leveraged loan experience.
Annual rate = 1 minus (1 minus cumulative rate) to the power one over the number of years. A 25.71 per cent cumulative break-even over five years is 5.77 per cent a year; 37.14 per cent is 8.87 per cent a year. Going the other way, 3.00 per cent a year for five years compounds to 14.13 per cent cumulative.
This article is one calculation from The Credit Investor. 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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: credit, private credit and distressed debt → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.