The first-loss classes are bought on a loss scenario, not a spread, and moving the losses three years earlier costs almost as much as an extra point of loss.
A B-piece buyer prices the first-loss classes by writing down the expected pool losses against them, year by year, and discounting what is left at a target yield. On an illustrative $65.0M B-piece with a 4.75 per cent coupon, a 3.00 per cent cumulative pool loss written off in years 5 to 7 and a 14.00 per cent target, the price is $22.97M, 35.35 cents on the dollar. Without the losses the same bond would be worth 51.75 cents, and bought at 35.35 it would show a 20.36 per cent yield that nobody should expect to earn.
Worked in full in CMBS and CRE CLOs by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The B-piece is the set of classes below investment grade in a conduit deal, usually the last six or seven per cent of the pool. Because losses are allocated reverse-sequentially, every dollar of pool loss up to its size lands on it first, which is why it is priced on a loss scenario rather than on a spread.
| Input | Value |
|---|---|
| Pool balance | $1,000.00M |
| B-piece face, share of pool | $65.00M, 6.50% |
| B-piece coupon, on the written-down balance | 4.75% |
| Term, principal paid last (sequential pay) | 10 years |
| Cumulative pool loss | $30.00M, 3.00% |
| Timing of the write-downs | equal, years 5 to 7 |
| Target loss-adjusted yield | 14.00% |
Price = Σ (interest on the written-down balancet + principalt) ÷ (1 + y)t
Each year the balance falls by the losses allocated to it, interest is paid on what remains, and the surviving face comes back at the end. In Excel: =NPV(14%,CashFlows), with the yield at a given price from =IRR on the price and the same row.
The pool loss of 30.00 is 46.15 per cent of the B-piece. Written off at 10.00 a year, the balance goes from 65.00 to 55.00, 45.00 and 35.00.
| Year | Balance | Interest | Principal | Cash |
|---|---|---|---|---|
| 1 to 4, each | 65.00 | 3.09 | 0.00 | 3.09 |
| 5 | 55.00 | 2.61 | 0.00 | 2.61 |
| 6 | 45.00 | 2.14 | 0.00 | 2.14 |
| 7 to 9, each | 35.00 | 1.66 | 0.00 | 1.66 |
| 10 | 35.00 | 1.66 | 35.00 | 36.66 |
| Total, undiscounted | 58.75 |
Discounted at 14.00 per cent, the row is worth 22.97, or 35.35 cents. The same bond with no losses is worth 33.64, or 51.75 cents, so the loss scenario costs 10.66 of price. At 35.35 cents the year-1 coupon of 3.09 is a current yield of 13.44 per cent: almost all of the return is running cash until the write-downs begin.
The buyer bids 35.35 cents. If the pool loses nothing, the bond returns 20.36 per cent; if it loses 3.00 per cent on schedule, 14.00 per cent. The spread between the two is the buyer's whole view of credit, which is why a B-piece buyer re-underwrites every loan in the pool and can kick loans out before pricing: each loan removed is loss removed from its own class.
The pool loss that wipes out the B-piece is its own thickness. Here that is 6.50 per cent of the pool, $65.00M. At 5.00 per cent cumulative loss the bond still returns 6.48 per cent at the base price, but the margin above that is thin.
| Cumulative pool loss | Price, cents | Yield at 35.35 |
|---|---|---|
| 0.00% | 51.75 | 20.36% |
| 1.00% | 46.28 | 18.57% |
| 2.00% | 40.81 | 16.49% |
| 3.00% | 35.35 | 14.00% |
| 4.00% | 29.88 | 10.85% |
| 5.00% | 24.41 | 6.48% |
| Write-downs in | Price, cents | Yield at 35.35 |
|---|---|---|
| Years 2 to 4 | 31.41 | 12.04% |
| Years 5 to 7 | 35.35 | 14.00% |
| Years 8 to 10 | 38.00 | 15.31% |
Each point of pool loss is worth about 5.47 cents of price, and timing is worth almost as much as a point of loss: the same loss arriving three years earlier costs 3.94 cents, because the coupon is lost on the written-down balance for longer. That is why appraisal reductions matter to a first-loss buyer long before any loss is realised: they cut the interest the class receives while the loan is still being worked out. Moving the target yield from 10.00 to 18.00 per cent takes the price from 44.75 to 28.59 cents.
The common mistake is to quote the yield on the bond's contractual cash flows, 20.36 per cent at the 35.35 price, as if it were the return. That number assumes no pool losses at all, in the one class designed to absorb them. Compare B-piece bids on the loss-adjusted yield, and state the loss scenario and its timing next to it. The second mistake is to model losses as a single write-down at maturity: the same 3.00 per cent loss is worth 38.00 cents if it arrives late and 31.41 if it arrives early.
The loss the B-piece absorbs depends on how severity is measured: realised severity runs above appraisal severity, and the classes above the B-piece are protected by exactly the subordination it provides, as in how credit enhancement is calculated.
Price a B-piece on a stated loss scenario: write the losses down against the class in the years they are expected, pay interest only on what survives and discount at the target. Here that gives 35.35 cents. The free workbook for this case takes a target yield and a loss scenario and returns the bid, with the timing grid live so you can find your own indifference points.
It is the set of classes below investment grade, usually the bottom six or seven per cent of a conduit pool, which absorbs losses first under reverse-sequential allocation. In the illustrative deal it is 6.50 per cent of a 1,000.00M pool, so a cumulative pool loss of 65.00M wipes it out entirely.
Because once a loss is written down, the class stops earning its coupon on that amount. The same 30.00M of loss written down in years 2 to 4 gives a price of 31.41 cents at a 14.00 per cent target, against 38.00 cents if it arrives in years 8 to 10.
Much more than its loss-adjusted yield. Bought at 35.35 cents on a 4.75 per cent coupon, the illustrative B-piece returns 20.36 per cent with no losses and 14.00 per cent with the 3.00 per cent pool loss priced in. Only the loss-adjusted figure is comparable between bids.
This article is one calculation from CMBS and CRE CLOs. 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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