An IO class has no principal: it owns the excess interest the loans pay over the bonds, and it shrinks as the deal pays down.
The X-A coupon is the pool's net weighted average coupon less the balance-weighted coupon of the classes it references, paid on a notional equal to their outstanding balance. On an illustrative $1,000M conduit, a net WAC of 6.225 per cent against an A-class average of 5.710 per cent gives a strip of 0.515 per cent on $700.0M, $3.605M in year 1. The strip and the notional both shrink as the deal pays down, and at a 7.00 per cent yield the class is worth 2.81 points.
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 →
Every conduit CMBS issues one or more interest-only classes, usually labelled X-A and X-B. They have no principal of their own. They exist because the loans pay more interest than the fixed-rate bonds need: the senior classes are sold at coupons below the pool's rate, and the difference, the excess interest, is carved off and sold separately. The calculation is a subtraction, but both sides of it move every month.
| Item | Balance, $M | Rate | Term / note |
|---|---|---|---|
| 5-year interest-only loans | 150.0 | 6.50% | 5 years |
| 7-year interest-only loans | 50.0 | 6.40% | 7 years |
| 10-year interest-only loans | 500.0 | 6.20% | 10 years |
| 10-year loans, 30-year amortisation | 300.0 | 6.25% | 10 years |
| Top-of-pool fees (servicer, trustee, administration) | 0.045% | a year | |
| A-1 / A-2 / A-3 | 30.0 / 160.0 / 60.0 | 4.90% / 5.55% / 5.70% | fixed |
| A-4 / A-5 | 250.0 / 200.0 | 5.80% / 5.85% | fixed |
| Subordinate classes | 300.0 | not in X-A |
X-A references the five A classes, $700.0M in all. Principal is paid sequentially, A-1 first; the pool pays down on the same schedule as in the weighted average life example.
Net WACt = Σ(loan balance × loan rate) ÷ pool balance − fees
X-A ratet = net WACt − Σ(class balance × class coupon) ÷ Σ class balance
X-A interestt = X-A ratet × notionalt, notional = sum of the A-class balances
In Excel, per period: =SUMPRODUCT(LoanBal,LoanRate)/SUM(LoanBal)-Fees-SUMPRODUCT(ClassBal,ClassCpn)/SUM(ClassBal), then multiply by SUM(ClassBal).
Year 1: the gross WAC is 6.270 per cent, 6.225 per cent after fees. The A classes average 5.710 per cent by balance. The strip is 0.515 per cent, 51.5 basis points, on $700.0M: $3.605M.
| Year | Net WAC | A-class coupon | Strip | Notional | X-A interest |
|---|---|---|---|---|---|
| 1 | 6.225% | 5.710% | 0.515% | 700.00 | 3.605 |
| 3 | 6.225% | 5.719% | 0.506% | 692.51 | 3.507 |
| 5 | 6.225% | 5.729% | 0.496% | 684.06 | 3.396 |
| 6 | 6.184% | 5.798% | 0.386% | 529.43 | 2.041 |
| 8 | 6.173% | 5.817% | 0.355% | 469.29 | 1.667 |
| 10 | 6.172% | 5.820% | 0.352% | 457.84 | 1.611 |
| Ten years, undiscounted | 26.49 |
Two things erode the strip. The low-coupon A-1 retires first, so the weighted coupon of the A classes drifts up from 5.710 to 5.820 per cent. And in year 5 the 6.50 per cent loans repay, which pulls the pool's net WAC down from 6.225 to 6.184 per cent: WAC drift. Between them the strip falls from 51.5 to 35.2 basis points while the notional falls by a third. Discounted at 7.00 per cent, the ten years of interest are worth $19.687M, 2.81 per cent of the initial notional, which is how an IO price is quoted.
| Yield | Base | Maturities extended | $100M liquidated in year 3 |
|---|---|---|---|
| 6.00% | 2.93 | 3.22 | 2.67 |
| 7.00% | 2.81 | 3.09 | 2.58 |
| 8.00% | 2.71 | 2.97 | 2.48 |
The extension case takes the five-year loans out two years and the 10-year interest-only loans one year. The IO gains 0.28 points: the notional stays outstanding longer and keeps earning the strip. The liquidation case defaults $100.0M of the 10-year interest-only loans, recovering 70 per cent at the end of year 3. The $30.0M loss is written off the subordinate classes, so it never touches X-A's notional, but the $70.0M recovery pays down A-1 and A-2 years early. The notional drops to $618.41M in year 4, the strip earns on less, and the IO loses 0.24 points, $2.54M of interest, undiscounted, that is never paid.
That asymmetry is the point of owning an IO. It has no credit loss in the usual sense and no principal to lose. It loses when principal comes back early, through liquidation, a prepayment that escapes call protection or a loan repaid ahead of its schedule, and it gains when principal comes back late.
The common mistake is to price the year-1 strip as if it lasted: 51.5 basis points on $700.0M for ten years, discounted at 7.00 per cent, gives 3.62 points against the true 2.81, an overpayment of nearly 30 per cent of the price. It ignores both the paydown of the notional and the drift in the two rates. The strip has to be recomputed every period from the balances then outstanding, which means the IO cannot be modelled without the full loan-level principal and coupon schedule behind it.
Check the reconciliation. In every period, interest on the loans less fees should equal interest on all principal classes plus the IO classes, before any shortfall. If the X-A rate is set as a residual against only the A classes, the subordinate classes must be paid at or below the net WAC for the sum to close.
The X-A coupon is net WAC less the weighted coupon of the classes it references, on their balance: 0.515 per cent on $700.0M at issue in this deal, falling to 0.352 per cent on $457.84M by year 10, for a price of 2.81 points at 7.00 per cent. Price it from the full schedule, and run the early-paydown case beside the base. The free companion workbooks for the book carry the loan tape and the net pool coupon after top-of-pool fees that the calculation starts from.
Because a liquidation returns principal early. Losses are written off the subordinate classes, but the recovery pays down the senior classes that make up the IO notional. In the illustrative deal a $100.0M default recovered at 70 per cent in year 3 cuts the X-A notional to $618.41M a year later and the price by 0.24 points.
The change in a pool's weighted average coupon as loans with different rates pay off. When the illustrative pool's 6.50 per cent five-year loans repay, its net WAC falls from 6.225 to 6.184 per cent, and since the bond coupons are fixed, the fall comes straight out of the interest-only strip.
As the present value of the projected strip interest, in points per 100 of initial notional. On the illustrative X-A, $19.687M of discounted interest on $700.0M is 2.81 points at a 7.00 per cent yield, 2.93 at 6.00 per cent and 2.71 at 8.00 per cent.
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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