The cap turns a fixed-rate bond into a bet on which loans stay in the pool, and the bondholder only ever loses that bet.
A WAC-capped CMBS bond pays the lesser of its stated coupon and the pool's net weighted average coupon, so when the highest-coupon loans leave the pool the bond's coupon falls with the pool. On an illustrative $500.0M pool with a net WAC of 5.11 per cent, a class with a stated 5.00 per cent coupon is paid in full only while the highest-coupon loans stay; once the two highest-coupon loans repay, the net WAC drops to 4.85 per cent, and the $30.0M class loses 14.6 basis points, $43,929 a year, without a single loss being allocated.
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 cap is a line in the prospectus that most investors read once. It matters because it turns a fixed-rate bond into one that depends on which loans survive, and the loans that leave a pool early are rarely a random sample.
A conduit pool cut down to six loans, so the arithmetic can be followed by hand. All figures are illustrative.
| Loan | Balance | Mortgage rate | Annual interest |
|---|---|---|---|
| Office, 1 | 120.0 | 5.60% | 6.72 |
| Retail, 2 | 100.0 | 5.35% | 5.35 |
| Multifamily, 3 | 90.0 | 5.10% | 4.59 |
| Industrial, 4 | 80.0 | 4.95% | 3.96 |
| Hotel, 5 | 60.0 | 4.80% | 2.88 |
| Self storage, 6 | 50.0 | 4.60% | 2.30 |
| Pool | 500.0 | 5.16% | 25.80 |
WAC = Σ(loan balance × mortgage rate) ÷ pool balance = 25.80 ÷ 500.0 = 5.16%
Net WAC = WAC − administrative fee rate = 5.16% − 0.05% = 5.11%
Strictly, each loan's net mortgage rate is its rate less its own fee strip, and the pool figure is the balance-weighted average of those net rates. With one fee rate across the pool the two give the same answer.
Class C coupon = MIN(5.00%, net WAC) = MIN(5.00%, 5.11%) = 5.00%
Excel, with balances in B2:B7, rates in C2:C7 and the fee in F1: =MIN(5%,SUMPRODUCT(B2:B7,C2:C7)/SUM(B2:B7)-F1)
At issue the class has 11 basis points of cushion, worth $33,000 a year on $30.0M. That cushion is not the bondholder's: in a typical conduit it is part of what the interest-only strip receives. The cap only binds once the cushion is gone.
Recompute the net WAC on the loans that remain. When loans 1 and 2 mature at the end of year one and repay, $220.0M of the highest-coupon collateral leaves, carrying 12.07 of the 25.80 of annual interest. The 280.0 that remains earns 4.9036 per cent gross, 4.85 per cent net, and the cap now binds.
| Loans that have repaid | Pool, $M | Net WAC | Class C coupon | Lost, bp | Lost, $ a year |
|---|---|---|---|---|---|
| None | 500.0 | 5.11% | 5.00% | 0.0 | 0 |
| Loan 1 | 380.0 | 4.97% | 4.97% | 2.9 | 8,684 |
| Loans 1 and 2 | 280.0 | 4.85% | 4.85% | 14.6 | 43,929 |
| Loan 6 | 450.0 | 5.17% | 5.00% | 0.0 | 0 |
| Loans 1, 2 and 6 | 230.0 | 4.92% | 4.92% | 8.0 | 24,130 |
The lost interest is $3,661 a month in the second case. It is not a shortfall to be reimbursed later, and it is not covered by servicer advances: the coupon has simply been redefined by the pool. Lost in each of years two to six and discounted at an illustrative 6.50 per cent, the second case is worth $171,411, or 0.57 points of price on the class. A buyer who paid a premium for a 5.00 per cent bond has paid for coupon that will not arrive.
The asymmetry in the table is the whole point. A low-coupon loan repaying, loan 6, raises the net WAC to 5.17 per cent, but the class cannot go above 5.00 per cent, so the bondholder gains nothing. A high-coupon loan repaying cuts the coupon. The cap is a short option on the pool's mix, and the bondholder wrote it.
Conduit loans are usually locked out of voluntary prepayment and then open only to defeasance or yield maintenance, so early payoffs come mostly from three places:
Read the definition. Many pooling and servicing agreements compute the net mortgage rate without regard to later modifications, so a rate cut in a workout does not flow into the cap; others differ. Loans that accrue on an actual/360 basis also have their net rate adjusted month by month so that a 31-day month and February pay the right amount to 30/360 bonds, which makes the monthly net WAC move even when no loan has left.
The same pool supports three kinds of coupon. A fixed WAC-capped class, like class C, is fixed until the cap binds. A WAC class pays the net WAC itself, 5.11 per cent at issue and 4.85 per cent after loans 1 and 2 repay, so it moves in both directions. A WAC-minus class pays the net WAC less a spread, 0.30 per cent here, so 4.81 per cent at issue and 4.55 per cent later: it has the same exposure as the WAC class at a lower level. Only the fixed capped class has the one-sided profile, which is why the cushion at issue is the number to price. Where the interest-only strip sits in this, and how it shrinks first, is worked in how the coupon on a CMBS X-A class is calculated.
Treating the stated coupon as the coupon. Yield tables that run the bond at 5.00 per cent to maturity assume the cushion survives every payoff. The test is to rerun the net WAC with the highest-coupon loans removed, then with the shorter-term loans removed, and see whether the class stays above its stated rate. Here the cushion is 11 basis points, and loan 1 alone, 24 per cent of the pool, takes 13.9 basis points off the net WAC, more than the whole cushion.
A WAC-capped bond is fixed rate only while the pool's mix holds. Measure the cushion between the net WAC and the stated coupon, rank the loans by rate and expected payoff date, and recompute. On this pool two maturities cost the class 14.6 basis points a year for the last five years of its life. The full tape, stack and waterfall these figures sit inside are in the free workbook for this case, and the order in which interest reaches each class is in how a CMBS waterfall works.
The net weighted average coupon is the balance-weighted average mortgage rate of the loans in the pool, less the administrative fees taken off the top: servicing, trustee and similar strips. On an illustrative $500.0M pool earning 25.80 a year, the gross WAC is 5.16 per cent and, after a 0.05 per cent fee rate, the net WAC is 5.11 per cent. It is recomputed every month on the loans still in the pool.
Because its coupon is defined as the lesser of a fixed rate and the net WAC, or as the net WAC itself. When higher-coupon loans mature, are liquidated or otherwise leave, the average rate of what remains falls. In the illustrative pool, two loans paying 5.60 and 5.35 per cent repaying take the net WAC from 5.11 to 4.85 per cent, below a 5.00 per cent stated coupon.
Usually not. A defeased loan stays in the pool at its original mortgage rate, with payments now made from a portfolio of government securities, so its rate keeps counting in the net WAC. Loans that actually repay or are liquidated leave the calculation. That is why a defeasance is neutral for a WAC-capped class while a liquidation of a 5.60 per cent loan can cost it several basis points.
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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