Mortgage-Backed Sector of the Bond Market
A mortgage-backed security (MBS) turns a pool of home loans into a tradeable bond. The catch is that borrowers can prepay, so the cash flows are uncertain even without default — the dominant risk here is prepayment risk, not credit. This lesson covers the mortgage itself and its amortisation, passthrough securities, how prepayments are measured (SMM, CPR, the PSA benchmark), average life, and how collateralised mortgage obligations (CMOs) slice the cash flows into tranches that redistribute that risk — sequential, accrual, floater/inverse, IO, PAC and support — plus stripped MBS and commercial MBS.
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Residential MBS come in three forms: mortgage passthrough securities, collateralised mortgage obligations (CMOs), and stripped MBS — the latter two being derivative MBS built by redistributing a passthrough's cash flows. Before the 2008 crisis, agency MBS were viewed as carrying essentially no credit risk, so the focus was prepayment risk and how to redistribute it. We keep that focus, then add the credit dimension for non-agency and commercial MBS.
Learning outcomes
- Describe a mortgage and the cash flows of a fixed-rate, level-payment, fully amortised loan.
- Describe passthrough securities and compute WAC and WAM.
- Calculate the prepayment for a month from the SMM, and relate SMM, CPR and the PSA benchmark.
- Explain why average life is more relevant than maturity, and the factors driving prepayments.
- Distinguish sequential-pay, accrual, PAC and support tranches and their risk under rate changes.
- Explain stripped (IO/PO) MBS, and contrast agency, non-agency and commercial MBS.
2 · Residential mortgage loans
A mortgage is a loan secured by specified real estate that obliges the borrower to make a set series of payments. The interest rate is the mortgage (contract) rate; the lender may foreclose and seize the property on default. The standard U.S. design is the fixed-rate, level-payment, fully amortised mortgage: the rate is fixed for life, every monthly payment is identical, and the final payment leaves a zero balance. Each payment splits into interest (1/12 of the annual rate on the outstanding balance) and a scheduled principal repayment (amortisation). Alternative designs — adjustable-rate, balloon, growing-equity, reverse and tiered-payment mortgages — are the riskier "speculative/Ponzi" units.
Amortisation of a $100,000 mortgage
30-year (360-month) \$100,000 loan, 8.125% rate, level payment \$742.50. Split month 1 into interest and principal, and find the month-2 interest.
Show solution
Monthly rate \(=0.08125/12=0.0067708\). Month-1 interest \(=\$100{,}000\times0.0067708=\$677.08\); principal \(=\$742.50-\$677.08=\$65.41\); end balance \(=\$99{,}934.59\). Month-2 interest \(=0.0067708\times\$99{,}934.59=\$676.64\). As the balance falls, the interest portion declines and the principal portion rises each month. A servicing fee (e.g. 50 bp) is taken from the mortgage rate, so an 8.125% loan pays the investor a 7.625% net coupon. Any payment above the scheduled amount is a prepayment — the source of prepayment risk.
Mo.1: $677.08 interest + $65.41 principal; Mo.2 interest $676.643 · Mortgage passthrough securities
A passthrough is created when holders of a pool of mortgages sell participation certificates in the pool; the mortgages are then securitised. Monthly cash flows pass through to investors less servicing and other fees, so the passthrough rate is below the loans' rates. Because the pooled loans differ, the pool is described by a weighted-average coupon (WAC) and a weighted-average maturity (WAM), each weighted by outstanding balance.
WAC and WAM of a pool
Five loans with weights 22.12%, 15.04%, 30.97%, 19.47%, 12.39%; rates 7.5%, 7.2%, 7.0%, 7.8%, 6.9%; months remaining 275, 260, 290, 285, 270.
Show solution
$$ \text{WAC}=0.2212(7.5)+0.1504(7.2)+0.3097(7.0)+0.1947(7.8)+0.1239(6.9)=7.28\% $$
$$ \text{WAM}=0.2212(275)+0.1504(260)+0.3097(290)+0.1947(285)+0.1239(270)=279\ \text{months} $$
WAC = 7.28%; WAM = 279 monthsThe three U.S. agency guarantors are Ginnie Mae (a federally related institution — full faith and credit of the U.S. government), and Fannie Mae and Freddie Mac (government-sponsored enterprises — guarantee not backed by full faith and credit). A conforming loan meets agency underwriting standards; non-conforming loans fail them and back non-agency securities. Prices are quoted like Treasuries (a quote of 94-05 = 94 + 5/32 = 94.15625% of par), and the pool factor gives the % of the original balance still outstanding.
E.g. a price of 92 on \$1,000,000 par with pool factor 0.85 costs \(0.92\times\$1{,}000{,}000\times0.85=\$782{,}000\).
3.4 · Measuring the prepayment rate
The single monthly mortality rate (SMM) is the month's prepayment as a fraction of the amount available to prepay (beginning balance less scheduled principal). The conditional prepayment rate (CPR) annualises the SMM:
SMM, prepayment and CPR
(a) Month 33: beginning balance \$358,326,766; scheduled principal \$297,825; prepayment \$1,841,347. Find SMM. (b) If next month's balance is \$290m, scheduled principal \$3m and SMM 0.5143%, find the prepayment. (c) Annualise SMM = 0.5143% to a CPR.
Show solution
(a) $$ \text{SMM}_{33}=\frac{1{,}841{,}347}{358{,}326{,}766-297{,}825}=0.5143\%. $$
(b) $$ \text{Prepay}=0.005143\times(290{,}000{,}000-3{,}000{,}000)=\$1{,}476{,}041. $$
(c) $$ \text{CPR}=1-(1-0.005143)^{12}=6\%. $$
SMM = 0.5143%; prepayment ≈ $1.476m; CPR = 6%The 100% PSA benchmark assumes prepayments start slow on new loans and "season": a CPR of 0.2% in month 1, rising 0.2%/month for 30 months until it hits 6%, then a flat 6% thereafter. Formally, \(\text{CPR}=6\%\times(t/30)\) for \(t<30\) and \(6\%\) for \(t\ge30\). Other speeds scale this: "165 PSA" is 1.65× the benchmark CPR at each month, "50 PSA" is half.
3.5 · Average life, and contraction vs extension risk
Because principal arrives gradually (and unpredictably), final maturity is misleading. The average life — the weighted-average time to receive principal — is the relevant measure, and it depends entirely on the prepayment assumption:
For one illustrative passthrough, average life falls from 15.11 years at 50 PSA to 11.66 (100), 8.76 (165), 5.63 (300) and just 2.78 years at 700 PSA — faster prepayments pull cash forward. Prepayments are driven by the prevailing mortgage rate (refinancing incentive), housing turnover, and loan characteristics.
Contraction risk: rates fall → prepayments speed up → the passthrough shortens (cash returns just when reinvestment rates are low). Extension risk: rates rise → prepayments slow → the passthrough lengthens (you are stuck in a below-market bond). This two-sided uncertainty is exactly what CMOs are built to redistribute.
4 · Collateralised mortgage obligations (CMOs)
A CMO redistributes a passthrough's cash flows to different bond classes (tranches) with different prepayment exposures. A CMO cannot eliminate prepayment risk — it reallocates it so each tranche suits a different investor.
Sequential-pay and accrual (Z) tranches
Sequential-pay: all principal (scheduled + prepayments) goes to Tranche A until it is retired, then to B, then C, and so on — so A has the shortest, last tranche the longest, average life. An accrual (Z) tranche receives no current interest; its accrued interest is instead used to pay down the earlier tranches faster. Adding a Z bond therefore shortens A, B and C (e.g. at 165 PSA, tranche A falls from 3.48 to 2.90 years) while the Z bond itself runs long.
Floater and inverse-floater tranches
A fixed-rate tranche can be split into a floater and an inverse floater whose coupons sum to the tranche's fixed interest. The inverse floater pays \(K-L\times\text{LIBOR}\), where \(K\) is the cap and \(L\) the leverage (higher \(L\) → bigger coupon swings):
Splitting tranche C into FL + IFL
Tranche C: \$96.5m at 7.5%. Carve a \$72.375m floater (LIBOR + 0.50%) and a \$24.125m inverse floater. Find the inverse floater's coupon if LIBOR = 3.75%, and verify the cap \(K\).
Show solution
With \(K=28.5\%\) and \(L=3\): coupon \(=28.5\%-3\times3.75\%=17.25\%\). To check \(K\): if LIBOR \(=0\), the floater takes \(0.5\%\times\$72.375\text{m}=\$361{,}875\); tranche C's total interest is \(7.5\%\times\$96.5\text{m}=\$7{,}237{,}500\), leaving the inverse floater \(\$7{,}237{,}500-\$361{,}875=\$6{,}875{,}625\). Then \(K=\$6{,}875{,}625/\$24{,}125{,}000=28.5\%.\)
IFL coupon = 17.25%; cap K = 28.5%Structured IO tranches
Setting a tranche's coupon below the collateral coupon frees excess interest, which can be packaged as a structured interest-only (IO) tranche with a notional principal:
E.g. tranche A (\$194.5m, 6.0% coupon, excess 1.5%) gives \(\$194.5\text{m}\times0.015/0.075=\$38.9\text{m}\) of 7.5% IO notional; summed over the deal, \$52.57m.
4.5 · PAC and support tranches
A planned amortisation class (PAC) bond follows a fixed principal-repayment schedule as long as prepayments stay within a chosen band — the PAC collar (e.g. 90–300 PSA). PAC holders have priority on principal, giving them two-sided protection against both contraction and extension risk. That certainty is bought at the expense of the support (companion) tranches, which absorb the prepayment variability and therefore carry the most prepayment risk. The PAC window is the span over which principal is repaid; a narrow window resembles a bullet bond. As the deal seasons, the band that can still keep the schedule changes — the effective collar. A PAC can be split into a series of sequential PAC tranches (P-A … P-F), and even support tranches can themselves be carved into scheduled (PAC-like) pieces.
5 · Stripped mortgage-backed securities
A stripped MBS (a type of CMO) divides the cash flows into a principal-only (PO) strip and an interest-only (IO) strip, so each is extremely sensitive to prepayments — in opposite directions:
PO is bought at a deep discount; the investor wants fast prepayments — falling rates bring par forward, raising the return. It is an extreme discount security. IO has no par value; it receives interest only on the principal still outstanding, so the investor wants slow prepayments — rising rates (and slower prepayments) help. It is an extreme premium security and can fail to return the amount invested if rates fall. Unusually, an IO's price can rise with rising mortgage rates.
7 · Non-agency and commercial MBS
Non-agency securities carry no government guarantee, so the investor bears credit risk and the deal must be credit-enhanced. Agency underwriting standards govern the maximum loan-to-value (LTV) ratio, payment-to-income ratio, and loan amount.
Commercial MBS (CMBS) are backed by loans on income-producing property and are non-recourse — the lender can look only to the property, not the borrower, for repayment. Each property is assessed as a stand-alone business; the two key credit measures are the debt-service-coverage ratio and the LTV ratio. Deal structures are multi-property single-borrower or multi-property conduit.
Unlike residential borrowers, commercial borrowers face call protection. At the loan level: prepayment lockout, defeasance (substitute a Treasury portfolio replicating the cash flows), prepayment penalty points, and yield-maintenance charges (make the lender indifferent to prepayment timing). At the structure level: sequential-pay-by-rating means an AA tranche cannot pay down until the AAA is retired, and so on. Many CMBS loans are balloon loans, adding balloon risk — the borrower may be unable to refinance or sell to make the final lump-sum payment.
An MBS converts pooled mortgages into bonds whose dominant risk is prepayment, not default. Prepayments are measured by SMM, annualised to CPR and benchmarked against PSA; because they make cash flows uncertain, average life beats maturity, and falling/rising rates create contraction/extension risk. A CMO cannot remove that risk but reallocates it across tranches — sequential, accrual (Z), floater / inverse floater, structured IO, and the two-sided-protected PAC bonds backed by risk-absorbing support tranches. Stripped MBS split it into opposite-facing PO and IO bets, while non-agency and commercial MBS add the credit dimension and their own call protection.