Mortgage-Backed Securities

A bank writes a 30-year mortgage and its money is gone for 30 years. Do that a few thousand times and the bank has no capacity left to lend. Securitization is the escape hatch: gather the loans into a pool, sell slices of that pool to investors, and get the cash back to lend again. The slices are mortgage-backed securities.

Picture yourself owning one thousandth of a pool of 3,000 mortgages. Every month those households post their cheques. A servicer collects them, takes a small fee, and forwards your one-thousandth share of everything that arrived. That is a pass-through: you are not lending to anyone in particular, you are buying a fraction of a very large, very predictable stream of household payments.

Except it is not predictable, and that is the whole subject.

What actually lands in your account each month

Three things arrive, and it pays to keep them separate.

• Interest on the outstanding balance, at the pass-through rate — the loans' coupon minus the servicing and guarantee fees.
• Scheduled principal, the small amount of the level monthly payment that is not interest.
• Prepayments, unscheduled principal from anyone who refinanced, sold their house, or defaulted (an agency guarantee turns a default into a prepayment at par).

The share of the original balance still outstanding is the pool factor. A pool factor of 0.62 means 38 percent of the original loans have gone, through some mix of amortisation and prepayment.

Worked example: one month of a pool

Take a $400 million pool with a 6.00 percent weighted-average coupon and 0.50 percent of fees, so investors receive a 5.50 percent pass-through rate.

1. Interest to investors. $400{,}000{,}000 \times 0.055 / 12 = 1{,}833{,}333$, so about $1.83 million.
2. Scheduled principal. The level payment on $400 million at 6 percent over 360 months is about $2,398,196. Of that, $400{,}000{,}000 \times 0.06/12 = 2{,}000{,}000$ is interest, leaving roughly $398,000 of scheduled principal.
3. Prepayments. Suppose the pool is running at an 8 percent CPR (conditional prepayment rate — the fraction of the surviving balance expected to prepay over a year). The monthly equivalent, the SMM, is

$$\text{SMM} = 1 - (1 - \text{CPR})^{1/12} = 1 - 0.92^{1/12} = 0.00693$$

In plain terms: if 8 percent of what is left disappears over a year, about 0.693 percent of it disappears each month. Applied to the balance after scheduled principal, $0.00693 \times 399{,}602{,}000 \approx 2{,}767{,}000$, so about $2.77 million of prepayments.

Total principal returned this month is roughly $3.17 million, of which prepayments are seven-eighths. Prepayment is not a footnote to an MBS; it is the dominant cash flow.

Worked example: what a refinancing wave does

Now mortgage rates fall a point and the pool starts paying at a 40 percent CPR. The same arithmetic gives $\text{SMM} = 1 - 0.60^{1/12} = 0.0417$, and prepayments of $0.0417 \times 399{,}602{,}000 \approx 16{,}650{,}000$ — about $16.65 million in a single month, six times the earlier figure.

Read what just happened. Rates fell, so a normal bond would have gone up in price. Instead your high-coupon MBS handed you a pile of cash back at par, precisely when the only place to reinvest it is at the new, lower rate. That is contraction risk. Push rates the other way and the mirror image appears: nobody refinances, prepayments dry up, and you are stuck holding a below-market coupon for far longer than you planned. That is extension risk.

The shape this produces

An ordinary bond's price-yield curve bends upward: it gains more on a rally than it loses on an equal sell-off, and that free asymmetry is positive convexity. The MBS curve bends the other way. Its duration shortens when rates fall and lengthens when rates rise — short when you want to be long, long when you want to be short, every single time.

Where you meet it in practice

Agency MBS carry a US government-linked guarantee against default, so the risk that remains is almost purely prepayment; non-agency deals carry credit risk too and are sliced into tranches. Because negative convexity has to be re-hedged constantly, MBS investors are forced buyers of duration when rates rise and forced sellers when rates fall, which amplifies moves in the Treasury market. The universe is enormous and the liquid front end trades on a TBA basis, where you agree on coupon and settlement month and only learn which specific pools you got two days before delivery.

Key terms

• Pass-through — a security paying a pro-rata share of a pool's collections.
• Pass-through rate — the loan coupon minus servicing and guarantee fees.
• Pool factor — fraction of the original balance still outstanding.
• CPR / SMM — annual and monthly prepayment speeds.
• Contraction / extension risk — getting cash back too fast when rates fall, too slowly when they rise.
• Negative convexity — a price-yield curve that bends downward, so duration moves the wrong way.