Credit · C11 · 10 min
Mortgage-backed securities I: prepayment
See how home loans become a bond, why homeowners repaying early is the investor’s main risk, and how to measure the speed.
In the news: “Mortgage rates drop and refinancing jumps”: holders of mortgage bonds are about to get their money back early.
The essentials
- Pass-through MBS
- A bond that passes a pool of home loans’ monthly interest and principal to investors, less fees: 6.85% mortgages might pay 6.0%. In the US most are guaranteed by Fannie Mae, Freddie Mac or Ginnie Mae, so default losses are slight.
- Prepayment and extension risk
- US homeowners can repay a fixed-rate mortgage early without a penalty. When rates fall they refinance and money comes back early, to be reinvested lower; when rates rise repayments slow and the bond lasts longer as its value falls.
- Negative convexity
- An shortens when fall, capping its gains, and lengthens when they rise, deepening its losses, because its holder is short the homeowners’ option to repay. MBS pay extra yield to make up for it.
- CPR and SMM
- is the share of remaining loans repaid early in a year; SMM is the monthly rate, so 6% CPR is about 0.514%. Faster speeds shorten the : about 9 years at 8% CPR, under 3 at 30%, for one pool.
- What sets the speed
- Speeds rise when mortgage rates sit well below the loans’ rate and when more people move house; they are slower for new loans and for pools already through a refinancing wave. 100% ramps CPR to 6% by month 30.
- UK mortgages
- Most UK mortgages fix their rate for two or five years, with a fee for repaying early during the fix. So borrowers refinance when the fix ends, not whenever rates fall, and UK mortgage bonds carry far less prepayment risk.
Monthly prepayment speed
SMM = 1 − (1 − CPR)^(1/12)
- CPR
- share of the remaining balance repaid early over a year
- SMM
- the same speed per month (single monthly mortality)
How it works
1. A bond made of mortgages
Thousands of home loans can be pooled into one bond. Each month the homeowners’ payments, interest plus some of the loan itself (the principal), flow through to the bond’s owners. That is a mortgage-backed security, or MBS.
2. The guarantee and the fees
In the US, government-backed agencies guarantee most of these bonds, so investors face almost no losses from homeowners defaulting: . Ginnie Mae’s guarantee is backed by the US government itself. Fees are taken out along the way, so mortgages at 6.85% might pay investors 6.0%.
3. Homeowners can repay early
US homeowners can usually pay off a fixed-rate mortgage at any time without a penalty. When mortgage rates fall, many refinance, and the investor gets money back early, just when it can only be reinvested at lower rates. That is .
4. Or later than expected
When rates rise, almost nobody refinances and fewer people move house, so repayments slow down. The bond lasts longer just as its value is falling. That is .
5. Negative convexity
Put the two together: an MBS shortens when yields fall, capping its gains, and lengthens when yields rise, deepening its losses. An ordinary bond does the reverse. This is , and MBS pay extra yield to make up for it.
6. Measuring speed: CPR
Repayment speed is quoted as : the share of the remaining loans repaid early over a year. A faster speed shortens the pool’s , the average time until its principal comes back: an illustrative 6.5% pool has about 9 years at 8% CPR but under 3 years at 30%.
7. Monthly speed: SMM
Payments arrive monthly, so convert CPR to a monthly rate, the single monthly mortality (SMM): SMM = 1 − (1 − CPR)^(1/12). 6% CPR is 0.514% a month, a little more than 6% ÷ 12. This month’s early repayment = SMM × (balance − this month’s scheduled principal).
8. PSA and what drives speed
A standard curve, the , has CPR rising 0.2% a month to 6% at month 30; 200% PSA doubles it. Speeds rise when today’s mortgage rates are well below the loans’ rate and when more people move. They are slower for new loans, and for pools that have already been through a refinancing wave.
9. The UK is different
Most UK mortgages fix their rate for two or five years, and repaying early during the fix usually costs a fee. So UK borrowers refinance when the fix ends rather than whenever rates fall, and UK mortgage bonds carry far less prepayment risk than US agency MBS.
Try it
This is an ordinary bond: its gains grow faster as yields fall. An MBS does the opposite at low yields, because homeowners refinance.
5% coupon at par · duration 7.72
- Duration says
- −11.58%
- True change
- −10.78%
- Gap (convexity)
- +0.80pts
Worked example
A $100m pool of 6.5% 30-year mortgages prepays at 8% CPR, and this month’s scheduled principal is $0.10m. Then mortgage rates fall 1.5 points and speeds jump to 30% CPR.
- At 8% CPR: SMM = 1 − 0.92^(1/12) = 0.692% a month.
- Early repayment: 0.692% × ($100m − $0.1m) ≈ $0.69m.
- At 30% CPR: SMM = 1 − 0.70^(1/12) = 2.93% a month.
- Early repayment: 2.93% × $99.9m ≈ $2.93m, four times as much, just as rates have fallen.
Monthly early repayments jump from about $0.69m to $2.93m: the bond shortens just as rates fall.
Check yourself
9 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
What are the two big risks of owning MBS?
Why is an MBS negatively convex?
Why might UK mortgage securities behave differently from US agency MBS?
Remember
SMM = 1 − (1 − CPR)^(1/12)
MBS holders are short the homeowner’s option: the bond shortens when rates fall and lengthens when they rise.
Sources
- Ginnie Mae — Overview: Ginnie Mae guaranty agreement, key components
- Bank of England — Monetary policy and mortgage fixation lengths (Staff Working Paper No. 1,158)
Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.