Prepayment risk and time tranching

What is prepayment risk?

The prepayment risk in a mortgage bond is the risk that borrowers repay principal at a different pace from the contractual schedule. It has two parts, and both are driven by the general level of interest rates. Mortgage investors care because a mortgage bond is a bundle of cash flows whose timing the borrowers control.

It comes in two forms, and the direction of rates tells you which one you face.

Prepayment riskprincipal repaid at a different pace than scheduled

• Contraction risk Memorize repaid faster; rates fall, borrowers refinance
  • Reinvest at lower rates Memorize the cash comes back when yields are low
  • Capped price gain Memorize the prepayment option limits the rise in price
• Extension risk Memorize repaid slower; rates rise, borrowers stay put
  • Stuck with a low coupon Memorize for longer than expected
  • Discounted at higher rates Memorize and the payments are stretched out

When rates fall, homeowners refinance at the lower rate. Here contraction risk is the risk that principal comes back faster than expected, so the bond’s life shortens. It hurts twice: the cash must be reinvested at lower rates, and the borrowers’ option to repay at par limits how far the bond’s price can rise.

When rates rise, nobody refinances and some people even delay buying a new home. Here extension risk is the risk that principal comes back slower than expected, so the bond’s life lengthens. You hold a below-market coupon for longer, and the stretched payments are discounted at a higher rate.

	Contraction risk	Extension risk
Trigger	Rates fall; borrowers refinance	Rates rise; borrowers stop prepaying
What happens	Principal returns early; average life shortens	Principal returns late; average life lengthens
Why it hurts	Reinvest at lower rates; price gain is capped	Low coupon for longer; discounted at higher rates

Exam tip Rates down means contraction, rates up means extension. Mortgages in the US carry few prepayment penalties, which is why refinancing waves are so large there. Penalties, common in Europe, reduce contraction risk.

Why does the legal maturity not tell you much?

Scheduled payments and prepayments both reduce the balance, so a mortgage-backed security (MBS) with a 30-year legal maturity may be repaid far sooner or, at times, somewhat later. The market works with the weighted average life (average life): the expected time until principal is repaid, given an assumed prepayment speed.

Use it

$$\text{WAL} = \frac{\sum_t t \times \text{Principal}_t}{\text{Total principal}}$$

Weight each year by the share of principal paid in it. The calculation is the same as any weighted average, with years as the values and principal paid as the weights.

Go deeper Why the US 30-year mortgage creates so much contraction risk

A US borrower can usually repay a fixed-rate 30-year loan at any time with no penalty. The borrower holds a free option: if rates fall, repay and refinance; if rates rise, keep the cheap loan. The investor in the bond has written that option. The result is an asymmetry. When rates fall, the investor’s gain is capped because the bond is repaid at par; when rates rise, the bond falls in price in full and lengthens. This is the origin of negative convexity, which the curve-based risk measures module turns into effective duration and effective convexity.

Go deeper Average life as the MBS investor's working maturity

For an option-free bond, maturity and the timing of cash flows are known. For an MBS they depend on a prepayment assumption, so two investors can quote different average lives for the same bond. The measure is useful because it tells you roughly when you expect to be repaid. It is not a promise: change the assumption and the average life moves, as the three scenarios above show.

What is time tranching?

With time tranching , one pool is cut into bond classes with different expected maturities. In a sequential-pay structure , all principal from the pool, scheduled and prepaid, goes first to Tranche A until it is retired, then to Tranche B, then to Tranche C. Every class still receives its own interest.

Because A is repaid first, B and C stand behind it. If prepayments slow, A still collects before the others, so its life stays short: A is protected against extension risk. C is repaid last, so A and B absorb early prepayments before C is touched: C is protected against contraction risk. Nobody gains for free. The risk the early tranches shed goes to the late ones, and the reverse.

Do not confuse the two ways to cut a pool. Credit tranching ranks classes by who absorbs losses first. Time tranching ranks them by who receives principal first. Many deals combine both.

Tranchingone pool, several bond classes

• Credit tranching Memorize decides who absorbs losses first
  • Senior loses last, paid first on default
  • Subordinated loses first, higher yield
• Time tranching Memorize decides who receives principal first
  • Short tranche (A) short, steady life; protected from extension
  • Middle tranche (B) in between
  • Long tranche (C) long life; protected from contraction

Go deeper Idiosyncratic risks hit the whole pool, whatever the tranching

Time tranching reshuffles timing risk, but it cannot protect a pool from a risk that hits every loan in it. Suppose a pool finances rooftop heat pumps from a single manufacturer, and that manufacturer goes bankrupt. Warranties lapse, repair costs rise and the units lose resale value, so defaults rise and recoveries fall across the whole pool at once. The structure decides who bears a risk, not whether the risk exists.