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Explain prepayment modeling and its four components (curtailments, defaults, turnover and refinancing), and outline the mortgage prepayment option together with the factors influencing it.

FRM® Part I · Financial Markets and Products · Mortgages and Mortgage-Backed Securities · FRM1.FM.18.h

The idea

Prepayment models split prepayments into four components. Curtailments are partial extra principal payments. Defaults, for agency pass-throughs, are repaid to investors by the guarantor, so they act as involuntary prepayments at par. Turnover is full repayment when a home is sold. It depends on mobility and season rather than on rates. Refinancing is driven by the incentive, usually the pool coupon relative to the current mortgage rate. It is S-shaped, with little response until the incentive exceeds transaction costs. The prepayment option is the borrower's right to repay at par, so the investor is short a call, which produces negative convexity. Seasoning, home prices, loan size and burnout shift behaviour. Burnout is the lower response of a pool that has already been through a refinancing wave. The exam point is that borrowers exercise imperfectly and not every prepayment is rate-driven.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which list gives the four components of a prepayment model?

  1. Seasoning, burnout, seasonality and the media effect.Why not: These are factors that shift prepayment speed, not the components of prepayments.
  2. Scheduled amortization, curtailments, turnover and refinancing.Why not: Scheduled amortization is not a prepayment, and defaults are left out.
  3. Curtailments, defaults, turnover and refinancing. - correct
  4. Refinancing, turnover, delinquencies and extensions.Why not: Delinquencies and extensions are not prepayment components.

Total prepayment is modelled as the sum of partial extra payments (curtailments), involuntary repayment from default, home-sale turnover and rate-driven refinancing.

A harder one

Two pools have the same coupon and age, and both are in the money today with a current mortgage rate 150 basis points below the coupon. Pool X went through a refinancing wave earlier when rates dipped. Pool Y has never had an incentive until now. Which pool should prepay faster?

  1. Pool X, because its borrowers have seen low rates before and are more alert.Why not: Reverses burnout: the alert borrowers have already left the pool.
  2. Pool Y, because X is burned out; its responsive borrowers have already left. - correct
  3. Both the same, because they share a coupon and today's incentive.Why not: Ignores path dependence; the rate history matters.
  4. Neither, because burnout applies only to discount pools.Why not: Burnout is a feature of in-the-money (premium) pools such as these.

Burnout means the remaining borrowers in a pool that has been through earlier incentives are less likely to refinance. Prepayment depends on the history of rates as well as today's incentive.

The hardest tier

A borrower has a 30-year mortgage with an original balance of USD 300,000 at 6.00%. She can refinance into a new 30-year loan at 5.00% for the same balance, paying USD 6,000 of closing costs. Ignoring discounting and the small reduction in balance from payments already made, the break-even period is closest to:

  1. 24.0 monthsWhy not: Uses the interest saving on the balance (300,000 x 1% / 12 = 250) instead of the payment saving.
  2. 3.3 monthsWhy not: Divides the costs by the whole old payment instead of the saving.
  3. 2.7 monthsWhy not: Multiplies the saving by 12 and treats the result as months.
  4. 31.9 months - correct

Old payment = 1,798.65; new payment = 1,610.46; saving = 188.19 a month. Break-even = 6,000 / 188.19 = 31.9 months.

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