Cover the techniques for forecasting prepayments, and compute the PSA (Public Securities Association) rate along with the CPR (constant prepayment rate).

FRM® Part II · Credit Risk Measurement and Management · An Introduction to Securitisation · FRM2.CR.23.h

The idea

Prepayments are forecast from the borrowers' refinancing incentive, which rises as market rates fall below pool coupons. Other drivers are seasoning, seasonality, burnout and housing turnover. Speeds are quoted against the PSA benchmark. The constant prepayment rate, CPR, is the annualized fraction of the balance prepaid. 100 PSA assumes CPR rises by 0.2% per month of pool age until month 30, and is 6% thereafter. Other speeds scale this, so 150 PSA is 1.5 times those rates. The single monthly mortality rate, written SMM, turns an annual CPR into a monthly figure as follows: SMM = 1 − (1 − CPR)^(1/12). The prepayment in a month is SMM times the balance after scheduled principal. To get an implied PSA speed, convert SMM to CPR and divide by the 100 PSA CPR for that month. The usual errors are dividing CPR by 12 instead of using the twelfth root, and forgetting to stop the ramp at month 30.

Formulas

CPR under a PSA speed

CPR = (PSA ÷ 100) × 0.2% × min(t, 30)

PSA: the prepayment speed, 100 being the benchmark
t: the pool's age in months

The ramp stops at month 30, after which 100 PSA is a flat 6%. Forgetting the cap is the usual error.

Single monthly mortality from CPR

SMM = 1 − (1 − CPR)^(1 ÷ 12)

CPR: the annual constant prepayment rate, as a decimal

Take the twelfth root; CPR ÷ 12 understates SMM. Apply SMM to the balance after scheduled principal.

Conditional prepayment rate from SMM

CPR = 1 − (1 − SMM)¹²

SMM: the single monthly mortality rate, as a decimal

Monthly compounding. SMM × 12 overstates CPR; the reverse is SMM = 1 − (1 − CPR)^(1 ÷ 12).

A practice question

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

In prepayment modeling, burnout describes the tendency for:

A new pool to prepay very slowly in its first months and then speed up as it agesWhy not: That describes seasoning, the ramp-up of prepayments with pool age.
Prepayments to rise in summer months, when housing turnover is highWhy not: That describes seasonality, which is calendar related.
Defaults to rise when borrowers lose their jobs, returning principal to investorsWhy not: That describes involuntary prepayment through default, not burnout.
A pool that has already been exposed to a refinancing opportunity to prepay more slowly afterwards, because the remaining borrowers are less able or willing to refinance - correct

Burnout means the borrowers who are most rate sensitive have already refinanced, leaving a pool that responds less to further rate declines.

A harder one

A pool prepays at a CPR of 9%. The corresponding single monthly mortality rate is closest to:

0.75%Why not: Divides the CPR by 12 instead of using the twelfth root.
2.3%Why not: Uses the fourth root, a quarterly conversion, instead of the twelfth root.
0.78% - correct
67.8%Why not: Raises the survival rate to the 12th power instead of taking the 12th root.

SMM = 1 - (1 - 0.09)^(1/12) = 0.78%. Compounding means CPR divided by 12 slightly understates SMM.

The hardest tier

A mortgage pool is in month 30 and prepays at 400 PSA. The balance at the start of the month is USD 500 million and scheduled principal is USD 2.0 million. The expected prepayment during the month is closest to:

USD 9.96 millionWhy not: Uses CPR divided by 12 (2.0%) instead of the SMM.
USD 2.56 millionWhy not: Forgets the 400% multiplier and uses 100 PSA at month 30, a CPR of 6%.
USD 5.28 millionWhy not: Assumes the ramp lasts 60 months, so that CPR at month 30 is only half of the plateau times four.
USD 11.26 million - correct

CPR = 6% x 4 = 24%. SMM = 1 - 0.76^(1/12) = 2.261%. Prepayment = 2.261% x (500 - 2.0) = 11.26 million.

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