conditional prepayment rate CPR

[narayananvenkat]

David.

Consider a pool of mortgages that were issued exactly 22 months ago(they are beginning 23rd month) Whatis the CPR and what is the SMM assuming 150 PSA.

CPR SMM

A. 4,2 % ,74%
B.4.1% .48%
C.4.6 .59%
D.4.9 .63%

How do we start? I find from the solutions CPR considered at 6% to be calibrated for the period of 23 rd month over 30 years. and adjusted further over 150 PSA.Is this a default one that needs to be assumed?

Help..help..help..

venkat

 

[David Harper CFA FRM]

Hi venkat,

CPR 6% * 23 months / 30 months = 4.6%; i.e., CPR at 100 PSA
150 PSA = 4.6% * 1.5 = 6.9%
SSM = (1-(1-6.9%)^(1/12)) = 0.00594 single monthly mortality

David

 

[narayananvenkat]

David..

thanks. my question is the base CPR 6% .Is it a constant/ ie a default % to be considered in all case? I still feel I am missing something.
venkat

 

[David Harper CFA FRM]

venkat,

I started an XLS b/c it would be good to have in the library...i'll link back when i post it

but (source: Fabozzi MBS):

up to month 30: CPR = 6% * (month t /30)
then after month 30: CPR = 6%

...so CPR starts at 0% and takes a straight line (+0.2% per month) up to 6% at month 30 then flat @ 6%

David

 

[narayananvenkat]

David..

Great.. David..to be frank I got clairified on this now.This is an important note all we guys have to remember!!

venkat

 

[shanlane]

This is a little out of left field, but CPR is an annual rate, correct? So the 0.2% in month 1 means that if nothing changed (prepayment rate stayed constant) then 0.2% of the total loan pool would be paid off at the end of the first year, correct?

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon, Yes, that is correct. This is by definition as CPR is the annual rate, expressed as in monthly discrete compound frequency terms, that informs the single monthly mortality rate (SMM): SMM = 1 - (1-CPR)^(1/12). As this SMM is used in the prepayment model to assume the rate of monthly prepayments, by definition, CPR = 1 - (1-SMM)^12, is the true rate of annual prepayment.

The "trap" is in the SMM. A CRP of 6% implies 6% prepaid at the end of one year. But if the CPR is 6%, we do not use a monthly SMM of 6%/12 = 0.5% because that implies a CPR of 1-(1-0.5%)^12 = 5.84% <> 6%. Rather the SMM is the correct monthly rate that "proves" the CPR is the true/effective annual rate.

 

[shanlane]

Perfect.

Thanks!

Shannon

 

[EIA]

Hi David,

Is the CPR 6.9% or 4.6% and why?

Because 6.9% was used in calculating SMM while the answer for CPR is 4.6%.

From your answer is there a difference between CPR at 150% PSA and CPR @ 23 month?

Please clarify.

BR

EIA

 

[David Harper CFA FRM]

Hi EIA,

Good point. I guess you might argue the question is framed imprecisely. The CPR is 4.6% under an assumption of 100% PSA; but 150% implies CPR of 1.5 * 4.6 = CPR 6.9%; the CPR here is 6.9%. The 4.6% is merely the input benchmark that is scaled by the PSA multiplier. It is the CPR of 6.9% that informs the modeled SMM monthly default rate.