Hello, I am from Argentina and I have a doubt trying to calculate this. First of all, I am writing about Fixed Income - Mortgage Backed Securities I understand SMM, CPR and PSA but I dont understand how you can calculate the Theorical Mortgage Payment after you have a prepayment. I mean at the begging you know how mortgage payment is by definition of the pool of mortgages and its WAM and WAC but I dont undertand how, after some prepayment, you can recalculate your new theorical mortgage payment. CFA books refers to this with this note: “the formula is presented in Chapter 19 of Frank J. Fabozzi, Fixed Income Mathematics”. That book is unreachable in Argentina and it is not online. What I am trying to understand actually is the theorical interest loss due to the prepayment that shorten the average life of the pool of loans; because of prepayment there is a difference of accrued interest between theorical interest at begging and actual interest at the end of the loan repayment. Thanks in advance for any help. Martín
instead of looking at it with a formula – think of it this way.
when you prepay - your principal is paid down.
that principal - if it had not been paid down - would have continued to accrue interest for the provider of the mortgage loan - for the period of time that it was still outstanding.
so an imputed value = PV(Principal Paydown , interest rate, # of periods)
and add on the compounding effect.
Adding to what cpk123 said, when a loan is prepaid, the principal balance will be lower, and the WAC and WAM might change (slightly). Simply use the new pirncipal balance, the new WAC, and the new WAM, and compute the payment, just as you did at the outset of the mortgage pool.
In essence, you forget about the past, and do your calculations starting from today forward.
Thanks to both but in order to achieve that you are supposed to know which loan and how it has prepaid. Imagine a mortgage backed security that has with 100 loans, what you are doing by calculating WAC and WAM is an average of that pool and then when you multiple this by an average prepayment rate you get a number of capital prepayment but you do not know how that prepayment actualy is, maybe the longest loans have prepaid or maybe those that were up to be completely canceled have prepaid, you only know the amount of prepayment but it does not tell anything about the new WAC or WAM of the pool at t+1. Maybe you can make an assumption that the new pool at t+1 has the same WAC and WAM than at t (I mean it will be lower because 1 period has passed but it has the same distribution) but it would be an assumption. Maybe Fabozzis book has a demonstration of this… and maybe it has a easier way to recalculate the new theorical mortgage payment at t+1 with an easier formula to apply. Thanks again!
Thanks to both but in order to achieve that you are supposed to know which loan and how it has prepaid. Imagine a mortgage backed security that has with 100 loans, what you are doing by calculating WAC and WAM is an average of that pool and then when you multiple this by an average prepayment rate you get a number of capital prepayment but you do not know how that prepayment actualy is, maybe the longest loans have prepaid or maybe those that were up to be completely canceled have prepaid, you only know the amount of prepayment but it does not tell anything about the new WAC or WAM of the pool at t+1. Maybe you can make an assumption that the new pool at t+1 has the same WAC and WAM than at t (I mean it will be lower because 1 period has passed but it has the same distribution) but it would be an assumption. Maybe Fabozzis book has a demonstration of this… and maybe it has a easier way to recalculate the new theorical mortgage payment at t+1 with an easier formula to apply. Thanks again!
the MBS investor does not have anything to do with the loans that have been pooled to create the MBS. He invested in the MBS hoping to get a pattern of payments over the life of the MBS - and this pattern is disrupted by the prepayments received.
- Loans (read you and I with a home mortgage) make a payment to bank
- Bank takes its servicing fee
- makes the remaining payment to investor - and this payment is part principal, part interest
- when a prepayment happens - the servicing fee does not change. but the principal portion received by the investor “increases” - which means he gets lower interest over the remaining life of the investment.
Thanks but that does not work at all to resolve my question… but thanks again!
I mean, what I am trying to calculate if you see it from investors perspective is the interest lost in the remaining life but without knowing how prepayment really was, you only know the absolute number at t but not which capital in the time has prepaid… it is a mathematical issue not a logical one… again thanks anyway…
again from investor’s perspective - he lost x amount of principal on which he would have earned y% interest for N periods… accumulate that (and in theory you are close to your answer). Here X is the amount of prepayment that was received.
pretty much what you do when you refinance your mortgage.