Question

Given a pool of 30 year fully-amortizing FRMs making monthly payments to investors with the following characteristics: WAC: 6% Pass-through rate: 5.5% Prepayment assumption: 200 PSA Loans were not seasoned before entering pool This MBS has been active for a few years in collecting payments from borrowers and making payments to investors. It's currently month 26 in the pool.(t=26) Starting pool balance month in month 26: 72,534,232

What is the prepayment amount for month 26, and starting pool balance for month 27?

Answer 1

As the prepayments does not occur at the same rate always, Public Securities Association (PSA) and Conditional Prepayment Rate (CPR) are the two industry conventions adopted as benchmark for prepayment rates.

PSA: A prepayment benchmark which is expressed as a montly series of CPRs.

CPR: Annual Rate at which a Mortgage Pool is assumed to be Pre-paid during the life of the Pool.

Single Monthly Mortality Rate (SMM) = 1 - (1-CPR)^1/12

SMM: When CPR is converted into monthly prepayment rate it is called Single Monthly Mortality rate.

For example: 20% SMM rate means, 20% of the Starting pool balance less scheduled payments, will be prepaid during the month.

Now realising the CPR for 100 PSA for a 30-year mortgages which is standard benchmark is as follows:

• CPR = 0.2% for the first month after origination, increasing by 0.2% per month up to 30 months.
• CPR = 6% for months 30 to 360

Therefore as in the question given, the CPR for 200 PSA for the month 26 is as follows:

CPR (month 26) = 26 x 0.2%= 0.052 (This is for 100 PSA)

CPR (month 26 for 200 PSA) = 2 x 0.052 = 0.104 or 10.4%

SMM = 1 - (1 - 0.104)^1/12 = 1 - (0.896)^1/12 = 1 - 0.99089 =0.00911 or 0.911%

Given Starting Pool balance : 72,534,232

Pre-payment for month 26 = 0.00911 x (72,534,232 - Scheduled Prepayment amount)

For Calculating the Scheduled Prepayment amount; we use excel formula with the following formula:

=-PMT(6/100,26, 72,534,232) = 5,578,198

Therefore the Prepayment for month 26 = 0.00911 x (72,534,232 - 5,578,198) = 6,069,969.5

The Starting Pool Balance for Month 27 = (72,534,232 - 5,578,198) - 6,069,969.5 = 60,886,064.5