Question

Given a pool of 30 year fully-amortizing FRMs making monthly payments to investors with the following characteristics: WAC: 5% Pass-through rate: 4.5% Prepayment assumption: 300 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 32 in the pool. (t=32) Starting pool balance month in month 32: 54,234,988 What is the starting pool balance for month 33 of this security? (Hint: N=360 when t=1, N=359 when t=2, N=358 when t=3....etc) please provide step by step

Answer 1

Soln : PSA stands for Prepayment standard Model

We can calculate the conditional prepayment rate CPR from PSA

Upto 30 months the CPR can vary but after 30 months the CPR will be constant i.e. 6% for 100 PSA

For 300 PSA, CPR = 300% of CPR = 3*6% = 18%

From CPR we can calculate the Single mortgage mortality rate (SMM)

SMM = 1-(1-CPR)^1/12, SMM = 1- (1-0.18)^1/12 = 1.64%

Balance at the start of the 32 month = $54234988, Now using interest rate of 4.5%, and time to maturity = 360-31 = 329

We can calculate the monthly payment using PMT in excel, we will get monthly payment as $287209

Interest paid monthly = 4.5%/12 *54234988 = $203381 , So principle paid in 32nd month = 287209-203381 = $83828

Pool balance at the start of the month 33rd = 54234988*(1-SMM) - 83828 = $5,32, 61,706