Question

Consider the following tables:

a. CPR Assuming

month	100% PSA	70% PSA	320% PSA
1
4
27
40

b. SMM Assuming

Month	100% PSa	70% PSA	320% PSA
1
4
27
40

Complete the tables.

Answer 1

Conditional Prepayment Rate (CPR)

CPR is the annualized percentage of the existing mortgage pool that is expected to be prepaid in a year.

Single Monthly Mortality rate (SMM)

CPR is an annual rate. However, since the mortgage payments happen monthly we need to calculate the monthly prepayment rate. SMM is a measure of monthly mortgage prepayment rate of the security's mortgage pool

CPR assuming

Month	100% PSA	70% PSA	320% PSA
1	0.2%	0.14%	0.64%
4	0.8%	0.56%	2.56%
27	5.4%	3.78%	17.28%
40	6%	4.20%	19.20%

The PSA benchmark assumes the following CPR's for 30-year mortgages

a CPR of 0.2% for the first month, increased by0.2% per year per month for the next 390 months when it reaches 6%

and a 6% CPR for remaining years. This benchmark is called 100% PSA

If t less than or equal 30: CPR = 6%(t/30)

If t greater than 30 CPR = 6% where t is the number of months

For ex 75 PSA means .75 times of the PSA benchmark prepayment rate

320 PSA means 3.2 times of the CPR of the PS benchmark prepayment rate

With 100 PSA, we get below CPR values

Month1 : CPR = 6%(1/30) = 0.2%; 100 PSA = 1.00(0.2%) = 0.2%

Month4 : CPR = 6%(4/30) = 0.8% ; 100 PSA = 1.00(0.8%) = 0.8%

Month 27 : CPR = 6%(27/30) = 5.4% ; 100 PSA = 1.00(5.4%) = 5.4%

Month 40 : CPR = 6% ; 100 PSA = 1.00(6%) = 6.0%

With 70 PSA

Month1 : CPR = 6%(1/30) = 0.2%; 70 PSA = .70(0.2%) = 0.14%

Month4 : CPR = 6%(4/30) = 0.8% ; 70 PSA = .70(0.8%) = 0.56%

Month 27 : CPR = 6%(27/30) = 5.4% ; 70 PSA = .70(5.4%) = 3.78%

Month 40 : CPR = 6% ; 70 PSA = .70(6%) = 4.20%

With 320 PSA

Month1 : CPR = 6%(1/30) = 0.2%; 320PSA = 3.2(0.2%) = 0.64%

Month4 : CPR = 6%(4/30) = 0.8% ; 320 PSA = 3.2(0.8%) = 2.56%

Month 27 : CPR = 6%(27/30) = 5.4% ; 320 PSA = 3.2(5.4%) = 17.28%

Month 40 : CPR = 6% ; 320 PSA = 3.2(6%) = 19.20%

With 100% PS we get the below SMM values

SMM = 1 - (1-CPR)^1/12

Month1 : CPR = 6%(1/30) = 0.2%; 100 PSA = 1.00(0.002%) = 0.002%

SMM = 1 - (1 - 0.002)^1/12 = 1 - (0.998)^0.83333 = 0.01668%

Month4 : CPR = 6%(4/30) = 0.8% ; 100 PSA = 1.00(0.008%) = 0.008%

SMM = 1 - (1 - 0.008)^1/12 = 1 - (0.992)^0.83333 = 0.06691%

Month 27 : CPR = 6%(27/30) = 5.4% ; 100 PSA = 1.00(.054%) = .054%

SMM = 1 - (1 - 0.054)^1/12 = 1 - (0.946)^0.83333 = 0.46154%

Month 40 : CPR = 6% ; 100 PSA = 1.00(.06%) = .06%

SMM = 1 - (1 - 0.06)^1/12 = 1 - (0.94)^0.83333 = 0.51430%

With 70 PSA

Month1 : CPR = 6%(1/30) = 0.2%; 70 PSA = .70(0.002%) = 0.0014%

SMM = 1 - (1 - 0.0014)^1/12 = 1 - (0.9986)^0.83333 = 0.01667%

Month4 : CPR = 6%(4/30) = 0.8% ; 70 PSA = .70(0.008%) = 0.056%

SMM = 1 - (1 - 0.0056)^1/12 = 1 - (0.9944)^0.83333 = 0.04679%

Month 27 : CPR = 6%(27/30) = 5.4% ; 70 PSA = .70(.054%) = .0378%

SMM = 1 - (1 - 0.0378)^1/12 = 1 - (0.9622)^0.83333 = 0.32059%

Month 40 : CPR = 6% ; 70 PSA = .70(.06%) = .0420%

SMM = 1 - (1 - 0.042)^1/12 = 1 - (0.958)^0.83333 = 0.35692%

With 320 PSA

Month1 : CPR = 6%(1/30) = 0.2%; 320PSA = 3.2(0.002%) = 0.0064%

SMM = 1 - (1 - 0.0056)^1/12 = 1 - (0.9936)^0.83333 = 0.05349%

Month4 : CPR = 6%(4/30) = 0.8% ; 320 PSA = 3.2(0.008%) = 0.0256%

SMM = 1 - (1 - 0.0256)^1/12 = 1 - (0.9744)^0.83333 = 0.21588%

Month 27 : CPR = 6%(27/30) = 5.4% ; 320 PSA = 3.2(.054%) = .01728%

SMM = 1 - (1 - 0.01728)^1/12 = 1 - (0.8272)^0.83333 = 1.56848%

Month 40 : CPR = 6% ; 320 PSA = 3.2(.06%) = .1920%

SMM = 1 - (1 - 0.1920)^1/12 = 1 - (0.8080)^0.83333 = 1.76092%

SMM assuming

Month	100% PSA	70% PSA	320% PSA
1	0.01668%	0.01167%	0.05349%
4	0.06691%	0.04679%	0.21588%
27	0.46154%	0.32059%	1.56848%
40	0.51430%	0.35692	1.76092