CPR/PSA/SMM calculation

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bartolia

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Hi,
I have a doubt on the CPR calculcation when you have to compute the CPR from any month from the 30th to 360th.
Here below, an example:
Let’s say with 150 PSA, compute the SMM for the 5th and 35th month.
SMM (5th month)
a) CPR (5th month): 5 x 0,2% = 0,01 (Since CPR = 0,2% from 1 to 30 month)
b) 150 PSA: 1,5 x CPR = 1,5 x 0,01 = 0,015
c) SMM (5th month): 1 - (1-0,015)^1/12
SMM (35th month)
a) CPR (35th month): 35 x 6%= 2,1 (Since CPR = 6% from 30 to 360 month)
b) 150 PSA: 1,5 x CPR= 1,5 x 2,1= 3,15
c) SMM (35th month): 1-(1-3,15)^1/12
The 2,1 does not make sense to me when it then comes to compute the SMM (35 month).
Would anyone clarify on this pls ?
Thanks
 
I wrote an article on this that may be of some help: http://financialexamhelp123.com/cpr-vs-smm-vs-psa/.
150 PSA in month 5 is:
150% × 5 × 0.2% = 1.5% CPR
1 – SMM = (1 – CPR)^(1/12)
1 – SMM = (1 – 0.015)^(1/12)
1 – SMM = 0.985^(1/12)
1 – SMM = 0.998741
SMM = 0.1259%
150 PSA in month 35 is:
150% × 6% = 9% CPR
1 – SMM = (1 – CPR)^(1/12)
1 – SMM = (1 – 0.09)^(1/12)
1 – SMM = 0.91^(1/12)
1 – SMM = 0.992172
SMM = 0.7828%
 
Thanks a lot S2000. Both your article and coment were very helpfull.
 
Just wanted to clarify something @S2000.
So assuming your PSA at 150% stays constant from month 30-360, does that mean that the SMM is constant as well throughout that range since the CPR is 6% throughout.
 
S2000magician, I still have a doubt.
On case Prutko (CFAI Mock Exam 2014) Question 1, the anwser provided by the CFAI does not match with our formula (see above):
According to CFAI:
CPR = PSA x 4/30 x 6% for Month 4 !
From my understanding and as per our last conv. above, the formula that shall b used is the following:
CPR= 0,2% x 4/30 x 6%
I am confused
 
nope. it should be 0.2% * 4
or
6%/30 * 4
which is the same thing.
CPR assumes a straight line from 0 to 6% in 30 months or 0.2% per month.
 
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