CPR/PSA/SMM calculation

CFA Level II Fixed Income
#1

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

#2

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%

#3

Thanks a lot S2000. Both your article and coment were very helpfull.

#4

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.

#5

Yes it should be.

#6

You’re quite welcome. Glad it helps.

#7

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

#8

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.