if SMM is the % of prepayment in a month and CPR is an annulizaion of this percent why isnt CPR calculated as

1+SMM^12

CFAI has it as 1- (1-SMM)^12

if SMM is the % of prepayment in a month and CPR is an annulizaion of this percent why isnt CPR calculated as

1+SMM^12

CFAI has it as 1- (1-SMM)^12

1+SMM^12 would be something very close to 1. Say SMM is 2%.

1 + .02^12 = 1 + 4.096 * 10^-12. How useful is that? None useful.

1 - (.98)^12 = 21.53% = CPR. It’s the annualized amount of the principal that is repaid.

You might have meant to say (1 + SMM)^12 - 1, but that would overstate CPR since you would be growing it over time instead of shrinking it. If the same % of principal is paid off each month, the annual % paid off is smaller than (but relatively close to) 12 * SMM because the remaining principal decreases every month.

Yes, I was thinking of (1+.02)^12 -1

And i do see your point on shrinking the value due to principle amort. wich is why we do not use SMM*12…and that was going to be my other question…so you answerd both. thanks