# Fixed Income - SMM - CPR

Does anyone understand the logic of this formula? SMM = 1 – (1 – CPR)^1/12 why do they use 1 - (minus) twice here?

Let’s say you have \$1 is mortgage balances AFTER scheduled payments of interest and principal. The SMM seeks to get a reduced number B which says if we regularly have SMM rate of PREPAYMENTS then the \$1 reduces to B Assume that the annualized CPR is given in: SMM = 1 – (1 – CPR)^1/12 i.e. CPR= 1 - (1 – SMM )^12 The B=(1-SMM)^12 is an annualized result of monthly prepayments at the SMM rate. This reduces the \$1 ( after scheduled payments ) balance of the mortgage geometrically throughout the year. Then B is a number very close to 1 And CPR is the difference between 1 and B. CPR=1-B i.e. CPR represents how much is prepaid on an annualized percentage basis Say B=0 , then CPR is 100% , all the balance ( after scheduled payments ) is paid off in 1 year. If B=1 , then CPR is 0 , and the homeowners are paying nothing beyond the scheduled payments ( a huge extension risk)