What is the formula to calculate the Single Monthly Mortality Rate (SMM)?

The formula for the Single Monthly Mortality Rate (SMM) is based on the Conditional Prepayment Rate (CPR). The correct formula, SMM = 1 - (1 - CPR)^(1/12), represents the probability of a mortgage loan being prepaid in a single month, considering the annualized CPR.

Understanding this formula involves recognizing that the CPR is typically an annualized rate of prepayment. To convert it into a monthly rate that calculates the likelihood of prepayment in just one month, we evaluate the complement of the survival rate (1 - CPR), which indicates the proportion of loans that are not prepaid. Raising this complement to the power of (1/12) adjusts the rate from an annual basis to a monthly basis. Finally, subtracting this value from 1 gives us the probability of prepayment occurring in that month, effectively deriving the SMM.

This approach captures the idea that as time progresses, the likelihood of a loan surviving without prepayment diminishes, which is essential in mortgage-backed security analysis and risk assessment.

Other formulations, like simply dividing CPR by 12 or adding CPR to 1, do not accurately reflect the relationship between monthly and annual prepayment rates and therefore do not provide the correct calculation for