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Glossary

# SMM to CPR

Category — Issue Parameters

## What is Single Monthly Mortality (SMM)?

Single monthly mortality rate (SMM) represents the prepayment rate of mortgage-backed security (MBS), reflecting the percentage of prepayment that occurs in a specific month.

For mortgage-backed securities investors in a high prepayment rate is generally undesirable as it means giving up potential future interest. Ideally, investors seek a lower or decreasing single monthly mortality for an MBS.

## What is the Conditional Prepayment Rate (CPR)?

The conditional prepayment rate (CPR) is a projected figure representing the expected percentage of a loan pool’s principal that is likely to be paid off ahead of schedule. This estimation takes into account various factors, including historical prepayment rates of similar loans in the pool and future economic forecasts. These calculations play a crucial role for investors when assessing assets like mortgage-backed securities or other securitized loan bundles.

## Correlation between SMM and CPR

The correlation between Single Monthly Mortality (SMM) and Conditional Prepayment Rate (CPR) is connected with differences in the context of mortgage-backed securities (MBS) and securitized bonds.

The Conditional Prepayment Rate (CPR) represents the estimated percentage of a loan pool’s principal that is expected to be prepaid ahead of schedule in a given year. It takes into account factors such as historical prepayment rates, economic outlooks, and the security’s mortgage pool balance. The CPR serves as a measure of the probability of prepayment in a specific year.

Meanwhile, Single Monthly Mortality (SMM) is a measure of the prepayment rate in a given month and is expressed as a percentage. It can be interpreted in two ways: the likelihood that an individual mortgage will be repaid in a given month or the rate of early repayment of the entire mortgage pool in that month. SMM is calculated using the following formula and involves scheduled payments and interest payments:

Monthly Mortality Rate (SMM) = (Interest Payments + Unscheduled Principal) / Mortgage Pool Balance

The relationship between SMM and CPR is mathematically connected through the formula:

SMM = 1 - (1 - CPR)^(1/12)

This formula shows how SMM is derived from the CPR, which is an annual measure. The SMM is calculated on a monthly basis, taking into account the CPR for the corresponding period.

Since both SMM and CPR are used to assess prepayment risks associated with securitized bonds, they are closely linked in evaluating the performance and behavior of mortgage-backed securities. Changes in the CPR can influence the SMM, affecting the pace of prepayment for the mortgage pool and vice versa. Investors analyze these metrics to gauge the potential impact of prepayments on the performance of their investments in MBS. These metrics are prevalent in the analysis conducted by the Public Securities Association to estimate the annual prepayment rate.

## How to Calculate Conditional Prepayment Rate from Single Monthly Mortality

Here’s how you can calculate the Conditional Prepayment Rate (CPR) from the Single Monthly Mortality (SMM):

Step 1. Calculate the Single Monthly Mortality (SMM)

SMM = Unscheduled Principal / Start of Month Balance - Scheduled Principal

Where:

• The unscheduled Principal is the actual principal paid less the scheduled principal, floored at zero.

• Scheduled Principal is the amount of principal due.

• Start of Month Balance is the sum of all active loan balances at the beginning of the month, excluding any defaulted/charged-off loans from previous periods.

Step 2. Annualize the SMM to obtain CPR

CPR = 1 - (1 - SMM)^12

The formula above is used to annualize the monthly prepayment rate SMM to get the Conditional Prepayment Rate (CPR). The CPR represents the expected percentage of the main balance of the mortgage pool that will be prepaid ahead of schedule for each year.

Remember that the scheduled principal is the regular monthly installment of principal that the borrower is required to pay, while the unscheduled principal represents any additional amount of principal that is paid, which exceeds the scheduled principal for the month. By calculating the SMM and then annualizing it, you can estimate the overall prepayment rate for the mortgage pool over the course of a year.

## Example of Conditional Prepayment Rate (CPR)

As an illustration, consider a pool of mortgages with a Conditional Prepayment Rate (CPR) of 8%. This indicates that approximately 8% of the outstanding principal in the pool is expected to be paid off before its scheduled maturity within a single year. The CPR serves as a valuable tool for investors as it enables them to foresee prepayment risk, which refers to the potential of early principal return on income-producing security. By understanding and factoring in the CPR, investors can better assess and manage the impact of prepayments on their investment strategies.

• ## What does a conditional prepayment rate of 8% mean?

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