# Conditional Prepayment Rate (CPR): Definition and Calculation

## What Is a Conditional Prepayment Rate (CPR)?

A conditional prepayment rate (CPR) is an estimate of the percentage of a loan pool's principal that is likely to be paid off prematurely. The estimate is calculated based on a number of factors, such as historical prepayment rates for previous loans similar to the ones in the pool and future economic outlooks. These calculations are important for investors in evaluating assets like mortgage-backed securities or other securitized bundles of loans.

### Key Takeaways

• A conditional prepayment rate (CPR) estimates the likely prepayment rate for a pool of loans, such as a mortgage backed security.
• The higher the CPR, the more prepayments are expected and the less interest the investor is likely to receive in total. This is called prepayment risk.
• CPR is expressed as an annual percentage rate, while the single monthly mortality (SMM) rate measures prepayment risk on a month to month basis.

## How to Calculate Conditional Prepayment Rates (CPRs)

The CPR can be used for a variety of loans. Pools of mortgages, student loans, and pass-through securities all use the CPR as estimates of prepayment. Typically, the CPR is expressed as an annual percentage.

For example, if a pool of mortgages has a CPR of 8%, that suggests that 8% of the pool's outstanding principal will be paid off prematurely in a given year.

The CPR helps investors anticipate prepayment risk, which is the risk involved with the premature return of principal on an income-producing security.

In simple terms, when a borrower pays a portion of their loan's principal off early that portion stops incurring interest and investors in that debt will no longer receive interest payments from it. The risk of prepayment is most prevalent in fixed-income securities such as callable bonds and mortgage-backed securities (MBSs).

## What Does the CPR Tell You?

The higher the CPR, the faster the associated debtors are likely to prepay on their loans.

A high prepayment rate means the debts associated with the security are being paid back at a faster rate than the required minimum. While this indicates that the investment is lower risk, since the amount that's owed is being paid back, it also means that the overall return on the investment is likely to be lower.

## Example of How to Use the CPR

The CPR can help investors gauge the likely return on an investment and their prepayment risk, especially in changing economic conditions.

For example, in a time of declining interest rates, homeowners often prepay their mortgages to refinance them at a lower rate. When that occurs, the mortgage-backed security that their mortgage is packaged into may be paid back sooner than expected, with the proceeds released back to the investor. The investor then needs to choose a new security to invest in, which is likely to have a lower rate of return since interest rates overall have dropped since their original investment.

Note that there is no prepayment risk with certain types of investments. Those include noncallable corporate bonds and United States Treasury bonds (T-bonds), which do not allow for it. Additionally, collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs), issued through investment banks, may be structured in such a way as to lower the risk of prepayment.

Further, debt investments associated with a higher-risk tranche often have a longer time to maturity than those with a lower-risk tranche and carry less risk of being paid off early.

## Single Monthly Mortality Rate (SMM) and CPR

In addition to the CPR, which expresses prepayment risk in annual terms, investors can look at an investment's single monthly mortality (SMM) rate. The SMM is determined by taking the total debt payment that's owed and comparing it against the actual amounts received for a particular month. It can be converted into a CPR and vice versa.

Suppose the total debt outstanding on a mortgage-backed security is \$1 million and the payment owed for the month is \$100,000 across all of the associated mortgages. But when the payments are received for that month the actual total is \$110,000. That translates into an SMM of 1% (0.01 x \$1,000,000).