# Prepayment Risk

A mortgage prepayment option works much like a call option for the borrower. Mortgage prepayments can take one of these two forms:

• the borrower increasing the amount/frequency of payments; or
• the borrower repaying/refinancing the entire outstanding balance.

Prepayment risk is the risk involved with the premature return of principal on a mortgage. A prepayment effectively renders the borrower free of mortgage obligations. Prepayment risk can take one of these two forms:

• contraction risk: the risk that interest rates decline. Homeowners will then refinance at the available lower interest rates.
• extension risk: the risk that when interest rates rise, prepayments will be lower than expected.

Prepayments are more likely to occur following a drop in interest rates. In such circumstances, the borrower may decide to refinance their existing mortgages at the lower rates. Other factors that influence prepayment include:

• seasonality: housing turnover increases at certain periods during the year, e.g., over summer when the weather is favorable;
• age of mortgage pool: borrowers prefer to refinance a significant number of years into the mortgage to minimize penalties and administrative charges that are usually tied to outstanding principal;
• housing prices: an increase in home prices may spur prepayments as borrowers scramble to take out some of the increased equity for personal use;
• refinancing burnout: prepayment risk decreases following a sustained period of refinancing activity.

## Modeling the Prepayment Rate

Prepayment is undoubtedly one of the key issues an investor in MBSs would want to keep an eye on. Prepayments speed up principal repayments and reduce the amount of interest paid over the life of a mortgage. Prepayments can, therefore, adversely affect the amount and timing of cash flows.

Markets have adopted two main benchmarks that are used to track prepayment risk – the Conditional Prepayment Rate (CPR) and the Public Securities Association (PSA) prepayment benchmark.

### Conditional Prepayment Rate (CPR)

The CPR is a proportion of a loan pool’s principal that is assumed to be paid off ahead of time in each period. It measures prepayments as a percentage of the current outstanding loan balance. It is always expressed as a percentage, compounded annually. For example, a 5% CPR means that 5% of the pool’s outstanding loan balance is likely to prepay over the next year. It is estimated based on historical prepayment rates for past loans with similar characteristics and future economic prospects.

The CPR can be converted to a single monthly mortality rate (SMM) as follows:

$$SMM=1-(1-CPR)^{1/12}$$

SMM is, in effect, the amount of principal on mortgage-backed securities that is prepaid in a given month.

Note: this also implies that:

$$CPR=1-(1-SMM)^{12}$$

and

Prepayment for month i (in \$) = SMM (beginning balance – scheduled principal repayment in month i)

### Public Securities Association (PSA) Prepayment Benchmark

The Public Securities Association prepayment benchmark model is used to estimate the monthly rate of prepayment. It is based on the assumption that rather than remaining constant, the monthly repayment rate gradually increases as a mortgage pool ages. The PSA is expressed as a monthly series of CPRs. The model assumes that:

• CPR = 0.2% for the first month after origination, and increases by 0.2% every subsequent month up to 30 months;
• CPR = 6% for months 30 to 360.

A mortgage pool whose prepayment speed (experience) is in line with the assumptions of the PSA model is said to be 100% PSA. Similarly, a mortgage pool whose prepayment experience is two times the CPR under the PSA model is said to be 200% PSA (or 200 PSA).

## Question

When interest rates decline, an investor who owns a mortgage pass-through security is most likely affected by:

1. Default risk.
2. Extraction risk.
3. Contraction risk.

Solution

Contraction risk is the risk occasioned by interest rates decline. Homeowners will then refinance at the available lower interest rates.

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