Why are we concerned with prepayments? With a debt obligation, nonpayment or delayed payment is an adverse economic consequence for the debt holder. In contrast, prepayment can be beneficial or harmful to the debt holder depending on the circumstances. Particularly in the case of for long-duration debt instruments such as residential mortgages, the mortgage not being allowed to continue until maturity but instead being prepaid may cause substantial loss of value to the mortgage lender, and upon securitization, to the mortgage-backed securities investor. What makes prepayment painful is that because it is an option granted to the borrower, it is always exercised to the benefit of the borrower and against the lender. For example, a fixed rate mortgage can be prepaid when mortgage rates decline below the loan rate paid by the borrower as the borrower can refinance the mortgage at the prevailing lower rate. An adjustable-rate mortgage may have a tendency to get prepaid when mortgage rates rise, making the mortgage unaffordable for the borrower. While prepayment is a risk for all debt obligations, the loss of value is particularly substantial, as mentioned before, in the case of mortgage products. Hence, prepayment is seen as a significant risk of mortgage investments.

In the residential MBS market, several conventions have been used as a benchmark for prepayment rates. Today the benchmarks used are the conditional prepayment rate and the Public Securities Association (PSA) prepayment benchmark.¹³

The conditional prepayment rate (CPR)³ as a measure of the speed of prepayments assumes that some fraction of the remaining principal in the mortgage pool is prepaid each month for the remaining term of the collateral. The CPR used for a particular deal is based on the characteristics of the collatral (including its historical prepayment experience) and the current and expected future economic environment.

The CPR is an annual prepayment rate. To estimate monthly prepayments, the CPR must be converted into a monthly prepayment rate, commonly referred to as the single-monthly mortality rate (SMM). The following formula is used to determine the SMM for a given CPR:

An SMM of w percent means that approximately w percent of the remaining mortgage balance at the beginning of the month, less the scheduled principal payment, will prepay that month. That is,

One problem with using the CPR is that it assumes a constant prepayment rate from the very outset of the origination of the loans. For example, it is not likely that prepayments might be the largest in dollar amount shortly after loans are originated than later on after loans have seasoned. Yet using a constant CPR makes that assumption. For residential mortgage loans, the PSA prepayment benchmark deals with this problem.¹⁴ The PSA prepayment benchmark is expressed as a monthly series of annual prepayment rates. The basic PSA benchmark model assumes that prepayment rates are low for newly originated loans, then will speed up as the mortgages become seasoned, and then reach a plateau and remain at that level.

The PSA standard benchmark assumes the following prepayment rates for 30-year residential mortgages loans: All months above are counted with reference to origination of the pool.

This benchmark is referred to as 100% PSA. Mathematically, 100 PSA can be expressed as follows: where t is the number of months since the mortgage originated.

Slower or faster speeds are then referred to as some percentage of PSA. For example, 50% PSA means one-half the CPR of the PSA benchmark prepayment rate and 165% PSA means 1.65 times the CPR of the PSA benchmark prepayment rate. A prepayment rate of 0% PSA means that no prepayments are assumed.

The PSA benchmark is commonly referred to as a prepayment model, suggesting that it can be used to estimate prepayment. However, it is important to note that characterizing this market convention for prepayments as a prepayment model is wrong.

With this background on prepayments conventions, we can now discuss the structuring of agency deals. To illustrate structuring and how it used to create bonds with different exposure to interest rate and prepayment risk via tranching, we will use a hypothetical pass-through security that will be the collateral for our illustrations. Let us look at the monthly cash flow for a hypothetical pass-through given a PSA assumption. We will assume the following for the underlying mortgages:The pass-through security has a coupon rate of 5.5% (WAC of 6% minus the servicing fee of 0.5%).

This first step in structuring requires a projection of the cash flow of the mortgage pool. The cash flow is decomposed into three components:To generate the cash flow for the hypothetical pass-through we will assume a prepayment speed of 165% PSA. The cash flow is shown in Table 3.1.

Column 2 shows the outstanding mortgage balance at the beginning of the month (i.e., outstanding balance at the beginning of the previous month reduced by the total principal payment in the previous month). Column 3 gives the SMM for 165% PSA.¹⁵ The aggregate monthly mortgage payment is reported in column 4. Notice that the total monthly mortgage payment declines over time, as prepayments reduce the mortgage balance outstanding.¹⁶ Column 5 shows the monthly interest that is determined by multiplying the outstanding mortgage balance at the beginning of the month by the passthrough rate of 5.5% and dividing by 12. The regularly scheduled principal repayment (amortization), shown in column 6 is the difference between the total monthly mortgage payment (column 4) and the gross coupon interest for the month (6.0% multiplied by the outstanding mortgage balance at the beginning of the month, then divided by 12). The prepayment for the month is reported in column 7 and is found by using equation (3.1). The sum of the regularly schedule principal and the prepayment is the total principal payment and is shown in column 8. The projected monthly cash flow is then the sum of the monthly interest plus the total principal payment as shown in the last column of the Table 3.1.

At 165% PSA the average life for this pass-through security is 8.6 years. We will use average life in our illustrations because the computation of the duration, more specifically effective duration, is much more complicated to compute. The average life is a weighted average of the principal cash flows divided by the par value where the weight is the month when the projected principal is expected to be received.