What does a conditional prepayment rate of 8% mean?

Question

What will be an ideal response?

Answer 1

One benchmark for projecting prepayments and the cash flow of a pass-through requires that one assumes some fraction of the remaining principal in the pool is prepaid each month for the remaining term of the mortgage.

The prepayment rate assumed for a pool, called the conditional prepayment rate (CPR), is based on the characteristics of the pool (including its historical prepayment experience) and the current and expected future economic environment. It is referred to as a conditional rate because it is conditional on the remaining mortgage balance.

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).

A formula can be used to determine the SMM for a given CPR:

SMM = 1 – (1 – CPR)1/12 .

For our problem we want to know what a conditional prepayment rate of 8% means. Assuming the CPR used to estimate prepayments is 8%, the corresponding SMM is

SMM = 1 – (1 – 0.08)1/12 = 1 – (0.92)0.08333 = 1 – 0.9930756 = 0.0069244 or 0.69244%.

An SMM of 0.69244% means that approximately 0.69244% of the remaining mortgage balance at the beginning of the month, less the scheduled principal payment, will prepay that month. That is, prepayment for month t is equal to

SMM = (beginning mortgage balance for month t – scheduled principal payment for month t).

For example, suppose that an investor owns a pass-through in which the remaining mortgage balance at the beginning of some month is $90 million. Assuming that the SMM is 0.69244% and the scheduled principal payment is $1 million, the estimated prepayment for the month is:

0.0069244($90,000,000 – $1,000,000) = 0.0069244($89,000,000) = $616,270.05 .