Do You Know CPR?

Prepayment rates are crucial in the analysis of mortgage backed securities. Measures such as yield, average life, and duration all require assumptions about the expected cash flows. The prepayment option with mortgages creates uncertain cash flows and, thus, requires careful consideration when estimating performance of pass-through securities. Two of the most commonly used methods for projecting principal prepayments are the Conditional Prepayment Rate (CPR) and the model designed by the Public Securities Association or PSA.

The CPR of a mortgage pool is the annual prepayment percentage. The CPR model assumes that a pool of mortgages will prepay at a fixed percentage rate, regardless of the age of the pool. Thus, a 0% CPR means no prepayments, a 10% CPR indicates that ten percent of the outstanding principal balance is expected to be prepaid in one year.

Any model that uses a fixed prepayment rate to project prepayments on a pool of newly issued mortgages, however, ignores the fact that prepayments tend to increase over time, especially in the first few years following origination. Consequently, a fixed rate will overestimate prepayments during the first few years. Addressing this limitation led to the derivation of the PSA model.

PSA specifies a standard percentage for each month and annualizes that percentage. The base for this model is known as 100% PSA, which assumes increasing annual prepayment rates beginning in the first month at .2% and increasing .2% per month until an annual rate of 6% is reached in the thirtieth month. From the thirtieth month until maturity, the base remains a constant 6% CPR (100% PSA). The base case is shown in the table below:

Mortgage Age	Annual Prepayment
in Months	Rate @ 100% PSA
1	0.2
2	0.4
3	0.6
4	0.8
.	.
.	.
28	5.6
29	5.8
30 and beyond	6.0

Calculating prepayments as multiples of PSA is relatively simple because it is a linear measure. When the PSA speeds vary from the 100% case, and they normally do, the conversion to an annual rate requires the simplest of mathematics. For example, the annual percentage rate at 200% PSA for month 4 is 1.6%, (2.00 x .8%). Similarly, a seasoned (more than 30 months old) pool prepaying at 75% PSA will prepay at 4.5%, (.75 x 6.0%).

The recognition of pool aging and the need for reliable cash flow information became a priority with the advent of Collateralized Mortgage Obligations (CMOs). The collateral for these derivatives are normally new pools of pass-throughs. The complexity of structuring the classes (or tranches) of projected cash flows lent itself to the PSA model. Thus, this model has become the industry standard for evaluating CMOs.

It should be noted that these models are not forecasting or predictive models. They merely quantify the expected cash flow to allow analysis of yield and average life expectancy of the pool. Extremely high or low prepayment rates can be misleading if an investor assumes that any prepayment rate will remain constant throughout the life of the pool.

Prepayment of principal can be caused by many different factors. Among these are natural disasters, shifts in population or geographic trends, sales, and refinancing. Analysis should be based on reasonable prepayment expectations. For those already owning pass-through securities, prepayments can and should be monitored periodically to determine if the investment is performing to expectations.