Many forms of consumer debt, such as home mortgages,
credit card debt and auto loans, permit the borrower to pay down the
indebtedness at an accelerated rate or to retire the debt early with a single
payment. If a homeowner decides to sell her home, she will use the
proceeds of the sale to retire any outstanding mortgage on the home. If
someone making payments on an auto loan receives a year-end bonus at work,
he may use it to pay down the debt.
For a lender, such prepayments
are desirable if interest rates have risen since a loan was made. They are
undesirable if interest rates have fallen. For most forms of consumer
debt, prepayment rates exhibit little correlation with interest rates.
They are a source of some uncertainty for the lender, but they do not pose
significant risk. An exception is mortgages. Because homeowners with
fixed-rate mortgages tend to refinance their mortgages when interest rates
drop, there is a pronounced negative correlation between the level of
interest rates and prepayment rates on fixed-rate mortgages. This poses a
prepayment risk—for mortgage originators. If an
originator transfers its mortgages to investors in the form of a
mortgage-backed security, it also transfers the prepayment risk to those
Because of the significance of prepayment for
mortgage-backed securities, the industry has developed metrics for
prepayment. These apply to a pool of fixed-rate mortgages collateralizing
a mortgage-backed security.
The most basic metric has a distinctly actuarial name. It
is called single monthly mortality
(SMM). It indicates, for any given month, the fraction of mortgages
principal that had not prepaid by the beginning of the month but does
prepay during the month. For computational purposes, if a mortgage does
prepay in a given month, its scheduled principal payment for that month is
not considered part of the prepayment.
A related concept is the
conditional prepayment rate
(CPR), which is annualized SMM. Specifically, CPR indicates, for any given
year, the fraction of mortgages principal that had not prepaid at the
beginning of the year that does prepay during the year.
If we know the 12 SMM rates, SMMi,
experienced by a pool of mortgages during a given year, the pool's CPR for
the year is obtained as
CPR = 1 – (1 – SMM1)(1 – SMM2)...(1 – SMM12).
We convert between SMM and CPR rates with
CPR = 1 – (1 – SMM)12.
A good approximation is
A simple way to communicate the potential for a pool of
mortgages to prepay over its lifetime is to project a constant CPR. A
constant CPR projection is not particularly realistic. However, it can be
useful for communicating the potential for a given pool to prepay.
Constant CPR projections facilitate comparisons between pools. A
shortcoming of such projections is that they ignore a tendency for
prepayments to be modest in the early years of a mortgage.
To address this shortcoming, the Public Securities
Association (PSA) introduced a metric for projecting prepayments over the
life of a pool. The metric is called, simply enough, PSA.
A pool is said to have 100% PSA if its CPR starts at 0 and increases by
0.2% each month until it reaches 6% in month 30. It is a constant 6% after
that. A PSA of 50% indicates CPRs that are half those of 100% PSA. A PSA
of 150% indicates CPRs that are one-and-a-half those of 100% PSA. This is
illustrated in Exhibit 1.
A pool of mortgages is said to have 100%
PSA if its CPR starts at 0 and increases by 0.2% each month until it
reaches 6% in month 30. It is a constant 6% after that. Other
prepayment scenarios can be specified as multiples of 100% PSA.
Note that PSA indicates prepayment rates. It
assumes a constant rate after 30 months, but actual cash flows due
to prepayment decline over time as outstanding principal is diminished.
This is illustrated in Exhibit 2.