Prepayment uncertaintyz

Now we turn to the another important source of risk in fixed-income markets,
prepayment uncertainty. Prepayment modeling is one of the most critical variables in
the mortgage-backed securities (MBS) market, as a prepayment forecast determines a
security’s value and its perceived ‘riskiness’ (where ‘risky’ is defined as having a large
degree of interest rate sensitivity, described by a large effective duration and/or
negative convexity). For those who may be unfamiliar with CMOs, certain types of
these securities (such as principal-only tranches, and inverse floaters) can have
effective durations that are two or three times greater than the duration of the
underlying mortgage collateral, while interest-only (IO) tranches typically have negative
durations, and many CMOs have substantial negative convexity. Changes in
prepayment expectations can have a considerable impact on the value of mortgagebacked
and asset-backed securities and therefore represents an important source
of risk.
Let’s briefly review how mortgage prepayment modeling affects the valuation of
mortgage-backed securities. To determine the expected future cash flows of a security,
a prepayment model must predict the impact of a change in interest rates on a
homeowner’s incentive to prepay (refinance) a mortgage; as rates decline, prepayments
typically increase, and vice versa. Prepayment models take into account the
age or ‘seasoning’ of the collateral, as a homeowner whose mortgage is relatively new
is less likely to refinance in the near-term than a homeowner who has not recently
refinanced. Prepayment models also typically incorporate ‘burnout’, a term that
reflects the fact that mortgage pools will contain a certain percentage of homeowners
who, despite a number of opportunities over the years, simply cannot or will not
refinance their mortgages. Many models also reflect the fact that prepayments tend
to peak in the summer months (a phenomenon referred to as ‘seasonality’), as
homeowners will often postpone moving until the school year is over to ease their
children’s transition to a new neighborhood. Prepayment models attempt to predict
the impact of these and other factors on the level of prepayments received from a
given pool of mortgages over the life of the collateral.
Earlier, we alluded to the fact that mortgage valuation is a path-dependent problem.
This is because the path that interest rates follow will determine the extent to which
a given collateral pool is ‘burned out’ when a new refinancing opportunity arises. For
example, consider a mortgage pool consisting of fairly new 7.00% mortgages, and
two interest rate paths generated by a Monte Carlo simulation. For simplicity, we
make the following assumptions:
Ω Treasury rates are at 5.25% across the term structure
Ω Mortgage lending rates are set at 150 bps over Treasuries
Ω Homeowners require at least a 75 bp incentive to refinance their mortgages.

Given this scenario, homeowners with a 7.00% mortgage do not currently have
sufficient incentive to trigger a wave of refinancings. Now, imagine that along the
first interest rate path Treasury rates rise to 6.00% over the first two years, then
decline to 4.75% at the end of year 3; therefore, mortgage lending rates at the end of
year 3 are at 6.25%, presenting homeowners with sufficient incentive to refinance at
a lower rate for the first time in three years. Along this path, we would expect a
significant amount of prepayments at the end of year 3. On the second path, imagine
that rates decline to 4.75% by the end of the first year and remain there. This gives
homeowners an opportunity to refinance their 7.00% mortgages for two full years
before a similar incentive exists on the first path. Consequently, by the end of year 3
we would expect that most homeowners who wish to refinance have already done so,
and the cash flows forecasted for the end of year 3 would differ markedly compared
to the first path, even though interest rates are the same on both paths at that point
in time.
Therefore, we cannot forecast the prepayments to be received at a given point in
time simply by observing the current level of interest rate; we must know the path
that rates followed prior to that point. In valuing mortgage-backed securities, this is
addressed by using some type of Monte Carlo simulation to generate a sufficient
number of different interest rate paths which provide the basis for a prepayment
model to predict cash flows from the collateral pool under a variety of possible paths,
based upon the history of interest rates experienced along each path.