Differences in prepayment models

Prepayment speed forecasts in the mortgage-backed securities market often differ
considerably across various reliable dealers. Table 7.2 shows the median prepayment
estimates provided to the Bond Market Association by ten dealer firms for different
types of mortgage collateral, along with the high and low estimates that contributed
to the median. Note that in many cases, the highest dealer prepayment forecast is
more than twice as fast as the lowest estimate for the same collateral type.
To illustrate the degree to which differences in prepayment model forecasts can
affect one’s estimate of a portfolio’s characteristics, we created a portfolio consisting
of the different mortgage collateral shown in Table 7.2, with equal par amounts of
eleven collateral pools with various coupons and maturities, using the ‘Low’ (slowest)
PSA% and the ‘High’ (fastest) PSA% for each collateral type. Using the ‘Low’ speed,
the portfolio had an average life of 6.85 years, with a duration of 4.73; using the
‘High’ speeds, the same portfolio had an average life of 3.67 years and a duration of
2.69. Clearly, the uncertainty in prepayment modeling can have a large impact on
one’s assessment of a portfolio’s risk profile.
There are a number of reasons why no two prepayment models will produce the
same forecast, even with the same information about the interest rate environment
and the characteristics of the mortgage collateral of interest. For example, different
firms’ prepayment models may be calibrated to different historical data sets – some
use five or even ten years of data, others may use data from only the past few years;
some models attach greater weight to more recent data, others attach equal weight
to all time periods; the variables used to explain and forecast prepayment behavior
differ across models, and so on. Therefore, differences in prepayment modeling across
well-respected providers is to be expected.4
In addition to differences in the way models are calibrated and specified, there is
some likelihood that the historical data used to fit the model no longer reflects
current prepayment behavior. When new prepayment data indicates that current
homeowner behavior is not adequately described by existing prepayment models,
prepayment forecasts will change as dealers and other market participants revise
their models in light of the new empirical evidence For example, in recent years
mortgage lenders have become more aggressive in offering low-cost or no-cost refinancing.
As a result, a smaller decline in interest rates is now sufficient to entice
homeowners to refinance their mortgages compared to five years ago (the required
‘refinance incentive’ has changed). Further developments in the marketplace (e.g. the
ability to easily compare lending rates and refinance a mortgage over the Internet)
will undoubtedly affect future prepayment patterns in ways that the historical data
used to fit today’s prepayment models does not reflect.
As mentioned previously, in the Fall of 1998 a combination of events wreaked
havoc in fixed-income markets. Traditional liquidity sources dried up in the MBS
market, which forced a number of private mortgage lenders to file for bankruptcy
over the course of a few days. At the same time, Treasury prices rose markedly as
investors sought the safe haven of US Treasuries in the wake of the uncertainties in
other markets. As a rule, when Treasury yields decline mortgage prepayments are
expected to increase, because mortgage lenders are expected to reduce borrowing
rates in response to the lower interest rate environment. This time, however, mortgage
lenders actually raised their rates, because the significant widening of spreads in
the secondary market meant that loans originated at more typical (narrower) spreads
over Treasury rates were no longer worth as much in the secondary market, and
many lenders rely on loan sales to the secondary market as their primary source of
funds. (Note that this episode is directly relevant to the earlier discussion of spread
duration for mortgage-backed securities.)
These conditions caused considerable uncertainty in prepayment forecasting.
Long-standing assumptions about the impact of a change in Treasury rates on
refinancing activity did not hold up but it was uncertain as to whether or not this
would be a short-lived phenomenon. Therefore, it was unclear whether prepayment
models should be revised to reflect the new environment or whether this was a
short-term aberration that did not warrant a permanent change to key modeling
parameters. During this time, the reported durations of well-known benchmark
mortgage indices, such as the Lehman Mortgage Index and Salomon Mortgage Index,
swung wildly (one benchmark index’s duration more than doubled over the course
of a week), indicating extreme uncertainty in risk assessments among leading MBS
dealers. In other words, there was little agreement as to prepayment expectations
for, and therefore the value of, mortgage-backed securities.
Therefore we must accept the fact that a prepayment model can only provide a
forecast, or an ‘educated guess’ about actual future prepayments. We also know that
the market consensus about expected future prepayments can change quickly,
affecting the valuation and risk measures (such as duration and convexity) that are
being used to manage a portfolio of these securities. Therefore, the effect of revised
prepayment expectations on the valuation of mortgage-backed securities constitutes
an additional source of risk for firms that trade and/or invest in these assets. This
risk, which we may call prepayment uncertainty risk, may be thought of as a ’model
risk’ since it derives from the inherent uncertainty of all prepayment models.
For an investment manager who is charged with managing a portfolio’s exposure
to mortgages relative to a benchmark, or for a risk manager who must evaluate a
firm’s interest rate risk including its exposure to mortgage-backed securities, this
episode clearly illustrates the importance of understanding the sensitivity of a
valuation or risk model’s output to a change in a key modeling assumption. We do
this by computing a ‘prepayment uncertainty’ measure that tests the ‘stability’ of a
model’s output given a change in prepayment forecasts.