Refinance and relocation uncertainty

One of the most important variables in a prepayment model is the minimum level or
‘threshold’ incentive it assumes a homeowner requires to go to the trouble of
refinancing a mortgage. The amount of the required incentive has certainly declined
over the past decade; in the early days of prepayment modeling, it was not unusual to
assume that new mortgage rates had to be at least 150 bps lower than a homeowner’s
mortgage rate before refinancings would occur. Today, a prepayment model may
assume that only a 75 bp incentive or less is necessary to trigger a wave of refinancings.
Therefore, we may wish to examine the amount of risk associated with a misestimate
in the minimum incentive the model assumes homeowners will require
before refinancing their mortgages.
To do so, we separate the total prepayment uncertainty measure into two components:
refinancing uncertainty and relocation uncertainty. The ‘refi’ measure
describes the sensitivity of a valuation to changes in the above-mentioned refinancing
incentive, and the ‘relo’ measure shows the sensitivity to a change in the level of
prepayments that are independent of the level of interest rates (i.e. due to demographic
factors such as a change in job status or location, birth of children, divorce,
retirement, and so on). Table 7.3 shows the overall and partial (‘refi’ and ‘relo’
prepayment uncertainties) for selected 30-year passthroughs.

At first glance, these prepayment uncertainty values appear to be rather small. For
example, we can see that a 10% increase or decrease in expected prepayments would
produce a 0.191% change in the value of a moderately seasoned 7.50% mortgage
pool. However, it is important to note that a 10% change in prepayment expectations
is a rather modest ‘stress test’ to impose on a model. Recall the earlier discussion of
differences in prepayment forecasts among Wall Street mortgage-backed securities
dealers, where the high versus low estimates for various collateral types differed by
more than 200%. Therefore, it is reasonable to multiply the prepayment uncertainty
percentages derived from a 10% change in a model by a factor of 2 or 3, or even
more.
It is interesting that there appears to be a negative correlation between total
prepayment uncertainty and effective duration; in other words, as prepayment
uncertainty increases, interest rate sensitivity decreases. Why would this be so?
Consider the ‘New 6.50%’ collateral with a slightly negative total prepay uncertainty
measure (ñ0.042). This collateral is currently priced at a slight discount to par, so
a slowdown in prepayments would cause the price to decline as the investor would
receive a somewhat below-market coupon longer than originally expected. Both the
‘refi’ and ‘relo’ components of this collateral’s total uncertainty measure are relatively
small, partly because these are new mortgages and we do not expect many
homeowners who have just recently taken out a new mortgage to relocate or even to
refinance in the near future, and partly because the collateral is priced slightly below
but close to par. Since the collateral is priced below par, even a noticeable increase
in the rate of response to a refinancing incentive would not have much impact on
homeowners in this mortgage pool so the ‘refi’ component is negligible. Also, since
the price of the collateral is so close to par it means the coupon rate on the security
is roughly equal to the currently demanded market rate of interest. An increase or
decrease in prepayments without any change in interest rates simply means the
investor will earn an at-market interest rate for a shorter or longer period of time;
the investor is be indifferent as to whether the principal is prepaid sooner or later
under these circumstances as there are reinvestment opportunities at the same
interest rate that is currently being earned.
In contrast, the effective duration is relatively large at 3.70 precisely because the
collateral is new and is priced close to par. Since the collateral is new, the remaining
cash flows extend further into the future than for older (seasoned) collateral pools
and a change in interest rates would have a large impact on the present value of
those cash flows. Also, since the price is so close to par a small decline in interest
rates could cause a substantial increase in prepayments as homeowners would have
a new-found incentive to refinance (in other words, the prepayment option is close
to at-the-money).
This highlights a subtle but important difference between the impact of a change
in refinance incentive due to a change in interest rates, which effective duration
reflects, and the impact of a prepayment model misestimate of refinancing activity
absent any change in interest rates. We should also note that since prepayment
uncertainty is positive for some types of collateral and negative for others, it is
possible to construct a portfolio with a prepayment uncertainty of close to zero by
diversifying across collateral types.