FRBSF Economic Letter
98-30; October 9, 1998
Mortgage Interest Rates, Valuation, and Prepayment Risk
Mortgage interest rates dropped in early 1998 to nearly the lowest level
in several decades. As mortgage rates moved down, refinancing activity
surged, flooding some mortgage investors with funds for reinvestment at
a time when a broader array of fixed-income investments also were offering
lower yields. On the other hand, investors in those mortgages that were
not prepaid generally have benefited from an appreciation in the value
of those mortgages. On balance, whether a given individual mortgage investor
suffered or benefited from recent changes in interest rates depended on
that investor's exposure to mortgage prepayment risk. This Economic
Letter explains important issues identified in the financial economics
literature on mortgage valuation and prepayment risk, including a new
line of research which relates regional variations in mortgage prepayment
risk to changes in local house prices.
Components of the mortgage rate spread
The goal of mortgage valuation theory is to determine the market value
of a given type of mortgage contract. Alternatively, if one fixes on a
given normal rate of profit in the mortgage origination business, mortgage
valuation theory can be used to describe the determination of mortgage
interest rates, including the spread between mortgage and Treasury interest
rates.
In recent years, the effective interest rate on 30-year fixed-rate residential
mortgages has exceeded the yield on 30-year U.S. Treasury bonds by more
than a full percentage point (Figure
1). This spread reflects several factors. In contrast to Treasury
bonds, mortgages require a lot of servicing, the handling of the monthly
payment of principal, interest, and escrow amounts. Mortgage lenders need
to receive additional revenues to cover these servicing costs. Second,
while the risk of default on U.S. government debt is nil, the default
risk on uninsured residential mortgages is substantial enough to contribute
noticeably to the spread. Third, the timing of regularly scheduled cash
flows differs between the two types of security. Treasury bonds pay a
stated interest rate semiannually, whereas mortgage payback is monthly
and amortizing; in a conventional 30-year mortgage, equal-sized monthly
payments of both principal and interest are paid over the 360 months of
the loan. The amortization and more frequent interest-payment features
reduce the effective "duration" of the mortgage; they make the timing
of mortgage cash flows most closely resemble those of a Treasury bond
with a term-to-maturity of much less than 30 years. Accordingly, medium-term
Treasury securities, such as 10-year bonds, in some ways are preferable
to 30-year Treasury bonds for defining a mortgage rate spread. Last, conventional
mortgages are prepayable at the option of the borrower. A portion of the
spread between 30-year mortgage rates and Treasury bond rates compensates
mortgage investors for granting borrowers a prepayment option which can
be exercised at any time, including when lenders reinvestment possibilities
are less favorable than at the date of mortgage origination.
Single-factor rational valuation paradigm
Standard option pricing methods have been used to calculate the value
of this mortgage prepayment option. One important early contribution to
the finance literature, Dunn and McConnell (1981), implemented such an
option pricing analysis on U.S. government agency-issued mortgage-backed-securities
(MBS). Such MBS are insured against loss of principal and interest from
homeowner default, and servicing costs are relatively uniform and clearly
specified. Thus, Dunn and McConnell were able to focus on the effects
of the amortization and call option features on the value of the MBS.
Valuation results depend on the modeler's assumption about the extent
of mortgage prepayment in various circumstances. Dunn and McConnell and
much of the subsequent literature assume that there are only two types
of prepayment, an "optimal" type which is triggered only when interest
rates move low enough to make exercise of the prepayment option the best
strategy, and a "suboptimal" background rate of early termination which
arises independently of the path of interest rates. The latter "suboptimal"
rate of exogenous termination captures features which are beyond the scope
of the model, such as homeowners' choosing to prepay in order to move.
Also, homeowners who default on the underlying mortgages trigger early
payments to MBS bondholders from insurers. In this model, "optimal" termination
represents refinancing, and there is only a single random factor-the short-term
riskless interest rate-determining MBS prepayment rates and MBS values.
Also, the model is frictionless in the sense that no transactions costs
impede the exercise of the option by the representative mortgage holder.
Recent history of mortgage rates and prepayment
rates on MBS
The Dunn and McConnell variant of the single-factor rational valuation
model captures some important features of the actual prepayment histories
of MBS, but the model also has severe limitations. Some of these limitations
can be inferred from the recent history of prepayment rates on passthrough
MBS shown in Figure 2. This
figure shows the percent of the pool value prepaid by month on four FreddieMac
reference pools, which are groups of MBS with a common year of origination
(1992 or 1993) and a common passthrough rate (7.0 to 8.5%). MBS passthrough
rates define how fast scheduled payments on the underlying mortages are
passed through to MBS bondholders as interest; the actual contract interest
rates on the underlying mortgages tend to be slightly above these passthrough
rates, as they include allowances for servicing and insurance charges.
As seen in the figures, when mortgage interest rates moved toward new
lows of about 7% in early 1996 and again in early 1998, a pickup in refinancing
showed through as a noticeable jump in overall prepayments on the two
reference pools with relatively high passthrough rates, the 1992 8.5s
and 8.0s. However, on the 1993 7.0s, prepayment rates remained low and
relatively stable.
In the broad sense of predicting high prepayment rates when current
interest rates fall well below the coupons on the outstanding mortgages
and predicting a relatively stable background rate of prepayment from
mobility and default, the single-factor model appears to succeed, at least
using this aggregate reference pool data. However, this frictionless rational
refinancing model implies that all mortgages in a given pool would prepay
in that single month when it first becomes optimal to exercise the call
option. In contrast, the peak rate of refinancing for these pools was
5% in this sample period. Thus, prepayment models need to make some allowance
for differences in the behavior of the mortgage borrowers within the pools.
Subsequent contributions to the literature introduce such heterogeneity
by assuming that borrowers face different "transactions costs" of exercising
the prepayment option.
Models with a distribution of transactions costs also are able to capture
another empirical regularity, the tendency of prepayment rates for a given
pool of mortgages to be higher the first time through a low interest rate
episode than in subsequent, similar episodes. In other words, MBS pools
tend to exhibit "burnout"; fast prepayers, those mortgage holders with
the lowest "transactions costs," exit the pools in the initial episodes,
leaving only sluggish prepayers in the remainder of the pool.
Recent advances in the literature
Rather than "burning out," the early 1998 spike in prepayment rates was
larger than the early 1996 jump in prepayment rates, even though the low
point for the conventional mortgage contract rates was about 7.0% in both
cases. One major difference between the two episodes is that the low rates
were sustained throughout early 1998, whereas the early 1996 decline in
mortgage rates was reversed quickly. Stanton's (1995) model, in which
only a portion of potential refinancers review this option each month,
incorporates this tendency for prepayment rates to depend on the duration
of interest rate lows.
Other research, such as Kau, et al. (1992), has extended the option pricing
framework to model the competing risks of refinancing and default. In
such models, housing prices appear as a second factor that is particularly
important to predicting defaults. In these models, when the value of the
house drops to below the level that would fully collateralize the outstanding
debt, a homeowner may rationally choose to default on the mortgage. The
broader literature on the relationship between house prices and mortgage
market activity suggests that declines in house prices also restrict mobility
and refinancing. In weak house price environments, mobility is reduced
because homeowners have less equity to use to trade up to larger houses,
and refinancing is held down because loan-to-value constraints tend to
bind. This literature suggests dropping the standard two-factor model's
restriction that excludes house prices from having a significant effect
on refinancing or mobility.
In Mattey and Wallace (1998), we analyze the benefits of using an unrestricted
two-factor model of mortgage terminations for mortgage-backed securities
valuation. To gather empirical evidence on how best to calibrate a Stanton
(1995) type of valuation model, we investigate the connection between
house prices and mortgage market activity in fifteen California counties
in 1992-96. During this period, house prices in Los Angeles area counties
were particularly depressed, but house prices held up better in San Francisco
Bay Area counties.
We find that overall mortgage terminations in many Los Angeles area counties
were depressed by the lack of housing collateral to use for refinancing
or for moving to another home. As might be expected, defaults were high
in the Los Angeles area counties with weak house prices. In terms of the
effect on total mortgage terminations, the increased defaults were a substantial,
but not complete, offset to the reduced mobility.
The Mattey and Wallace (1998) study also includes a simple model of the
dynamics of house prices in these counties. Given an assumed increase
in population flows to California's major metropolitan areas, the house
price model projects a moderate pickup in house prices beyond 1996, the
last year of the sample period used for estimation of the mortgage termination
model. Accordingly, holding interest rates constant, the model predicts
substantial increases in mortgage terminations in the out-of-sample period;
improved housing prices are projected to boost refinancing and home sales.
Although data are not yet available to check this out-of-sample projection
of county-specific mortgage termination rates, the in-sample results strongly
support the conclusion that regional variations in mortgage prepayment
risk are closely related to changes in local house prices.
Joe Mattey
Research Officer
References
Dunn, Kenneth, and John McConnell. 1981. "Valuation of GNMA Mortgage
Backed Securities." Journal of Finance 36, pp. 599-616.
Kau, James, Donald Keenan, Walter Muller II, and James Epperson. 1992.
"A Generalized Valuation Model for Fixed-Rate Residential Mortgages."
Journal of Money, Credit and Banking 24, pp. 279-299.
Mattey, Joe, and Nancy Wallace. 1998. "Housing
Prices and the (In)stability of Mortgage Prepayment Models: Evidence from
California." Federal Reserve Bank of San Francisco Working Paper 98-05.
Stanton, Richard. 1995. "Rational Prepayment and the Valuation of Mortgage-Backed
Securities." The Review of Financial Studies 8, pp. 677-708.
Opinions expressed in this newsletter do not necessarily reflect
the views of the management of the Federal Reserve Bank of San Francisco
or of the Board of Governors of the Federal Reserve System. Editorial
comments may be addressed to the editor or to the author. Mail comments
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Research Department
Federal Reserve Bank of San Francisco
P.O. Box 7702
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