FRBSF Economic Letter
1998-30 | October 9, 1998
Mortgage Interest Rates, Valuation, and Prepayment Risk
- Components of the mortgage rate spread
- Single-factor rational valuation paradigm
- Recent history of mortgage rates and prepayment rates on MBS
- Recent advances in the literature
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.
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.
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.
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.
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.
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 FRBSF Economic Letter 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. This publication is edited by Sam Zuckerman and Anita Todd. Permission to reprint must be obtained in writing.
Please send editorial comments and requests for reprint permission to
Attn: Research publications, MS 1140
Federal Reserve Bank of San Francisco
P.O. Box 7702
San Francisco, CA 94120