Reverse Mortgages and Prepayment Risk

This paper presents a detailed assessment of the Connecticut Housing Finance Authority (CHFA) reverse annuity mortgage (RAM) program. Because of the size and payment history of the program, the analysis provides an empirical framework on which to develop and assess other home equity conversion (HEC) programs. The program offers insights into the economic impact of these programs and the factors affecting prepayment. The program issued 765 annuities over five years, and 240 of these loans have terminated payments. The annuity payments had a demonstrable financial impact on the elderly participants, with an 88% average annual income increase. Prepayment rates varied across borrower and loan characteristics. The rates were most sensitive to marital status and were heavily affected by the age of the borrower and the term of the loan. Although default risk exists, the evidence indicates a low probability of the loan value exceeding the house value.     

Reverse Mortgages and Interest Rate Risk

We develop and apply a valuation model that quantifies the interest rate risk inherent in fixed-rate reverse mortgages. Consistent with intuition, our results show that the interest rate risk of a reverse mortgage is greater than that of either a typical coupon bond or a regular mortgage. Somewhat surprisingly, we find that this difference in interest rate risk is extremely large. In fact, the interest rate risk of a reverse mortgage often is several orders of magnitude greater than the interest rate risk of other fixed-income securities.     

Reverse Mortgages: Contracting and Crossover Risk

A pricing model is developed for a reverse mortgage contract where the borrower receives payments either as a lump sum or in an annuity while the loan balance accumulates as a claim against the house. No underwriting criteria on income are applied. One risk of default is that the borrower will remain in the house after the negatively amortizing loan balance exceeds the value of the house. An explicit pricing model of the reverse mortgage permits the evaluation of this default "crossover" option. Alternative methods involving life insurance contracts and securitization are compared as secondary market channels.     

Reverse Mortgages and the Liquidity of Housing Wealth

Housing wealth constitutes most of the non-pension wealth of the elderly population. This study analyzes the potential of reverse mortgages to increase the income and liquid wealth of the elderly by identifying households with relatively high levels of housing equity. Because this article looks at the whole distribution of elderly households and considers debt as well as income, it finds a larger potential market for reverse mortgages than previous studies.
Calculations from the 1990 Survey of Income and Program Participation and Census population estimates show that over six million homeowners in the United States could increase their effective monthly income by at least 20% by using a reverse mortgage. Of these, more than 1.3 million have no children. Furthermore, a reverse mortgage would allow over 1.4 million poor elderly persons to raise their incomes above the poverty line.     

Pricing Default Risk in Mortgages

This paper examines the valuation of fixed-rate mortgages and the pricing of insurance against default on such mortgages. Both the mortgage and the insurance are treated as compound European put options. A put is the right, but not the obligation, to turn over an asset to another party for a specified payment, and being a European put indicates that this can only occur at a specified expiration date. The mortgage contract, and hence the insurance on it, fit into a European option framework because no rational borrower would ever choose to default until a payment is due. Mortgages are compound options in nature because at each payment data prior to the last one, the borrower either defaults or purchases a new option to default at the next payment date by making the scheduled payment. Since the current value of the mortgage is affected by options to default in the future, the problem is solved working backwards in time with the value of later options feeding into the earlier ones, so that the process builds on itself in a recursive fashion. Using familiar arguments from option-pricing theory, the value of any of the assets in the model is expressed as the solution to a partial differential equation, where the terms of the contract yield the appropriate terminal conditions. Standard numerical procedures are then used to produce the value of the mortgage and the insurance under various economic conditions. The simulations indicate that the prime determinants of the value of the assets considered are the volatility of the house price and the volatility of the spot interest rate. Sensitivity tests show that changing either of these parameters affects the results substantially more than any of the other parameters examined. The paper completely analyzes the default option and insurance against default on the mortgage. It is one part of a complete model of fixed-rate mortgages that would allow for both prepayment and default and treat the interaction of the two options. The general approach outlined in this paper can be used to develop such a model as well as to value any mortgage-related security. In light of the increasing variety and the complexity of such instruments in the market today, the presentation of our approach to these valuation problems is perhaps the most important contribution of the paper.     

Interest-Rate Volatility, Basis Risk and Heteroscedasticity in Hedging Mortgages

This paper investigates the validity of the OLS regression to estimate the hedge ratio for mortgages (GNMA) and provides alternative methodologies. In particular, this paper is concerned with the variance structure (conditional and unconditional heteroscedasticities) and the misspecification (nonlinearities) of the simple linear regression model for direct as well as cross-hedging. Using data on spot prices of GNMA and futures prices of GNMAs and T-bills for the period September 1979 to January 1985, we show that there exists significant heteroscedasticity particularly for cross-hedging, and nonlinearity between cash and futures prices for direct as well as cross-hedging. Alternative hedge ratio estimates are provided using the Box-Cox transformation model and an autoregressive conditional heteroscedastic (ARCH) Model.     

Interest Rate Risk, Residential Mortgages and Financial Futures Markets

Residential mortgage markets in both the United States and Canada have recently been dominated by instruments such as variable-rate and short-term rollover mortgages which require borrowers to assume a greater burden of interest rate risk. An outstanding question is whether this approach to risk allocation is Pareto optimal or whether there are other more effective methods of dealing with the risk created by interest rate volatility. This study examines the potential for shifting this risk from the mortgage market to the financial futures market. After considering the rationale for expecting that neither mortgage borrowers nor lenders wish to absorb the high levels of risk present in the existing financial environment, this study discusses the hedging of interest rate risk through financial futures markets. Empirical tests are then performed to evaluate the effectiveness of U.S. futures markets for hedging positions from the U.S. mortgage market. These results indicate that the interest rate risk inherent in residential mortgages can be substantially shifted through one or more positions in the existing futures contracts and long-term, fixed-rate mortgages may still be financially feasible under conditions of interest rate volatility.     

Inflation Risk, Payment Tilt, and the Design of Partially Indexed Affordable Mortgages

This paper integrates two fundamentally important parameters into a theory of optimal mortgage design: the proportion of inflation risk borne by the lender / investor and the borrower and the amortization-graduation schedule for loan repayments. Equations are derived for a family of innovative mortgages, termed hybrid PLAMs, which offer advantages to borrowers and lenders over either the standard fixed rate mortgage (FRM) or the price level adjusted mortgage (PLAM). The superiority of the hybrid PLAMs lies in their ability to simultaneously and independently accommodate differing degrees of inflation-risk sharing and payment affordability. Inflation-risk sharing is represented by an indexation parameter set over a continuum of values such that the FRM has zero index variability and the PLAM has unit index variability. Similarly, payment tilt is represented by a tilt parameter such that the FRM has zero tilt and the PLAM has unit tilt. We demonstrate that these two parameters are independent and can each be continuously varied in a two-dimensional family of self-amortizing mortgages. A specific hybrid PLAM can be designed to partition inflation risk in any proportion between the borrower and the lender and to simultaneously prescribe any level of payment tilt between the extremes of the FRM and PLAM. The behavior of representative hybrid PLAMs is simulated and compared to FRMs and PLAMs for three different inflation scenarios, one of which uses actual market data from the period of 1960–1990.     

Borrower Credit and the Valuation of Mortgage-Backed Securities

We study the valuation of mortgage-backed securities when borrowers may have to refinance at premium rates because of their credit. The optimal refinancing strategy often results in prepayment being delayed significantly relative to traditional models. Furthermore, mortgage values can exceed par by much more than the cost of refinancing. Applying the model to an extensive sample of mortgage-backed security prices, we find that the implied credit spreads that match these prices closely parallel borrowers' actual spreads at the origination of the mortgage. These results suggest that models that incorporate borrower credit into the analysis may provide a promising alternative to the reduced-form prepayment models widely used in practice.     

Estimating Borrower Mobility from Observed Prepayments

This article describes a method used to estimate parameters describing the mobility of borrowers choosing fixed-rate mortgages. Using a mortgage valuation model that predicts prepayments contingent upon parameters describing the distribution of expected tenure in the home, the average mobility of borrowers can be estimated from observed prepayment behavior. This article estimates the mobility of borrowers who chose fixed-rate mortgages before 1980 and borrowers who chose similar mortgages in the second half of the 1980s, when adjustable-rate mortgages were widely available. The empirical results support the claim that the average mobility of fixed-rate borrowers has declined.     

Prepayment Risk in Adjustable Rate Mortgages Subject to Initial Year Discounts: Some New Evidence

This paper uses microlevel data to examine recent prepayment performance of adjustable rate mortgages (ARMs) employing the competing risk methodology developed by Deng, Quigley and Van Order (2000). We find support for the teaser rate and adjustment date effects implied by the theoretical model of Kau et al. (1993). In addition, we find that teased ARMs bear prepayment risk related to their discount, contrary to results reported by VanderHoff (1996) and Green and Shilling (1997). Finally, and contrary to the usual finding for fixed-rate mortgages, we find that loan age has a negative effect on prepayment risk for ARMs, consistent with the phenomenon that borrowers with high mobility and/or propensity to refinance exit the pool early.     

The Performance of Commercial Mortgages

This study examines the return characteristics of a large, well-diversified commercial mortgage portfolio. Mortgage-specific cash-flow histories are constructed for 2,480 loans originated over the period 1974 through 1990, and a contingent-claims approach to pricing risky debt is used to estimate inter-temporal market values. Quarterly holding-period returns are compared across selected mortgage groups and to alternate asset classes. Our findings suggest that both mortgage returns and volatility of return are comparable to those of other forms of fixed-income assets over the study period. Implied property price volatility is found to average 17%, a result significantly higher than reported in earlier studies. While mortgage returns are found to vary by property type and region of origin, cross correlation of returns is found to be high, illustrating the systematic effect of interest rates on the performance of commercial mortgages over the period 1974 through 1990. However, an increase in credit risk in the latter years of the study suggests that diversification may be a worthwhile objective for holders of these assets. We do not find evidence to suggest that abnormal returns were earned on commercial mortgage portfolios over the study period.     

A Note on Hybrid Mortgages

We extend previous research on traditional one-year adjustable-rate mortgages (ARMs) by analyzing the performance of 3/27 hybrid instruments. Under this contract innovation, which first appeared in the mid-1990s, note rates are fixed for three years after which they convert to a traditional one-year adjustment schedule with periodic and lifetime caps. We find high rates of prepayment, particularly at time of initial rate adjustment, and relatively high rates of default, as would be consistent with the payment shock that often affects adjustable-rate loans.     

Borrower Attitudes Toward Alternative Mortgage Instruments*

Much of the existing literature on homeownership assumes that financial markets work well enough to allow households to translate permanent income into effective demand. However, transaction costs, imperfections, and uncertainties all constrain the markets' operation so that people are often forced to choose a quantity of housing stock that diverges from their desired consumption level. Instead of being able to borrow against future income for the down payment or to make monthly payments in a pattern that matches future income, young families in their early years may be constrained from purchasing the size house they desire, and older households may remain in homes larger than they need. In light of these market imperfections, housing and tenure decisions depend not only on permanent income and the relative price of housing services, but also on such mortgage parameters as monthly payment patterns, down payment, and rate of equity accumulation. Models of the demand for housing and homeownership described in the existing literature do not include these parameters of mortgage finance. Mortgage terms are important factors in housing consumption and investment decisions. Because the standard mortgage no longer seems appropriate for all households under all economic conditions, the extent to which alternative mortgage instruments meet the requirements and preferences of different segments of the market becomes an important issue.     

Standardizing Yields on Mortgages and other Securities

The existence of a difference between the yield to maturity of a coupon bond and the expected holding period return on a coupon bond, referred to as coupon bias, is well recognized. This paper discusses the nature of coupon bias for mortgages, estimates the magnitude of the bias under different assumptions about the characteristics of the mortgage security and the term structure, and compares the magnitude of the coupon biases on mortgages and comparable coupon bonds. For a moderately upward sloping term structure at current levels of interest rates, coupon bias for a thirty-year mortgage can be on the order of 75 basis points.     

The Performance of Low-Income and Minority Mortgages

This article analyzes the performance of low-income and minority mortgages (LIMMs) from a large sample of fixed-rate conventional conforming mortgages. We find that low-income borrowers are less likely to prepay when it is optimal, whereas black and Hispanic borrowers prepay more slowly than other borrowers, regardless of the option's value. After controlling for equity, credit history and some other variables, LIMMs default slightly more frequently and have about the same loss severity as other loans. Our results suggest that, for most yield curve situations, differences in LIMM prepayment behavior have little effect on pricing.     

On the Design and Pareto-Optimality of Participating Mortgages

This paper develops a micro-economic model and proceeds with numerical simulation to demonstrate that participating mortgages can improve social welfare when the real estate ownership is shared among the different taxable entities. The optimal distribution of real estate ownership and lending will tend to be concentrated in taxable and nontaxable hands, respectively, with lending conducted via participating mortgages. This paper also demonstrates the violation of the well-known, risk-neutral valuation argument of the Black and Scholes (1973) model because of the lack of a riskless hedge due to the uniqueness of real estate.     

FHA, Racial Discrimination and Urban Mortgages

The empirical validity of two propositions regarding FHA unsubsidized single-family activity are explored at the neighborhood level in this paper. The propositions are first that FHA serves moderate-to-middle-income families, not low-income families who live in the inner city nor high-income families who live in the outer suburbs; and second that all other things being equal, black owner-occupants are more likely to have an FHA-insured mortgage than are whites
Two methods of analysis are performed: mapping and regression. First, 1974 FHA activity in the Philadelphia metropolitan area is mapped by race—black and white—and program—203(b), 221(d)(2), and 223(e)—at the census tract level. Then, the FHA activity by race and by program is regressed on 1970 neighborhood housing and population characteristics, again, using the census tract as the unit of observation. The results of the analysis provide support for both propositions. In Philadelphia in 1974, FHA is to a degree a border program differentially serving blacks.     

Rational Pricing of Adjustable Rate Mortgages

In this paper we develop a general method for valuing adjustable rate mortgages and by producing a set of simulation results, we show that our approach can be implemented. While the simulations are of interest in their own right, we view the approach itself as the major contribution of the paper.