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.     

Determinants of Credit Spreads in Commercial Mortgages

This article examines the cross-sectional and time-series determinants of commercial mortgage credit spreads as well as the terms of the mortgages. Consistent with theory, our empirical evidence indicates that mortgages on property types that tend to be riskier and have greater investment flexibility exhibit higher spreads. The relationship between the loan-to-value (LTV) ratio and spreads is relatively weak, which is probably due to the endogeneity of the LTV choice. However, the average LTV ratio per lender has a strong positive relation with credit spreads, which is consistent with the idea that lenders specialize in mortgages with either high or low levels of risk, and that high LTV mortgages require substantially higher spreads. Finally, we observe that spreads widen and mortgage terms become stricter after periods of poor performance of the real estate markets and after periods of greater default rates of outstanding real estate loans.     

Valuing the Defeasance Option in Securitized Commercial Mortgages

To protect the interests of investors, commercial mortgage loans pooled for the issuance of commercial mortgage-backed securities (CMBS) have restrictive covenants that discourage the borrower from refinancing. Such restrictions limit the borrower's ability to access any accumulated equity. The predominant means of accessing this equity today is defeasance. By defeasing a loan, the borrower substitutes the commercial mortgage with U.S. Treasury or agency obligations whose payments match those of the defeased mortgage. Therefore, defeasance is an exchange option whereby the borrower gives up the portfolio of Treasury or agency securities and in return receives the market value of the commercial mortgage plus the liquidity benefits arising from accessing the accumulated equity in the underlying property. The value of the option to defease is shown to depend critically on the rate of return that can be earned on the released equity, prevailing interest rate conditions, as well as the option's contractual features.     

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.     

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.     

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.     

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.     

Reverse Mortgages and Borrower Maintenance Risk

This paper develops a theoretical model of the problem of maintenance risk in reverse mortgages (RMs) and home equity conversion instruments generally. By maintenance risk, we refer to the incentive homeowners will have to reduce maintenance expenditures as their equity in the house falls during the term of the RM. The underlying reason for this tendency is the limited liability feature of RMs, given that a borrower's obligation to the lender at. maturity is limited to the value of the house.
The results of the model show that lenders will respond to this problem either by limiting the amount of RM loans to guarantee that maintenance risk is not a threat, or by charging an interest rate premium to cover the expected cost of default. Unfortunately, there do not exist data to test the importance of maintenance risk as a possible limitation on the extent of the RM market.     

The Termination of Subprime Hybrid and Fixed‐Rate Mortgages

Adjustable‐rate and hybrid loans have been a larger component of subprime mortgage lending in the mortgage market than prime lending. The typical adjustable‐rate loan in subprime is a hybrid of fixed and adjustable characteristics in which the first 2 years are fixed and the remaining 28 years adjustable. Hybrid loans terminate at elevated probabilities even before the first adjustment date. Hybrid loan terminations are sensitive to interest rates and teaser rates (payment shocks). Default probabilities increase dramatically when payment shocks are mixed with low or no equity in the home. This is the mixture of events that helped to trigger the 2007/2008 subprime mortgage crisis.     

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.     

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.     

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.     

Rate Level Indexed Mortgages: An Evaluation

In this paper, a new and superior alternative mortgage design is presented and evaluated. The mortgage design is motivated by a desire to reduce the exposure of both borrowers and lenders to risks that result from high and variable interest rates, while at the same time providing a mechanism by which changes in the real value of payments and rates of amortization can be controlled. In addition to a theoretical discussion of the merits of this design a simulation of the mortgage's performance is provided that uses market data from the period 1965 to 1983.     

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.     

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.     

A Contingent Claims Analysis of Price Level-Adjusted Mortgages

This paper examines the performance of alternative mortgage instruments in an environment of stochastic price fluctuations. The two most widely discussed contracts that deal with inflation are the adjustable-rate mortgage (ARM) and the price level-adjusted mortgage (PLAM). The former compensates for inflation by paying the nominal interest rate, which contains a component reflecting the rate of inflation. Nonetheless, even without explicit nominal amortization, this results in real amortization and hence a tilting effect. In addition, the inflation component of the nominal interest rate is shown to reflect only anticipated and not actual inflation, and so the real value of an ARM fluctuates due to unanticipated inflation. A PLAM suffers from none of these defects. To the extent that one is interested in a mortgage whose properties reflect the underlying real environment, the price level-adjusted mortgage is the ideal instrument.     

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.     

Pricing Life-of-Loan Rate Caps on Default-Free Adjustable-Rate Mortgages

A model is developed and utilized in this paper to value a life-of-loan interest-rate cap on an ARM that reprices monthly. The value of the cap is seen to depend importantly on both the slope of the term structure and the variance of the 1-month rate. However, the cap value is not sensitive to the source of the slope of the term structure — what precise combination of interest-rate expectations and risk aversion determined the slope. This insensitivity is fortunate because of the great difficulty of knowing at any point in time why the term structure is what it is.
Given the variation in the slope of the term structure and the variance of the 1-month rate that occurred over the 1979–84 period, the addition to the coupon rate on a 1-month ARM that lenders should have charged for a 5% life-of-loan cap has ranged from 5 to 40 basis points.     

The Impact of Interstate Foreclosure Cost Differences and the Value of Mortgages on Default Rates

Previous research on mortgage default has focused on the costs, benefits, and characteristics of the mortgagor. In such studies default rates have been taken as a measure of mortgage risk. In this paper we present a model where the position of the lender affects the default-foreclosure process. Important to the lender's decision to foreclose rather than renegotiate an existing loan are the value of mortgage and the legal costs associated with foreclosure.
The empirical evidence supports the hypothesis that both the value of the mortgage and legal foreclosure costs affect the foreclosure rate. In those states where legal foreclosure costs are high rates are significantly less than where costs are low. This suggests that previous models which include only the costs and benefits of default to the borrower are incomplete and that foreclosure rates can not be taken as a strict measure of mortgage risk. That is, low foreclosure rates may indicate that losses occur in other forms of loan negotiation rather than in expensive legal costs.