Mortgage Innovation, Mortgage Choice, and Housing Decisions
Chambers, Matthew S., Garriga, Carlos, Schlagenhauf, Don, Federal Reserve Bank of St. Louis Review
This paper examines some of the more recent mortgage products now available to borrowers. The authors describe how these products differ across important characteristics, such as the down payment requirement, repayment structure, and amortization schedule. The paper also presents a model with the potential to analyze the implications for various mortgage contracts for individual households, as well as to address many current housing market issues. In this paper, the authors use the model to examine the implications of alternative mortgages for homeownership. The authors use the model to show that interest rate-adjustable mortgages and combo loans can help explain the rise--and fall--in homeownership since 1994.
Housing is a big-ticket item in the U.S. economy. At the macro level, residential housing investment accounts for 20 to 25 percent of gross private investment. In the aggregate, this financing is about 8 trillion dollars and uses a sizable fraction of the financial resources of the economy. The importance of housing at the individual household level is more evident because the purchase of a house is the largest single consumer transaction and nearly always requires mortgage financing. This decision affects the overall expenditure patterns and asset allocation decisions of the household.
In recent years, interest in the role of housing in the U.S. economy has increased, influenced mainly by two events. During the economic downturn in 2000, the housing sector seemed to mitigate the slowdown in many other sectors of the economy as residential investment remained at high levels. More recently, the large number of foreclosures has again focused attention on the importance of housing. Fears have increased that mortgage market problems will have long-lasting effects on the credit market and thus continue to create a drag on the economy.
Events illustrating the important role of housing in the economy are not limited to those of the past decade. Housing foreclosures soared during the Great Depression as a result of two factors. The mortgage system was very restrictive: Homeowners were required to make down payments that averaged around 35 percent for loans lasting only five to ten years. At the end of the loan period, mortgage holders had to either pay off the loan or find new financing. The 1929 stock market collapse resulted in numerous bank failures. Mortgage issuance fell drastically, and homeowners were dragged into foreclosure. Faced with these problems, the government developed new housing policies as part of the New Deal legislation. The Home Owners' Loan Corporation (HOLC) and the Federal Housing Administration (FHA) were created along with a publicly supported noncommercial housing sector. The HOLC was designed to help distressed homeowners avert foreclosure by buying mortgages near or in foreclosure and replacing them with new mortgages with much longer durations. The HOLC financed these purchases by borrowing from the capital market and the U.S. Treasury. The FHA introduced new types of subsidized mortgage contracts by altering forms and terms, as well as mortgage insurance. In addition, Congress created Federal Home Loan Banks in 1932 and the Federal Home Loan Mortgage Corporation, commonly known as Fannie Mae, in 1938. The latter organization was allowed to purchase long-term mortgage loans from private banks and then bundle and securitize these loans as mortgage-backed securities. (1) These changes had an important impact on the economy: The stock of housing units increased 20 percent during the 1940s, and the homeownership rate increased approximately 20 percentage points from 1945 to 1965.
The need for increased understanding of housing markets, housing finance, and their linkage to the economy--the objective of this paper--should be obvious. We begin by examining the structure of a variety of mortgage contracts. Given the array of available mortgage products, mortgage choice can be a complex problem for potential home buyers. Buyers must consider many dimensions, such as the down payment, maturity of the contract, repayment structure, the ability to refinance the mortgage, and the impact of changes in interest rates and housing prices. We present examples to clarify key features of prominent mortgage contracts. The best mortgage for one household need not be the best mortgage for another. In fact, a model is needed to understand the mortgage decisionmaking process and what the aggregate implications are for the economy. This model must explicitly recognize the differences among households in age, income, and wealth. In addition, these decisions must reflect the complexities of the tax code that favor owner-occupied housing. Such a framework allows individual decisions to be aggregated so that the impact of mortgage decisions for the economy can be clearly identified.
The second part of this paper presents a model for understanding the impact of mortgage decisions on the economy. We use the model to show the role that adjustable-rate mortgages (ARMs) and combo loans have played since 1994 in the rapid rise--and subsequent decline--in homeownership.
A mortgage contract is a loan secured by real property. In real estate markets this debt instrument uses the structure (building) and land as collateral. In most countries mortgage lending is the primary mechanism to finance the acquisition of residential property. Mortgage loans typically are long-term contracts and require periodic payments that can cover interest and principal. Lenders provide the funds to finance the loans. Usually, such loans are sold to secondary market parties interested in receiving an income stream in the form of the borrower's payments.
The financial marketplace offers many types of mortgage loans, which are differentiated by three characteristics: the payment structure, the amortization schedule, and the term (duration) of the mortgage loan. The payment structure defines the amount and frequency of mortgage payments. The amortization schedule determines the amount of principal payments over the life of the mortgage. This schedule differs across types of mortgage loans and can be increasing, decreasing, or constant. Some contracts allow for no amortization of principal and full repayment of principal at a future, specified date. Other contracts allow negative amortization, usually in the initial years of the loan. (2) The term or duration usually refers to the maximum length of time allotted to repay the mortgage loan. The most common mortgage contracts are for 15 and 30 years. The combination of these three factors allows a large variety of distinct mortgage products.
Mortgage contracts affect consumer decisions. For example, some contracts are more effective in allowing increased homeownership for younger households. What types of mortgage contracts are actually held in the United States? According to the 2001 Residential Finance Survey (U.S. Census Bureau, 2001), roughly 97 percent of housing units were purchased through mortgage loans, whereas only 1.6 percent were purchased with cash. Table 1 summarizes the types of mortgage contracts used in the United States. The fixed-rate (payment) mortgage loan is the dominant contract, and the popularity of an adjustable (or floating) rate mortgage is substantially smaller. In contrast, in the United Kingdom and Spain, where the homeownership rate is 71 and 80 percent, respectively, the adjustable (or floating) rate contract is the dominant contract. The popularity of the fixed-rate contract in the United States is largely a result of the policies of the FHA, Veterans Administration, and various government incentives to sell the loan in the secondary market. This is the role of enterprises such as Fannie Mae and the Federal Home Loan Mortgage Corporation (Freddie Mac), two government-sponsored enterprises (GSEs) that are among the largest firms that securitize mortgages. Mortgage securitization occurs when a mortgage contract is resold in the secondary market as a mortgage-backed security. In the early 1990s, substantial changes occurred in the structure of the mortgage market in the United States. According to data in the 2007 Mortgage Market Statistical Annual, the market share of nontraditional mortgage contracts has increased since 2000. Nontraditional or alternative mortgage products include interest-only loans, option ARMs, loans that couple extended amortization with balloon-payment requirements, and other contracts of alternative lending. For example, in 2004 these products accounted for 12.5 percent of origination loans. By 2006, this segment increased to 32.1 percent of loan originations. Given the declining share of conventional and conforming loans, the structure of mortgage contracts merits further consideration.
General Structure of Mortgage Contracts
Despite all their differences, mortgage loans are just special cases of a general representation. Some form of notation is needed to characterize this representation. Consider the expenditure associated with the purchase of a house of size h and a unit price of p. We can consider h as the number of square feet in the house and p as the price per square foot. If buyers purchase a house with cash, the total expenditure is then denoted by ph. Most buyers do not have assets available that allow a check to be written for ph, and therefore they must acquire a loan to finance this large expenditure.
In general, a mortgage loan requires a down payment equal to [chi] percent of the value of the house. The amount [chi]ph represents the amount of equity in the house at the time of purchase, and [D.sub.0] = (1 - [chi])ph represents the initial amount of the loan. In a particular period, denoted by n, the borrower faces a payment amount [m.sub.n] (i.e., monthly or yearly payment) that depends on the size of the original loan, [D.sub.0], the length of the mortgage, N, and the mortgage interest rate, [r.sup.m]. This payment can be subdivided into an amortization (or principal) component, [A.sub.n], which is determined by the amortization schedule, and an interest component, [I.sub.n], which depends on the payment schedule. That is,
(1) [m.sub.n] = [A.sub.n] + [I.sub.n], [for all]n,
where the interest payments are calculated by [I.sub.n] = [r.sup.m][D.sub.n]. (3) An expression that determines how the remaining debt, [D.sub.n], changes over time can be written as
(2) [D.sub.n+1] = [D.sub.n] - [A.sub.n], [for all]n.
This formula shows that the level of outstanding debt at the start of period n is reduced by the amount of any principal payment. A principal payment increases the level of equity in the home. If the amount of equity in a home at the start of period n is defined as [H.sub.n], a payment of principal equal to [A.sub.n] increases equity in the house available in the next period to [H.sub.n+1]. Formally,
(3) [H.sub.n+1] = [H.sub.n] + [A.sub.n], [for all]n,
where [H.sub.0] = [chi]ph denotes the home equity in the initial period. (4)
This representation of mortgage contracts is very general and summarizes many of the different contracts available in the financial markets. For example, this formulation can accommodate a no-down-payment loan by setting [chi] = 0 so that the initial loan is equal to [D.sub.0] = ph. Because this framework can be used to characterize differences in the amortization terms and payment schedules, we use it to describe the characteristics of some prominent types of mortgage loans.
Mortgage Loans with Constant Payments
In the United States, fixed-rate mortgages (FRMs) typically are considered the standard mortgage contract. This loan product is characterized by a constant mortgage payment over the term of the mortgage, m [equivalent to] [m.sub.1] = ... = [m.sub.N]. This value, m, must be consistent with the condition that the present value of mortgage payments repays the initial loan. That is,
[D.sub.0] [equivalent to] [chi]ph = m/1 + r + ... + m/[(1 + r).sup.N-1] + m/[(1 + r).sup.N].
If this equation is solved for m, we can write
m = [lambda][D.sub.0],
where [lambda] = [r.sup.m][[1 - (1 + [[r.sup.m]).sup.-N]].sup.-1]. Because the mortgage payment is constant each period, and m = [A.sub.t] + [I.sub.t], the outstanding debt decreases over time [D.sub.0] > ... > [D.sub.n]. This means the fixed-payment contract front-loads interest rate payments,
[D.sub.n+1] = (1 + [r.sup.m])[D.sup.n] - m, [for all]n,
and, thus, back-loads principal payments,
[A.sub.n] = m - [r.sup.m][D.sub.n].
The equity in the house increases each period by the mortgage payment net of the interest payment component:
[H.sub.n+1] = [H.sub.n] + [m - [r.sup.m][D.sub.n]], [for all]n.
We now present some examples to illustrate key properties of the FRM contract.
Example 1. Consider the purchase of a house with a total cost of ph = $250,000 using a loan with a 20 percent down payment, [chi] = 0.20; an interest rate of 6 percent annually; and a 30-year maturity. This mortgage loan is for $200,000. (5) Table 2 illustrates the changes in interest and principal payments per month over the length of the mortgage contract.
The first two rows of Table 2 show the mortgage payment in the first and second months of the contract. The monthly payment on this mortgage is $1,178.74. In the first period, $973.51 of the monthly payment goes to interest rate payments. This means the principal payment is only $205.23. (6) Now, let us consider the mortgage payment 10 years into the mortgage. Although the monthly payment does not change, the principal payment has increased to $365.76 and the interest payment component has decreased to $812.98. After 10 years, the homeowner has paid off only $33,344.41 of the original $200,000 loan. The month after the halfway point in the mortgage occurs at period 181. The interest payment component of the monthly payment still exceeds the principal payment. In payment period 219--18 years and 3 months into the contract--the principal component of the monthly payment finally exceeds the interest payment component. From this point forward, the principal payment will be larger than the interest payment. At the end of 20 years, or period 240, the principal component of the $1,178.74 monthly payment is $655.01. However, $106,941.84 is still owed on the original $200,000 loan. The outstanding loan balance does not drop below $100,000 until payment period 251. With a standard 30-year mortgage contract, it takes nearly 22 years to pay off half the mortgage loan. The remaining half of the mortgage will be repaid in the final 8 years of this mortgage.
Example 2. Table 3 shows the standard 30-year mortgage contract if the mortgage interest rate increases from 6 percent to 7 percent. A 1 percent increase in the interest rate increases the monthly mortgage payment from $1,178.74 to $1,301.85--a $123.11 increase. Furthermore, the increase in the interest rate results in additional back-loading of principal payments. After 10 years, less than $30,000 of the original balance is paid off. The payment period when the principal component exceeds the interest component does not occur until period 239. In fact, the outstanding balance will not drop below $100,000 until payment 260-9 months later than if the interest rate is 6 percent (as in Example 1).
This table clearly illustrates the impact of interest rate changes on a mortgage loan. If the total interest payments on the mortgage contract presented in Table 2 are compared with those in Table 3, the 1 percent increase in the interest rate results in $44,320 of additional mortgage payments over the life of the mortgage.
Mortgage with Constant Amortization
As seen in Tables 2 and 3, the FRM accrues little equity in the initial years of the mortgage because most of the mortgage payment services interest payments. Some buyers would benefit by a combination of an FRM and faster equity accrual. Can a mortgage contract be designed to allow accrual of more equity in the initial periods, and what properties would be involved in such a contract? A mortgage contract with this benefit is known as a constant amortization mortgage (CAM). This loan contract allows constant contributions toward equity in each constant amortization mortgage period; that is, the amortization schedule is [A.sub.n] = [A.sub.n+1] = A. Because the interest repayment schedule depends on the size of outstanding level of debt, [D.sub.n], and the loan term, N, the mortgage payment, [m.sub.n], is no longer constant over the duration of the loan. Formally, the constant amortization term is calculated by
A = [D.sub.0]/N = (1 - X)ph/N.
If the expression for the interest payments is used, the monthly mortgage payment, [m.sub.n], will decrease over the length of the mortgage. This characteristic of the CAM follows from the decline in outstanding principal over the life of the contract. The monthly payment is determined by
[m.sub.n] = [D.sub.0]/N + [r.sup.m] [D.sub.n].
For this contract, the changes in the outstanding level of debt and home equity are represented by
[D.sub.n+1] = [D.sub.n] - [D.sub.0]/N, [for all]n,
[H.sub.n+1] = [H.sub.n] + [D.sub.0]/N, [for all]n.
Example 3. We consider a $250,000 30-year loan with a 20 percent down payment and a 6 percent annual interest rate to show the characteristics of this type of contract. Table 4 presents the monthly mortgage payment, principal component, and interest component.
The monthly payment with this contract has a much different profile than that of a fixed-payment mortgage loan. Clearly, the amount of the mortgage payment declines over the life of the loan. The initial payment is nearly three times the size of the payment in the last period. Principal payments are constant over the life of the loan, thus allowing for faster equity accumulation. Half of the original principal is repaid halfway through the loan. From a wealth accumulation perspective, this is an attractive feature. However, the declining payment profile is not positively correlated with a normal household's earning pattern during the first half of the life cycle: Mortgage payments are highest when earnings tend to be lower. From a household budget perspective, this could be a very unattractive option.
Balloon and Interest-Only Loans
The key property of the CAM is the payment of principal every period. In contrast, balloon and interest-only loans allow no amortization of principal throughout the term of the mortgage. A balloon loan is a very simple contract in which the entire principal borrowed is paid in full in the last payment period, N. This product tends to be more popular when mortgage rates are high and home buyers anticipate lower future mortgage rates. In addition, homeowners who expect to stay in their homes only for a short time may find this contract attractive as they are not concerned about paying principal. The amortization schedule for this contract can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
This means that the mortgage payment in all periods, except the last period, is equal to the interest rate payment, [I.sub.n] = [r.sup.m] [D.sub.0]. Hence, the mortgage payment for this contract can be specified as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [D.sub.0] = (1 - X)ph. The evolution of the outstanding level of debt can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
With an interest-only loan and no change in house prices, the homeowner never accrues equity beyond the initial down payment. Hence, [A.sub.n] = 0 and [m.sub.n] = [I.sub.n] = [r.sup.m] [D.sub.0] for all n. In essence, the homeowner effectively rents the property from the lender and the mortgage (interest) payments are the effective rental cost. As a result, the monthly mortgage payment is minimized because no periodic payments toward equity are made. A homeowner is fully leveraged with the bank with this type of mortgage contract. If capital gains are realized, the return on the housing investment is maximized. If the homeowner itemizes tax deductions, a large interest deduction is an attractive by-product of this contract.
Example 4. This example illustrates a balloon contract with a 15-year interest-only loan that is rolled into a 15-year fixed-payment mortgage. Table 5 shows the payment profiles for this contract. We also assume an interest rate of 6 percent and a 20 percent down payment.
The interest-only part of the loan requires 180 mortgage payments of $973.51 just to cover the interest obligations on the $200,000 loan. After 15 years, the mortgage payment increases to $1,670.59 because the 15-year balloon loan is rolled into a 15-year FRM. Payment number 219 denotes the month in which principal payments exceed interest payments. In period 290, half of the $200,000 debt will be paid off. With this type of mortgage contract, it takes more than 24 years to accrue $100,000 in equity.
Example 5. Some ARMs used in recent years have a very short period of interest-only payments. Table 6 presents the payment profiles for a 3-year interest-only ARM that rolls into a 27-year standard FRM. The assumptions for the interest rate, total contract length, and down payment remain unchanged.
The monthly interest payments for this interest-only ARM are $973.51. Once the standard 27-year contract takes effect, the monthly mortgage payment increases by $254.69 to $1,228.20. This increase is not caused by an interest rate increase, but rather payment toward principal.
Example 6. Mortgage interest rates have begun to increase recently. What effect does this have on an interest-only ARM? To show this effect, we allow the interest rate to increase to 7 percent for the standard FRM that is obtained after the 3-year ARM expires. Table 7 presents the various payment patterns. A 100-basis-point increase in the interest rate causes the monthly payment to increase to $1,347.72 from $1,228.20--a 38 percent increase in the mortgage payment from the interest-only payments. This example illustrates the risk facing homeowners when the interest rate increases before the transition to a standard FRM.
The repayment structures of the previous contract examples are relatively rigid. Payments are either constant during the entire contract or proportional to the outstanding level of debt. Mortgage contracts can be designed with a variable repayment schedule. This section focuses on mortgage loan payments that increase over time, [m.sub.1] < ... < [m.sub.N]. This feature could attract first-time buyers because payments are initially lower than payments in a standard contract. When a buyer's income grows over the life cycle, this loan product allows for stable housing expenditure as a ratio to income. However, the buyer's equity in the home builds at a slower rate than with the standard contract, which may explain this product's lack of popularity historically. Mortgage contracts with variable repayment schedules are known as graduated-payment mortgages (GPMs). These contracts are of special interest because their features are similar to those of mortgage contracts sold to subprime borrowers.
The repayment schedule for a GPM depends on the growth rate of these payments. The growth rate of payments is specified in the mortgage contract, and borrowers considering this contract must know this condition. We present examples to illustrate why knowledge of this parameter or condition is important. Typical GPM growth patterns are either geometric or arithmetic. We focus on GPMs with geometric growth patterns.
With this type of contract, mortgage payments evolve according to a constant geometric growth rate denoted by
[m.sub.n+1] = (1 + g)[m.sub.n],
where g > 0. This means the amortization and interest payments also increase as
[m.sub.n] = [A.sub.n] + [I.sub.n].
The initial mortgage payment is determined by
[m.sub.0] = [[lambda].sub.g][D.sub.0],
where [[lambda].sub.g] = ([r.sup.m] - g)[[1 - [(1 + [r.sup.m]).sup.-N]].sup.-1]. The law of motion for the outstanding debt satisfies
[D.sub.n+1] = (1 + [r.sup.m])[D.sub.n] - [(1 + g).sup.n] [m.sub.0],
and the amortization term is [A.sub.n] = [[lambda].sub.g][D.sub.0] - [r.sup.m][D.sub.n].
Example 7. Table 8 shows the implications for payments of a GPM contract when the mortgage payments grow at 1 percent per payment. We maintain the assumption of a 30-year contract with a 20 percent down payment and a 6 percent annual interest rate.
Clearly, the initial payments of this mortgage are very low, which explains why this contract is attractive for first-time buyers. However, these low payments come at a cost: The monthly payment does not cover the interest on the outstanding balance. Thus, the remaining principal increases. This mortgage contract exhibits negative amortization. In this example, the mortgage payment does not cover the interest on the principal for the first 219 months. The maximum remaining principal for this home purchase increases to more than $350,000 from the original $200,000 debt. It is interesting to note that the final $100,000 principal is paid in the final 16 months of this mortgage. Because the principal is back-loaded and must be paid off, the monthly payment must increase over time. The monthly mortgage payment tops out in the last month of the contract at $6,913.53. A homeowner who chooses this contract pays $482,149.10 in total interest payments. Compared with the FRM contract presented in Table 2, total interest payments are more than double. These characteristics make GPMs risky from a lender's perspective because the potential for default is greater, which is one reason this type of contract has not historically been a factor in the mortgage market.
Example 8. Table 9 shows the importance of the payment growth parameter by reducing the monthly growth rate from 1 percent to 0.1 percent. Negative amortization does not occur with a lower monthly growth rate. Perhaps the most striking result is the amount of total interest payments over the length of the mortgage contract. When the mortgage contract has a 1 percent monthly growth rate, total interest payments are $482,149.10. If the monthly growth rate falls to 0.1 percent, total interest payments are $246,356.77. Clearly there is a cost to loans with negative amortization.
In the late 1990s a new mortgage product became popular as a way to avoid large down payments and mortgage insurance. (7) This product is known as the combo loan and amounts to two different loans. Different types of CLs are offered in the mortgage industry; for example, an 80-15-5 loan implies a primary loan for 80 percent of the value, a secondary loan for 15 percent, and a 5 percent down payment. Another example is the so-called no-down-payment, or an 80-20 loan, which consists of a primary loan with a loan-to-value ratio of 80 percent and a second loan for the 20 percent down payment.
Formally, the primary loan covers a fraction of the total purchase, [D.sub.1]