Mortgage Financing: FHA Has Achieved Its Home Mortgage Capital Reserve Target
Released: 1996-04-22T00:00:00

Letter

Background

FHA was established in 1934 under the National Housing Act (P.L. 73-479). The primary purpose of FHA’s Fund is to insure private lenders against losses on mortgages that finance purchases of one to four housing units. There are two primary sources and three uses of cash for the Fund. The two sources of cash are income from mortgagees’ premiums and net proceeds from the sale of foreclosed properties. The three uses of cash are (1) payments associated with claims on foreclosed properties, (2) refunds of premiums on mortgages that are prepaid, and (3) administrative expenses for management of the program.

To cover losses, FHA deposits insurance premiums from participating borrowers in the Fund. According to 12 U.S.C. 1711, the Fund must meet or endeavor to meet statutory capital ratio requirements; that is, it must contain sufficient reserves and funding to cover estimated future losses resulting from the payment of claims on defaulted mortgages and administrative costs. A determination of reserves and funding to cover estimated future losses requires the use of an accrual basis of accounting. The accrual concept is particularly important for an entity such as FHA (or any insurance enterprise) because the actual payout or collection of cash may precede or follow the event that gave rise to the cash transaction by a substantial time period. Thus, a favorable cash position, or positive cash flow, at any given point may not reflect the true financial position of the entity.

The Fund remained relatively healthy until the 1980s, when losses were substantial primarily because foreclosure rates were high in economically stressed regions, particularly in the Rocky Mountain and Southwest regions. For example, in fiscal year 1988, the Fund lost $1.4 billion. If the Fund were to be exhausted, the U.S. Treasury would have to directly cover lenders’ claims and administrative costs.

Reforms designed to restore financial stability to the Fund and to correct problems in loan origination and property disposition were initiated by the Congress and HUD. The Omnibus Budget Reconciliation Act of 1990 (P.L. 101-508), enacted in November 1990, contained reforms to FHA’s single-family mortgage insurance program designed to place the Fund on a financially sound basis. The legislation, among other things, required FHA borrowers to pay more in insurance premiums over the life of the loans by adding a risk-based annual premium to the one-time, up-front premium. It effectively raised the present value of the insurance premium from 3.8 percent of the loan amount to from 5.5 to 6.8 percent, depending on the amount of the down payment made. It accomplished this change via two actions: lowering the up-front premium from 3.8 to 2.25 percent of the loan amount over a 4-year transitional period and, during the same period, phasing in a new annual premium of 0.5 percent of the loan balances. Those borrowers who make higher down payments pay the annual premium for a shorter period.

Other changes made by the legislation in response to the Fund’s financial problems included (1) limiting the loan-to-value ratio to a maximum of 97.75 percent of the value of homes appraised at more than $50,000 and (2) effectively suspending the payment of distributive shares (distribution of excess revenues to mortgagors) until the Fund is financially sound.

The legislation also required the Secretary of HUD to endeavor to ensure a capital ratio of 2 percent by November 2000 and maintain that ratio or a higher one at all times thereafter. The act defined the capital ratio as the ratio of the Fund’s capital, or economic net worth, to its unamortized insurance-in-force.

We and HUD’s Inspector General have been reporting on FHA’s management problems since the early 1980s. We have concluded in previous testimonies and reports that in addition to economic factors, poor program management and waste, fraud, and abuse contributed to the losses sustained by FHA’s Fund. For example, FHA did not have accounting data and internal controls in place to reconcile funds from the sales of government-owned properties with deposits to the U.S. Treasury. As a result, private real estate agents were able to steal millions of dollars by simply retaining the proceeds from the sale of FHA-owned properties rather than transferring the funds to the Treasury.

HUD’s efforts to improve the financial stability of the Fund have consisted of initiating several audits of the Fund; modifying the program, primarily to tighten controls and improve monitoring; and developing automated systems. For example, to reduce problems with loan origination, HUD tightened its screening of applicants, took steps to improve how it targets its efforts to monitor lenders, and strengthened appraisal requirements. To reduce problems with property disposition, HUD, among other things, tightened controls over closing agents and area management brokers and took actions to improve property pricing and automated accounting and management systems. Any success achieved by HUD and FHA in reducing FHA’s losses through better management will improve the Fund’s financial health.

Our Estimates of the Fund’s Economic Net Worth

The Fund had amortized insurance-in-force valued at about $305 billion as of September 30, 1994. To estimate the economic net worth of, and resulting capital ratio for, these loans over their life of up to 30 years, we developed an economic model of FHA’s home loan program. We generated three different economic scenarios, assuming for each a different rate of appreciation in house prices over the next 30 years. The actual economic net worth and capital ratios of the Fund and the validity of our estimates will depend on a number of future economic factors, including the rate of appreciation in house prices over the life of the FHA mortgages of up to 30 years. This factor is significant because, as house prices rise, the borrowers’ equity increases and the probability of defaults and subsequent foreclosures decreases. The house price appreciation, interest, and unemployment rates that we used were based on forecasts from DRI/McGraw-Hill, a private economic forecasting company.

Economic Net Worth Estimates of FHA’s Fund Under Three Scenarios

Table 1 presents our estimates of the economic net worth and resulting capital ratios for the FHA mortgage loans outstanding as of September 30, 1994, under each of our three economic scenarios. Although future rates of appreciation in house prices are uncertain, to be conservative, we placed greater reliance on our mid-range baseline economic scenario because it assumes slightly lower house price appreciation rates (1 percent annually) than the rates forecasted by DRI/McGraw-Hill. Under this scenario, we estimate that the Fund had an economic net worth of about $6.1 billion and resulting capital ratio of 2.02 percent at the end of fiscal year 1994. This estimate represents an improvement of about $8.8 billion from the lowest level reached by the Fund—a negative $2.7 billion economic net worth estimated by Price Waterhouse at the end of fiscal year 1990.

Under our low-case economic scenario, which assumes house price rates of appreciation of 2 percentage points lower than our baseline and a higher unemployment rate, we estimate that the Fund’s economic net worth would be $3 billion. Conversely, under our high-case economic scenario, which assumes house price rates of appreciation of 2 percentage points higher than our baseline, we estimated that the Fund’s economic net worth would be $7.4 billion.

Changes in the Fund’s Economic Net Worth During Fiscal Year 1994

We estimate that the economic net worth of the Fund increased under our baseline scenario by about $1.2 billion during fiscal year 1994, from $4.9 billion at the end of fiscal year 1993 to $6.1 billion at the end of fiscal year 1994. This increase occurred even though large numbers of FHA borrowers continued to lower their interest rates during fiscal year 1994 by refinancing their mortgages conventionally, which resulted in partial refunds of their insurance premiums. A detailed discussion of factors contributing to the $1.2 billion growth in the Fund’s economic net worth during fiscal year 1994 appears in appendix I.

Capital Ratio Target

We estimate that FHA’s Fund, with a capital reserve ratio of 2.02 percent of the amortized insurance-in-force, surpassed the November 2000 capital ratio target of 2 percent during fiscal year 1994. Therefore, the Fund has sufficient capital reserves to meet the capital ratio target.

Whether the Fund will be able to maintain the capital ratio will depend on a number of factors that will prevail in the future. These factors include (1) economic conditions, (2) changes to the program that affect the financial condition of the Fund, (3) the performance of FHA’s streamlined refinanced loans, and (4) risks associated with the demand for FHA’s loans. We did not attempt to project the economic net worth and capital ratio of the Fund to fiscal year 2000 because these factors are likely to change.

Economic Conditions

As shown in table 1, our estimates are sensitive to future economic conditions, particularly house price appreciation rates. The Fund will not perform as well if the economic conditions that prevail over the next 30 years replicate those we assumed in our low-case economic scenario. Our estimate of the Fund’s economic net worth for our low-case economic scenario is about $3 billion, or 49 percent, less than that of our baseline scenario. Under economic scenarios having generally favorable economic conditions but lower rates of appreciation in house prices, such as our low-case economic scenario, FHA’s Fund would likely experience higher claims. As a result, its economic net worth would decline.

Changes to the Program

FHA’s support of single-family mortgages could be altered by changes to the program proposed by the administration and others. The administration’s proposals, which are part of its efforts to “reinvent government,” would recreate FHA as a wholly owned government corporation. As such, the single-family insurance operations of a new FHA would be, among other things, free to introduce new product lines, enter into risk-sharing arrangements with private and public entities, and operate under more flexible personnel and procurement practices. Other proposals would limit FHA’s participation in single-family mortgages to low-income individuals and first-time home buyers only.

Specific information on the customers that a new FHA single-family mortgage insurance program would serve, the relationship that a new program would establish with partners in the housing market, and the mix of products that a new program would offer is not yet known. The extent to which this or some other restructuring alternative is implemented will have to be decided by the Congress through the legislative and appropriation processes. However, no matter what form FHA takes, these changes will likely have an affect on the Fund’s economic net worth.

Performance of Refinanced Loans

The substantial refinancing of FHA’s loans that occurred during fiscal years 1992 through 1994 has created a growing class of FHA borrowers whose future behavior is more difficult to predict than the typical FHA borrower’s. FHA’s streamlined refinanced mortgages accounted for about 40 percent of the loans originated by FHA in fiscal year 1994. About 19 percent of FHA’s amortized insurance-in-force at the end of fiscal year 1994 consisted of streamlined refinanced mortgages for which there is little experience with the tendency for such loans to be foreclosed and/or prepaid. Because FHA insured properties for which mortgages were streamlined refinanced were not required to be appraised, the initial loan-to-value ratio of these loans—a key predictor of the probability of foreclosure—is unknown. The impact of these loans on the financial health of the Fund is probably positive, since they represent preexisting FHA business whose risk has been reduced through lower interest rates and lower monthly payments. However, the lack of experience with these loans increases the uncertainty associated with their expected foreclosure rates.

This refinancing activity also raises questions about the credit quality of the loans that were not refinanced despite the fall in interest rates. Since, under these circumstances, most borrowers who could refinance would find it to their financial advantage to do so, those borrowers who did not refinance may not have been able to qualify for a new loan. This suggests that future foreclosure rates on these loans, which originated in previous years when interest rates were higher, may be greater than we have forecasted. As additional years of experience with these loans are gained, their effect on the Fund’s financial status will become more certain.

Risks Associated With FHA’s Loans

New developments in the private mortgage insurance market may increase the average risk of future FHA-insured loans. Home buyers’ demand for FHA-insured loans depends, in part, on the alternatives available to them. Some private mortgage insurers recently began offering mortgage insurance coverage on conventional mortgages with a 97-percent loan-to-value ratio, which brings their terms closer to FHA’s 97.75-percent loan-to-value ratio on loans for properties exceeding $50,000 in appraised value. While potential home buyers may consider many other factors when financing their mortgages, such as the fact that FHA will finance the up-front premium as part of the mortgage loan, this action by private mortgage insurers could reduce the demand for FHA-insured mortgage loans. In particular, by lowering the required down payment, private mortgage insurers may attract some borrowers who might have otherwise insured their mortgages with FHA. If by selectively offering these low down payment loans, private mortgage insurers are able to attract FHA’s lower-risk borrowers, such as borrowers with better-than-average credit histories or payment-to-income ratios, new FHA loans may become more risky on average. If this effect is substantial, the economic net worth of the Fund may be adversely affected, and it may be more difficult for the Fund to maintain a 2-percent capital ratio.

Price Waterhouse’s Estimates of the Fund’s Economic Net Worth

Price Waterhouse has performed annual actuarial reviews of the Fund for FHA since 1990. In its most recent report dated May 8, 1995, Price Waterhouse reported that the Fund had an economic net worth of about $6.68 billion—compared with our baseline estimate of $6.1 billion—and a resulting capital ratio of 1.99 percent of the unamortized insurance-in-force as of the end of fiscal year 1994—compared with our baseline estimate of 2.02 percent of the amortized insurance-in-force. It also reported that the Fund will meet the fiscal year 2000 capital ratio of 2 percent of the unamortized insurance-in-force with a capital ratio of 3.03 percent and that the economic net worth of the Fund will be about $15.2 billion. These projections are based on forecasted economic assumptions and the assumption that FHA does not change its premium and refund policies.

Although our estimate of the Fund’s economic net worth is lower than Price Waterhouse’s estimate by about 9 percent, in view of the uncertainty associated with any forecast of the performance of the Fund’s loans over their life of up to 30 years, these estimates can be considered roughly equivalent. Each of us used somewhat different modeling techniques and assumptions that account for some of the $580 million difference. However, in general, our model and Price Waterhouse’s rely on many of the same key factors, such as the rates of appreciation in house prices and changes in mortgage interest rates, as important determinants of mortgage terminations and the economic net worth of the Fund.

However, our estimate of the Fund’s capital ratio is slightly higher than Price Waterhouse’s estimate—2.02 percent compared with 1.99 percent—even though our estimate of economic net worth is lower that Price Waterhouse’s. The primary reason for this is the fact that we used a lower insurance-in-force amount ($305 billion of amortized insurance-in-force) to calculate the capital ratio than Price Waterhouse did ($335 billion of unamortized insurance-in-force). As discussed previously, the act defined the capital ratio as the ratio of the Fund’s economic net worth to its unamortized insurance-in-force. However, the act’s definition of unamortized insurance-in-force as the remaining obligation on outstanding mortgages is commonly understood to be the definition of the amortized insurance-in-force.

The insurance-in-force amount that we used differs from the amount used by Price Waterhouse primarily because we deleted the loan principal payments made on mortgages to date to arrive at an amortized insurance-in-force amount of $305 billion. We calculated the capital ratio on the basis of the amortized insurance-in-force and not on unamortized insurance-in-force, as did Price Waterhouse. We used the amortized insurance-in-force for our calculations because FHA-insured mortgages are in fact fully amortized over the 30-year life of the loans. Therefore, the amortized insurance-in-force represents a better measure of the Fund’s potential liability. Price Waterhouse used the unamortized insurance-in-force for its calculations to be consistent with its previous reports and because the data on unamortized insurance-in-force are considered more reliable than the data on amortized insurance-in-force. However, Price Waterhouse also reported that its estimate of the capital ratio using the amortized insurance-in-force was 2.16 rather than 1.99.

Conclusions

FHA’s Fund has accumulated the capital reserves needed to meet the legislative capital reserve target of 2 percent. Clearly, the legislative and other program changes have helped restore the Fund’s financial health and reverse the trend of the late 1980s and early 1990s toward insolvency. However, it should be recognized that fiscal year 1994 was a good year for FHA because actual economic conditions and forecasts of future economic conditions were favorable. Nevertheless, forecasting economic net worth and resulting capital ratios to determine whether FHA will have the funds it needs to cover its losses over the life of the loans it has insured for up to 30 years is uncertain. The performance of FHA’s loans, and therefore economic net worth and capital ratios, will depend on a number of economic and other factors, particularly on the rates of appreciation in house prices and the alternative, if any, that the Congress implements to restructure FHA.

Agency Comments

We provided a draft of this report to HUD and Price Waterhouse for their review and comment. We met with HUD officials, including the FHA Comptroller; HUD’s Director of the Program Evaluation Division, Office of Evaluation; and an official from HUD’s Office of Policy Development and Research, and obtained their comments. HUD officials generally agreed with the factual material and conclusions presented in the report. The comments by the Director, Program Evaluation Division, focused on (1) the effect of proposed changes to FHA’s program and (2) FHA’s actions to improve the financial health of the Fund. Specifically, the Director commented that the draft report’s discussion of proposed changes to the program implied that they would have an exclusively negative impact on the financial health of the Fund. He believes that many of the proposed changes will have a positive effect on the Fund’s financial health. The report was changed to eliminate this implication.

The Director also commented that the draft report attributed progress in achieving the capital reserve target to favorable actual economic conditions and favorable forecasts of future economic conditions. He pointed out that FHA had taken many actions to improve the financial health of the program, such as revising the premium refund schedule, and that this contribution to economic health should be recognized in our report. We agree. As pointed out in our October 1994 report on the economic net worth of the Fund as of September 30, 1993, we estimated that if FHA had not revised its premium refund schedule, the economic net worth of the Fund would have been about $500 million (10 percent) less than our baseline estimate. We added to our report information on additional actions taken by FHA to improve the financial health of the Fund.

However, we continue to believe that favorable prevailing and forecasted economic conditions were primarily responsible for this improvement. As noted in our report, under our low-case economic scenario, which assumes house price appreciation rates 2 percentage points lower than our baseline, we estimated that the Fund’s economic net worth would be $3 billion, rather than $6.1 billion.

HUD’s Office of Policy Development and Research official commented that the methodology we used is fundamentally sound and provides a welcome second opinion to Price Waterhouse’s actuarial review. This official also provided technical comments on our model’s specification and interpretation of statistical results. He commented that if the technical comments cannot be addressed in the report and the Congress asks us to estimate the economic net worth of the Fund in the future, we should consult further with the Office of Policy Development and Research on our cash flow and economic models. We have revised the report to address many of the issues concerning the model’s specification and interpretation that were raised by HUD’s Office of Policy Development and Research. If the Congress asks us to do more work in this area, we will consult further with HUD on our models.

We also met with a Price Waterhouse official, who commented that our economic model was solid. Price Waterhouse also provided technical comments, which we incorporated where appropriate.

Scope and Methodology

To estimate the economic net worth of FHA’s Fund as of September 30, 1994, and its resulting capital ratios under different economic scenarios, we examined existing studies on the single-family housing programs of both HUD and the Department of Veterans Affairs (VA), academic literature on the modeling of mortgage foreclosures and prepayments, and previous work performed by Price Waterhouse, HUD, VA, us, and others on modeling government mortgage programs. On the basis of this examination, we developed econometric and cash flow models to prepare our estimates. For these models, we used data supplied by FHA and DRI/McGraw-Hill, a private economic forecasting company.

Our econometric analysis estimated the historical relationships between the probability of loan foreclosure and prepayment and key explanatory factors, such as the borrower’s equity and the interest rate. To estimate these relationships, we used data on the performance of FHA-insured home mortgage loans—such as data on foreclosure, prepayment, and loss rates—originated from fiscal year 1975 through fiscal year 1994. Also, using our estimates of these relationships and of economic conditions, we developed a baseline forecast of future loan performance to estimate the Fund’s economic net worth and resulting capital ratio. We then developed additional estimates that assumed higher and lower future rates of appreciation in house prices; the scenario with the lower rates of appreciation of house prices also assumed higher unemployment.

To estimate the net present value of future cash flows of the Fund, we constructed a cash flow model to measure the primary sources and uses of cash for loans originated from fiscal year 1975 through fiscal year 1994. Our model was constructed to estimate cash flows for each policy year through the life of a mortgage. An important component of the model was the conversion of all income and expense streams—regardless of the period in which they actually occur—into 1994 dollars. In addition to estimating the economic net worth of the Fund as a whole, we also generated approximations of the economic net worth of the loans originated in the 2 most recent fiscal years. To conduct this analysis, it was necessary not only to project future cash flows but also to estimate the level of past cash flows.

To test the validity of our model, we examined how well our model predicted the actual rates of FHA’s loan foreclosures and prepayments through fiscal year 1994. We found that our predicted rates closely resembled the actual rates.

To compare our estimate of the Fund’s economic net worth with the estimate prepared for FHA by Price Waterhouse, we compared our economic model with the model developed by Price Waterhouse. We also discussed with Price Waterhouse officials differences in the models and methods for forecasting the Fund’s economic net worth. A detailed discussion of our models and methodology for forecasting the economic net worth of FHA’s Fund appears in appendix II. We conducted our work from April 1995 through February 1996 in accordance with generally accepted government auditing standards.

Unless you announce its contents earlier, we plan no further distribution of this report until 10 days from the date of this letter. At that time, we will send copies to interested congressional committees; the Secretary of HUD; and the Director, Office of Management and Budget. We will make copies available to others on request.

Please contact me at (202) 512-7631 if you or your staff have any questions. Major contributors to this report are listed in appendix III.

Factors Contributing to the Growth in the Mutual Mortgage Insurance Fund’s Economic Net Worth in Fiscal Year 1994

We estimate that during fiscal year 1994, the economic net worth of the Federal Housing Administration’s (FHA) Mutual Mortgage Insurance Fund increased by about $1.2 billion. This increase is attributable to our estimates of positive contributions to economic net worth made by two factors—the inclusion in our estimate of some fiscal year 1993 loans that had been excluded from our fiscal year 1993 estimate and loans insured by FHA in fiscal year 1994. The increase in economic net worth attributable to these two factors was offset to some extent by our estimate of a decrease in the Fund’s economic net worth from loans insured by FHA in fiscal year 1993 and earlier years. Table I.1 summarizes these factors.

Data provided by FHA last year and used in our September 30, 1993, economic net worth estimates did not include information on all loan originations and terminations occurring in fiscal year 1993. FHA subsequently updated its records to include the remaining fiscal year 1993 activity. As shown in table I.1, including this loan activity increases our estimate of the Fund’s economic net worth by about $260 million, resulting in a revised estimate of about $5.16 billion as of the end of fiscal year 1993. We also estimate that loans insured by FHA in fiscal year 1994 contributed about $1.4 billion to the economic net worth of the Fund. This represents the third consecutive year in which the Fund’s new loans made a positive contribution to the Fund’s economic net worth. However, this increase in economic net worth was reduced by a $460 million decrease in the economic net worth of loans insured by FHA in fiscal year 1993 and earlier years. As a result, a net increase of $940 million was realized in our baseline estimate during fiscal year 1994, bringing our baseline economic net worth estimate as of September 30, 1994, to $6.1 billion.

The $460 million decrease in the Fund’s estimated economic net worth for loans insured by FHA in fiscal year 1993 and earlier years is the result of several factors, some of which involved large increases or decreases in economic net worth. Table I.2 summarizes the factors contributing to changes in the economic net worth of loans made in fiscal year 1993 and earlier years.

We estimate that the economic net worth of the Fund’s loans made in fiscal year 1993 and earlier years increased by about $620 million because updated data showed that these loans performed better in fiscal year 1994 than previously forecasted. This occurred, in part, because during fiscal year 1994, house prices increased more rapidly, and the unemployment rate was lower than in previous economic forecasts. Interest earned on investments accounted for an estimated increase of $618 million.

Offsetting these increases were several factors that resulted in a decrease in the estimated economic net worth of the Fund’s loans made in fiscal year 1993 and earlier years. A $235 million decrease in economic net worth is attributable to our revised forecasts for loan foreclosures and prepayments for these loans during fiscal year 1995 and beyond. These revisions resulted largely from revised assumptions of future economic conditions that in combination, had a less favorable financial effect on the Fund. A $953 million decrease occurred because our 1994 forecast uses an economic model different from the model we used to derive our fiscal year 1993 estimate. Our revised model uses a different statistical approach and recognizes the higher risks associated with the performance of refinanced and adjustable rate mortgages rather than treating these mortgages like other FHA mortgages, as we have done in the past. The Fund’s economic net worth was also reduced by about $273 million because we updated our calculation of the present value of future cash flows using fiscal year 1994 instead of 1993 as our base, which increases the present value of future cash flows (which are negative) because they are discounted by 1 less year of interest. That is, because we are 1 year closer to paying claims associated with future foreclosures, the present value of these claims against the Fund is larger. The remaining $237 million decrease was attributable to other factors.

GAO’s Econometric and Cash Flow Models Used to Forecast FHA’s Economic Net Worth

This appendix describes the econometric and cash flow models that we built and the analysis we conducted to estimate the economic net worth of the Federal Housing Administration’s (FHA) Mutual Mortgage Insurance Fund (Fund) as of the end of fiscal year 1994. The goal of the econometric analysis was to forecast mortgage foreclosure and prepayment activity, which affect the flow of cash into and out of the Fund. We forecasted activity for all loans active at the end of fiscal year 1994 for each year from fiscal year 1995 through fiscal year 2024 on the basis of assumptions stated in this appendix. We estimated equations from data covering fiscal years 1975 through 1994 that included all 50 states and the District of Columbia but excluded U.S. territories.

Our forecasting models used observations on loan-quarters, that is, information on the characteristics and status of an insured loan during each quarter of its life to predict conditional foreclosure and prepayment probabilities. More specifically, our model used a continuous time estimation routine, CTM to jointly predict the probabilities of a loan terminating in a claim or a prepayment at a given time, as a function of interest and unemployment rates, the borrower’s equity (computed using a house’s price and current and contract interest rates as well as a loan’s duration), the loan-to-value (LTV) ratio, the house price, the geographic location of the house, and the length of time that the loan has been active.

Cash flows out of the Fund when FHA pays a claim on a foreclosed mortgage and when a prepaid mortgage results in the partial refund of a premium. Cash flows into the Fund when FHA sells the foreclosed property and when borrowers pay the premium for the mortgage insurance. We forecasted the cash flows into and out of the Fund on the basis of our foreclosure and prepayment models and key economic variables provided by DRI/McGraw-Hill, a leading economic forecasting firm. We then used the forecasted cash flows, including an estimate of interest that would be earned or foregone, and the Fund’s capital resources to estimate the economic net worth of the Fund.

We conducted separate estimations for investors’ mortgages, fixed-rate mortgages with terms of 25 years or more (hereafter referred to as 30-year mortgages), fixed-rate mortgages with terms of less than 25 years (hereafter referred to as 15-year mortgages), and adjustable-rate mortgages (ARMs). The 30-year fixed-rate mortgages and investor mortgages were further divided into new (purchase money) and refinancing mortgage samples. A complete description of the data we used, our models, and the results we obtained are discussed in detail in the following sections.

Data and Sample Selection

For our analysis, we selected from FHA’s computerized files a random sample of 1.4 million mortgages insured by FHA from fiscal year 1975 through fiscal year 1994. From FHA’s records, we obtained information on the initial characteristics of each loan, such as the year of the loan’s origination and state in which the loan originated; the LTV ratio; the loan’s amount; and the contract’s interest rate. We categorized the loans as either foreclosed, prepaid, or active as of the end of fiscal year 1994.

To describe macroeconomic conditions at the national and state levels, we obtained data from the 1995 Economic Report of the President on the implicit price deflator for personal consumption expenditures. The Federal Home Loan Mortgage Corporation’s quarterly interest rates for 30-year fixed-rate mortgages were used, along with DRI/McGraw-Hill’s data at the state level, on the median house price appreciation and civilian unemployment rates and on interest rates on 1-year and 10-year U.S. Treasury bonds.

Specification for Model

People buy homes for consumption and investment purposes. Normally, people do not plan to default on loans. However, conditions that lead to defaults occur. Defaults may be triggered by a number of events: unemployment, divorce, death, and so forth. These events are not likely to trigger foreclosure if the owner has positive equity in his/her home because the sale of the home with realization of a profit is better than the loss of the home through foreclosure. However, if the property is worth less than the mortgage, these events may trigger default.

Prepayments to financial institutions may be triggered by other events—declining interest rates, which prompt refinancing; rising house prices, which prompt the take-out of accumulated equity; or the sale of the residence. Because FHA’s mortgages are assumable, the sale of a residence does not automatically trigger prepayment. For example, if interest rates have risen substantially since the time the mortgage was originated, a new purchaser may prefer to assume the seller’s mortgage.

We hypothesized that foreclosure behavior is influenced by the level of unemployment, price of the house, value of the home, current interest rates, contract interest rates, home equity, and region of the country within which the home is located. We hypothesized that prepayment is influenced by (1) a function of the difference between the interest rate specified in the mortgage contract and the mortgage rates generally prevailing in each subsequent year, (2) the amount of accumulated equity, (3) the price of the house, and (4) the region of the country in which the home is located.

The estimated model also allows for the presence of unobserved heterogeneity, that is, the possibility that individual borrowers will refinance (or default) at different interest rate differentials (or levels of equity) for reasons not recorded in the data. Such reasons might include differences in financial sophistication, differences in moving plans, or differences in the value attached to a good credit rating. In models that do not allow for the presence of heterogeneity, the impact of time on termination probabilities will be overstated, since the loans most likely to terminate will terminate first. Additionally, estimating a heterogeneity distribution provides a method of capturing the effect of refinancing waves, such as those that occurred during 1986-87 and 1992-93, on the termination probabilities of the mortgages that remain.

Our first set of coefficients estimate conditional mortgage foreclosure probabilities as a function of a variety of explanatory variables. Our second set of coefficients estimate conditional prepayment probabilities. The model estimated is a competing risks hazard model. The probability of prepaying or terminating with a loss to the Fund over the course of a quarter is jointly estimated as a function of time (the baseline hazard) multiplied by a linear function of the independent variables. The baseline hazards are estimated as a Box-Cox transformation of time measured in months. - 1)/l when l is not zero, and ln(x) when l =0. termination (claim or prepayment), CTM also estimates a coefficient by which those points are multiplied, referred to as the factor loading. In effect, CTM estimates a distribution of intercepts for each termination probability. This incorporates the assumption that mortgage borrowers differ in their probabilities of mortgage termination in unobservable ways. While the different probabilities are not attached to individual borrowers, the heterogeneity parameters produce an estimate of the proportions of borrowers with high or low termination propensities. The methodology is analogous to a random effects model for the analysis of panel data.

The variables we used to predict foreclosures and prepayments fall into two general categories: descriptions of states of the economy and characteristics of the loan. In choosing explanatory variables, we relied on the results of our own and others’ previous efforts to model foreclosure and prepayment probabilities and on implications drawn from economic principles. We allowed for many of the same variables to affect both foreclosure and prepayment.

Equity

The single most important determinant of a loan’s foreclosure is the borrower’s equity in the property, which changes over time because (1) payments reduce the amount owed on the mortgage, (2) property values can increase or decrease, and (3) prevailing mortgage interest rates change, while the rate on a fixed-rate mortgage remains constant. Equity is a measure of the current value of a property compared with the current value of the mortgage on that property. Previous research strongly indicates that borrowers with small amounts of equity or even negative equity are more likely than other borrowers to default. We computed equity as the difference between the value of the property and the value of the mortgage, expressed as a percentage of the value of the property. For example, if the value of a property is $100,000 and the value of the mortgage is $80,000, then equity is 20 percent, or 0.2. To measure equity for modeling the foreclosure behavior of fixed-rate mortgages, we calculated the value of the mortgage as the present value of the remaining mortgage payments (up to a maximum of 10 years), evaluated at the current quarter’s fixed-rate mortgage interest rate, and added the book value of the mortgage at the end of 10 years, thus assuming a prepayment 10 years into the future. We calculated the value of the property by multiplying the value of the property at the time of the loan’s origination by the change in the state’s median nominal house price between the year of origination and the current year. Because the effects on claims of small changes in equity may differ depending on whether the level of equity is high or low, we used a pair of equity variables, LAGEQHI and LAGEQLOW, in our foreclosure regression. The effect of equity is lagged 1 year, since we are predicting the time of foreclosure, which usually occurs many months after a loan first defaults.

We also included lagged equity in our prepayment regression. We anticipated that higher levels of equity would be associated with an increased likelihood of prepayment. Borrowers with substantial equity in their home may be interested in prepaying their existing mortgage and taking out a larger one to obtain cash for other purposes. Borrowers with little or no equity may be less likely to prepay because they may have to take money from other savings to pay off their loan and cover transaction costs.

For the prepayment regression, we defined equity as book equity (LAGBKHI and LAGBKLOW). Book equity was defined as the estimated property value less the amortized balance of the loan. It is book value that the borrower must pay to retire the debt. Additionally, the effect of interest rate changes on prepayment are captured by the relative interest variables, RELEQHI and RELEQLO.

Down Payment

In addition to LAGEQHI and LAGEQLOW, we included another variable in our regressions related to equity: the initial DOWNPAY, calculated as 1 minus the LTV ratio. In some years, FHA measured the LTV ratio as the loan amount less the financed portion of the mortgage insurance premium in the numerator and appraised value plus closing costs in the denominator. To reflect true economic LTV, we adjusted FHA’s measure by removing closing costs from the denominator and including financed premiums in the numerator.

DOWNPAY measures a borrower’s initial equity, so we anticipate that it will be negatively related to the probability of foreclosure. One reason for including DOWNPAY is that it measures initial equity accurately. Our measures of current equity are less accurate because we do not have data on the rate of change for the price of each borrower’s house.

Another reason for including DOWNPAY and expecting it to have a negative sign in our foreclosure equation is that it may capture the effects of income constraints. We are unable to include borrowers’ incomes or payment-to-income ratios directly because data on borrowers’ incomes were not available for every year in the sample period. However, it seems likely that borrowers with little or no down payment are more likely to be financially stretched in meeting their payments and, therefore, more likely to default. The anticipated relationship between DOWNPAY and the probability of prepayment is uncertain.

Unemployment

We used the natural logarithm of the annual unemployment rate for each state for the period from 1975 through 1994 to describe the condition of the economy in the state where a loan was made. We anticipated that foreclosures would be higher in years and states with higher unemployment rates and that prepayments would be lower because property sales slow down during recessions. The actual variable we used in our regressions, LAGUNEMP, is defined as the logarithm of the preceding year’s unemployment rate in that state.

Interest Rates

We included the logarithm of the interest rate on the mortgage as an explanatory variable in the foreclosure equation. We expected a higher interest rate to be associated with a higher probability of foreclosure because a higher interest rate causes a higher monthly payment. However, in explaining the likelihood of prepayment, our model uses a function of the ratio of current mortgage rates to the contract rate on the borrower’s mortgage. A borrower’s incentive to prepay is high when the interest rate on a loan is greater than the rate at which money can now be borrowed, and it diminishes as current interest rates increase. To capture the relative attractiveness of prepaying, we calculated the present value of the mortgage payments over the remaining term of the mortgage (up to 10 years) using the currently prevailing mortgage interest rate to estimate the market value of the mortgage. This value was divided by the book value of the mortgage (the unpaid principal balance), and the relative balance was used as an explanatory variable for prepayment.

In our prepayment regression, we used the two relative interest rate variables defined above, RELEQHI and RELEQLO, so that the effect of changes in relative interest rates could be different over different ranges. RELEQHI is defined as the ratio of the market value of the mortgage to the book value of the mortgage but is never smaller than 1. RELEQLO is also defined as the ratio of the market value of the mortgage to the book value but is never larger than 1. Thus, RELEQHI captures a borrower’s incentive to refinance, and RELEQLO captures a new buyer’s incentive to assume the seller’s mortgage.

We created two variables, REFIN and REFIN2, that measure how many quarters have passed in which the borrower had not taken advantage of a refinancing opportunity. We defined a refinancing opportunity as having occurred if the interest rate on fixed-rate mortgages in any previous quarter in which a loan was active was at least 150 basis points below the contract rate on the mortgage. REFIN counts the number of quarters in which the loan has been active and a refinancing opportunity has not been seized, up to a maximum of eight quarters. REFIN2 counts the number of passed refinancing opportunities in excess of eight quarters, up to a maximum of eight more quarters.

Several reasons might explain why borrowers passed up apparently profitable refinancing opportunities. For example, if they had been unemployed or their property had fallen in value, they might have had difficulty obtaining refinancing. This reasoning suggests that REFIN and REFIN2 would be positively related to the probability of foreclosure; that is, a borrower unable to obtain refinancing previously because of poor financial status might be more likely to default.

Similar reasoning suggests a negative relationship between REFIN and REFIN2 and the probability of prepayment; a borrower unable to obtain refinancing previously might also be unlikely to obtain refinancing currently. A negative relationship might also exist if a borrower’s passing up of one profitable refinancing opportunity reflected a lack of financial sophistication that in turn, would be associated with passing up additional opportunities. However, a borrower who anticipated moving soon might pass up an apparently profitable refinancing opportunity to avoid the transaction costs associated with refinancing. A positive relationship might exist in this case, with the probability of prepayment if the borrower fulfilled his/her anticipation and moved, thereby prepaying the loan.

Another explanatory variable is the volatility of interest rates, INTVOL, defined as the standard deviation of the monthly average of the Federal Home Loan Mortgage Corporation’s series of 30-year fixed-rate mortgage effective interest rates. We calculated the standard deviation over the previous 12 months. Financial theory predicts that borrowers are likely to refinance more slowly at times of volatile rates because there is a larger incentive to wait for a still-lower interest rate.

We also included the slope of the yield curve, YIELDCUR, in our prepayment estimates, which we calculated as the difference between the 1-year and the 10-year Treasury rates of interest. We then subtracted 250 basis points from this difference and set differences that were less than zero to zero. This variable measured the relative attractiveness of adjustable-rate mortgages versus fixed-rate mortgages. When ARMs have low rates, borrowers with fixed-rate mortgages may be induced into refinancing into ARMs to lower their monthly payments.

For adjustable-rate mortgages, we did not use relative equity variables as we did with fixed-rate mortgages. Instead, we defined four variables, CHANGEPOS, CHANGENEG, CAPPEDPOS, and CAPPEDNEG, to capture the relationship between current interest rates and the interest rate paid on each mortgage. CHANGEPOS measures how far the interest rate on the mortgage has increased since origination, with a minimum of zero, while CHANGENEG measures how far the rate has decreased, with a maximum of zero. CAPPEDPOS measures how much farther the interest rate on the mortgage will rise, if prevailing interest rates in the market do not change, while CAPPEDNEG measures how much farther the mortgage’s rate will fall if prevailing interest rates do not change. For example, if an ARM is originated at 7 percent and interest rates have increased by 250 basis points 1 year later, CHANGEPOS will equal 100 because FHA’s ARMs can increase by no more than 100 basis points in a year. CAPPEDPOS will equal 150 basis points, since the mortgage rate will eventually increase by another 150 basis points if market interest rates do not change, and CHANGENEG and CAPPEDNEG will equal zero. As interest rates have generally trended downwards since FHA introduced ARMs, there is very little experience with ARMs in an increasing interest rate environment.

Geographic Regions

We created four 0-1 variables to reflect the geographic distribution of FHA loans and included them in both regressions. Locational differences may capture the effects of differences in borrowers’ income, rates of appreciation in house prices, underwriting standards by lenders, economic conditions not captured by the unemployment rate, or other factors that may affect foreclosure and prepayment rates. We assigned each loan to one of the four Bureau of the Census regions on the basis of the state in which the borrower resided. The West Region was the omitted category, that is, the regression coefficients show how each of the regions was different from the West Region. We also created a variable, JUDICIAL, to indicate states that allowed judicial foreclosure procedures in place of nonjudicial foreclosures.

House Price

To obtain an insight into the differential effect of relatively larger loans on mortgage foreclosures and prepayments, we used the logarithm of the initial house price as an explanatory variable. This variable was divided into three ranges—below $60,000, $60,000 to $120,000, and $120,000 and over—to allow the effect of house price to change over its range. The three ranges were called LOGPRICL, LOGPRICM, and LOGPRICH, respectively. All dollar amounts are inflation adjusted and represent 1994 dollars.

Time

Finally, to capture the time pattern of foreclosures and prepayments (given the effects of equity and the other explanatory variables), we defined two variables on the basis of the number of quarters that had passed since the year of the loan’s origination. We refer to these variables as YEAR12 and YEAR34. YEAR12 counts the number of quarters since origination, up to the sixth quarter. YEAR34 counts the number of quarters since origination from the 7th to the 14th quarter. TIME measures the number of months elapsed since origination, and EXPONENT is the estimated value of a Box-Cox transformation of TIME. We created the variables YEAR12 and YEAR34 to allow for the passage of time to have much stronger impacts on termination probabilities in the early months of a mortgage’s life.

Table II.1 summarizes the variables we used to predict claims and prepayments along with their corresponding means. These means are for investor mortgages, both for purchase and for refinancing purposes; 30-year fixed-rate mortgages, both for purchase and for refinancing purposes; 15-year fixed-rate mortgages; and adjustable-rate mortgages.

Log of house price if ^æM\Q $60,000 Log of house price 0.32 $60,000 but $60,000 but ^æM\Q$120,000 Log of house price $120,000 Log of contract interest rate The volatility of mortgage rates, defined as the standard deviation of 30-year fixed mortgage rates over the prior 12 months The slope of the yield curve, defined as the difference between 1-year and 10-year Treasury interest rates minus 250 basis points, but not less than zero The ratio of the market value of the mortgage to the book value if the market value is below the book value, else 1 The ratio of the market value of the mortgage to the book value if the market value is above the book value, else 1 Number of quarters that the prevailing mortgage interest rate had been at least 150 basis points below the contract rate and the borrower had not refinanced, up to eight quarters Number of quarters that the above situation prevailed, beyond eight quarters (continued)

The logarithm of the previous year’s unemployment rate in the state Number of quarters since origination, up to six Number of quarters since the 6th, up to 14 The down payment, expressed as a percentage of the purchase price of the house. The values reported in FHA’s database were adjusted to ensure that closing costs were included in the loan amount and excluded from the house price.

The value of equity, defined as 1 minus the ratio of the present value of the loan balance, evaluated at the current mortgage interest rate, to the current estimated house price, if equity is less than 20 percent, else 20 percent The value of equity, defined as 1 minus the ratio of the present value of the loan balance, evaluated at the current mortgage interest rate, to the current estimated house price, minus 20 percent, but no less than zero The value of equity, defined as 1 minus the ratio of the amortized loan balance to the current estimated house price, if equity is less than 20 percent, else 20 percent (continued)

The value of equity, defined as 1 minus the ratio of the amortized loan balance to the current estimated house price, minus 20 percent, but no less than zero 1, if the loan was in the East (Conn., Maine, Mass., N.H., N.J., N.Y., Pa., R.I., and Vt.), else zero 1, if the loan was in the South (Ala., Ark., D.C., Del., Ga., Ky., La., Md., Miss., N.C., Okla., S.C., Tenn., Tex., Va., and W.Va.), else zero 1, if the loan was in the Midwest (Ill., Ind., Iowa, Kans., Mich., Minn., Mo., Nebr., N.D., Ohio, S.D., and Wis.), else zero 1, if state allowed judicial foreclosure (list of states varies by year)

N/A = not applicable.

Estimation Results

As described above, we used competing risks hazard rate models to estimate loan foreclosures and prepayments as a function of a variety of predictor variables. We estimated separate regressions for 30-year fixed-rate mortgages, 15-year fixed-rate mortgages, investors’ loans, and adjustable-rate mortgages originated (made) from fiscal year 1983 to fiscal year 1993. The 30-year fixed-rate mortgages and investors’ mortgages were further divided into samples of purchase money loans and loans made for the purpose of refinancing. Although FHA was given authority to insure streamlined refinancing loans in 1983, FHA’s database cannot reliably identify refinancing loans before 1991. Therefore, we placed any loan written after fiscal year 1982 with an LTV ratio of zero into the refinanced loan sample, along with loans that FHA’s database identified as refinancing loans. We estimated quarterly termination probabilities throughout the life of the loan or the end of fiscal year 1994, whichever came first.

Tables II.2 and II.3 present the estimated coefficients for all of the predictor variables for foreclosure and prepayment equations. Table II.4 displays the estimated heterogeneity distributions for the regression results in the previous tables. ARM loan regression results are presented in table II.5. A heterogeneity distribution was not estimated for ARMs. All loan categories except for the refinanced investor loans were estimated with hundreds of thousands of observations, so most coefficients are significant at standard levels.

In general, our results are consistent with the economic reasoning that underlies our models. Most importantly, the probability of foreclosure declines as current equity and down payment increase, and the probability of prepayment increases as the current mortgage interest rate falls below the contract mortgage interest rate. Both of these effects are very strong. As expected, the unemployment rate is positively related to the probability of foreclosure and negatively related to the probability of prepayment. Our results also indicate that the probability of foreclosure is higher when the contract rate of interest is higher. Mortgages on more-expensive houses have higher prepayment probabilities. For purchase money mortgages, foreclosure probability declines with the price of a house, but for refinanced mortgages foreclosure probability rises with price. For 30-year fixed mortgages and for investor mortgages, passing up a profitable refinancing opportunity raises the probability of foreclosure. For all mortgages, passing up profitable refinancing opportunities lowers prepayment probabilities.

The heterogeneity distributions presented in table II.4 indicate substantial differences in intercepts among different classifications of borrowers. For instance, among new 30-year fixed-rate borrowers, 62.9 percent are estimated to have a foreclosure intercept of 17.739, 24.8 percent (87.7 percent minus 62.9 percent) are estimated to have a foreclosure intercept of 17.202 (a location of 0.169 times a factor loading of –3.179, added to the intercept of 17.739), 5.9 percent are estimated to have a foreclosure intercept of 16.503, and 6.4 percent are estimated to have a foreclosure intercept of 14.56. This indicates that about 6.4 percent of borrowers have substantially lower termination probabilities than do most borrowers.

Forecast of Loan Foreclosures and Early Payments

To test the validity of our model, we examined how well the model predicted actual patterns of FHA’s claim and prepayment rates through fiscal year 1994. Using a sample of 10 percent of FHA’s loans made from fiscal year 1975 through fiscal year 1994, we found that our predicted rates closely resembled actual rates.

To predict the probabilities of claim payment and prepayment, we combined the model’s coefficients with the information on a loan’s characteristics and information on economic conditions described by our predictor variables in each quarter between a loan’s origination and fiscal year 1994. For each loan-quarter, we predicted termination probabilities and compared them with random numbers from a uniform distribution. If the termination probability was greater than the random number, the loan was assumed to terminate in that quarter. If our model predicted a foreclosure or prepayment termination, we determined the loan’s balance during that quarter to indicate the dollar amount associated with the foreclosure or prepayment. We estimated cumulative claim and prepayment rates by summing the predicted claim and prepayment dollar amounts for all loans originated in each of the fiscal years 1975 through 1994. We compared these predictions with the actual cumulative (through fiscal year 1994) claim and prepayment rates for the loans in our sample. Figure II.1 compares predicted and actual cumulative foreclosure rates, and figure II.2 compares predicted and actual cumulative prepayment rates.

We then forecasted future loan activity (claims and prepayments) on the basis of the regression results described above and on DRI/McGraw-Hill’s forecasts of the key economic and housing market variables. DRI/McGraw-Hill forecasts the median sales price of existing housing, by state and year, through fiscal year 1998. We subtracted 2 percentage points per year to adjust for improvements in the quality of housing over time and the depreciation of individual housing units. After fiscal year 1998, we assumed that prices would rise at 3 percent per year. For our base case, we made DRI/McGraw-Hill’s forecasts of appreciation rates less optimistic by subtracting another 1 percentage point per year from the company’s forecasts. DRI/McGraw-Hill also forecast each state’s unemployment rate through fiscal year 2002. For our base case, we used DRI/McGraw-Hill’s forecasts of each state’s unemployment rate and assumed that rates from fiscal year 2003 on would equal the rate in fiscal year 2002. We also used DRI/McGraw-Hill’s forecasts of interest rates on 30-year fixed-rate mortgages.

Estimating Economic Value

The economic value of the Fund is defined in the Omnibus Budget Reconciliation Act of 1990 as the “current cash available to the Fund, plus the net present value of all future cash inflows and outflows expected to result from the outstanding mortgages in the Fund.” Information on the capital resources of the Fund as of September 30, 1994, was obtained from the audited financial statements for fiscal year 1994. Capital resources were reported to be $10.8 billion.

To estimate the net present value of future cash flows of the Fund, we constructed a cash flow model to measure the five primary sources and uses of cash for loans originated in fiscal years 1975 through 1994. The two sources of cash are income from mortgagees’ premiums and net proceeds from the sale of foreclosed properties. The three uses of cash are payments associated with claims on foreclosed properties, refunds of premiums on mortgages that are prepaid, and administrative expenses for management of the program.

In addition to estimating the economic value of the Fund as a whole, we also generated approximations of the economic value of the loans originated in the 2 most recent fiscal years. To conduct this analysis, it was necessary not only to project future cash flows but also to estimate the level of past cash flows.

Our model was constructed to estimate cash flows for each policy year through the life of a mortgage. An important component of the model is its ability to convert all income and expense streams—regardless of the period in which they actually occur—into a 1994 present value. We applied discount rates to match as closely as possible the rate of return that FHA likely earned in the past or would earn in the future from its investment in U.S. Treasury securities. As an approximation of what FHA earned for each book of business, we used a rate of return comparable to the yield on 7-year U.S. Treasury securities prevailing when that book was written to discount all cash flows occurring in the first 7 years of that book’s existence. We assumed that after 7 years, the Fund’s investment was rolled over into new Treasury securities at the interest rate prevailing at that time and used that rate to discount cash flows to the rollover date. For rollover dates occurring in fiscal year 1994 and beyond, we used 7 percent as the new discount rate. As an example, cash flows associated with the fiscal year 1992 book of business and occurring from fiscal year 1992 through fiscal year 1998 (i.e, the first 7 policy years) were discounted at the 7-year Treasury rate prevailing in fiscal year 1992. Cash flows associated with the fiscal year 1992 book of business but occurring in fiscal year 1999 and beyond are discounted at a rate of 7 percent.

Our methodology for estimating each of the five principal cash flows is described below.

Premium Income

Because FHA’s premium policy has changed over time, our calculations of premium income to the Fund changes depending on the date of the mortgage’s origination.

For fiscal years 1975 through 1983: Premium = annual outstanding principal balance x 0.5%.

For fiscal years 1984 through June 30, 1991: Premium = original loan amount x mortgage insurance premium.

The mortgage insurance premium during this period is equal to 3.8 percent for 30-year mortgages and 2.4 percent for 15-year mortgages. For the purposes of this analysis, mortgages of other lengths of time are grouped with those they most closely approximate.

Effective July 1, 1991, legislation mandated that FHA add an annual premium of 0.5 percent of the outstanding principal balance to its up-front premiums. The number of years for which a borrower would be liable for making premium payments depended on the LTV ratio at the time of origination. (See table II.6.)

For the period July 1, 1991, through September 30, 1992: Premium = (original loan amount x 3.8%) + (annual outstanding principal balance x 0.5%).

For the period October 1, 1992, through December 31, 1992: Premium = (original loan amount x 3.0%) + (annual outstanding principal balance x 0.5%).

For the period January 1, 1993, through April 17, 1994: 30-year mortgages: Premium = (original loan amount x 3.0%) + (annual outstanding principal balance x 0.5%). 15-year mortgages: Premium = (original loan amount x 2.0%) + (annual outstanding principal balance x 0.25%).

For the period April 18, 1994, through September 30, 1994: 30-year mortgages: Premium = (original loan amount x 2.25%) + (annual outstanding principal balance x 0.5%). 15-year mortgages: Premium = (original loan amount x 2.00%) + (annual outstanding principal balance x 0.25%).

For 15-year mortgages, annual premiums are payable for 8, 4, or zero years depending on the LTV category of the mortgage at loan origination.

Claims Payments

Claims Payments = outstanding principal balance on foreclosed mortgages x acquisition cost ratio.

We define the acquisition cost ratio as being equal to the total amount paid by FHA to settle a claim and acquire a property (i.e., FHA’s “acquisition cost” as reported in its database) divided by the outstanding principal balance on the mortgage at the time of foreclosure. For the purpose of our analysis, we calculated an average acquisition cost ratio for each year’s book of business using actual data for fiscal years 1975 through 1992 and applied that average to projected claims. Beginning in fiscal year 1993, FHA’s A43 database no longer contained the information needed to calculate the acquisition cost ratio. Therefore, we used the fiscal year 1992 ratio for fiscal years 1993 and 1994. (See tables II.7 and II.8.)

Net Proceeds

Net proceeds = (5.9/12) x claims payments from previous period x (1 - loss ratio) + (6.1/12) x claims payments from current period x (1 - loss ratio).

We assumed the lag time between the payment of a claim and the receipt of proceeds from the disposition of the property to be 5.9 months on the basis of the latest available information reported by Price Waterhouse in its fiscal year 1994 financial audit of FHA. We define the loss ratio as being equal to FHA’s reported dollar loss after the disposition of property divided by the reported acquisition cost. For forecast periods, we applied a loss rate of 38 percent, which is the average loss reported by FHA’s financial auditors for fiscal year 1994. This is comparable to the weighted average of losses for fiscal years 1975 through 1989.

Refunded Premiums

The amount of premium refunds paid by FHA’s Fund depends on the policy year in which the mortgage is prepaid and the type of mortgage. For mortgages prepaid from October 1, 1983, to December 31, 1993, we used the refund rate schedule that FHA published in the April 1984 edition of Mortgage Banking. In 1993, FHA changed its refund policy to affect mortgages prepaid on or after January 1, 1994. The refund rates that we used from the new schedule—which assume prepayment at mid-year—are found in table II.9.

For loans prepaying through December 31, 1993: Refunds = original loan amount x refund rate.

For loans prepaying on or after January 1, 1994: Refunds = up-front mortgage insurance premium x refund rate.

Administrative Expenses

Administrative expenses = outstanding principal balance x 0.1% Our estimate of administrative expenses as 0.1 percent of the outstanding principal balances was based on data in recent years’ financial statements.

Sensitivity Analysis

We conducted additional analyses to determine the sensitivity of our forecasts to the values of certain key variables. Because we found that projected losses from foreclosures are sensitive to the rate of unemployment and the rate of appreciation of house prices, we adjusted the forecasts of unemployment and price appreciation to provide a range of economic value estimates under alternative economic scenarios. Our starting points for forecasts of the key economic variables were forecasts made by DRI/McGraw-Hill.

We used DRI/McGraw-Hill’s forecasts of house prices in each state, adjusted as described above, as the basis for our estimation of future equity. We subtracted 2 percentage points per year from DRI/McGraw-Hill’s projected price increases to adjust for quality improvements over time. For our base case, we made DRI/McGraw-Hill’s forecasts of appreciation rates less optimistic by subtracting 1 percentage point per year from its forecasts. For our high case, we added 2 percentage points per year to our base case. For our low case, we subtracted 2 percentage points from our base case.

DRI/McGraw-Hill also forecast each state’s unemployment rate through fiscal year 2002. For our high case and our base case, we used DRI/McGraw-Hill’s forecasts of each state’s unemployment rate and assumed that rates from fiscal year 2003 on would equal the rate in fiscal year 2002. For our low case, we added 1 percentage point to the forecasted unemployment rate during 1995 and beyond.

Table II.10 summarizes the three economic scenarios. The rates of house price appreciation and unemployment are based on DRI/McGraw-Hill’s forecasts. The numbers in the table are our weighted averages of DRI/McGraw-Hill’s state-level forecasts; each state’s number is weighted by the state’s share of FHA’s fiscal year 1993 business.

To assess the impact of our assumptions of the loss and discount rates on the economic value of the Fund, we operated our cash flow model with alternative values for these variables. We found that for the economic scenario of our base case, a 1-percentage-point increase in the loss rate (from our assumption of 38 to 39 percent) resulted in a $201 million decline in our estimate of the economic value of the Fund. With respect to the discount rate, we found that for our base case economic scenario, a 1-percentage-point increase in the interest rate that was applied to most periods’ future cash flow (from our assumption of 7 to 8 percent) resulted in a $90 million increase in our estimate of economic value.

Major Contributors to This Report

Resources, Community, and Economic Development Division, Washington, D.C.

Related GAO Products

Mortgage Financing: Financial Health of FHA’s Home Mortgage Insurance Program Has Improved (GAO/RCED-95-20, Oct. 18, 1994).

Mortgage Financing: Financial Health of FHA’s Home Mortgage Insurance Program Has Improved (GAO/T-RCED-94-255, June 30, 1994).

Homeownership: Actuarial Soundness of FHA’s Single-Family Mortgage Insurance Program (GAO/T-RCED-93-64, July 27, 1993).

Homeownership: Loan Policy Changes Made to Strengthen FHA’s Mortgage Insurance Program (GAO/RCED-91-61, Mar. 1, 1991).

Impact of FHA Loan Policy Changes on Financial Losses and Homebuyers (GAO/T-RCED-90-94, July 24, 1990).

Impact of FHA Loan Policy Changes on Financial Losses and Homebuyers (GAO/T-RCED-90-95, July 10, 1990).

Impact of FHA Loan Policy Changes on Its Cash Position (GAO/T-RCED-90-70, June 6, 1990).

Impact of FHA Loan Policy Changes (GAO/T-RCED-90-17, Nov. 16, 1989).

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