GAO

United States General Accounting Office

Report to Congressional Committees

February 2001 MORTGAGE 

FINANCING

FHA’s Fund Has 

Grown, but Options 

for Drawing on the 

Fund Have Uncertain 

Outcomes

GAO-01-460

Page 1 GAO-01-460 Mortgage Financing

Contents

Letter 3

Appendixes Appendix I: Scope and Methodology 34

Appendix II: Models Used to Estimate the Economic Value of 

FHA’s Mutual Mortgage Insurance Fund 38

Appendix III: Development of Scenarios of Adverse Economic 

Conditions Used to Estimate the Economic Value 

of the Fund 69

Appendix IV: Comments From the Department of Housing and 

Urban Development 76

Appendix V: GAO Contacts and Staff Acknowledgments 80

Related GAO Products 81

Tables Table 1: Estimates of Capital Ratios for FHA's Mutual Mortgage 

Insurance Fund by GAO and Deloitte & Touche, End of 

FY 1999 13

Table 2: Capital Ratios Under Expected and Historical Economic 

Scenarios 17

Table 3: Capital Ratios Under Expected and More Severe Economic 

Scenarios in Selected Locations 18

Table 4: Variable Names and Descriptions 48

Table 5: Means of Predictor Variables 50

Table 6: Coefficients From Foreclosure Equations and Summary 

Statistics 54

Table 7: Coefficients From Prepayment Equations and Summary 

Statistics 56

Table 8: Premium Schedule for 30-Year Non-Streamline Mortgages, 

by Date of Mortgage Origination 63

Table 9: Premium Schedule for 15-Year Non-Streamline Mortgages, 

by Date of Mortgage Origination 64

Table 10: Premium Schedule for 15- and 30-Year Streamline Refinanced 

Mortgages That Originated Before July 1, 1991 64

Table 11: Premium Refund Rates for Loans That Were Terminated After 

October 1, 1983 66

Table 12: Alternative Estimates of Capital Ratios for FHA's Mutual 

Mortgage Insurance Fund 68
Contents

Page 2 GAO-01-460 Mortgage Financing

Table 13: Historical Median House Price and Unemployment 

Experience in States Representing Regional Downturns 71

Table 14: National Results of Alternative Scenarios 74

Figures Figure 1: Cash Flows of the Mutual Mortgage Insurance Fund 8

Figure 2: Comparison of Estimated Economic Value and 2 Percent 

of Insurance-in-Force, 1989-2000 10

Figure 3: Capital Ratios Resulting From Applying the Average 

1986-90 Foreclosure Rates in the West South Central 

Census Division to Varying Proportions of FHA's Insurance 

Portfolio in 2000-04 21

Figure 4: Cumulative Foreclosure Rates by Book of Business for 

30-Year, Fixed-Rate, Nonrefinanced, Mortgages; Actual and 

Predicted, Fiscal Years 1975-99 59

Figure 5: Cumulative Prepayment Rates by Book of Business, for 

30-Year, Fixed-Rate, Nonrefinanced, Mortgages: Actual and 

Predicted, Fiscal Years 1975-99 60

Abbreviations

ARM Adjustable rate mortgage

FHA Federal Housing Administration

HUD Department of Housing and Urban Development

LTV Loan-to-value
Page 3 GAO-01-460 Mortgage Financing

United States General Accounting Office

Washington, D.C. 20548

Letr

February 28, 2001

The Honorable Wayne Allard

Chairman, Subcommittee on Housing

and Transportation

Committee on Banking, Housing and

Urban Affairs

United States Senate

The Honorable Marge Roukema 

Chairman, Subcommittee on Housing 

and Community Opportunity

Committee on Financial Services

House of Representatives

According to the Department of Housing and Urban Development (HUD), 

the economic value of the Mutual Mortgage Insurance Fund (Fund) grew 

by about $5 billion in 1999, apparently reaching its highest level in at least 

the last 20 years.1

 Under this Fund, HUD's Federal Housing Administration 

(FHA) provides insurance for private lenders against losses on home 

mortgages. Borrowers who obtain FHA-insured mortgages pay insurance 

premiums, which are deposited into the Fund. Although the Fund has been 

financially self-sufficient for most of its history, it experienced substantial 

losses during the 1980s, primarily because foreclosure rates on singlefamily homes supported by the Fund were high in economically stressed 

regions. To help place the Fund on a financially sound basis, the Congress 

enacted legislation in November 1990 that required the Secretary of HUD 

to, among other things, take steps to ensure that the Fund achieves and 

maintains an economic value of at least 2 percent of the Fund's insurancein-force. The 1990 reforms also required that an independent actuarial 

study be conducted annually to measure this capital ratio. In January 2000, 

HUD reported that, according to an independent study by Deloitte & 

Touche, the estimated capital ratio was 3.66 percent at the end of fiscal 

1

 The economic value of the Fund is the sum of existing capital resources plus the net 

present value of future cash flows. 
Page 4 GAO-01-460 Mortgage Financing

year 1999.2 With the Fund's capital ratio now substantially above the 

minimum required level, proposals have surfaced to reduce the ratio either 

by spending some of the Fund's current resources or by reducing the net 

cash flows into the Fund.

Concerned about the adequacy of the minimum 2-percent requirement and 

about proposals to spend what some were calling excess reserves, you 

asked us to determine the conditions under which an estimated capital 

ratio of 2 percent would be adequate to maintain the actuarial soundness of 

the Fund. Specifically, you asked us to (1) estimate the value of the Fund at 

the end of fiscal year 1999, given expected economic conditions, and 

compare our estimate to the estimate of the value of the Fund reported by 

HUD for that year; (2) determine the extent to which a 2-percent capital 

ratio would allow the Fund to withstand worse-than-expected loan 

performance due to economic and other factors; and (3) describe some 

options for adjusting the size of the Fund if the estimated capital ratio is 

different than the amount needed, and describe the impact that these 

options might have on the Fund, FHA mortgagors, and the federal budget.

To meet these objectives, we reviewed the laws and regulations governing 

FHA's insurance program. In addition, to estimate the value of the Fund 

and determine the extent to which a 2-percent reserve would allow the 

Fund to withstand worse-than-expected loan performance, we developed 

economic models. We also met with HUD officials who administer FHA's 

single-family insurance program, the independent contractors that have 

analyzed the Fund throughout the 1990s, and other experts to better 

understand methodologies used to estimate the value of the Fund. In 

addition, we met with officials at the Office of Management and Budget and 

the Congressional Budget Office who are building economic models of 

FHA's insurance program to provide better information about the Fund's 

impact on the federal budget. To explore options for changing the size of 

the Fund, we met with HUD officials and other interested parties. To 

determine the impact of these changes on the Federal budget, we relied on 

our own experts as well as budget experts familiar with FHA's program and 

mortgage models at the Office of Management and Budget and the 

Congressional Budget Office.

2 Actuarial Review of MMI Fund as of FY 1999, Deloitte & Touche. In its January 2001 

actuarial review, Deloitte & Touche estimated a capital ratio of 3.51 percent at the end of 

fiscal year 2000. This estimate should not be compared with its reported estimate for 1999 

because, in its latest report, Deloitte revised downward its estimate of the value of the Fund 

at the beginning of fiscal year 2000. 
Page 5 GAO-01-460 Mortgage Financing

We conducted our work between December 1999 and February 2001 in 

accordance with generally accepted government auditing standards. See 

appendix I for a further discussion of our scope and methodology. 

Results in Brief We estimated that the Mutual Mortgage Insurance Fund had an economic 

value of about $15.8 billion at the end of fiscal year 1999. This estimate 

implies a capital ratio of 3.20 percent of the unamortized insurance-inforce. The relatively large economic value and high capital ratio reflect the 

strong economic conditions that prevailed during most of the 1990s and the 

good economic performance expected for the future as well as the 

increased insurance premiums put in place in 1990. HUD reported that 

Deloitte & Touche, using a different method of analysis, estimated an 

economic value of about $16.6 billion for fiscal year 1999, which on the 

basis of its estimate of the unamortized insurance-in-force implied a capital 

ratio of about 3.66 percent. Although there is uncertainty associated with 

any forecast, both of these estimates easily exceed the minimum required 

capital ratio of 2 percent that the Congress set in 1990. The difference 

between these estimates is due in part to differences in the timing of the 

analyses and the assumptions used. Nonetheless, given the uncertainty 

inherent in forecasting and the number of professional judgments made in 

this type of analysis, we conclude that these estimates are comparable.

Given the economic value of the Fund and the state of the economy at the 

end of fiscal year 1999, a 2-percent capital ratio appears sufficient to 

withstand moderately severe economic downturns that could lead to 

worse-than-expected loan performance. That is, such conditions would not 

cause the estimated value of the Fund at the end of fiscal year 1999 to 

decline by more than 2 percent of the Fund's insurance-in-force. Under 

economic scenarios that we developed to represent regional and national 

economic downturns that the nation experienced between 1975 and 1999, 

the estimated capital ratio fell by only slightly less than 0.4 percentage 

points. Some more severe downturns that we analyzed also did not cause 

the estimated capital ratio to decline by as much as 2 percentage points. 

However, in three of the scenarios with more severe economic conditions, 

an economic value of 2 percent of insurance-in-force would not be 

adequate. These included (1) a scenario in which the entire nation 

experiences a downturn similar to the one New England experienced 

during the late 1980s and early 1990s, (2) a scenario in which FHA 

experiences foreclosure rates similar to those it experienced in the late 

1980s, and (3) a scenario in which 35.6 percent or more of FHA loans 

experience foreclosure rates similar to those experienced by FHA in the 
Page 6 GAO-01-460 Mortgage Financing

west south central portion of the United States in the late 1980s. Because of 

the uncertainty and professional judgment associated with this type of 

analysis, we caution against relying on any one estimate or even on a group 

of estimates at a point in time to determine the adequacy of the Fund's 

reserves over the longer term. For example, recent and future FHA-insured 

loans might perform worse than our estimates assume for several reasons, 

including recent and future changes in FHA's programs and the 

conventional mortgage market. To the extent that this is the case, the Fund 

could be less able to withstand adverse economic scenarios than some of 

our estimates suggest. In fact, the Fund had an even higher capital ratio in 

1979 when the economic value of the Fund equaled 5.3 percent of 

insurance-in-force, but in little more than a decade—after a national 

recession, the substitution of an up-front premium for annual insurance 

premiums, and regional real estate declines—the economic value of the 

Fund was negative. This report contains a recommendation that the 

Secretary of HUD address these limitations in evaluating the health of the 

Fund.

There are several options available to the Secretary of HUD under current 

legislative authority that could result in a lower capital ratio for the Fund. 

Other options would require legislative action. However, in either case, it is 

difficult to reliably measure the full impact of policy changes on the Fund's 

capital ratio and FHA borrowers without using tools designed to estimate 

the multiple impacts that policy changes often have. The extent to which 

policy changes will affect the Fund's capital ratio and FHA borrowers is 

difficult to estimate because the impact often depends not only on the 

direct effect of the changes but also on the degree to which the changes 

affect the volume of FHA-insured loans and the riskiness of those loans. A 

complete estimate would require that economic models be used to estimate 

these indirect effects. At this time, however, neither the models used by 

HUD to assess the financial health of the Fund, nor those used by others, 

explicitly recognize the indirect effects of policy changes on the volume 

and riskiness of FHA's loans. As a result, HUD cannot reliably estimate nor 

evaluate the full impact of policy changes on the Fund. Further, the 

difficulty of estimating the impact of the various policy options on the 

capital ratio also makes it difficult to measure precisely the impact on the 

federal budget. Nonetheless, any option that results in a reduction in the 

Fund’s reserve, if not accompanied by a similar reduction in other 

government spending or by an increase in receipts, would result in either a 

reduction in the budget surplus or an increase in any existing deficit. This 

report contains a recommendation that the Secretary of HUD develop 

better tools for assessing the impact of policy changes on the Fund.
Page 7 GAO-01-460 Mortgage Financing

Background FHA was established in 1934 under the National Housing Act (P.L. 73-479) 

to broaden homeownership, shore up and protect lending institutions, and 

stimulate employment in the building industry. FHA insures private lenders 

against losses on mortgages that finance purchases of properties with one 

to four housing units. Many FHA-insured loans are made to low-income, 

minority, and first-time homebuyers. 

Generally, borrowers are required to purchase single-family mortgage 

insurance when the value of the mortgage is large relative to the price of 

the house. FHA, the Department of Veterans Affairs, and private mortgage 

insurers provide virtually all of this insurance. In recent years private 

mortgage insurers and conventional mortgage lenders have begun to offer 

alternatives to borrowers who want to make little or no down payment.3

FHA provides most of its single-family insurance through a program 

supported by the Mutual Mortgage Insurance Fund. The Fund is organized 

as a mutual insurance fund in that any income received in excess of the 

amounts required to cover initial insuring costs, operating expenses, and 

losses due to claims may be paid to borrowers in the form of distributive 

shares after they pay their mortgages in full or voluntarily terminate their 

FHA insurance. The economic value of the Fund depends on the relative 

sizes of cash outflows and inflows over time. Cash flows out of the Fund 

from payments associated with claims on foreclosed properties, refunds of 

up-front premiums on mortgages that are prepaid, and administrative 

expenses for management of the program (see fig. 1). To cover these 

outflows, FHA deposits cash inflows—up-front and annual insurance 

premiums from participating homebuyers and net proceeds from the sale 

of foreclosed properties—into the Fund. If the Fund were to be exhausted, 

the U.S. Treasury would have to cover lenders' claims and administrative 

costs directly.

3

 Generally, borrowers are required to purchase mortgage insurance when the value of the 

mortgage is over 80 percent of the price of the house. Many private mortgage insurers will 

now insure a mortgage up to 97 percent of the value of the house being purchased. In 

addition, conventional mortgage lenders by offering second mortgages of up to 23 percent 

of the value of the house, sometimes allow borrowers to borrow more than the value of the 

house without obtaining mortgage insurance. 
Page 8 GAO-01-460 Mortgage Financing

Figure 1: Cash Flows of the Mutual Mortgage Insurance Fund

The Fund remained relatively healthy from its inception until the 1980s 

when losses were substantial, primarily because of high foreclosure rates 

in regions experiencing economic stress, particularly the oil-producing 

states in the west south central section of the United States. These losses 

prompted the reforms that were first enacted in November 1990 as part of 
Page 9 GAO-01-460 Mortgage Financing

the Omnibus Budget Reconciliation Act of 1990 (P.L. 101-508). The reforms 

that were designed to place the Fund on an actuarially sound basis required 

• the Secretary of HUD to take steps to ensure that the Fund attains a 

capital ratio of 2 percent of the insurance-in-force4

 by November 2000 

and maintains that ratio at a minimum at all times thereafter; 

• an independent contractor to conduct an annual actuarial review of the 

Fund;5

• the Secretary of HUD to suspend the payment of distributive shares, 

which had been paid continuously from 1943 to 1990, until the Fund is 

actuarially sound; and 

• FHA borrowers to pay more in insurance premiums over the life of their 

loans by adding a risk-adjusted annual premium to the one time, upfront premium. 

The Federal Credit Reform Act of 1990, enacted as part of the Omnibus 

Budget Reconciliation Act of 1990, also reformed budgeting methods for 

federal credit programs including FHA's mutual insurance program. The 

1990 credit reforms were intended to ensure that the full cost of credit 

activities for the current budget year would be reflected in the federal 

budget so that the executive branch and the Congress could consider these 

costs when making annual budget decisions. As a result, FHA's budget is 

required to reflect the subsidy cost to the government—the estimated longterm cost calculated on a net present value basis—of FHA's loan insurance 

activities for that year. During the 1990s, the estimated economic value of 

the Fund—comprised of capital resources and the net present value of 

future cash flows—grew substantially. As figure 2 shows, by the end of 

fiscal year 1995, the Fund had attained an estimated economic value that 

slightly exceeded the amount required for a 2-percent capital ratio. Since 

that time, the estimated economic value of the Fund has continued to grow 

and has always exceeded the amount required for a 2-percent capital ratio. 

4

 The Omnibus Budget Reconciliation Act of 1990 defined the capital ratio as the ratio of the 

Fund's capital, or economic net worth (economic value), to its unamortized insurance-inforce. However, the act defined unamortized insurance-in-force as the remaining obligation 

on outstanding mortgages—a definition generally understood to apply to amortized 

insurance-in-force. HUD has calculated the 2-percent capital ratio using unamortized 

insurance-in-force as it is generally understood—which is the initial amount of mortgages. 

Unless otherwise noted, the capital ratios in this report are calculated using unamortized 

insurance-in-force.

5

 From 1989 to 1998, Price Waterhouse performed this review; in 1999, Deloitte & Touche 

was awarded the contract.
Page 10 GAO-01-460 Mortgage Financing

Figure 2: Comparison of Estimated Economic Value and 2 Percent of Insurance-in-Force, 1989-2000

Source: GAO analysis of Price Waterhouse (now PricewaterhouseCoopers) and Deloitte & Touche 

data.

As a result of the 1990 housing reforms, the Fund must not only meet 

capital ratio requirements, but it must also achieve actuarial soundness; 

that is, the Fund must contain sufficient reserves and funding to cover 

estimated future losses resulting from the payment of claims on foreclosed 

mortgages and administrative costs. However, neither the legislation nor 

the actuarial profession defines actuarial soundness. Price Waterhouse 

(now PricewaterhouseCoopers) in 1989 concluded that for the Fund to be 

actuarially sound, it should have capital resources that could withstand 

losses from reasonably adverse, but not catastrophic, economic 

downturns. The Price Waterhouse report did not clearly distinguish 

adverse from catastrophic downturns; however, they said that private 

mortgage insurers are required to hold contingency reserves to protect 

against catastrophic losses. In turn, rating agencies require that private 

mortgage insurers have enough capital on hand to withstand severe losses 

Dollars in billions

-5

0

5

10

15

20

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Fiscal years

Estimated value

2% of insurance-in-force
Page 11 GAO-01-460 Mortgage Financing

that would occur if loans they insure across the entire nation had losses 

similar to those experienced in the west south central states in the 1980s.

Because economic downturns put downward pressure on house prices and 

incomes, they can stress FHA's ability to meet its obligations. Thus, it is 

reasonable that measures of the financial soundness of the Fund would be 

based on tests of the Fund's ability to withstand recent recessions or 

regional economic downturns. In the last 25 years, we have experienced a 

national recession and regional economic declines that did or could have 

placed stress on FHA. For example, the nation experienced a recession in 

1981 and 1982 that strained mortgage markets. Regionally, states in the 

west south central portion of the nation experienced an economic decline 

in 1986 through 1989 precipitated by a sharp drop in the price of crude oil. 

Similarly, the economic decline experienced by California from 1992 

through 1995 placed stress on FHA. Because FHA does substantial 

business in these regions of the country, these experiences led to 

substantial losses for FHA. In contrast, the economic decline experienced 

by the New England states from 1989 through 1991 placed little strain on 

FHA because insured mortgages in this region do not make up a large 

portion of FHA's total portfolio. However, experiences similar to the New 

England downturn, during which the unemployment rate increased by 

almost 140 percent and house prices decreased by 5.5 percent, could place 

stress on FHA if they occurred in other regions or the nation as a whole.

The Fund's Estimated 

Economic Value 

Exceeds 3 Percent of 

Insurance-in-Force

On the basis of our economic model of FHA's home loan program and 

forecasts of several key economic factors, we estimate that at the end of 

fiscal year 1999, the Fund had an economic value of about $15.8 billion. 

This value, which is 3.20 percent of the unamortized insurance-in-force, 

reflects the robust economy and relatively high premium rates prevailing 

through most of the 1990s and the good economic performance forecast for 

the future. In comparison, Deloitte & Touche estimated that the Fund's 

1999 economic value was over $800 million larger than our estimate—or 

about 3.66 percent of its estimate of FHA's unamortized insurance-in-force. 

Although we did not evaluate the quality of Deloitte's estimates, we believe 

that Deloitte's and our estimates are comparable because of the 

uncertainty inherent in forecasting and the professional judgments made in 

this type of analysis. However, Deloitte's analysis and ours differ in several 

ways, including the time when the analyses were performed and some of 

the assumptions made. 
Page 12 GAO-01-460 Mortgage Financing

The Estimated Economic 

Value of the Fund Reflects 

the Robust Economy and 

Increased Premium Rates

Using conservative assumptions, we estimate that at the end of fiscal year 

1999, the Fund had an economic value of about $15.8 billion. The economic 

value of the Fund consists of the capital resources on hand and the net 

present value of future cash flows. Documents used to prepare FHA's 1999 

financial statements show that the Fund had capital resources of about 

$14.3 billion at the end of that fiscal year. We estimated the relationship 

between historical FHA foreclosures and prepayments and certain key 

economic factors to forecast foreclosures and prepayments and the 

resulting cash flows over the next 30-year period for mortgages insured by 

FHA before the end of fiscal 1999. As a result of this analysis, we estimate 

that at the end of 1999 the net present value of future cash flows was about 

$1.5 billion. Summing the capital resources and future cash flows gives us 

an economic value of about $15.8 billion. See appendix II for a detailed 

discussion of the forecasting and cash flow models used to estimate the 

economic value of the Fund. 

We also estimate that the Fund's capital ratio—the Fund's economic value 

divided by its insurance-in-force—exceeded 3-percent at the end of fiscal 

year 1999. From the individual loan data provided by HUD, we calculated 

that the unamortized insurance-in-force at the end of fiscal year 1999 was 

about $494 billion and that the amortized value of that insurance, an 

estimate of the outstanding balance of the loans and thus FHA's insurance 

liability, was about $455.8 billion. Therefore, the economic value of the 

Fund represented 3.20 percent of the unamortized insurance-in-force and 

about 3.47 percent of the amortized insurance-in-force on September 30, 

1999. 

The robust economy and the increased premium rates established by the 

1990 legislation contributed to the strength of the Fund at the end of fiscal 

year 1999. The Fund's economic value principally reflects the large amount 

of capital resources that the Fund has accrued. Because current capital 

resources are the result of previous cash flows, the robustness of the 

economy and the higher premium rates throughout most of the 1990s 

accounted for the accumulation of these substantial capital resources. 

Good economic times that are accompanied by relatively low interest rates 

and relatively high levels of employment are usually associated with high 

levels of mortgage activity and relatively low levels of foreclosure; 

therefore, cash inflows have been high relative to outflows during this 

period. 

The estimated value of future cash flows also contributed to the strength of 

the Fund at the end of fiscal 1999. As a result of relatively low interest rates 
Page 13 GAO-01-460 Mortgage Financing

and the robust economy, FHA insured a relatively large number of 

mortgages in fiscal years 1998 and 1999. These loans make up a large 

portion of FHA's insurance-in-force, because many borrowers refinanced 

their FHA-insured mortgages originated in earlier years, probably as a 

result of interest rates having fallen to relatively low levels in 1998 and 

1999. Because these recent loans have low interest rates and because 

forecasts of economic variables for the near future show house prices 

rising while unemployment and interest rates remain fairly stable, our 

models predict that these new loans will have low levels of foreclosure and 

prepayment. As a result, our models predict that future cash flows out of 

the Fund will be relatively small. At the same time, we assume that FHAinsured homebuyers will continue to pay the annual premiums that were 

reinstituted in 1991. Thus, our models predict that cash flowing into the 

Fund from mortgages already in FHA's portfolio at the end of fiscal year 

1999 will be more than sufficient to cover the cash outflows associated 

with these loans. As a result, the estimated economic value of the Fund is 

even higher than the level of its current capital resources.

Deloitte's Estimates Are 

Comparable to Ours, but the 

Analyses Differ in Several 

Ways

As table 1 shows, Deloitte's independent actuarial analysis of the Fund for 

fiscal year 1999 estimated a capital ratio that was somewhat higher than 

ours, 3.66 percent rather than 3.20 percent of unamortized insurance-inforce. Although we did not evaluate the quality of Deloitte's estimates, we 

did identify some reasons that its estimate of the capital ratio was higher 

than ours. The ratio is higher because Deloitte estimates both a higher 

economic value of the Fund and a lower amount of insurance-in-force. 

Deloitte's higher estimated economic value of the Fund includes a higher 

estimated value for capital resources on hand that is somewhat offset by a 

lower estimate of the net present value of future cash flows.

Table 1: Estimates of Capital Ratios for FHA's Mutual Mortgage Insurance Fund by GAO and Deloitte & Touche, End of FY 1999

Source: GAO analysis and Actuarial Review of MMI Fund as of FY 1999, Deloitte & Touche.

Our estimate and that of Deloitte rely on forecasts of foreclosures and 

prepayments over the next 30 years, and, in turn, these forecasts 

Dollars in millions

Estimate

Total capital

resources

Future

cash flows

Economic

value

Unamortized

insurance-in-force

Capital ratio

(percent)

GAO $14,326 $1,484 $15,810 $493,990 3.20

Deloitte 15,331 1,306 16,637 454,184 3.66
Page 14 GAO-01-460 Mortgage Financing

necessarily rest on forecasts of certain economic factors. In addition, the 

estimates depend on the choices made concerning a variety of other 

assumptions. As a result of the inherent uncertainty and the need for 

professional judgment in this type of analysis, we believe that our estimates 

and Deloitte's estimates of the Fund's economic value and capital ratio are 

comparable. 

Although the estimates are comparable, Deloitte's estimates of capital 

resources and insurance-in-force differ from ours primarily because the 

analyses were conducted at different times. Because Deloitte performed its 

analysis before the end of 1999, it had to estimate some data for which we 

had year-end values. In particular, Deloitte overestimated the 1999 value of 

capital resources by extrapolating from the 1998 value. In contrast, we used 

values developed for FHA's 1999 financial statements that were about $1 

billion lower than Deloitte's estimate. Using our value for capital resources, 

Deloitte's estimated capital ratio would be 3.44 percent rather than 3.66 

percent of insurance-in-force.6

 Similarly, Deloitte underestimated the 

number of loans that FHA insured in the fourth quarter of fiscal year 1999 

and, thus, underestimated the value of loans insured for all of fiscal year 

1999 by about $33 billion, though this appears to have had little effect on 

the estimated capital ratio. 

Our analysis of the net present value of future cash flows and that of 

Deloitte also differ in several respects. Both our estimates and Deloitte's 

rely on forecasts of future foreclosures and prepayments. In turn, these 

forecasts are generated from models that are based on estimated 

relationships between the probability of loan foreclosure and prepayment 

and key explanatory factors, such as borrowers' home equity and interest 

and unemployment rates. Our model differs from Deloitte's in the way that 

it specifies these relationships. For example, Deloitte specified changes in 

household income as one of the key explanatory factors, while we did not.7

6

 In its 2000 actuarial review, Deloitte recognized that its 1999 estimate of capital resources 

was about $1 billion higher than the actual year-end value. In addition, Deloitte revised 

upward its measure of up-front mortgage insurance premiums and downward the net 

present value of future cash flows calculated at the beginning of fiscal year 2000. As a 

result, Deloitte estimates an economic value of the Fund of $14.1 billion at the beginning of 

fiscal year 2000, which would have resulted in a capital ratio even lower than 3.44 percent at 

the beginning of fiscal year 2000, that is, the end of fiscal year 1999.

7

 We did not include changes in household income because we believe that unemployment 

rates are more directly connected to changes in the ability of borrowers to make mortgage 

payments and are sufficient to capture those changes. 
Page 15 GAO-01-460 Mortgage Financing

The analyses also differ in the assumptions made about some future 

economic values and costs associated with FHA's insurance program. For 

example, we assumed lower house price appreciation rates and higher 

discount rates for calculating net present values than did Deloitte.8

 In 

addition, the analyses differ in the way that they use HUD's data. We used a 

sample of individual loans while Deloitte grouped loans into categories to 

do its analysis. Although these factors could be important in identifying 

why the two estimates differ, we could not quantify their impact because 

we did not have access to Deloitte's models. 

A 2-percent Capital 

Ratio Appears 

Sufficient to Withstand 

Some Worse-ThanExpected Loan 

Performance

According to our estimates, worse-than-expected loan performance that 

could be brought on by moderately severe economic conditions would not 

cause the estimated value of the fund at the end of fiscal year 1999 to 

decline by more than 2 percent of insurance-in-force. However, a few more 

severe economic scenarios that we examined could result in such poor 

loan performance that the estimated value of the fund at the end of fiscal 

year 1999 could decline by more than 2 percent of insurance-in-force. Two 

of the three scenarios that showed such a large decline extended adverse 

conditions more widely than the moderately severe scenarios and, 

therefore, are less likely to occur. While these estimates suggest that the 

capital ratios are more than sufficient to protect the Fund at this time from 

many worse-than-expected loan performance scenarios, factors not fully 

captured in our models could affect the Fund's ability to withstand worsethan-expected experiences over time. These factors include recent changes 

in FHA's insurance program and the conventional mortgage market that 

could affect the likelihood of poor loan performance and the ability of the 

Fund to withstand that performance. For example, conventional mortgage 

lenders and private mortgage insurers have recently lowered the required 

down payment on loans. Such actions may have attracted some lower risk 

borrowers who would otherwise have insured their loans with FHA. As a 

result, the overall riskiness of FHA's portfolio may be greater than we have 

estimated, making a given amount of capital less likely to withstand future 

economic downturns than we have predicted. 

8

 Appendix II discusses the sensitivity of our results to some of the assumptions we made in 

our analysis.
Page 16 GAO-01-460 Mortgage Financing

At This Time, the Capital 

Ratio Appears Sufficient to 

Withstand Moderately 

Severe Economic Scenarios 

That Are Based on Recent 

Historical Experience

Beginning with the robust economy and the value of the Fund in 1999, our 

analysis shows that a 2-percent capital ratio appears sufficient to withstand 

worse-than-expected loan performance that results from moderately 

severe economic scenarios similar to those experienced over the last 25 

years. Our model and others that are based on historical experience 

suggest that falling house prices and high levels of unemployment are likely 

to produce poor mortgage performance. Thus, to test the Fund's ability to 

withstand worse-than-expected loan performance, we developed economic 

scenarios that are based on certain regional downturns and the 1981-82 

national recession.

We tested the adequacy of the capital ratio using economic scenarios that 

were based on three recent regional economic downturns—one in the west 

south central region of the United States that began in 1986, one in New 

England that began in 1989, and one in California that began in 1992—that 

produced high mortgage foreclosure rates in those regions.9

 The degree to 

which these downturns affected the Fund depended on their severity as 

well as on the volume of mortgages insured by FHA in that region. Thus, 

while New England suffered a severe downturn in the late 1980s and early 

1990s, the Fund did not suffer significantly because the volume of loans 

that FHA insures in New England represents a small share of FHA's total 

volume of insured loans. Because regional averages diminish the impact of 

the adverse economic experience, from each region we selected a state 

with particularly poor experience as the basis for our scenarios. We also 

adjusted the scenarios to recognize that the forecasts start from the 

economic conditions that existed at the end of 1999. See appendix III for 

further discussion of the scenarios that we used to test the adequacy of 

FHA's capital ratio. 

As can be seen in table 2, neither the scenarios that are based on regional 

downturns nor the scenario that is based on the 1981-82 national recession 

had much of an effect on the value of the Fund. More specifically, in these 

worse-than-expected scenarios that are based on specific historical 

experiences, the estimated capital ratio never falls below 2.8 percent, 

which is only 0.4 percentage points below our estimated capital ratio using 

9

 The west south central region includes those states in the west south central Bureau of the 

Census division—Arkansas, Louisiana, Oklahoma, and Texas. The New England region 

includes Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont. 

California is part of the Pacific region, which corresponds to the Pacific census division and 

also includes Alaska, Hawaii, Oregon, and Washington.
Page 17 GAO-01-460 Mortgage Financing

expected economic conditions. However, the national recession had the 

greatest impact because it affected FHA's entire portfolio. 

Table 2: Capital Ratios Under Expected and Historical Economic Scenarios

a

In estimating these capital ratios, we assume that the scenario begins in the first year after the most 

recent loans were originated. In our data, the most recent loans were originated in fiscal year 1999; 

therefore, scenarios start in fiscal year 2000. We knew when we performed this analysis that none of 

these scenarios actually occurred in fiscal year 2000, but we wanted to test the ability of the Fund to 

withstand an economic downturn when many of FHA's loans were new and the borrowers had not 

accumulated much equity. In addition, results for scenarios beginning a year later had less of an effect 

on the Fund. 

b

Standard and Poor's DRI is a private economic forecasting company.

Source: GAO analysis.

Under More Severe 

Economic Scenarios, the 

Capital Ratio Could Fall by 

More Than 2 Percentage 

Points

Although the Fund's estimated capital ratio at the end of fiscal year 1999 

fell by considerably less than 2 percentage points under economic 

scenarios that are based on recent regional experiences and the 1981-82 

national recession, our model suggests that extensions of some historical 

regional scenarios to broader regions of the country could cause the capital 

ratio to fall by more than 2 percentage points. Specifically, to test whether a 

2-percent capital ratio could withstand more severe economic conditions, 

we extended the regional scenarios to two regions and then to the nation as 

a whole. However, we recognize that these extensions are less likely to 

occur than the historical scenarios that affected a single region. As table 3 

shows, if any of these downturns simultaneously hit two regions where 

FHA has significant business—the west south central and Pacific regions—

the estimated capital ratio would be less than 2 percentage points lower 

than it would be with expected loan performance. In addition, even if the 

Scenario Description

Capital ratioa

(percent)

Expected economic conditions Unemployment and interest rates vary as Standard & Poor's DRI 

forecasts; house price growth is adjusted for constant quality and 

slower growth.b

3.20

West south central downturn House prices and unemployment change as they did in Louisiana from 

1986 through 1990.

3.06

New England downturn House prices and unemployment change as they did in Massachusetts 

from 1988 through 1992. 

3.14

Pacific downturn House prices and unemployment change as they did in California from 

1991 through 1995. 

2.89

1981-82 national recession For each state, house prices, unemployment rates, and interest rates 

change as they did from 1981 through 1985.

2.81
Page 18 GAO-01-460 Mortgage Financing

entire nation experienced a downturn similar to two of the three regional 

downturns that we analyzed, the estimated capital ratio would still fall by 

less than 2 percentage points. However, a national downturn as severe as 

that experienced by Massachusetts from 1989 through 1992 would cause 

our estimate of the 1999 capital ratio to fall by more than 2 percentage 

points. 

Table 3: Capital Ratios Under Expected and More Severe Economic Scenarios in Selected Locations

a

The two regions are the Pacific and west south central census divisions.

b

Standard & Poor's DRI is a private economic forecasting company.

Scenario Description

Capital ratio for

scenarios in two

regionsa

 (percent)

Capital ratio for

national scenarios

(percent)

Expected econom 

conditions

Unemployment and interest rates 

vary as DRI forecasts; house price 

growth is adjusted for constant 

quality and slower growth.b

NA 3.20

Extensions of historical regional downturns

West south central 

downturn 

House prices and unemployment 

rates change as they did in 

Louisiana from 1986 through 1990.

2.81 2.31

New England downturn House prices and unemployment 

rates change as they did in 

Massachusetts from 1988 through 

1992. 

2.14 0.81

Pacific downturn House prices and unemployment 

rates change as they did in 

California from 1991 through 1995. 

2.59 2.16

National scenarios with interest rate changes or high foreclosure rates

Induced refinancing 

followed by a recession

Mortgage interest rates fall, 

inducing borrowers to refinance, 

and then a recession sets in, such 

that the unemployment rate rises 

and house prices fall. 

NA 1.37

Rising interest rate 

scenario

Mortgage and other interest rates 

are higher from 2000 through 2004 

than under expected economic 

conditions.

NA 3.36

Scenario with foreclosure 

rates from the 1980s

Foreclosure rates in 2000 through 

2004 equal foreclosure rates from 

1986 to 1990 for mortgages 

originated in most recent 10-year 

periodc

NA 0.92
Page 19 GAO-01-460 Mortgage Financing

c

This scenario does not vary foreclosure rates for streamline refinanced or adjustable rate mortgages 

because there are no data on these products for the 10-year period prior to 1986.

Source: GAO analysis.

Because we were concerned that the historical scenarios we were 

considering might not be adequate to test the effect of changes in interest 

rates, we developed two additional scenarios: one in which mortgage 

interest rates fall and then a recession sets in and one in which mortgage 

and other interest rates rise to levels that are higher than those in the 

expected economic conditions scenario. The first scenario is more likely to 

exhaust a 2-percent capital ratio.

Under a scenario in which mortgage interest rates fall and then a recession 

sets in, the drop in interest rates might induce some homeowners to 

refinance their mortgages. For those homeowners who refinance outside of 

FHA, the fund would no longer be accumulating revenue in the form of 

annual premiums; if the homeowners have not had their mortgages for 

long, they would receive some premium refunds. Moreover, those 

borrowers who use FHA's streamline refinance provision that allows 

borrowers to refinance their mortgages without a new appraisal of their 

home will likely pay annual premiums for fewer years than if they had not 

refinanced.10 So, cash outflows would have increased and cash inflows 

would have decreased before the recession hits. When the recession hits, 

cash outflows would increase further because of increased foreclosures 

among the remaining borrowers. As table 3 shows, our model predicts that 

the capital ratio would fall substantially—by almost 2 percentage points—

under this scenario.

A scenario with rising mortgage interest rates will affect various loan types 

differently. Because the payments on adjustable rate mortgages increase as 

interest rates rise, there is an increased likelihood that borrowers with 

these types of mortgages will default. However, since FHA-insured 

mortgages are assumable, rising interest rates make fixed-rate mortgages 

10 Borrowers with 30-year mortgages who borrow more than 95 percent of the value of their 

home are required to pay annual premiums equal to 0.5 percent of the remaining balance of 

their mortgage for 30 years. However, if these borrowers refinance their mortgages using 

FHA's streamline program, they will have to pay annual premiums for no more than 7 years. 

In “Mortgage Refinancing, Adverse Selection, and FHA’s Streamline Program”, Journal of 

Real Estate Finance and Economics (vol. 21, issue 2), David Brickman and Patric 

Hendershott estimated that borrowers who borrowed 97 percent of the value of their homes 

in 1994 and immediately refinanced would have reduced the net present value of their 

premium payments by 32 percent.
Page 20 GAO-01-460 Mortgage Financing

more valuable to those borrowers holding them. This decreases the 

likelihood that borrowers with these types of mortgages will default. 

Insurance on loans originated in 1998 and 1999 make up 42 percent of 

FHA's portfolio at the end of fiscal year 1999, and the insured loans are 

predominately fixed rate mortgages. Consequently, it is not surprising that 

a rising interest rate scenario leads to an increase in the value of the Fund. 

Because our economic model did not predict regional or national 

foreclosure rates as high as those experienced during the 1980s in any of 

our scenarios, we estimated cash flows using foreclosure rates that more 

closely matched regional experience during the 1980s. Specifically, we 

assumed that for mortgages originated from 1989 through 1999, foreclosure 

rates in 2000 through 2004 would equal those experienced from 1986 

through 1990 by FHA-insured loans that originated between 1975 and 1985 

in a given region. As table 3 shows, the capital ratio fell to 0.92 percent 

under this scenario. To test an even more severe scenario, one similar to 

that used by rating agencies for private mortgage insurers,11 we also 

calculated future cash flows assuming that foreclosure rates in 2000 

through 2004 extended the very poor performance of the west south central 

mortgages in the 1980s to ever larger portions of FHA's insurance portfolio. 

As figure 3 shows, we found that if 36.5 percent of FHA-insured mortgages 

experienced these high default rates, the estimated capital ratio for fiscal 

year 1999 would fall by 2 percentage points. If about 55 percent of FHA's 

portfolio experienced these conditions, a less likely event, the capital ratio 

would be 0. 

11 For example, Standard & Poor’s assumes that over the next 10 years, default rates for 

fixed rate mortgages will equal those from the west south central states in the 1980s. In 

addition, they assume that no new loans will be insured. The rating for private mortgage 

insurers depends on how much capital a company has at the end of this 10-year experience.
Page 21 GAO-01-460 Mortgage Financing

Figure 3: Capital Ratios Resulting From Applying the Average 1986-90 Foreclosure 

Rates in the West South Central Census Division to Varying Proportions of FHA's 

Insurance Portfolio in 2000-04

Note: West south central mortgages made up 9 percent of FHA's portfolio in 1999. This analysis does 

not change foreclosure rates for streamline refinanced or adjustable rate mortgages because there are 

no data on these products for the 10-year period prior to 1986.

Source: GAO analysis.

Other Factors May Affect 

the Adequacy of the Capital 

Ratio 

Because our models are based on the relationship between foreclosures 

and prepayments and certain economic factors from fiscal years 1975 

through 1999, they do not account for the potential impact of recent events, 

such as changes in FHA's program or in the behavior of the conventional 

mortgage market. In addition, our models assume that no additional 

changes in FHA's program or the conventional mortgage market that would 

affect FHA-insured loans originated through 1999 take place during the 

forecast period, which extends from fiscal years 2000 through 2028. To the 

extent that any such changes cause foreclosure and prepayment rates on 

existing FHA-insured loans to be higher or lower than we have predicted, 

0 20 40 60 80 100

Percentage of FHA’s portfolio

-3

-2

-1

0

1

2

3

4 Capital ratio (percent)

Point at which the capital ratio would fall by 2 percentage points

Capital ratio with 1986 to 1990 foreclosure rates
Page 22 GAO-01-460 Mortgage Financing

the Fund's capital ratio would be different under the various scenarios we 

have discussed. Furthermore, our analysis does not attempt to predict how 

loans insured by FHA after fiscal year 1999 will behave. Future changes in 

FHA's program, such as the premium changes adopted as of January 1, 

2001,12 or in the conventional mortgage market may make future loans 

perform better or worse than we might expect from past experience. In 

addition, these changes may increase or reduce the amount of cash flowing 

into the Fund and thus its ability to withstand worse-than-expected loan 

performance in the future. 

Changes in FHA's Insurance 

Program 

HUD and the Congress can change FHA's insurance program in a variety of 

ways, including changes in refund policy and underwriting standards. In 

fact, HUD and the Congress have taken the following actions in recent 

years that could affect the Fund in ways that are not accounted for in our 

models: 

• HUD has suggested that it will reinstitute distributive shares and 

Members of Congress have introduced bills requiring HUD to take that 

action. The immediate consequence of this action would be that cash 

flows out of the Fund would be higher than our estimates. 

• During the late 1990s, the Congress required that FHA implement a new 

loss mitigation program that encourages lenders to take actions to lower 

defaults on FHA-insured mortgages. The program requires that lenders 

provide homebuyers with certain options to avoid foreclosure. While it 

is hoped that losses from foreclosures will decline as a result of this 

program, if foreclosure is simply delayed as a result of forbearance, 

losses could ultimately be larger in the long run. In either case, actual 

cash flows would likely be different than our estimates. 

• FHA has also reduced up-front premiums for new homeowners who 

receive financial counseling before buying a home. If the program 

reduces the likelihood that these homeowners will default, losses would 

be lower than we have estimated.13

12 These changes include reducing the up-front premium for all homebuyers to 1.5 percent (a 

reduction of up to 0.75 percentage points) and canceling the annual mortgage insurance 

premiums for most borrowers when the value of the mortgage reaches 78 percent of the 

original price of the house.

13 As a result of the reduction in up-front premiums for all borrowers on January 1, 2001, 

borrowers receiving financial counseling before purchasing a home will no longer pay lower 

up-front premiums than other borrowers.
Page 23 GAO-01-460 Mortgage Financing

• HUD has taken action to improve the oversight of lenders and better 

dispose of properties and is continuing to implement new programs in 

these areas. Better oversight of lenders could mean that losses on 

existing business would be lower than we have predicted, and better 

practices for disposing of property could reduce losses associated with 

foreclosed properties below the level we have estimated.

Our models do not look at cash flows associated with loans that FHA 

would insure after fiscal year 1999. However, recent and future changes in 

FHA's insurance program will affect the likelihood that these loans will 

perform differently than past experience suggests they will. If, for example, 

FHA loosens underwriting standards, there is a greater likelihood that 

future loans would perform worse than past experience suggests. In 

addition, changes in premiums, such as the recent reductions in up-front 

premiums, could reduce cash inflows into the Fund and, therefore, reduce 

the Fund's ability to withstand poor loan performance. However, this 

premium change could also lower the riskiness of the loans FHA insures. 

Changes in the Conventional 

Mortgage Market

Recent changes in the conventional mortgage market, especially changes in 

FHA's competitors' behavior, may also affect the estimates we have made 

concerning the Fund's ability to withstand adverse economic conditions 

over the long run. Homebuyers' demand for FHA-insured loans depends, in 

part, on the alternatives available to them. In recent years, FHA's 

competitors in the conventional mortgage market—private mortgage 

insurers and conventional mortgage lenders—are increasingly offering 

products that compete with FHA's for those homebuyers who are 

borrowing more than 95 percent of the value of their home. These 

developments in the conventional mortgage market may have increased the 

average risk of FHA-insured loans in the late 1990s. In particular, by 

lowering the required down payment, conventional mortgage lenders and 

private mortgage insurers may have attracted some borrowers who might 

otherwise have insured their mortgages with FHA. If, by selectively offering 

these low down payment loans, conventional mortgage lenders and private 

mortgage insurers were able to attract FHA's lower-risk borrowers, recent 

FHA loans with down payments of less than 5 percent may be more risky 

on average than they have been historically. If this effect, known as adverse 

selection, has been substantial, the economic value of the Fund may be 

lower than we estimate, and it may be more difficult for the Fund to 

withstand worse-than-expected loan performance than our estimates 

suggest. In addition, should these competitive pressures persist, newly 

insured loans are likely to perform worse than prior experience would 

suggest, and then any given capital ratio would be less able to withstand 
Page 24 GAO-01-460 Mortgage Financing

such performance. FHA is taking some action to more effectively compete. 

For example, FHA is attempting to implement an automated underwriting 

system that could enhance the ability of lenders underwriting FHA-insured 

mortgages to distinguish better credit risks from poorer ones. Although this 

effort is likely to increase the speed with which lenders process FHAinsured loans, it may not improve the risk profile of FHA borrowers unless 

lenders can lower the price of insurance for better credit risks.

The Impacts of Options 

for Reducing FHA's 

Capital Ratio Are 

Difficult to Predict

Several options are available to the Secretary of HUD under current 

legislative authority that could result in reducing FHA's capital ratio. Other 

options would require legislative action. Reliably measuring the impacts of 

these options on the Fund's capital ratio and FHA borrowers is difficult 

without using tools designed to estimate the multiple impacts that policy 

changes often have. While HUD has substantially improved its ability to 

monitor the financial condition of the Fund, neither the models used by 

HUD to assess the financial health of the Fund, nor those used by others, 

explicitly recognize the indirect effects of policy changes on the volume 

and riskiness of FHA's loans. As a result, the impacts of the various policy 

options on the federal budget are difficult to discern. However, any option 

that results in a reduction in the Fund’s reserve, if not accompanied by a 

similar reduction in other government spending or by an increase in 

receipts, would result in either a reduction in the surplus or an increase in 

any existing deficit. 

The Secretary of HUD and 

the Congress Have 

Numerous Options 

Available to Reduce the 

Capital Ratio 

There are several changes to the FHA single-family loan program that could 

be adopted if the Secretary of HUD or the Congress believes that the 

economic value of the Fund is higher than the amount needed to ensure 

actuarial soundness. For example, actions that the Secretary could take 

that could reduce the value of the fund include lowering insurance 

premiums, adjusting underwriting standards, and reinstituting distributive 

shares.14 However, congressional action in the form of new legislation 

would be required to make other program changes that are not now 

14 Between 1943 and 1990, FHA rebated these so-called excess funds to borrowers as 

distributive shares. In 1990, however, the Congress suspended the payment of these shares 

until the Secretary of HUD determines that the Fund is actuarially sound. HUD has 

announced that it will resume paying distributive shares. HUD officials said that they are 

developing systems to facilitate the payment of these shares and expect to be ready to 

resume paying them in mid-2001.
Page 25 GAO-01-460 Mortgage Financing

authorized or clearly contemplated by the statute. These would include 

actions such as changing the maximum amount FHA-insured homebuyers 

may borrow relative to the price of the house they are purchasing and using 

the Fund's reserves for other federal programs.15 Generally, the Secretary 

of HUD, in making any authorized changes to the FHA single-family 

program, must meet certain operational goals. These operational goals 

include (1) maintaining an adequate capital ratio, (2) meeting the needs of 

homebuyers with low down payments and first-time homebuyers by 

providing access to mortgage credit, (3) minimizing the risk to the Fund 

and to homeowners from homeowner default, and (4) avoiding adverse 

selection. 

Potential Effects of Options 

on the Fund's Capital Ratio 

and FHA Borrowers Are 

Difficult to Measure

Reliably estimating the potential effect of various options on the Fund's 

capital ratio and FHA borrowers is difficult because the impacts of these 

policy changes are complex and tools available for handling these 

complexities may not be adequate. Policy changes have not only 

immediate, straightforward impacts on the Fund and FHA's borrowers, but 

also more indirect impacts that may intensify or offset the original effect. 

Implementing these options could affect both the volume and the average 

riskiness of loans made, which, in turn, could affect any future estimate of 

the Fund's economic value. As a result of this complexity, obtaining a 

reliable estimate would likely require that economic models be used to 

estimate the indirect effects of policy changes. In 1990, the Congress 

enacted legislation designed to provide better information on the Fund's 

financial condition. The Omnibus Budget Reconciliation Act requires 

annual independent actuarial reviews of the Fund and includes credit 

reforms that require HUD to estimate, for loans originated in a given year, 

the net present value of the anticipated cash flows over all the years that 

the loans will be in existence. The models developed by HUD to comply 

with these requirements are based on detailed analyses of the Fund's 

historical claim and loss rates and have improved HUD's ability to monitor 

the financial condition of the Fund. At this time, however, neither the 

models used by HUD to assess the financial health of the Fund, nor those 

used by others, explicitly recognize the indirect effects of policy changes 

on the volume and riskiness of FHA's loans. As a result, HUD cannot 

reliably estimate the impact of policy changes on the Fund. Although it is 

difficult to predict the overall impact of a change on the Fund's capital ratio 

15 During the 106th Congress, legislation was introduced that proposed using the Fund's 

resources to fund affordable rental housing (see S. 2997).
Page 26 GAO-01-460 Mortgage Financing

and thus on FHA borrowers as a whole, different options would likely have 

different impacts on current and prospective FHA-insured borrowers.

Effect on the Fund's Capital 

Ratio 

Many of the proposals to reduce the capital ratio, such as lowering 

premiums or reinstituting distributive shares, will reduce the price of FHA 

insurance to the borrower. If no change in the volume of loans FHA insures 

is considered, then the effect of lowering premiums, for example, clearly 

would be to lower the economic value of the Fund. However, for two 

reasons, this price reduction is likely to increase the volume of FHA loans 

originated, which would increase both premium income and claims against 

the Fund when some of these new loans default. First, by lowering the 

price of FHA insurance relative to the price of private mortgage insurance, 

this premium reduction would likely induce some borrowers who 

otherwise would have obtained private mortgage insurance to obtain FHA 

insurance instead, thereby increasing FHA's market share. Second, people 

who were deferring home purchases because of the high price of FHA 

insurance might buy homes with FHA insurance once the price is lower. 

Without a complete analysis of the impact on the volume of loans, reliably 

estimating the effect of lowering the premiums on the Fund's economic 

value is difficult. 

Furthermore, the economic value of the Fund is influenced not only by the 

volume of loans FHA insures, but also by the riskiness of those loans. 

Therefore, determining the effect a policy change will have on the 

economic value of the Fund requires determining how the policy will affect 

the riskiness of FHA-insured loans. In the case of lowering up-front 

premiums, for example, the new FHA-insured loans could be less risky than 

FHA's existing loans. As a result, the new loans would be profitable and 

offset the direct impact of lower premiums. Generally, private mortgage 

insurers require that borrowers meet higher credit standards than does 

FHA. So, to the extent that these new FHA borrowers would have obtained 

private mortgage insurance without the lower premiums, they are likely to 

have lower risk profiles than the average for all current FHA borrowers. At 

the same time, lowering up-front premiums is not likely to attract many 
Page 27 GAO-01-460 Mortgage Financing

additional higher-risk borrowers who would previously not have qualified 

for FHA-insured loans.16

Because HUD does not have adequate tools to handle the complexities of 

estimating the ultimate impact of policy changes on the volume of FHAinsured loans and the riskiness of those loans, these factors are not always 

considered in assessing the impact of policy changes. For example, 

assuming that the volume and riskiness of FHA-insured loans will not 

change, HUD estimates that the recent reductions in up-front premiums 

combined with the introduction of mortgage insurance cancellation 

policies will lower the estimated value of the Fund by almost $6 billion over 

the next 6 years. Because this estimate does not consider the possible 

changes in the volume of loans that will be insured and the riskiness of 

those loans, it is an estimate only of the direct impact rather than the full 

impact of policy changes. Similarly, a recent study presents estimates that 

lowering up-front premiums to 1.5 percent would result in an almost 

fivefold increase in the likelihood that cash inflows would be less than 

outflows over a random 10-year period.17 However, this study notes that it 

did not look at how these changes would affect the riskiness of new loans. 

The complexity of estimating the impact of policy changes on the Fund 

implies that economic models would be needed to reliably estimate the 

likely outcomes. The most likely sources for such models would be the 

studies that compute the economic value of the Fund; however, the models 

HUD and others have been using to assess the financial health of the Fund 

do not explicitly recognize the impact of policy changes on the economic 

value of the Fund. Instead, they assume that FHA's market share remains 

static.

Effect on Borrowers Although it is difficult to predict the overall impact of a change on the 

Fund's capital ratio and thus on FHA borrowers as a whole, different 

options would likely have different impacts on various FHA-insured 

borrowers. Some proposals would more likely benefit existing and future 

16 Most FHA borrowers finance their up-front premiums over the life of their loans 

(generally 30 years), rather than paying them up-front. As a result, lowering the up-front 

premiums would not substantially reduce the amount of cash required from borrowers at 

settlement. However, those borrowers who could not qualify for a mortgage because their 

monthly payments would have been too high relative to their income, might then qualify 

because the reduction in up-front premiums would lower the monthly payment.

17 See “Credit Risk, Capital, and FHA Mortgage Insurance,” by Charles A. Capone, Jr., 

forthcoming in the Journal of Housing Research (vol. 11, issue 2). 
Page 28 GAO-01-460 Mortgage Financing

FHA-insured borrowers, while others would benefit only future borrowers, 

and still others would benefit neither of these groups. One interpretation of 

the higher premiums that borrowers paid during the period in which the 

economic value of the fund has been rising is that borrowers during the 

1990s “overpaid” for their insurance. Some options for reducing the capital 

ratio, such as reinstituting distributive shares, would be more likely to 

compensate these borrowers. Paying distributive shares would benefit 

certain existing borrowers who voluntarily terminate their mortgages. If 

these policies continued into the future, they would also benefit future 

policyholders. Alternatively, reducing up-front premiums, reducing the 

number of years over which annual insurance premiums must be paid, or 

relaxing underwriting standards would tend to benefit only future 

borrowers. Policy options that propose to use some of FHA's capital 

resources for spending on other programs would benefit neither existing 

nor future FHA-insured borrowers, but would instead benefit the recipients 

of those programs receiving the new expenditures. For example, reducing 

the capital ratio by shifting funds from the Fund to subsidize multifamily 

housing may primarily benefit renters rather than single-family 

homeowners. However, over time such a policy could be sustained only so 

long as FHA borrowers continue to pay premiums higher than the cost to 

FHA of insuring single-family mortgages. 

Potential Impact of Options 

on the Federal Budget Is 

Difficult to Discern 

Because of the difficulty in reliably measuring the effect of most actions 

that could be taken either by the Secretary of HUD or the Congress on the 

Fund's capital ratio, we cannot precisely measure the effect of these 

policies on the budget.18 However, any actions taken by the Secretary or the 

Congress that influence the Fund's capital ratio will have a similar effect on 

the federal budget. Specifically, any proposal that results in a reduction in 

the Fund’s reserve, if not accompanied by a similar reduction in other 

government spending or by an increase in receipts, would result in either a 

reduction in the surplus or an increase in any existing deficit. 

If the Secretary or the Congress adopts policies, such as paying distributive 

shares or relaxing underwriting standards, that could reduce the 

profitability of the Fund, both the negative subsidy amount reported in 

FHA's budget submission and the Fund's reserve would be lower. Some of 

18 However, the Congressional Budget Office has begun building a model that it believes will 

allow it to forecast simulations and what-if analyses with the objective of making FHA's 

budget reporting more transparent and informative.
Page 29 GAO-01-460 Mortgage Financing

these policies—such as paying distributive shares—would affect FHA's 

cash flows immediately. Thus, the amount of money available for FHA to 

invest in Treasury securities would be lower. The Treasury, in turn, would 

have less money available for other purposes, and any overall surplus 

would decline or any deficit would rise. If the amounts of cash flowing out 

of the Fund exceeded current receipts, FHA would be required to redeem 

its investments in Treasury securities to make the required payments. The 

Treasury, then, would be required to either increase borrowing from the 

public or use general tax revenues to meet its financial obligations to FHA. 

In either case, any annual budget surplus would be lower or deficit higher. 

Conclusions At the end of fiscal year 1999, the Fund had a capital ratio that exceeded 2 

percent of FHA's insurance-in-force—the minimum required by law; 

however, whether the fund was actuarially sound is not so clear. Neither 

the statute nor HUD has established criteria to determine how severe of a 

stress the Fund should be able to withstand, that is, what constitutes 

actuarial soundness. Our results show that as of the end of fiscal year 1999, 

only the most severe circumstances that we analyzed would cause the 

current economic value of the Fund to fall below 0. 

One method of determining actuarial soundness would be to estimate the 

value of the Fund under various economic and other scenarios. In our 

analysis, the required minimum capital ratio of 2 percent appears sufficient 

to cover most of the adverse economic scenarios we tested, although it 

would not be possible to maintain the minimum under all scenarios. 

Nonetheless, we urge caution in concluding that the estimated value of the 

Fund today implies that the Fund could withstand the specified economic 

scenarios regardless of the future activities of FHA or the market. Our 

estimates and those of others are valid only under a certain set of 

conditions, including that loans FHA recently insured respond to economic 

conditions similarly to those it insured in the more distant past, and that 

cash inflows associated with future loans at least offset outflows 

associated with those loans. However, HUD is changing several policies 

that may affect the volume and quality of its future business. Further, 

adverse economic events cannot be predicted with certainty; therefore, we 

cannot attach a likelihood to any of the scenarios that we tested (even 

though we recognize that it is less likely that a severe economic downturn 

will affect the whole nation than one or two regions). It is instructive to 

remember in considering the uncertainty of the future, that the Fund had 

an even higher capital ratio in 1979 when the economic value of the Fund 

equaled 5.3 percent of insurance-in-force, but in little more than a decade—
Page 30 GAO-01-460 Mortgage Financing

after a national recession, the substitution of an up-front premium for 

annual insurance premiums, and regional real estate declines—the 

economic value of the Fund was negative. Thus, it is important to 

periodically reevaluate the actuarial soundness of the Fund.

Today, FHA knows more about the condition of the Fund but could still 

improve its evaluation of the impact that unexpected economic downturns 

and policy changes may have on the Fund. HUD has already taken some 

action that it estimates will lower the value of the Fund, including reducing 

up-front insurance premiums on newly insured mortgages. HUD has done 

so without the tools necessary to reliably measure the multiple impacts 

that these policies are likely to have. While the direct impact of policies 

that are likely to reduce the Fund's capital ratio can be estimated with the 

models used in the actuarial reviews, those models cannot isolate the 

indirect effects on the volume of loans insured by FHA and the riskiness of 

those loans. 

Matters for 

Congressional 

Consideration 

The Congress may want to consider taking action to amend the laws 

governing the Fund to specify criteria for determining when the Fund is 

actuarially sound. Because we believe that actuarial soundness depends on 

a variety of factors that could vary over time, setting a minimum or target 

capital ratio will not guarantee that the Fund will be actuarially sound over 

time. For example, if the Fund were comprised primarily of seasoned loans 

with known characteristics, a capital ratio below the current 2-percent 

minimum might be adequate, but under conditions such as those that 

prevail today, when the Fund is comprised of many new loans, a 2-percent 

ratio might be inadequate if recent and future loans perform considerably 

worse than expected. Thus, the Congress may want to consider defining 

the types of economic conditions under which the Fund would be expected 

to meet its commitments without borrowing from the Treasury.

Recommendations If the Congress decides that no further guidance is necessary, to better 

evaluate the health of the Fund and determine the appropriate types and 

timing of policy changes, we recommend that HUD develop criteria for 

measuring the actuarial soundness of the Fund. These criteria should 

specify the economic conditions that the Fund would be expected to 

withstand and may specify capital ratios currently consistent with those 

criteria. 
Page 31 GAO-01-460 Mortgage Financing

Because many conditions affect the adequacy of a given capital ratio, we 

recommend that the independent annual actuarial analysis give more 

attention to tests of the Fund's ability to withstand appropriate stresses. 

These tests should include more severe scenarios that capture worse-thanexpected loan performance that may be due to economic conditions and 

other factors, such as changes in policy and the conventional mortgage 

market.

To more fully assess the impact of policy changes that are likely to 

permanently affect the profitability of certain FHA-insured loans, we 

recommend that the Secretary of HUD develop better tools for assessing 

the impact these changes may have on the volume and riskiness of loans 

that FHA insures. Such analysis is particularly important where the policy 

change permanently affects certain loans, as in the case of underwriting 

and premium changes. Without a better analytical framework to assess the 

full impact of policy changes that permanently affect certain loans, we 

recommend that such changes be made in small increments so that their 

impact can be monitored and adjustments can be made over time.

Agency Comments and 

Our Evaluation

We provided a draft of this report to the Secretary of HUD for his review 

and comment. HUD agreed with the report's findings regarding the 

estimated value of the fund, and the ability of the fund to withstand 

moderately severe economic downturns that could lead to worse-thanexpected loan performance. However, HUD expressed concern that the 

report did not note the probability of the most stressful scenarios we tested 

and FHA's ability to react to adverse developments. HUD also thought our 

reference to the substantial decline in the capital ratio that occurred during 

the 1980s left a false impression that the Fund is currently in jeopardy. In 

addition, HUD expressed concern that the report did not fully recognize the 

improvements it has made in analyzing policy changes and monitoring the 

performance of the Fund and disagreed with our recommendations. HUD's 

letter is reproduced in appendix IV.

In response, we clarified that scenarios in which we extend historical 

adverse economic conditions more widely are less likely to occur. 

However, we cannot attribute a probability to any scenario we used. We 

also acknowledge that the annual actuarial reviews and the annual 

reestimates of the Fund required under the housing and credit reforms of 

1990 enable HUD to better monitor the performance of the Fund and, 

therefore, react to adverse developments. However, we remain concerned 

that HUD's analyses of policy changes do not fully recognize the impact 
Page 32 GAO-01-460 Mortgage Financing

that these policy changes may have on the volume of loans FHA will insure 

and the riskiness of those loans. We also disagree that the reference to the 

decline in the capital ratio experienced in the 1980s implies that the Fund is 

in jeopardy today. In fact, this example serves to illustrate that changes in 

the economy and HUD policy can have a dramatic impact on the value of 

the Fund. 

With regard to our recommendation that HUD develop criteria for 

measuring the actuarial soundness of the Fund, HUD seems to infer that we 

believe a static capital ratio should be the criterion for measuring actuarial 

soundness. We do not recommend a static capital ratio for measuring 

actuarial soundness. Rather, we believe that it is important to measure 

actuarial soundness under different economic and other scenarios; 

therefore, we recommend that HUD specify the conditions that the Fund 

would be expected to withstand. We revised this recommendation to make 

clear that the definition of actuarial soundness should consider the 

economic conditions that the Fund would be expected to withstand.

Regarding our recommendation that the independent annual actuarial 

analysis give more attention to tests of the Fund's ability to withstand 

appropriate stresses, HUD noted that it believed it was already complying 

with this recommendation and asked that our report define more 

specifically what tests are needed. In response, we clarified that the annual 

actuarial review should include more severe scenarios that capture worsethan-expected loan performance that may be due to economic conditions 

and other factors, such as changes in HUD policy and the conventional 

mortgage market. HUD's recent actuarial analysis included two 

scenarios—an interest rate spike scenario and a lower house price 

appreciation scenario—for testing the value of the Fund under a stressed 

economic state, and in neither scenario do house prices decline or 

unemployment rates rise.19

With regard to our recommendation concerning tools for assessing the 

impact of policy changes, HUD disagreed that any tools are needed beyond 

those that it already has. Specifically, HUD cites the annual analyses done 

in compliance with the Federal Credit Reform Act of 1990 and its annual 

actuarial reviews that already focus on policy changes. Further, HUD notes 

that it has made its program data more accessible for policy analysis 

19 These scenarios are in addition to the three forecasts of key economic variables provided 

by Standard & Poor's DRI that Deloitte did not consider to be stressed economic states.
Page 33 GAO-01-460 Mortgage Financing

through the creation of the Single Family Data Warehouse. However, we 

remain concerned that HUD does not have adequate tools for assessing the 

full impact that policy changes may have. Tools such as models for 

estimating the change in demand and the risk characteristics of future 

loans would enable HUD to better estimate the full impact that policy 

changes may have on the value of the Fund. HUD also disagreed with the 

idea that any policy actions it takes should be only incremental and 

reversible. We revised our recommendation to make clear that incremental 

changes are appropriate where a policy change permanently affects certain 

loans. 

Copies of this report will be distributed to interested congressional 

committees; the Honorable Mel Martinez, Secretary of the Department of 

Housing and Urban Development; the Honorable Mitchell E. Daniels, Jr., 

the Director of the Office of Management and Budget; and the Honorable 

Dan L. Crippen, the Director of the Congressional Budget Office. We will 

also make copies available to others on request.

If you or your staff have any questions about this report, please contact me 

at (202) 512-8678. Key contributors to this report are listed in appendix V. 

Thomas J. McCool

Managing Director, Financial Markets and

 Community Investment
Page 34 GAO-01-460 Mortgage Financing

Appendix I

Scope and Methodology ApApenednxidxeiIs

To estimate the economic value of the Federal Housing Administration's 

(FHA) Fund as of September 30, 1999, and its resulting capital ratio, we 

developed econometric and cash flow models. These models were based 

on models that we developed several years ago for this purpose. In 

developing the earlier models, we examined existing studies of the singlefamily housing programs of both the Department of Housing and Urban 

Development (HUD) and the Department of Veterans Affairs (VA); 

academic literature on the modeling of mortgage foreclosures and 

prepayments; and previous work that Price Waterhouse (now 

PricewaterhouseCoopers), HUD, VA, ourselves, and others had performed 

on modeling government mortgage programs. For our current analysis, we 

modified our previous models on the basis of our examination of work 

performed recently by PricewaterhouseCoopers, Deloitte & Touche, and 

others; discussions we held with analysts familiar with modeling mortgage 

foreclosures and prepayments; and program changes made by FHA since 

our previous work was performed. For these models, we used data 

supplied by FHA and Standard & Poor’s DRI, a private economic 

forecasting company. We also used information from FHA’s independent 

actuarial reviews in our analysis.

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 HUD’s A-43 data on the default and 

prepayment experience of FHA-insured home mortgage loans that 

originated from fiscal years 1975 through 1999. To test the validity of our 

econometric models, we examined how well the models predicted the 

actual rates of FHA's loan foreclosures and prepayments through fiscal 

year 1999. We found that our predicted rates closely resembled the actual 

rates. Next, we used our estimates of these relationships and forecasts of 

future economic conditions provided by Standard & Poor’s DRI to develop 

a baseline forecast of future loan foreclosures and prepayments for loans 

that were active at the end of fiscal year 1999. 

To estimate the net present value of future cash flows of the Fund under 

expected economic conditions, we used our forecast of future loan 

foreclosures and prepayments in conjunction with a cash flow model that 

we developed to measure the primary sources and uses of cash for loans 

that originated from fiscal years 1975 through 1999. Our cash flow 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 
Appendix I

Scope and Methodology

Page 35 GAO-01-460 Mortgage Financing

are actually forecasted to occur—into their 1999 present value equivalents. 

We then added the forecasted 1999 present values of the future cash flows 

to the current cash available to the Fund, which we obtained from 

documents used to prepare FHA's 1999 audited financial statements, to 

estimate the Fund's economic value and resulting capital ratio. A detailed 

discussion of our models and methodology for estimating the economic 

value and capital ratio of the Fund appears in appendix II.

To compare our estimates of the Fund's economic value and capital ratio 

with the estimates prepared for FHA by Deloitte & Touche, we reviewed 

Deloitte's report and met with its analysts and HUD officials to learn more 

about that study's methodology, data, and assumptions.

To determine the extent to which a capital ratio of 2 percent would allow 

the Fund to withstand worse-than-expected loan performance, we 

developed various scenarios for future economic conditions that we 

anticipated would result in substantially worse loan performance than we 

forecasted in our scenario using expected economic conditions. We based 

these scenarios on the economic conditions that led to episodes of 

relatively high foreclosure rates for FHA single-family loans in certain 

regions of the country at different times during the 1975 through 1999 

period and on those experienced nationally during the 1981-82 recession. 

We developed additional scenarios that extended the adverse regional 

economic conditions to larger sections of the country to analyze how well 

the Fund could withstand conditions even worse than what we had 

experienced in the past 25 years. We also developed some additional 

scenarios with even higher foreclosure rates to further analyze the Fund's 

ability to withstand adverse conditions.

Under each of the scenarios that we developed, we used our estimated 

relationships between foreclosure and prepayment rates and various 

explanatory factors, and the future economic conditions implied by the 

scenarios, to forecast future foreclosures and prepayments for loans that 

were active at the end of fiscal year 1999. We then used these forecasts, in 

conjunction with our cash flow model, to estimate the economic value and 

capital ratio of the Fund under each scenario. The difference between 

these estimates and our estimate under expected economic conditions 

shows whether each scenario is likely to result in a reduction of the Fund's 

economic value of more than 2 percent and, therefore, whether a 2-percent 

capital ratio is likely to be sufficient to allow the Fund to withstand the 

worse-than-expected loan performance associated with such a scenario.
Appendix I

Scope and Methodology

Page 36 GAO-01-460 Mortgage Financing

Our analysis of the adequacy of FHA’s capital ratio is limited to the 

performance of loans in FHA's portfolio as of the end of fiscal year 1999. 

That is, our analysis assesses the likelihood that an economic value of 2 

percent of the unamortized insurance-in-force would be sufficient to cover 

the excess of future payments over future cash inflows (on a net present 

value basis) on those loans if they perform worse than expected. Our 

analysis of the ability of the Fund to withstand various adverse economic 

conditions requires making the assumption that the adverse conditions 

would not also cause loans insured by FHA after fiscal year 1999 to be an 

economic drain on the Fund. Since the 1990 reforms, the cash flows 

associated with each year’s loans have been estimated to have a positive 

economic value, thereby adding to the economic value of the entire Fund. 

However, during adverse economic times, new loans might perform worse 

than loans that were insured by FHA during the 1990s. If the newly insured 

loans perform so poorly that they have a negative economic value, then the 

loss to the Fund in any of the adverse economic scenarios that we have 

considered would be greater than what we have estimated. Alternatively, if 

the newly insured loans have positive economic values, then the Fund 

would continue to grow.

To identify other factors, such as recent program and market changes, that 

could cause worse-than-expected loan performance, we reviewed the laws 

and regulations governing FHA’s insurance program, studied recent 

actuarial reviews of the Fund, and interviewed experts. We considered 

these other factors because the relationships estimated in our econometric 

models are based on historical relationships since 1975. As a result, these 

models might not capture the effects of recent changes in FHA programs or 

the conventional mortgage market on the likelihood that loans insured in 

the late 1990s will foreclose or prepay. In addition, our forecasts of future 

cash flows assume that FHA’s program and the private mortgage market 

will not change over the 30-year forecast period in any way that would 

affect FHA-insured loans originated through 1999.

To identify options for adjusting the size of the Fund and determining the 

impact that these options might have, we reviewed the laws and 

regulations governing FHA’s insurance program and proposals to use the 

Fund’s economic value or otherwise change FHA’s insurance program. 

Additionally, we interviewed experts both within and outside the federal 

government. When available, we collected HUD’s estimates of the impact 

of various options on the Fund and the estimates of other experts. To 

determine the impact of these changes on the federal budget, we relied on 
Appendix I

Scope and Methodology

Page 37 GAO-01-460 Mortgage Financing

our own experts as well as those at the Office of Management and Budget 

and the Congressional Budget Office.

We conducted our review from December 1999 to February 2001 in 

accordance with generally accepted government auditing standards.
Page 38 GAO-01-460 Mortgage Financing

Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund ApendxiI

We built econometric and cash flow models to estimate the economic value 

of HUD's FHA's Mutual Mortgage Insurance Fund (Fund) as of the end of 

fiscal year 1999. 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 1999 for each year from fiscal years 2000 to 2028 on 

the basis of assumptions stated in this appendix. We estimated equations 

from data covering fiscal years 1975 through 1999 that included all 50 states 

and the District of Columbia, but excluded U.S. territories.

Our econometric models used observations on loan years—that is, 

information on the characteristics and status of an insured loan during 

each year of its life—to estimate conditional foreclosure and prepayment 

probabilities.1

 These probabilities were estimated using observed patterns 

of prepayments and foreclosures in a large set of FHA-insured loans. More 

specifically, our model used logistic equations to estimate the logarithm of 

the odds ratio,2

 from which the probability of a loan's payment (or a loan's 

prepayment) in a given year can be calculated. These equations are 

expressed 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 loan's size, the geographic location of the house, and the number 

of years that the loan has been active. The results of the logistic 

regressions were used to estimate the probabilities of a loan being 

foreclosed or prepaid in each year.

FHA pays a claim on a foreclosed mortgage and sometimes, depending on 

the age of the loan, refunds a portion of the up-front premium when a 

mortgage prepays. These two actions contribute to cash outflows. Cash 

inflows are generated when FHA sells foreclosed properties and when 

borrowers pay mortgage insurance premiums. We forecasted the cash 

flows into and out of the Fund on the basis of our foreclosure and 

1

 These probabilities are conditional because they are subject to the condition that 

the loan has remained active until a given year.

2 If “P” is the probability that an event will occur, the “odds ratio” is defined as P/(1-

P). The logistic transformation is the natural logarithm of the odds ratio, or 

LN[P/(1-P)], of which the logistic regression provides an estimate. See G.S. 

Maddala, Limited Dependent Variables and Qualitative Variables in Econometrics

(Cambridge : Cambridge Univ. Press, 1983). Also see John H. Aldrich and Forrest 

D. Nelson, Linear Probability, Logit, and Probit Models (SAGE Publications: 

Beverly Hills, London, and New York, 1984), pp. 41-44.
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 39 GAO-01-460 Mortgage Financing

prepayment models and key economic variables. We then used the 

forecasted cash flows, including an estimate of interest that would be 

earned, and the Fund's capital resources to estimate the economic value of 

the Fund.

We prepared separate estimates for fixed-rate mortgages, adjustable rate 

mortgages (ARMs), and investor loans. The fixed-rate mortgages with 

terms of 25 years or more (long-term loans) were divided between those 

that refinanced and those that were purchase money mortgages (mortgages 

associated with home purchase). Separate estimates were prepared for 

each group of long-term loans. Likewise, investor loans were divided 

between mortgages that refinanced and the loans that were purchase 

money mortgages. We prepared separate estimates for each group of 

investor loans (refinanced and purchase money mortgages). A separate 

analysis was also prepared for loans with terms that were less than 25 years 

(short-term loans). 

A complete description of our models, the data that we used, and the 

results that we obtained is presented in detail in the following sections. In 

particular, this appendix describes (1) the sample data that we used; (2) our 

model specification and the independent variables in the regression 

models; (3) the model results; (4) the cash flow model, with emphasis on 

key economic variables; and (5) a sensitivity analysis that demonstrates the 

sensitivity of our forecasts to the values of some key variables.

Data and Sample 

Selection

For our analysis, we selected from FHA's computerized files a 10-percent 

sample of records of mortgages insured by FHA from fiscal years 1975 

through 1999 (1,465,852 loans). For the econometric models related to 

long-term, fixed-rate mortgages, we used 25 percent of the long-term loans 

in our sample. From the FHA records, we obtained information on the 

initial characteristics of each loan, such as the year of the loan's origination 

and the state in which the loan originated; LTV ratio; loan amount; and 

contract interest rates. We categorized the loans as foreclosed, prepaid, or 

active as of the end of fiscal year 1999.

To describe macroeconomic conditions at the national and state levels, we 

obtained data from Standard & Poor's DRI,3

 by state, on annual civilian 

3

 Formerly DRI/McGraw-Hill, Standard & Poor's DRI is a leading economic forecasting firm.
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 40 GAO-01-460 Mortgage Financing

unemployment rates and data from the 2000 Economic Report of the 

President on the implicit price deflator for personal consumption 

expenditures. We used Standard & Poor's DRI data on quarterly interest 

rates for 30-year mortgages on existing housing along with its forecast data, 

at the state level, on median house prices and civilian unemployment rates, 

and at the national level, on interest rates on 1- and 10-year U.S. Treasury 

securities.

Specification of the 

Model

People buy houses for consumption and investment purposes. Normally, 

people do not plan to default on loans. However, conditions that lead to 

defaults do occur. Defaults may be triggered by a number of events, 

including unemployment, divorce, or death. These events are not likely to 

trigger defaults 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 defaults.

Prepayments of home mortgages can also occur. These may be triggered 

by events such as declining interest rates, which prompts refinancing, and 

rising house prices, which prompts the take out of accumulated equity or 

the sale of the residence. Because FHA mortgages are assumable, the sale 

of a residence does not automatically trigger prepayment. For example, if 

interest rates have risen substantially since the time that the mortgage was 

originated, a new purchaser may prefer to assume the seller's mortgage.

We hypothesized that foreclosure behavior is influenced by, among other 

things, the (1) level of unemployment, (2) size of the loan, (3) value of the 

home, (4) current interest rates, (5) contract interest rates, (6) home equity, 

and (7) region of the country within which the home is located. We 

hypothesized that prepayment behavior is influenced by, among other 

things, the (1) difference between the interest rate specified in the 

mortgage contract and the mortgage rates generally prevailing in each 

subsequent year, (2) amount of accumulated equity, (3) size of the loan, and 

(4) region of the country in which the home is located.

Our first regression model estimated conditional mortgage foreclosure 

probabilities as a function of a variety of explanatory variables. In this 

regression, the dependent variable is a 0/1 indicator of whether a given loan 

was foreclosed in a given year. The outstanding mortgage balance, 

expressed in inflation-adjusted dollars, weighted each loan-year 

observation.
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 41 GAO-01-460 Mortgage Financing

Our foreclosure rates were conditional on whether the loan survives an 

additional year. We estimated conditional foreclosures in a logistic 

regression equation. Logistic regression is commonly used when the 

variable to be estimated is the probability that an event, such as a loan's 

foreclosure, will occur. We regressed the dependent variable (whose value 

is 1 if foreclosure occurs and 0 otherwise) on the explanatory variables 

previously listed.

Our second regression model estimated conditional prepayment 

probabilities. The independent variables included a measure that is based 

on the relationship between the current mortgage interest rate and the 

contract rate, the primary determinant of a mortgage's refinance activity. 

We further separated this variable between ratios above and below 1 to 

allow for the possibility of different marginal impacts in higher and lower 

ranges.

The variables that 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 and (2) property 

values can increase or decrease. 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.4

We computed the percentage of equity 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. For example, if the current estimated 

house price is $100,000, and the value of the mortgage at the current 

4

 When we discuss the likely effects of one of our explanatory variables, we are describing 

the marginal effects of that variable, while holding the effects of other variables constant. 
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 42 GAO-01-460 Mortgage Financing

interest rate is $80,000, then equity is .2 (20 percent), or 1-(80/100). To 

measure equity, we calculated the value of the mortgage as the present 

value of the remaining mortgage, evaluated at the current year's fixed-rate 

mortgage interest rate. We calculated the value of a property by 

multiplying the value of that property at the time of the loan’s origination by 

the change in the state's median nominal house price, adjusted for quality 

changes, between the year of origination and the current year.5

 Because the 

effects on foreclosure of small changes in equity may differ depending on 

whether the level of equity is large or small, we used a pair of equity 

variables, LAGEQHIGH and LAGEQLOW,6

 in our foreclosure regression. 

The effect of equity is lagged 1 year, as we are predicting the time of 

foreclosure, which usually occurs many months after a loan first defaults.

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 more 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 used a variable that measures book 

equity—the estimated property value less the amortized balance of the 

loan—instead of market equity. It is book value, not market value, that the 

borrower must pay to retire the debt.7

 Additionally, the important effect of 

interest rate changes on prepayment is captured by two other equity 

variables, RELEQHI and RELEQLO, which are sensitive to the difference 

between a loan's contract rate and the interest rate on 30-year mortgages 

available in the current year. These variables are described below.

5

 The estimated rate of appreciation in nominal median house prices, obtained from 

Standard & Poor's DRI, was revised downward by 2 percentage points per year to account 

for depreciation and the gradual improvement in the quality of the existing housing stock 

over time. Also, to ensure that our estimates were conservative, we subtracted an 

additional 1 percent annually from Standard & Poor's DRI’s forecasts. 

6

 Essentially, LAGEQHIGH takes the value of equity minus .2 if equity is greater than 20 

percent or 0 if equity is less than or equal to 20 percent. LAGEQLOW takes the value of 

equity if equity is 20 percent or less and .2 if equity is greater than 20 percent. 

7

 Similarly, for foreclosures within the ARM equations, we defined equity as book equity (the 

estimated property value less the amortized balance of the loan) and not market equity. The 

effects of interest rate changes in the ARM equations were estimated using a separate 

variable.
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 43 GAO-01-460 Mortgage Financing

LTV Ratio We included an additional set of variables in our regressions related to 

equity: the initial LTV ratio. We entered LTV as a series of dummy variables, 

depending on its size. Loans fit into eight discrete LTV categories. In some 

years, FHA measured LTV as the loan amount less mortgage insurance 

premium financed in the numerator of the ratio 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.

A borrower’s initial equity can be expressed as a function of LTV, so we 

anticipated that if LTV was an important predictor in an equation that also 

includes a variable measuring current equity, it would probably be 

positively related to the probability of foreclosure. One reason for 

including LTV is that it measures initial equity accurately. Our measures of 

current equity are less accurate because we do not have data on the actual 

rate of change in the mortgage loan balance or the actual rate of house 

price change for a specific house. 

Loans with higher LTVs are more likely to foreclose. For the long-term 

nonrefinanced equation, the ARM equation, and the short-term equation, 

we deleted the lower category of LTV loans. We expected LTV to have a 

positive sign in the foreclosure equations at higher levels of LTV. LTV in 

our foreclosure equations may capture the effects of income constraints. 

We were unable to include borrowers’ income or payment-to-income ratio 

directly because data on borrowers’ income were not available.8

 However, 

it seems likely that borrowers with little or no down payment (high LTV) 

are more likely to be financially stretched in meeting their payments and, 

therefore, more likely to default. The anticipated relationship between LTV 

and the probability of prepayment is uncertain. 

For some loan type categories, we used down payment information 

directly, rather than the series of LTV variables. We defined down payment 

to ensure that closing costs were included in the loan amount and excluded 

from the house price.

8

 We also did not know whether individual borrowers had subsequently acquired a second 

mortgage or other obligations that would affect prepayment or foreclosure probabilities. 
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 44 GAO-01-460 Mortgage Financing

Unemployment We used the annual unemployment rates for each state for the period from 

fiscal years 1975 through 1999 to measure the relative 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 high interest rates cause a higher monthly payment. However, in 

explaining the likelihood of prepayment, our model uses information on 

the level of current mortgage rates relative 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. In our 

prepayment regression, we defined two variables, RELEQHI and 

RELEQLO. 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. When currently available 

mortgage rates are lower than the contract interest rate, market equity 

exceeds book equity because the present value of the remaining payments 

evaluated at the current rate exceeds the present value of the remaining 

payments evaluated at the contract rate. 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 0/1 variables, REFIN and REFIN2, that take on a value of 1 

if a borrower had not taken advantage of a refinancing opportunity in the 

past and 0 otherwise. We defined a refinancing opportunity as having 

occurred if the interest rate on fixed-rate mortgages in any previous year in 

which a loan was active was at least 200 basis points9

 below the rate on the 

mortgage in any year up through 1994 or 150 basis points below the rate on 

9

 A basis point equals 1/100 of a percentage point. 
Appendix II

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Page 45 GAO-01-460 Mortgage Financing

the mortgage in any year after 1994.10 REFIN takes a value of 1 if the 

borrower had passed up a refinancing opportunity at least once in the past. 

REFIN2 takes on a value of 1 if the borrower had passed up two or more 

refinancing opportunities in the past. 

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 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. In this case, there might be a 

positive relationship, with the probability of prepayment being higher if the 

borrower fulfilled his/her anticipation and moved, thereby prepaying the 

loan. 

Another explanatory variable is the volatility of interest rates, INTVOL, 

which is 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, YC, in our prepayment 

estimates, which we calculated as the difference between the 1- and 10-

year Treasury rates of interest. We then subtracted 250 basis points from 

this difference and set differences that were less than 0 to 0. This variable 

10 Transaction costs associated with refinancing have fallen in recent years, making it more 

profitable than before to refinance at a smaller decrease in interest rates.
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Page 46 GAO-01-460 Mortgage Financing

measured the relative attractiveness of ARMs versus fixed-rate mortgages; 

the steeper the yield curve, the more attractive ARMs would be. When 

ARMs have low rates, borrowers with fixed-rate mortgages may be induced 

into refinancing into ARMs to lower their monthly payments. 

For ARMs, 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 0, while 

CHANGENEG measures how far the rate has decreased, with a maximum 

of 0. CAPPEDPOS measures how much farther the interest rate on the 

mortgage would rise, if prevailing interest rates in the market did not 

change, while CAPPEDNEG measures how much farther the mortgage’s 

rate would fall, if prevailing interest rates did not change. For example, if 

an ARM was originated at 7 percent and interest rates increased by 250 

basis points 1 year later, CHANGEPOS would equal 100 because FHA’s 

ARMs can increase by no more than 100 basis points in a year. 

CAPPEDPOS would equal 150 basis points, since the mortgage rate would 

eventually increase by another 150 basis points if market interest rates did 

not change, and CHANGENEG and CAPPEDNEG would equal 0. Because 

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 nine 0/1 variables to reflect the geographic distribution of FHA 

loans and included them in both regressions. Location differences may 

capture the effects of differences in borrowers’ income, 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 nine Bureau of the 

Census (Census) divisions on the basis of the state in which the borrower 

resided. The Pacific division was the omitted category; that is, the 

regression coefficients show how each of the regions was different from 

the Pacific division. We also created a variable, JUDICIAL, to indicate 

states that allowed judicial foreclosure procedures in place of nonjudicial 

foreclosures. We anticipated that the probability of foreclosure would be 

lower where judicial foreclosure procedures were allowed because of the 

greater time and expense required for the lender to foreclose on a loan.
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Page 47 GAO-01-460 Mortgage Financing

Loan Size To obtain an insight into the differential effect of relatively larger loans on 

mortgage foreclosures and prepayments, we assigned each loan to 1 of 10 

loan-size categorical variables (LOAN1 to LOAN10). The omitted category 

in our regressions was loans between $80,000 and $90,000, and results on 

loan size are relative to those loans between $80,000 and $90,000. All dollar 

amounts are inflation-adjusted and represent 1999 dollars. 

Number of Units The number of units covered by a single mortgage was a key determinate in 

deciding which loans were more likely to be investor loans. Loans were 

noted as investor loans if the LTV ratio was between specific values, 

depending on the year of the loan, or if there were two or more units 

covered by the loan. Once a loan was identified as an investor loan, we 

separated the refinanced loans from the purchase money mortgages and 

performed foreclosure and payoff analyses on each. For each of the 

investor equations, we used two dummy variables defined according to the 

number of units in the dwelling. LIVUNT2 has the value of 1 when a 

property has two dwelling units and a value of 0 otherwise. LIVUNT3 has a 

value of 1 when a property has three or more dwelling units and a value of 0 

otherwise. The missing category in our regressions was investors with one 

unit. Our database covers only loans with no more than four units. 

Policy Year and Refinance 

Indicator

To capture the time pattern of foreclosures and prepayments (given the 

effects of equity and the other explanatory variables), we defined seven 

variables on the basis of the number of years that had passed since the year 

of the loan’s origination. We refer to these variables as YEAR1 to YEAR7 

and set them equal to 1 during the corresponding policy year and 0 

otherwise. Finally, for those loan type categories for which we did not 

estimate separate models for refinancing loans and nonrefinancing loans, 

we created a variable called REFINANCE DUMMY to indicate whether a 

loan was a refinancing loan.

Table 4 summarizes the variables that we used to predict foreclosures and 

prepayments. Table 5 presents mean values for our predictor variables for 

each mortgage type for which we ran a separate regression. 
Appendix II

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Page 48 GAO-01-460 Mortgage Financing

Table 4: Variable Names and Descriptions

Variable name Variable description

Loan size dummy variables

LOAN1 1 if loan amount is less than $40,000, else 0

LOAN2 1 if loan amount is $40,000 or above but below $50,000, else 0

LOAN3 1 if loan amount is $50,000 or above but below $60,000, else 0

LOAN4 1 if loan amount is $60,000 or above but below $70,000, else 0

LOAN5 1 if loan amount is $70,000 or above but below $80,000, else 0

LOAN6 1 if loan amount is $80,000 or above but below $90,000, else 0

LOAN7 1 if loan amount is $90,000 or above but below $100,000, else 0

LOAN8 1 if loan amount is $100,000 or above but below $110,000, else 0

LOAN9 1 if loan amount is $110,000 or above but below $130,000, else 0

LOAN10 1 if loan amount is at least $130,000, else 0

Economic variables

LOGINT Log of the contract mortgage interest rate

REFINANCE DUMMY 1 if the loan is a refinancing loan, else 0

RELEQLO The ratio of the market value of the mortgage to the book value if the market 

value is below the book value, else 1

RELEQHI The ratio of the market value of the mortgage to the book value if the market 

value is above the book value, else 1

REFIN 1 if, in at least 1 previous year, the mortgage interest rate had been at least 

200 basis points below the contract rate in any year prior to 1995 or 150 basis 

points below the contract rate after 1994 and the borrower had not 

refinanced, else 0

REFIN2 1 if, in at least 2 previous years, the above situation prevailed, else 0

INTVOL The volatility of mortgage rates, defined as the standard deviation of 30-year 

fixed-rate mortgage interest rates over the previous 12 months

YC The slope of the yield curve, defined as the difference between 1- and 10-

year U.S. Treasury interest rates minus 250 basis points, but not less than 0

LIVUNT2 1 if the property has two housing units, else 0

LIVUNT3 1 if the property has three or more housing units, else 0

LAGUNEMP The log of the previous year’s unemployment rate in each state

JUDICIAL 1 if state allowed judicial foreclosure (list of states varies by year), else 0

Policy year dummy variables

YEAR1 1 if in loan’s first year, else 0 

YEAR2 1 if in loan’s second year, else 0 

YEAR3 1 if in loan’s third year, else 0 

YEAR4 1 if in loan’s fourth year, else 0 

YEAR5 1 if in loan’s fifth year, else 0 
Appendix II

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Page 49 GAO-01-460 Mortgage Financing

YEAR6 1 if in loan’s sixth year, else 0 

YEAR7 1 if in loan’s seventh year, else 0

Loan-to-value dummy variables

LTV0 1 if LTV equals 0, assumed missing data, else 0 

LTV1 1 if LTV is above 0 and less than 60, else 0 

LTV2 1 if LTV is greater than or equal to 60, but less than 85, else 0

LTV3 1 if LTV is greater than or equal to 85, but less than 92, else 0

LTV4 1 if LTV is greater than or equal to 92, but less than 96, else 0

LTV5 1 if LTV is greater than or equal to 96, but less than 98, else 0

LTV6 1 if LTV is greater than or equal to 98, but less than 100, else 0

LTV7 1 if LTV is greater than or equal to 100, but less than 102, else 0

Equity variables

LAGEQLOW The lagged value of market 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 or equal to 20 

percent, else .2

LAGEQHIGH The lagged value of market 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 .2) if equity is greater than 20 

percent, else 0

BOOKNEG The lagged value of book equity (defined as 1 minus the ratio of the 

amortized loan balance to the current estimated house price) if equity is less 

than or equal to 20 percent, else .2

BOOKPOS The lagged value of book equity (defined as 1 minus the ratio of the 

amortized loan balance to the current estimated house price minus .2), if 

equity is greater than 20 percent, else 0

CHANGEPOS The amount by which the interest rate of an ARM has increased since 

origination, with a minimum of 0

CHANGENEG The amount by which the interest rate of an ARM has decreased since 

origination, with a maximum of 0

CAPPEDPOS The amount by which the interest rate of an ARM could still rise, if prevailing 

interest rates in the market did not change, with a minimum of 0

CAPPEDNEG The amount by which the interest rate of an ARM could still decline, if 

prevailing interest rates in the market did not change, with a maximum of 0

DOWNPAY The down payment, expressed as a percentage of the purchase price of the 

house. Closing costs were excluded from the house price and included in the 

loan amount

Census division dummy variables

DV_Aa 1 if the loan is in the Mid-Atlantic states (NY, PA, NJ), else 0

DV_E 1 if the loan is in the east south central states (KY, TN, AL, MS), else 0

DV_G 1 if the loan is in the west north central states (MN, MO, IA, NB, KS, SD, ND), 

else 0

(Continued From Previous Page)

Variable name Variable description
Appendix II

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Page 50 GAO-01-460 Mortgage Financing

a

 DV = Division. 

Table 5: Means of Predictor Variables

DV_M 1 if the loan is in the Mountain states (CO, UT, AZ, NM, NV, ID, WY, MT), else 

0

DV_N 1 if the loan is in the New England states (MA, CT, RI, NH, ME, VT), else 0

DV_R 1 if the loan is in the east north central states (IL, MI, OH, IN, WI), else 0

DV_S 1 if the loan is in the South Atlantic states (GA, NC, SC, VA, MD, DC, DE, 

WV), else 0

DV_W 1 if the loan is in the west south central states (TX, OK, LA, AR), else 0

(Continued From Previous Page)

Variable name Variable description

Loan type

Predictor

variable name Long-term FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance

Loan size dummy variables

LOAN1 0.0635 0.0160 0.1531 0.0044 0.0617 0.0267

LOAN2 0.0860 0.0355 0.1253 0.0148 0.0789 0.0504

LOAN3 0.1197 0.0648 0.1369 0.0336 0.1038 0.0829

LOAN4 0.1338 0.1043 0.1391 0.0577 0.1165 0.1175

LOAN5 0.1292 0.1294 0.1216 0.0849 0.1253 0.1337

LOAN6 0.1130 0.1434 0.1034 0.1087 0.1189 0.1293

LOAN7 0.0980 0.1362 0.0774 0.1231 0.1102 0.1102

LOAN8 0.0862 0.1171 0.0575 0.1228 0.0886 0.0858

LOAN9 0.1033 0.1461 0.0582 0.2032 0.1070 0.1272

LOAN10 0.0673 0.1070 0.0276 0.2468 0.0891 0.1363

Economic variables

LOGINT -2.3773 -2.4890 -2.4165 -2.6864 -2.3025 -2.5168

REFINANCE DUMMY - - 0.3650 0.1088 - -

RELEQHI 1.0613 1.0535 1.0286 - 1.0793 1.0461

RELEQLO 0.9450 0.9855 0.9745 - 0.9601 0.9845

REFIN 0.1174 0.0506 0.1082 0.0734 0.1892 0.0453

REFIN2 0.0779 0.0237 0.0734 0.0281 0.1302 0.0240

LIVUNT2 - - - - 0.3085 0.2396

LIVUNT3 - - - - 0.0859 0.0944
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Page 51 GAO-01-460 Mortgage Financing

LAGUNEMP -2.8063 -2.8870 -2.8379 -2.9155 -2.7788 -2.9044

Policy year dummy variables

YEAR1 0.1514 0.2527 0.1634 0.2453 0.1363 0.2729

YEAR2 0.1384 0.1993 0.1509 0.2299 0.1299 0.2048

YEAR3 0.1227 0.1501 0.1354 0.1820 0.1185 0.1495

YEAR4 0.1054 0.1285 0.1210 0.1206 0.1043 0.1228

YEAR5 0.0873 0.1059 0.1047 0.0850 0.0900 0.0972

YEAR6 0.0734 0.0903 0.0911 0.0597 0.0784 0.0817

YEAR7 0.0603 0.0431 0.0628 0.0337 0.0672 0.0435

Loan-to-value dummy variables

LTV0 0.0327 0.7301 0.2551 0.0555 0.0099 0.2330

LTV1 0.0097 0.0067 0.0620 0.0017 0.0054 0.0064

LTV2 0.0842 0.0621 0.2366 0.0517 0.2321 0.6263

LTV3 0.0976 0.0892 0.0970 0.1231 0.5280 0.1027

LTV4 0.2038 0.0654 0.1146 0.2898 0.0689 0.0158

LTV5 0.1937 0.0326 0.0770 0.3673 0.0526 0.0093

LTV6 0.1683 0.0025 0.0855 0.0464 0.0463 0.0009

LTV7 0.1476 0.0081 0.0576 0.0518 0.0411 0.0036

LTV8 0.0624 0.0034 0.0146 0.0126 0.0157 0.0019

Equity variables

LAGEQLOW 0.1226 0.0718 0.1649 - 0.1518 0.1429

LAGEQHIGH 0.1049 0.0131 0.1470 - 0.1068 0.0412

BOOKNEG 0.1312 0.0943 0.1628 0.1142 0.1652 0.1628

BOOKPOS 0.0903 0.0153 0.1438 0.0112 0.1063 0.0386

CHANGEPOS - - - 0.8844 - -

CHANGENEG - - - -0.4940 - -

CAPPEDPOS - - - 0.1462 - -

CAPPEDNEG - - - -0.0860 - -

DOWNPAY - 0.0337 - - - 0.1173

Census division dummy variables

DV_Aa 0.0725 0.0536 0.0757 0.0578 0.1579 0.1181

DV_E 0.0737 0.0394 0.0890 0.0454 0.0499 0.0713

DV_G 0.0874 0.1063 0.1242 0.1036 0.0700 0.0796

DV_M 0.1344 0.1932 0.1286 0.1377 0.1418 0.1708

DV_N 0.0098 0.0137 0.0077 0.0320 0.0274 0.0294

(Continued From Previous Page)

Loan type

Predictor

variable name Long-term FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance
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Page 52 GAO-01-460 Mortgage Financing

a

ARM = Adjustable rate mortgage; DV = Division; FRM = Fixed-rate mortgage. 

Estimation Results As previously described, we used logistic regressions to model loan 

foreclosures and prepayments as a function of a variety of predictor 

variables. We estimated separate regressions for fixed-rate purchase 

money mortgages (and refinanced loans) with terms over and under 25 

years, ARMs, and investor loans. We used data on loan activity throughout 

the life of the loans for loans originated from fiscal years 1975 through 

1999. The outstanding loan balance of the observation weighted the 

regressions. 

The logistic regressions estimated the probability of a loan being 

foreclosed or prepaid in each year. The standard errors of the regression 

coefficients are biased downward because the errors in the regressions are 

not independent. The observations are on loan years, and the error terms 

are correlated because the same underlying loan can appear several times. 

However, we did not view this downward bias as a problem because our 

purpose was to forecast the dependent variables, not to test hypotheses 

concerning the effects of independent variables. 

In general, our results are consistent with the economic reasoning that 

underlies our models. Most importantly, the probability of foreclosure 

declines as equity increases, and the probability of prepayment increases 

as the current mortgage interest rate falls below the contract mortgage 

interest rate. As shown in tables 6 and 7, both of these effects occur in 

each regression model and are very strong. These tables present the 

estimated coefficients for all of the predictor variables for the foreclosure 

and prepayment equations.

Table 6 shows our foreclosure regression results. As expected, the 

unemployment rate is positively related to the probability of foreclosure 

and negatively related to the probability of prepayment. Our results also 

DV_P 0.1425 0.1589 0.0726 0.2050 0.1471 0.1305

DV_R 0.1164 0.0822 0.1315 0.1711 0.1300 0.1362

DV_S 0.2060 0.2152 0.1575 0.2043 0.1706 0.1792

DV_W 0.1574 0.1375 0.2132 0.0432 0.1054 0.0848

(Continued From Previous Page)

Loan type

Predictor

variable name Long-term FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance
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Page 53 GAO-01-460 Mortgage Financing

indicate that generally the probability of foreclosure is higher when LTV 

and contract interest rate are higher. The overall goodness of fit was 

satisfactory: Chi-Square statistics were significant on all regressions at the 

0.01-percent level. 

Because the coefficients from a nonlinear regression can be difficult to 

interpret, we transformed some of the coefficients for the long-term, 

nonrefinanced, fixed-rate regressions into statements about changes in the 

probabilities of foreclosure and prepayment. Overall conditional 

foreclosure probabilities for this mortgage type are estimated to be about 

0.5 percent.11,12 In other words, on average, there is a 1⁄2 of a 1-percent 

chance for a loan of this type to result in a claim payment in any particular 

year.13 By holding other predictor variables at their mean values, we can 

describe the effect on the conditional foreclosure probability of changes in 

the values of predictor variables of interest. For example, if the average 

value of the unemployment rate were to increase by 1 percentage point 

from its mean value (in our sample) of about 6 percent to about 7 percent, 

the conditional foreclosure probability would increase by about 20 percent 

(from 0.5 percent to about 0.6 percent). Similarly, a 1-percentage-point 

increase in the mortgage contract rate from its mean value of about 9.25 to 

about 10.25 would also raise the conditional foreclosure probability by 20 

percent (from about 0.5 percent to about 0.6 percent). Values of 

homeowners' equity of 10 percent, 20 percent, 30 percent, and 40 percent 

result in conditional foreclosure probabilities of 0.8 percent, 0.7 percent, 

0.5 percent, and 0.3 percent, respectively, illustrating the importance of 

increased equity in reducing the probability of foreclosure. 

Table 7 shows our prepayment regression results. The overall conditional 

prepayment probability for long-term, fixed-rate mortgages is estimated to 

be 4.8 percent. This means that, in any particular year, about 5 percent of 

11 The conditional foreclosure probability is calculated as F(Z) = EXP(Z)/[1+EXP(Z)], 

where Z = Σι (Xi*Bi), where Xi refers to the mean value of the ith explanatory variable and the 

Bi

s are the estimated coefficients. 

12 Conditional foreclosure probabilities for the other mortgage types were estimated as 

follows: long-term, fixed-rate, refinancing mortgages (0.3); short-term, fixed-rate mortgages 

(0.2); ARMs (0.3); investor, nonrefinancing mortgages (0.6); and investor, refinancing 

mortgages (0.2).

13 This average is for the dollar worth of a loan, not the number of loans. 
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Page 54 GAO-01-460 Mortgage Financing

the loan dollars outstanding will prepay, on average.14 Prepayment 

probability is quite sensitive to the relationship between the contract 

interest rate and the currently available mortgage rates. We modeled this 

relationship using RELEQHI and RELEQLO. Holding other variables at 

their mean values, if the spread between mortgage rates available in each 

year and the contract interest rate widened by one percentage point, the 

conditional prepayment probability would increase by about 80 percent to 

8.6 percent. 

Table 6: Coefficients From Foreclosure Equations and Summary Statistics

14 Conditional prepayment probabilities for the other mortgage types were estimated as 

follows: long-term, fixed-rate, refinancing mortgages (7.7); short-term, fixed-rate mortgages 

(5.9); ARMs (8.2); investor, nonrefinancing mortgages (5.3); and investor, refinancing 

mortgages (6.6).

Loan type

Predictor variable name

Long-term

FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance

INTERCEPT 2.8424 8.4917 5.1918 5.7426 4.4798 6.1160

Loan size dummy variables

LOAN1 0.4559 0.2015 0.6280 0.3699 0.2301 0.1214

LOAN2 0.2089 0.3401 0.3577 0.5417 0.1367 0.4806

LOAN3 0.1238 0.1857 0.2741 0.4112 0.0957 0.0825

LOAN4 0.0630 0.0670 0.1755 0.1728 0.0019 -0.1074

LOAN5 -0.0077 0.1196 -0.0346 0.0389 0.1093 0.1611

LOAN7 0.0533 0.0941 0.0829 -0.0570 -0.0522 -0.0088

LOAN8 -0.0116 0.2417 0.0100 -0.0213 -0.0226 0.3838

LOAN9 0.0499 0.3755 0.3107 -0.0142 -0.1076 0.2515

LOAN10 0.1640 0.6596 0.2550 -0.0841 0.1166 0.5903

Economic variables

LOGINT 1.7604 2.8065 3.3779 1.3074 2.5642 2.3067

REFINANCE DUMMY - - -0.1033 0.0806 - -

REFIN 0.2757 0.1427 -0.0690 - 0.3024 0.2010

REFIN2 -0.0467 - -0.1968 - 0.1159 -

LIVUNT2 - - - - 0.2031 -0.6954

LIVUNT3 - - - - 0.3245 -0.5352

LAGUNEMP 1.1322 1.8867 1.2634 1.1528 1.1581 1.3849
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INTVOL 0.0661 -0.2651 0.2815 -1.8350 0.1054 -0.4593

Policy year dummy variables

YEAR1 -3.6549 -4.2892 -3.9423 -5.1043 -3.4559 -3.7991

YEAR2 -1.1583 -1.5378 -1.6170 -1.6688 -0.6838 -1.5670

YEAR3 -0.1734 -0.3399 -0.5061 -0.3611 0.2215 -0.5058

YEAR4 0.1139 -0.0013 -0.2101 0.1190 0.3735 -0.1317

YEAR5 0.2077 0.1734 -0.1072 0.3006 0.4455 -0.1305

YEAR6 0.1868 0.0751 -0.0328 0.3101 0.4040 0.1324

YEAR7 0.1154 -0.0667 -0.0601 0.0950 0.2865 0.0287

Loan-to-value dummy variables

LTV0 0.5864 -0.0349 1.3391 -0.7377 0.0208 0.2826

LTV1 - - - - 0.2383 -

LTV2 -0.0521 - 0.9851 -0.7269 0.3093 -

LTV3 0.2225 - 1.2587 -1.0359 0.3037 -

LTV4 0.3585 - 1.5278 -0.8733 0.2516 -

LTV5 0.4427 - 1.7433 -0.8449 0.1997 -

LTV6 0.4746 - 1.8241 -0.8075 0.2456 -

LTV7 0.4290 - 1.7740 -1.0976 0.3345 -

LTV8 0.4634 - 1.4832 -1.1230 - -

Equity variables

DOWNPAY - 0.1062 - - - -0.3661

LAGEQLOW -1.5913 -1.7065 -1.3388 - -1.7707 -0.9796

LAGEQHIGH -3.9061 -4.8967 -3.4301 - -4.0435 -8.4771

BOOKNEG - - - -3.3058 - -

BOOKPOS - - - -7.8496 - -

CHANGENEG - - - -0.1630 - -

CHANGEPOS - - - -0.2325 - -

CAPPEDNEG - - - 0.4445 - -

CAPPEDPOS - - - 0.0120 - -

Census division dummy variables

DV_A a -0.0961 -0.6324 0.0873 -0.7830 -0.3807 0.1808

DV_E -0.2442 -0.6969 0.0282 -1.0519 0.1646 -0.3263

DV_G 0.0559 -0.4792 0.1847 -1.1353 0.2876 -0.3948

DV_M 0.3434 -0.4969 0.4345 -0.7531 0.6335 -0.2241

DV_N 0.2225 0.1393 1.0141 -0.2386 0.4703 1.0258

(Continued From Previous Page)

Loan type

Predictor variable name

Long-term

FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 56 GAO-01-460 Mortgage Financing

a

ARM = Adjustable rate mortgage; DV = Division; FRM = Fixed-rate mortgage.

Table 7: Coefficients From Prepayment Equations and Summary Statistics

DV_R -0.0896 -0.7246 -0.0257 -0.6189 -0.1482 -0.5150

DV_S 0.1450 -0.3786 0.1830 -0.4121 0.3052 -0.1798

DV_W 0.3436 -0.3450 0.5660 -0.8390 0.7350 -0.2109

JUDICIAL -0.1350 -0.2168 -0.0671 -0.3836 -0.1600 -0.6095

Summary statistics

Percentage of concordant pairs 76.1 82.6 78.2 80.0 78.4 83.0

Percentage of tied pairs 3.6 3.3 9.1 3.1 2.7 4.4

Number of unweighted 

observations

1,526,825 503,253 498,723 473,573 660,253 52,715

(Continued From Previous Page)

Loan type

Predictor variable name

Long-term

FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance

Loan type

Predictor variable name

Long-term

FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance

INTERCEPT -16.4264 -18.1645 -24.7363 -5.2631 -16.9717 -16.4240

Loan size dummy variables

LOAN1 -0.4966 -0.7217 -0.5502 -0.5199 -0.6714 -0.5439

LOAN2 -0.3867 -0.5551 -0.3690 -0.4400 -0.4162 -0.2566

LOAN3 -0.2690 -0.3367 -0.2361 -0.3412 -0.2607 -0.1642

LOAN4 -0.1513 -0.2250 -0.1493 -0.2173 -0.1544 -0.0420

LOAN5 -0.0965 -0.1058 -0.0535 -0.1171 -0.0624 -0.0518

LOAN7 0.0786 0.0739 0.0717 0.1057 0.0866 0.0984

LOAN8 0.1645 0.1680 0.1333 0.1553 0.1433 0.1179

LOAN9 0.2682 0.2349 0.2028 0.2360 0.2433 0.2469

LOAN10 0.3601 0.3576 0.2155 0.3823 0.3287 0.3947

Economic variables

JUDICIAL - - - 0.0834 - -

RELEQHI 8.6248 10.6524 10.8280 - 6.5717 9.7379

RELEQLO 4.0974 0.5224 9.9514 - 6.8953 1.1596

REFINANCE DUMMY - - 0.1667 0.0511 - -
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 57 GAO-01-460 Mortgage Financing

REFIN -0.4126 -0.7985 -0.4159 - -0.2148 -0.6270

REFIN2 -0.9690 - -0.4800 - -0.8893 -

LIVUNT2 - - - - -0.2852 -0.3853

LIVUNT3 - - - - -0.3735 -0.3973

LAGUNEMP -0.3093 -0.9917 -0.3465 -1.3883 -0.3207 -0.6892

INTVOL -0.1532 -0.9027 0.0953 -1.4628 0.2270 -0.4564

YC 0.6490 0.9190 1.0536 -1.9892 0.9197 0.7492

Policy year dummy variables

YEAR1 -1.8664 0.0919 -1.3950 -1.7499 -1.5846 -0.0012

YEAR2 -0.3667 0.8526 -0.2351 -0.0641 -0.3511 0.8935

YEAR3 0.1074 0.9118 0.0214 0.2971 -0.0011 0.9970

YEAR4 0.2406 0.6924 0.0387 0.2847 0.1072 0.7482

YEAR5 0.1514 0.4692 0.0234 0.3413 0.0246 0.7789

YEAR6 0.0957 0.4168 -0.0102 0.2567 -0.0519 0.6648

YEAR7 0.2151 0.2470 0.0501 0.2376 0.2114 0.4584

Loan-to-value dummy variables

LTV0 0.0623 0.8115 0.2864 0.4611 -0.3276 0.0329

LTV1 -0.1218 - 0.0824 - -0.2461 -

LTV2 -0.0816 0.3427 0.2249 -0.2133 -0.3234 -

LTV3 -0.0370 0.4700 0.2172 -0.1507 -0.0841 -

LTV4 -0.0471 0.4921 0.2534 -0.1352 -0.2134 -

LTV5 -0.1297 0.4100 0.1665 -0.1460 -0.2729 -

LTV6 -0.1679 0.9448 0.1273 -0.4552 -0.3270 -

LTV7 -0.2416 0.7392 0.0910 -0.5858 -0.3709 -

LTV8 - 0.7018 - -0.4581 - -

Equity variables

BOOKNEG 1.3572 1.1104 0.8176 2.2369 1.2333 1.1330

BOOKPOS 0.7731 1.9607 1.3009 1.1137 0.6994 3.3660

CHANGENEG - - - 0.1549 - -

CHANGEPOS - - - -0.1754 - -

CAPPEDNEG - - - -0.2042 - -

CAPPEDPOS - - - -0.1181 - -

DOWNPAY - - - - - -1.7804

Census division dummy variables

DV_A a -0.4397 -0.3413 -0.3437 -0.5644 -0.2616 -0.4401

(Continued From Previous Page)

Loan type

Predictor variable name

Long-term

FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 58 GAO-01-460 Mortgage Financing

a

ARM = Adjustable rate mortgage; DV = Division; FRM = Fixed-rate mortgage.

Model Predictions for 

Historical Period

To test the validity of our model, we examined how well the model 

predicted actual patterns of FHA’s foreclosure and prepayment rates 

through fiscal year 1999. Using a sample of 10 percent of FHA’s loans made 

from fiscal years 1975 to 1999, we found that our predicted rates closely 

resembled actual rates. 

To predict the probabilities of foreclosure and prepayment in the historical 

period, 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 year from a loan’s origination through 

fiscal year 1999. If our model predicted foreclosure or prepayment in any 

year, we determined the loan’s balance during that year to indicate the 

dollar amount associated with the foreclosure or prepayment. We 

estimated cumulative foreclosure and prepayment rates by summing the 

predicted claim and prepayment dollar amounts for all loans originated in 

each of the fiscal years 1975 through 1999. We compared these predictions 

with the actual cumulative (through fiscal year 1999) foreclosure and 

prepayment rates for the loans in our sample. Figure 4 compares actual 

and predicted cumulative foreclosure rates, and figure 5 compares actual 

and predicted cumulative prepayment rates. 

DV_E -0.1071 0.2771 0.1027 -0.1597 -0.0949 0.0914

DV_G 0.1191 0.2663 0.0900 -0.4870 0.0932 0.1025

DV_M 0.1169 0.4774 0.2433 0.0334 0.0118 0.3155

DV_N -0.2030 -0.4385 0.0817 -0.6094 -0.0892 -0.0299

DV_R 0.0951 0.3203 0.2295 -0.2247 0.1049 0.2867

DV_S -0.2746 -0.0977 -0.1176 -0.5520 -0.2545 -0.1784

DV_W -0.3377 0.0109 -0.2565 -0.4196 -0.3003 -0.0208

Summary statistics

Percentage of concordant pairs 78.5 72.5 73.7 74.1 76.3 73.3

Percentage of tied pairs 0.5 0.8 0.7 0.5 0.6 0.8

Number of unweighted 

observations

1,526,825 503,253 498,723 473,573 660,253 52,715

(Continued From Previous Page)

Loan type

Predictor variable name

Long-term

FRMa

Long-term

FRM refinance

Short-term

FRM ARMa Investor

Investor

refinance
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 59 GAO-01-460 Mortgage Financing

Figure 4: Cumulative Foreclosure Rates by Book of Business for 30-Year, Fixed-Rate, Nonrefinanced, Mortgages; Actual and 

Predicted, Fiscal Years 1975-99 

Percentage terminating in foreclosure

0

5

10

15

20

25

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999

Fiscal year of origination

Predicted

Actual
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 60 GAO-01-460 Mortgage Financing

Figure 5: Cumulative Prepayment Rates by Book of Business, for 30-Year, Fixed-Rate, Nonrefinanced, Mortgages: Actual and 

Predicted, Fiscal Years 1975-99

Estimation of the 

Economic Value of the 

Fund

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.” We obtained 

information on the capital resources of the Fund from documents used to 

prepare FHA’s audited financial statements. These capital resources were 

reported to be $14.3 billion.

To estimate the net present value of future cash flows of the Fund, we 

constructed a cash flow model to estimate the five primary future outflows 

and inflows of cash through 2028 resulting from the books of business 

written from fiscal years 1975 through 1999. Cash flows out of the fund 

from payments associated with claims on foreclosed properties, refunds of 

up-front premiums on mortgages that are prepaid, and administrative 

Percentage terminating in prepayment

0

10

20

30

40

50

60

70

80

90

1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999

Fiscal year of origination

Predicted

Actual
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 61 GAO-01-460 Mortgage Financing

expenses for management of the program. Cash flows into the fund from 

income from mortgagees' insurance premiums and from the net proceeds 

from the sale of foreclosed properties.

To estimate the Fund's cash flow, we first forecasted, for active loans at the 

end of 1999, the dollar value of loans predicted to foreclose or prepay in 

any year through 2028. From those estimates, we derived estimates of the 

outstanding principal balances for the loans remaining active for each year 

in the forecast period. Our cash flow model used these estimates of 

foreclosure and prepayment dollars and outstanding principal balances to 

derive estimates of each of the primary cash flows.

We forecasted future loan activity (foreclosures and prepayments) on the 

basis of the regression results described above and forecasts of the key 

economic and housing market variables made by Standard & Poor's DRI. 

Standard & Poor's DRI forecasts the median sales price of existing housing, 

by state and year, through fiscal year 2005. We assumed that after 2005 

those prices would rise at 3 percent per year. In creating the borrower's 

equity variable, we used DRI forecasts of existing housing prices by state 

and subtracted 2 percentage points per year to adjust for improvements in 

the quality of housing over time and the depreciation of individual housing 

units. We also subtracted another 1 percentage point per year from the 

company’s forecasts, to be conservative. We made similar adjustments to 

our assumed value of median house price change for the years beyond the 

range of these forecasts. We used DRI forecasts of each state’s 

unemployment rate and assumed that rates from fiscal year 2026 on would 

equal the rates in 2025. We also used Standard & Poor's DRI forecasts of 

interest rates on 30-year mortgages and 1- and 10-year Treasury securities. 

Using the results of the econometric model, the cash flow model estimates 

cash flows for each policy year through the life of a mortgage. An 

important component of the model is converting all income and expense 

streams—regardless of the period in which they actually occurred—into 

1999 present value dollars. We applied discount rates to match as closely as 

possible the rate of return FHA likely earned in the past or would earn in 

the future from its investment in Treasury securities.15 As an 

15 Actual rates vary by the specific date on which the investment is made and the length of 

maturity of the note. Precise data on the length of maturity of FHA's investments were 

unavailable, but we estimated the average to be approximately 7 years and used this 

estimate as the basis for our selection of discount rates.
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 62 GAO-01-460 Mortgage Financing

approximation of what FHA earned for each book of business,16 we used a 

rate of return comparable to the yield on 7-year 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 1999 

and beyond, we used 6 percent as the new discount rate. As an example, 

cash flows associated with the fiscal year 1992 book of business and 

occurring from fiscal years 1992 through 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 6 

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 change depending on the date of the 

mortgage’s origination. We describe all premium income, including upfront premiums, even though they play no role in estimating the future cash 

flows for the Fund at the end of fiscal year 1999.

For loans originating from fiscal years 1975 through 1983, premiums equal 

the annual outstanding principal balance times 0.5 percent. For loans 

originating from fiscal years 1984 through June 30, 1991, premiums equal 

the original loan amount times the mortgage insurance premium. The 

mortgage insurance premium during this period was equal to 3.8 percent 

for 30-year mortgages and 2.4 percent for 15-year mortgages. Because 

there are no annual premiums for this group of loans, the future cash flows 

would include no premium income. For the purposes of this analysis, 

mortgages of other lengths of time are grouped with those they most 

closely approximate. Effective July 1, 1991, FHA added 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 tables 8 and 9.) For loans originating from July 1, 1991, 

16 New mortgage loans insured by FHA in a given fiscal year.
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 63 GAO-01-460 Mortgage Financing

through the time of our review, premiums equal the original loan amount 

times the respective up-front premium plus the product of the annual 

outstanding principal balance times the respective annual premium rate for 

as many years as annual premiums were required.

Table 8: Premium Schedule for 30-Year Non-Streamline Mortgages, by Date of 

Mortgage Origination

a

From September 3, 1996, to January 1, 2000, new homeowners who received financial counseling 

before buying an FHA-insured home were eligible for reduced up-front premiums.

Applicable dates

Up-front premium

rates for 30-year

non-streamline

loans

Annual premium

rates and

durations for

30-year nonstreamline loansApplicable LTV

ratio

10/1/74 - 9/30/83 None 0.5% for 30 years All loans

10/1/83 - 6/30/91 3.80% None -

7/1/91 - 9/30/92 3.80% 0.5% for 5 years

0.5% for 8 years

0.5% for 10 years

Under 90%

90% through 95%

Over 95%

10/1/92 - 4/16/94 3.00% 0.5% for 7 years

0.5% for 12 years

0.5% for 30 years

Under 90%

90% through 95%

Over 95%

4/17/94 - present 2.25%a 0.5% for 7 years

0.5% for 12 years

0.5% for 30 years

Under 90%

90% through 95%

Over 95%
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 64 GAO-01-460 Mortgage Financing

Table 9: Premium Schedule for 15-Year Non-Streamline Mortgages, by Date of 

Mortgage Origination

Some loans that originated in the 1990s are streamline refinanced 

mortgages that are subject to different premium rates. Since streamline 

refinances do not require an appraisal, we decided that mortgages coded in 

FHA’s database with an LTV of 0 could reasonably be assumed to represent 

streamline refinance business. For streamline refinance mortgages that 

originated before July 1, 1991, we applied the premium rates from table 10. 

Table 10: Premium Schedule for 15- and 30-Year Streamline Refinanced Mortgages 

That Originated Before July 1, 1991 

Applicable dates

Up-front premium

rates for 15-year

non-streamline

loans

Annual premium

rates and

durations for

15-year nonstreamline loansApplicable LTV

ratio

10/1/74 - 9/30/83 None 0.50% for 15 years All loans

10/1/83 - 6/30/91 2.40% None -

7/1/91 - 9/30/92 3.80% 0.5% for 5 years

0.5% for 8 years

0.5% for 10 years

Under 90%

90% through 95%

Over 95%

10/1/92 - 12/25/92 3.00% 0.5% for 7 years

0.5% for 12 years

0.5% for 15 years

Under 90%

90% through 95%

Over 95%

12/26/92 − present 2.00% . None

0.25% for 4 years

0.25% for 8 years

Under 90%

90% through 95%

Over 95%

Applicable 

refinancing dates

Up-front

premium rates

for 30-year

loans

Annual

premium

rates for 30-

year loans

 Up-front

premium rates

for 15-year

loans

Annual

premium

rates for 15-

year loans

Before 7/1/91 3.80% None 2.40% None

7/1/91 - 4/24/92 3.80% 0.5% for 5

years

3.80% 0.5% for 5

years

4/24/92 − 12/25/92 3.80% None 3.80% None

12/26/92 − present 3.80% None 2.40% None
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 65 GAO-01-460 Mortgage Financing

For all streamline refinance mortgages that originated after July 1, 1991, we 

applied the premium rates for non-streamline loans. That is, for up-front 

premium rates, we followed the 15-year or 30-year non-streamline premium 

schedule for loans of those maturities. For annual premium rates and 

number of years that annual premiums are paid, we applied the rates for 

loans with an LTV of less than 90 percent.

Claim Payments Claim payments equal the outstanding principal balance on foreclosed 

mortgages times the acquisition cost ratio. We defined 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 purposes 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 1999. Acquisition cost ratios generally decreased 

over time from a high of 1.51 for loans originating in 1975 to a low of 1.09 

for loans originating in 1999. 

Net Proceeds FHA’s net proceeds from the sale of foreclosed properties depend on both 

the lag rate—the proportion of a year that passes between the time of a 

foreclosure and the time the proceeds are received—and the loss rate—the 

proportion of the cost of the property acquired that is not recovered when 

the property is sold. These are calculated as follows:

Net Proceeds = Lag rate x claim payments from previous period x (1 - loss 

rate) + (12-lag rate) x claim payments from the current period x (1 - loss 

rate). 

The lag, which is the number of months between the payment of a claim 

and the receipt of proceeds from the disposition of the property, varied as 

follows. Before 1995, the lag was 5.9 months; in 1995, 5.35 months; in 1996, 

4.7 months; and in 1997, 5.26 months. For the years after 1997, we used a 

lag of 5.26 months. To calculate the lag rate for each period, we divided the 

lag by 12.

We defined the loss rate as equal to FHA’s reported dollar loss after the 

disposition of property divided by the reported acquisition cost over the 

historical period. We determined a loss rate for each year per book of 

business for years 1 through 25. We used an auto-regressive model to 

forecast future loss rates. In addition to past values of loss rates, we used 
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 66 GAO-01-460 Mortgage Financing

the origination year and policy year of the loan as independent variables in 

this model. Using the results of this model, we forecast loss rates over the 

period from fiscal years 2000 through 2023. For fiscal years 2024 through 

2028, we used the estimated rate for 2023. Our loss rates averaged 37 

percent over the forecast period. 

Refunded Premiums The amount of premium refunds paid by FHA depends on the policy year in 

which the mortgage is prepaid and the type of mortgage. For mortgages 

prepaid between October 1, 1983, and December 31, 1993, refunds were 

equal to the original loan amount times the refund rate. However, we 

converted these rates to express them as a percentage of the up-front 

premium. In 1993, FHA changed its refund policy to affect mortgages 

prepaid on or after January 1, 1994. For loans prepaying on or after 

January 1, 1994, refunds are equal to the up-front mortgage insurance 

premium times the refund rate. (See table 11.)

Table 11: Premium Refund Rates for Loans That Were Terminated After October 1, 

1983

Refund rates on loans prepaid between 

10/1/83 and 12/31/93

Year 15-year loans 30-year loans

Refund rates

on all loans

prepaid after 1/1/94

1 99.0% 99.0% 95.0%

2 93.0% 94.0% 85.0%

3 81.0% 82.0% 70.1%

4 66.0% 67.0% 49.4%

5 51.0% 54.0% 30.2%

6 39.0% 43.0% 15.1%

7 29.0% 35.0% 4.2%

8 21.0% 29.0% 0.0%

9 15.0% 24.0% 0.0%

10 11.0% 21.0% 0.0%

11 8.0% 18.0% 0.0%

12 6.0% 16.0% 0.0%

13 4.0% 15.0% 0.0%

14 3.0% 13.0% 0.0%

15 2.0% 12.0% 0.0%
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 67 GAO-01-460 Mortgage Financing

Administrative Expenses Administrative expenses equal the outstanding principal balance times the 

administrative expense rate. The estimates of the administrative expense 

rates were 0.098 percent for the years before 1995, 0.113 percent for 1995, 

0.097 percent for 1996, 0.102 percent for 1997, and 0.103 percent for 1998 

and all future years. 

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 rates of 

unemployment and house price appreciation, we adjusted the forecasts of 

unemployment and price appreciation to provide a range of estimates of 

the Fund's economic value under alternative economic scenarios. Our 

starting points for forecasts of the key economic variables were forecasts 

made by Standard & Poor's DRI, as previously described. 

For our low case scenario, we made these forecasts more pessimistic by 

subtracting 2 percentage points per year from the forecasts of house price 

appreciation rates and adding 1 percentage point per year to the 

16 0.0% 11.0% 0.0%

17 0.0% 10.0% 0.0%

18 0.0% 9.0% 0.0%

19 0.0% 9.0% 0.0%

20 0.0% 8.0% 0.0%

21 0.0% 7.0% 0.0%

22 0.0% 7.0% 0.0%

23 0.0% 6.0% 0.0%

24 0.0% 5.0% 0.0%

25 0.0% 5.0% 0.0%

26 0.0% 4.0% 0.0%

27 0.0% 4.0% 0.0%

28 0.0% 4.0% 0.0%

29 0.0% 4.0% 0.0%

30 0.0% 0.0% 0.0%

Refund rates on loans prepaid between 

10/1/83 and 12/31/93

Year 15-year loans 30-year loans

Refund rates

on all loans

prepaid after 1/1/94
Appendix II

Models Used to Estimate the Economic Value 

of FHA’s Mutual Mortgage Insurance Fund

Page 68 GAO-01-460 Mortgage Financing

unemployment rate forecasts. For our high case scenario, we added 2 

percentage points per year to our base case forecast of house price 

appreciation rates. Under these alternatives, we estimated economic 

values of about $13.6 billion and about $16.4 billion, respectively, for the 

low and high cases, compared with about $15.8 billion for our base case. 

These estimates correspond to estimates of the capital ratio of about 2.75 

percent and 3.32 percent, respectively, for the low and high cases, 

compared with our base case estimate for the capital ratio of 3.20 percent. 

These estimates are shown in table 12.

Table 12: Alternative Estimates of Capital Ratios for FHA's Mutual Mortgage 

Insurance Fund

Source: GAO analysis.

To assess the impact of our assumptions about 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 forecasted 

loss rate resulted in a 0.7-percent decline in our estimate of the economic 

value of the Fund. Conversely, each percentage point decrease in the loss 

rate resulted in a 0.7-percent increase in our estimate of economic value. 

With respect to the discount rate, we found that for our base case economic 

scenario, a 1-percentage-point increase in the interest rate applied to most 

periods’ future cash flow resulted in a 0.3-percent increase in our estimate 

of economic value. Conversely, each percentage point decrease in the 

discount rate resulted in a 0.4-percent decrease in our estimate of 

economic value. 

Dollars in billions

Scenario Economic value

Capital ratio

 (percent)

Most likely economic 

conditions

$15.8 3.20

Low case scenario 13.6 2.75

High case scenario 16.4 3.32
Page 69 GAO-01-460 Mortgage Financing

Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund ApendxiI

This appendix describes the scenarios that we used to estimate the ability 

of the Fund to withstand adverse future economic conditions. Each 

scenario specifies values of key economic variables, which our models 

indicate are associated with mortgage claims and prepayments, during the 

forecast period. We used these values with the forecasting models 

presented in appendix II to estimate future mortgage claims and 

prepayments. We then used these forecasted values of claim and 

prepayment dollars in our cash flow model to estimate the economic value 

of the Fund and the capital ratio under each scenario. 

We developed two types of scenarios—historical and judgmental. We 

designed the historical scenarios to test the ability of the Fund to withstand 

adverse economic conditions similar to those that adversely affected the 

Fund in the 1980s and 1990s. Because some of these adverse conditions 

affected only certain regions, in some scenarios we expanded our analysis 

to include estimates of the capital ratio when the historical conditions were 

assumed to affect a larger share of FHA's business, including when they 

were assumed to affect the entire nation. In contrast, the judgmental 

scenarios that we developed are not based on historical experience. 

Instead, they represent conditions that we believe might place stress on the 

Fund.

The key economic variables for which we forecast different values in the 

different scenarios are the rate of house price appreciation; the 

unemployment rate; and, in some instances, certain interest rates, 

especially the mortgage interest rate. In addition, we assumed that FHA's 

loss per claim (the loss rate), expressed as a percentage of the claim 

amount, was greater than the loss rate that we used in our base case 

analysis under expected economic conditions. We assumed that FHA 

would experience higher loss rates when foreclosures were substantially 

higher because of the difficulty of managing and disposing of a large 

number of properties at the same time. In addition, the demand for housing 

would be likely to fall during an economic downturn, making it more 

difficult to dispose of properties than in the base case.

Historical Scenarios Three regional economic downturns and the 1981-82 national recession 

form the bases of our historical scenarios. Each regional downturn was 

associated with a regional decline in house prices. Declining house prices 

represent a particularly adverse condition for the Fund because of the 

strong negative relationship between borrowers' equity and the probability 

of defaults leading to foreclosures. The three regional economic 
Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund

Page 70 GAO-01-460 Mortgage Financing

downturns, and associated housing price declines, that we used were (1) 

the late 1980s' decline in the oil-producing states of the west south central 

region; (2) the late 1980s' and early 1990s' decline in New England; and (3) 

the early to mid-1990s' decline in the Pacific region, particularly in 

California.1

For each scenario that is based on a regional downturn, we assumed that 

for 4 years the rate of house price change for the part of the nation assumed 

to be affected by the downturn equaled the rate of house price change in 

the state in that region that we selected to represent the regional 

experience. We selected the experiences of (1) Louisiana, beginning in 

1986, to represent the oil price downturn; (2) Massachusetts, beginning in 

1988, to represent the New England economic downturn; and (3) 

California, beginning in 1991, to represent the California housing market 

downturn. Table 13 shows the median house prices for existing houses in 

these states during their economic downturns. In calculating homeowner's 

equity, we made the same adjustment to annual changes in median house 

prices that we did in our base case, as described in appendix II. Similarly, in 

our scenarios that are based on regional downturns, we assumed that 

unemployment rates would change in the affected area for 4 years by the 

same percentages as those rates changed in Louisiana; Massachusetts; and 

California, respectively.

1

 The west south central region is comprised of Arkansas, Louisiana, Oklahoma, and Texas. 

The Pacific region is comprised of Alaska, California, Hawaii, Oregon, and Washington. The 

New England region is comprised of Connecticut, Maine, Massachusetts, New Hampshire, 

Rhode Island, and Vermont.
Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund

Page 71 GAO-01-460 Mortgage Financing

Table 13: Historical Median House Price and Unemployment Experience in States Representing Regional Downturns

a

For Unemployment rates in Louisiana, we used 1985 as the base year (year 0) and used changes in 

the unemployment rate for 3 years (1986 through 1988) only.

We developed six separate scenarios that are based on each regional 

downturn, by varying the scope (i.e., the number of states assumed to be 

affected) and timing of the adverse economic conditions in the forecast 

period. Specifically, we used three different scopes. In the narrowest 

scope, we assumed that only the particular region was affected. That is, for 

the scenario based on the downturn in the west south central region in the 

late 1980s, we assumed that during 4 years of the forecast period, all of the 

states in the west south central region experienced the same changes in 

key economic variables as Louisiana experienced from 1987 through 1990. 

We then expanded the scope by assuming that two regions in which FHA 

has a lot of borrowers, the west south central and Pacific regions, were 

House price Unemployment rate

State Year

Ordinal

year Amount

Percentage

of year 0 Percent

Percentage

of year 0

Louisiana 1986 0 $75.3 100.0 11.2a 100.0

1987 1 78.7 104.5 12.8 114.1

1988 2 73.5 97.6 12.5 113.4

1989 3 69.6 92.4 11.2 100.1

1990 4 67.3 89.4 - -

Massachusetts 1988 0 142.3 100.0 3.1 100.0

1989 1 137.5 96.6 3.7 118.7

1990 2 135.4 95.1 5.4 171.2

1991 3 128.0 90.0 8.6 274.1

1992 4 133.1 93.5 8.7 277.7

California 1991 0 199.9 100.0 7.4 100.0

1992 1 198.9 99.5 8.9 120.1

1993 2 191.6 95.8 9.5 128.6

1994 3 183.7 91.9 8.9 120.9

1995 4 183.0 91.5 7.9 106.6
Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund

Page 72 GAO-01-460 Mortgage Financing

affected.2 Finally, we then expanded the scope to the entire nation, by 

assuming that all states were affected. 

Regarding timing, for each scope we developed two scenarios, one in 

which the downturn began in 2000 and one in which it began in 2001. 

Although we know that an economic downturn did not begin in 2000, we 

developed scenarios starting then to test the ability of the Fund to 

withstand an economic downturn that occurs when the portfolio contains 

many recent loans. Scenarios in which the downturn does not begin until 

2001 would be expected to be less adverse because most of the large 

number of borrowers who took out mortgages in 1998 and 1999 would have 

seen substantial price appreciation in 2000, thereby reducing the likelihood 

of default.

We developed two historical scenarios that are based on the 1981-82 

recession and subsequent recovery. In those scenarios, we assumed that in 

each state, the rates of change in house price appreciation and 

unemployment for 5 years during the forecast period are the same as they 

were from 1981 through 1985. In one scenario, we assumed that these 

adverse conditions replicating 1981 through 1985 began in 2000; in the 

other scenario, we assumed that they began in 2001. Under these 

scenarios, some states fared better than in the base case scenario.

Because it will be more difficult to manage and dispose of foreclosed 

properties during an economic downturn, we increased the loss rates on 

the proportion of mortgages affected by a given scenario during the years 

the scenario runs. We assumed that losses on affected foreclosed 

properties would rise to 45 percent of the property’s value. Without this, 

loss rates average about 37 percent. 

Our estimates of the economic value of the Fund and the capital ratio for 

the historical scenarios are presented in table 14.

2

 We used these two regions for each set of scenarios, even the set that is based on the New 

England decline, because FHA does relatively little business in New England, and we 

wanted to test the ability of the Fund to withstand a downturn like the one a decade ago in 

New England, if it occurred simultaneously in two regions in which FHA does a lot of 

business.
Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund

Page 73 GAO-01-460 Mortgage Financing

Judgmental Scenarios We developed several judgmental scenarios to test the ability of the Fund to 

withstand various types of economic conditions that might adversely affect 

the Fund without regard to their relationship to historical experience. In 

one scenario, we assumed that median existing house prices declined by 5 

percent per year for 3 consecutive years—an extremely steep rate of 

decline3

—and that unemployment increased compared with the base case, 

with both changes beginning in 2001. Specifically, we increased the 

unemployment rates in each state from forecasted levels by 2 percentage 

points in 2001; 5 percentage points in 2002, 2003, and 2004; and 2 

percentage points in 2005. In a second scenario, we allowed the mortgage 

interest rate to decline in 2000—by 2 percentage points from its forecasted 

level—and then to return to forecasted levels. We did this to precipitate a 

wave of refinancing. We also assumed declining house prices and rising 

unemployment beginning in 2001, as in the previous judgmental scenario. 

We used this scenario to test what might happen if premium income turns 

out to be substantially less than expected and premium refunds 

substantially more than expected because of rapid prepayment of loans, 

most of which would not default. In our third scenario, we added 1 

percentage point to the base case forecasts of the mortgage interest rate, 

and 1- and 10-year Treasury rates for the year 2000, 3 percentage points to 

the forecasts of these interest rates between 2001 and 2003, and 1 

percentage point in 2004. We used this scenario to test what might happen 

if interest rates were to rise more than anticipated. In a fourth scenario, we 

used the same rising interest rates as in the third scenario and also added 

one percentage point to the forecasts of median existing house prices over 

that period. 

Our estimates of the economic value of the Fund and the capital ratio for 

the judgmental scenarios are also presented in table 14.

3

 Since we adjusted growth in median house prices for quality improvements, as described 

in appendix II, the decline in house prices facing individual borrowers is even greater.
Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund

Page 74 GAO-01-460 Mortgage Financing

Table 14: National Results of Alternative Scenarios

Geographic extent

Starting

year

Number of

loan years

Average

house price

Average

unemployment rate

(percent)

Average

equity

(percent)

Economic

value

(millions)

Capital ratio

(percent)

Base Case

National NA 3,974,076 $124,076 4.3 49.9 $15,810 3.20

Historical scenarios that were based on the Louisiana experience of 1986-90

One region (WSC) 2000 4,010,385 $116,739 4.3 45.6 $15,130 3.06

Two regions (WSC and PAC) 2000 4,058,778 111,618 4.4 43.2 13,861 2.81

Nation 2000 4,308,066 85,005 4.4 29.1 11,430 2.31

One region (WSC) 2001 4,003,327 117,360 4.3 46.2 15,320 3.10

Two regions (WSC and PAC) 2001 4,040,790 112,900 4.3 44.2 14,606 2.96

Nation 2001 4,233,621 89,016 4.3 32.2 12,848 2.60

Historical scenarios that were based on the Massachusetts experience of 1988-92

One region (NE) 2000 3,991,873 122,936 4.3 49.3 15,510 3.14

Two regions (WSC and PAC) 2000 4,024,416 112,829 4.9 43.9 10,566 2.14

Nation 2000 4,261,430 88,058 5.8 31.2 4,020 0.81

One region (NE) 2001 3,985,822 123,108 4.3 49.5 15,623 3.16

Two regions (WSC and PAC) 2001 4,020,651 113,934 4.8 44.8 12,291 2.49

Nation 2001 4,211,557 91,832 5.5 33.9 7,759 1.57

Historical scenarios that were based on the California Experience of 1991-95

One region (PAC) 2000 4,026,719 118,921 4.4 47.5 14,281 2.89

Two regions (WSC and PAC) 2000 4,057,387 112,031 4.4 43.5 12,815 2.59

Nation 2000 4,304,672 86,298 4.5 30.1 10,683 2.16

One region (PAC) 2001 4,013,887 119,695 4.3 48.0 14,912 3.02

Two regions (WSC and PAC) 2001 4,041,526 113,280 4.4 44.4 14,353 2.91

Nation 2001 4,231,923 90,223 4.4 33.0 12,319 2.49

Historical scenarios that were based on state-by-state experiences during the 1981-82 recession

Nation 2000 4,025,522 123,503 4.7 49.1 13,876 2.81

Nation 2001 3,997,043 127,824 4.5 50.2 14,673 2.97

Judgmental scenario: mortgage rate decline in 2000 followed by 3 years of 5 percent declines in house prices and increased 

unemployment starting in 2001

Nation 2000 3,795,878 86,731 5.4 29.5 6,779 1.37

Judgmental scenario: 3 years of 5 percent declines in house prices and increased unemployment starting in 2001

Nation 2001 4,285,284 87,005 5.4 30.3 6,918 1.40

Judgmental scenario: higher mortgage rates early in forecast period

Nation 2000 4,594,178 125,287 4.3 53.9 16,608 3.36
Appendix III

Development of Scenarios of Adverse 

Economic Conditions Used to Estimate the 

Economic Value of the Fund

Page 75 GAO-01-460 Mortgage Financing

In another type of judgmental scenario, we did not forecast the economic 

variables and then use the forecasted claims and prepayments from our 

econometric model, as we did with all of our other scenarios, both 

judgmental and historical. Instead, because none of our other scenarios 

produced foreclosure rates nearly as high as FHA experienced in the 1980s, 

we developed two scenarios in which we directly assumed higher 

foreclosure rates. First, we assumed that in 2000 through 2004, the 

proportion of loans insured in each region experienced for the 1989 

through 1999 books of business the same foreclosure rates that the 1975 

through 1985 books of business experienced in that region in 1986 through 

1990. This scenario produced a capital ratio of 0.92 percent. Second, we 

assumed that in 2000 through 2004, varying proportions of FHA’s portfolio 

experienced for the 1989 through 1999 books of business the same 

foreclosure rates that the 1975 through 1985 books of business experienced 

in the west south central states in 1986 through 1990. Because streamline 

refinanced mortgages and ARMs did not exist or were minimal parts of 

FHA’s portfolio from 1975 through 1985, foreclosure rates were not 

adjusted for these types of loans. For the other products—30-year fixedrate, 15-year fixed-rate, investor, and graduated payment mortgages—

foreclosure rates were adjusted accordingly for each type of product. For 

this scenario, we found that if 36.5 percent of FHA-insured mortgages 

experienced these high default rates, the estimated capital ratio for fiscal 

year 1999 would fall by 2 percentage points, and if about 55 percent of 

FHA's portfolio experienced these conditions, the economic value would 

be depleted.

Judgmental scenario: higher mortgage rates early in forecast period, accompanied by faster house price growth

Nation 2000 4,538,531 139,330 4.3 58.1 16,818 3.40

(Continued From Previous Page)

Geographic extent

Starting

year

Number of

loan years

Average

house price

Average

unemployment rate

(percent)

Average

equity

(percent)

Economic

value

(millions)

Capital ratio

(percent)
Page 76 GAO-01-460 Mortgage Financing

Appendix IV

Comments From the Department of Housing 

and Urban Development ApendxiIV
Appendix IV

Comments From the Department of Housing 

and Urban Development

Page 77 GAO-01-460 Mortgage Financing
Appendix IV

Comments From the Department of Housing 

and Urban Development

Page 78 GAO-01-460 Mortgage Financing
Appendix IV

Comments From the Department of Housing 

and Urban Development

Page 79 GAO-01-460 Mortgage Financing
Page 80 GAO-01-460 Mortgage Financing

Appendix V

GAO Contacts and Staff Acknowledgments ApendxiV

GAO Contacts Thomas J. McCool, (202) 512-8678

Mathew Sciré, (202) 512-6794

Acknowledgments In addition to those named above, Nancy Barry, Elaine Boudreau, Steve 

Brown, Jay Cherlow, Kimberly Granger, DuEwa Kamara, John McDonough, 

Salvatore F. Sorebllo Jr., Mark Stover, and Patrick Valentine made key 

contributions to this report.
Page 81 GAO-01-460 Mortgage Financing

Related GAO Products

Financial Health of the Federal Housing Administration's Mutual Mortgage 

Insurance Fund (GAO/T-RCED-00-287, Sept. 12, 2000).

Level of Annual Premiums That Place a Ceiling on Distributions to FHA 

Policyholders (GAO/RCED-00-280R, Sept. 8, 2000).

Single-Family Housing: Stronger Measures Needed to Encourage Better 

Performance by Management and Marketing Contractors (GAO/T-RCED00-180, May 16, 2000, and GAO/RCED-00-117, May 12, 2000).

Single-Family Housing: Stronger Oversight of FHA Lenders Could Reduce 

HUD's Insurance Risk (GAO/RCED-00-112, Apr. 28, 2000).

Homeownership: Results of and Challenges Faced by FHA's Single-Family 

Mortgage Insurance Program (GAO/T-RCED-99-133, Mar. 25, 1999).

Homeownership: Achievements of and Challenges Faced by FHA's SingleFamily Mortgage Insurance Program (GAO/T-RCED-98-217, June 2, 1998).

Homeownership: Management Challenges Facing FHA's Single-Family 

Housing Operations (GAO/T-RCED-98-121, Apr. 1, 1998).

Homeownership: Mixed Results and High Costs Raise Concerns about 

HUD's Mortgage Assignment Program (GAO/RCED-96-2, Oct. 18, 1995).

Homeownership: Information on Single Family Loans Sold by HUD

(GAO/RCED-99-145, June 15, 1999).

Homeownership: Information on Foreclosed FHA-Insured Loans and HUDOwned Properties in Six Cities (GAO/RCED-98-2, Oct. 8, 1997).

Homeownership: Potential Effects of Reducing FHA's Insurance Coverage 

for Home Mortgages (GAO/RCED-97-93, May 1, 1997).

Homeownership: FHA's Role in Helping People Obtain Home Mortgages

(GAO/RCED-96-123, Aug. 13, 1996).

Mortgage Financing: FHA Has Achieved Its Home Mortgage Capital 

Reserve Target (GAO/RCED-96-50, Apr. 12, 1996).

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