Mortgage Financing: Financial Health of FHA's Home Mortgage Insurance
Program Has Improved (Letter Report, 10/18/94, GAO/RCED-95-20).
Through its Federal Housing Administration (FHA), the Department of
Housing and Urban Development insures private lenders against losses on
home mortgages financed through its Mutual Mortgage Insurance Fund.
These mortgages are now valued at nearly $270 billion. Although the Fund
has historically been financially self-sufficient, it began to
experience substantial losses during the 1980s, mainly because of high
foreclosure rates on single-family homes supported by the fund in
economically depressed areas. This report (1) summarizes GAO's
assessment of the economic net worth of the Fund at the end of fiscal
year 1993 and (3) describes GAO's econometric and cash flow modeling
approach for forecasting the economic net worth of the Fund.
--------------------------- Indexing Terms -----------------------------
REPORTNUM: RCED-95-20
TITLE: Mortgage Financing: Financial Health of FHA's Home Mortgage
Insurance Program Has Improved
DATE: 10/18/94
SUBJECT: Mortgage programs
Mortgage protection insurance
Revolving funds
Internal controls
Financial management
Financial analysis
Homeowners insurance
Budgetary reserves
Funds management
Econometric modeling
IDENTIFIER: Mutual Mortgage Insurance Fund
HUD Single-Family Mortgage Insurance Program
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Cover
================================================================ COVER
Report to the Chairman, Subcommittee on Housing and Community
Development,Committee on Banking, Finance, and Urban Affairs, House
of Representatives
October 1994
MORTGAGE FINANCING - FINANCIAL
HEALTH OF FHA'S HOME MORTGAGE
INSURANCE PROGRAM HAS IMPROVED
GAO/RCED-95-20
Financial Health of FHA
Abbreviations
=============================================================== ABBREV
FHA - Federal Housing Administration
GAO - General Accounting Office
HUD - Department of Housing and Urban Development
LTV - loan-to-value
VA - Department of Veterans Affairs
Letter
=============================================================== LETTER
B-258141
October 18, 1994
The Honorable Henry B. Gonzalez
Chairman, Subcommittee on Housing
and Community Development
Committee on Banking, Finance,
and Urban Affairs
House of Representatives
Dear Mr. Chairman:
Through its Federal Housing Administration (FHA), the Department of
Housing and Urban Development (HUD) provides insurance for private
lenders against losses on home mortgages financed through its Mutual
Mortgage Insurance Fund (Fund). These mortgages are currently valued
at about $269 billion. Although the Fund has historically been
financially self-sufficient, it began to experience substantial
losses during the 1980s, primarily because foreclosure rates on
single-family homes supported by the Fund were high in economically
stressed regions. To help place the Fund on an actuarially sound
basis, legislative reforms, such as requiring FHA borrowers to pay
more in insurance premiums, were made in November 1990.
Concerned about the current financial health of FHA's Fund and the
impact of the reforms on FHA, you asked us to assess the actuarial
soundness of the Fund. On June 30, 1994, we presented our assessment
in testimony before your Subcommittee.\1 Our testimony also included
a brief description of our econometric modeling approach for
forecasting the actuarial soundness of the Fund. This report (1)
summarizes our assessment of the economic net worth of the Fund\2 as
of the end of fiscal year 1993 and (2) presents a complete
description of our econometric and cash flow modeling approach for
forecasting the economic net worth of the Fund.
--------------------
\1 Mortgage Financing: Financial Health of FHA's Home Mortgage
Insurance Program Has Improved (GAO/T-RCED-94-255, June 30, 1994).
\2 The current cash available to the Fund, plus the net present value
of all future cash inflows and outflows expected to result from
outstanding mortgages in the Fund.
RESULTS IN BRIEF
------------------------------------------------------------ Letter :1
Although there is uncertainty associated with any forecast, the
economic value of FHA's Fund clearly has improved significantly in
recent years, and the Fund is on the way to accumulating sufficient
capital reserves to be considered actuarially sound under the law.
Legislative and other changes to FHA's single-family mortgage
insurance program have helped restore the Fund's financial health,
but favorable prevailing and forecasted economic conditions in fiscal
year 1993 were primarily responsible for this improvement. While the
Fund fell short of achieving the legislative mandate for capital
reserves of 1.25 percent of amortized insurance-in-force by the
November 1992 deadline, the Fund's 1.83-percent capital reserve ratio
at the end of fiscal year 1993 surpassed the mandate. Whether the
Fund can sustain this progress; attain the legislative target of 2
percent for capital reserves by November 2000, thereby achieving
actuarial soundness under the law; and maintain that ratio thereafter
will depend on many economic and program-related factors that will
affect the financial health of the Fund this year and over the next 6
years.
Our model consists of econometric and cash flow models of FHA's
single-family mortgage insurance program that we used to estimate the
economic net worth of and resulting capital ratios for FHA's loans
over their life of up to 30 years. Our econometric model was used to
predict, among other things, the probability of loan foreclosures and
prepayments on the basis of historical relationships between these
events and key explanatory variables such as the borrower's equity.
Our cash flow model was used to predict the net present value of all
future cash inflows and outflows expected to result from the
outstanding mortgages in the Fund as of the end of fiscal years 1992
and 1993. The actual economic net worth and capital ratios of the
Fund--and the validity of our estimates--will depend on a number of
future economic and program-related factors, including the rate of
appreciation in house prices over the life of the FHA mortgages.
This factor is significant because, as house prices rise, the
borrowers' equity increases and the probability of defaults and
subsequent foreclosures decreases.
BACKGROUND
------------------------------------------------------------ Letter :2
FHA was established in 1934 under the National Housing Act (P.L.
73-479). The primary purpose of FHA's Fund is to insure private
lenders against losses on mortgages that finance purchases of one to
four housing units. To cover these losses, FHA deposits insurance
premiums from participating home buyers in the Fund. According to 12
U.S.C. 1711, the Fund must meet or endeavor to meet statutory
capital ratio requirements designed to achieve actuarial soundness;
that is, it must contain sufficient reserves and funding to cover
estimated future losses resulting from the payment of claims on
defaulted mortgages and administrative costs.
The Fund remained relatively healthy until the 1980s, when losses
were substantial, primarily because foreclosure rates were high in
economically stressed regions, particularly in the Rocky Mountain and
Southwest regions. For example, in fiscal year 1988 the Fund lost
$1.4 billion. If the Fund were to be exhausted, the U.S. Treasury
would have to directly cover lenders' claims and administrative
costs.
Reforms designed to restore financial stability to the Fund and to
correct problems in loan origination and property disposition were
initiated by the Congress and HUD. The Omnibus Budget Reconciliation
Act of 1990 (P.L. 101-508), enacted in November 1990, contained
reforms to FHA's single-family mortgage insurance program designed to
place the Fund on an actuarially sound basis. The legislation, among
other things, required FHA borrowers to pay more in insurance
premiums over the life of the loans by adding a risk-based annual
premium to the one-time, up-front premium. Other changes made by the
legislation in response to the Fund's financial problems included (1)
limiting the loan-to-value ratio to a maximum of 97.75 percent of
appraised value on homes whose appraised value exceeds $50,000 and
(2) effectively suspending payment of distributive shares
(distribution of excess revenues to mortgagors) until the Fund is
actuarially sound.
The legislation also mandated that the Fund attain a capital ratio
(ratio of the Fund's economic net worth to its insurance-in-force) of
1.25 percent by November 1992 and required the Secretary of HUD to
endeavor to ensure a capital ratio of 2 percent by November 2000 and
maintain that ratio at a minimum at all times thereafter.
HUD's efforts to improve the financial stability of the Fund
consisted of initiating several audits of the Fund; making program
modifications, primarily to tighten controls and improve monitoring;
and developing automated systems. We have concluded that in addition
to economic factors, poor program management and waste, fraud, and
abuse contributed to the losses sustained by FHA's Fund. The full
extent of losses attributable to these factors is not known. As we
have pointed out in previous testimonies and reports, some of the
major management problems facing HUD concern FHA's single-family
program. For example, the absence of internal controls over FHA's
management systems for single-family property disposition allowed
private real estate agents to steal millions of dollars in FHA funds.
Moreover, we reported that a direct correlation exists between the
effectiveness of internal controls, the accuracy and timeliness of
financial information, and the magnitude of the losses incurred by
FHA as well as by other HUD programs.\3
We and HUD's Inspector General have been reporting on these
management problems since the early 1980s. HUD has taken steps to
address some of these problems and to strengthen FHA's financial
position. To reduce problems with loan origination, HUD tightened
its screening of applicants, took steps to improve how it targets its
efforts to monitor lenders, and strengthened appraisal requirements.
To reduce problems with property disposition, HUD, among other
things, tightened controls over closing agents and area management
brokers and took actions to improve property pricing and automated
accounting and management systems. However, we have concluded that
much work remains to be done by HUD and FHA to resolve the underlying
causes of FHA's problems, such as inadequate information and
financial management systems. Any success achieved by HUD and FHA in
reducing FHA's losses through better management will improve the
financial health of the FHA Fund.
--------------------
\3 See Impacts of FHA Loan Policy Changes on Its Cash Position
(GAO/T-RCED-90-70, June 6, 1990); HUD Reforms: Progress Made Since
the HUD Scandals but Much Work Remains (GAO/RCED-92-46, Jan. 31,
1992); and Letter to the Ranking Minority Member, Subcommittee on
Housing and Community Development, House Committee on Banking,
Finance, and Urban Affairs (B-249052, Sept. 30, 1992).
OUR ESTIMATES OF THE FUND'S
ECONOMIC NET WORTH
------------------------------------------------------------ Letter :3
In assessing the actuarial soundness of FHA's Fund, we (1) estimated,
under different economic scenarios, the economic net worth of the
Fund as of the end of fiscal years 1992 and 1993 and (2) assessed the
progress made by the Fund in achieving the legislatively prescribed
capital ratios.
FHA's Fund made significant progress during fiscal year 1993 toward
achieving the capital reserves needed for actuarial soundness under
the law. As shown in table 1, under our baseline economic scenario,
we estimated that the Fund had an economic net worth of about $4.9
billion\4 and a resulting capital ratio of 1.83 percent at the end of
fiscal year 1993. This estimate represents an improvement of about
$7.6 billion from the lowest level reached by the Fund--a negative
$2.7 billion estimated by Price Waterhouse at the end of fiscal year
1990.
As of September 30, 1993, the Fund had capital resources of about
$9.7 billion, which were sufficient to cover the $4.8 billion in
expenses that we estimate the Fund will incur in excess of
anticipated revenues ($19.3 billion in expenses less $14.5 billion in
anticipated revenues) over the life of the loans outstanding at that
time. The remaining $4.9 billion represents the Fund's economic net
worth, or capital. We also estimated, under our baseline economic
scenario shown in table 1, that the Fund had an economic net worth of
about $600 million and a resulting capital ratio of 0.21 percent at
the end of fiscal year 1992.
Table 1
GAO's Estimates of the Economic Net
Worth and Capital Ratios of FHA's Fund
as of September 30, 1992, and September
30, 1993
(Dollars in Billions)
FY FY FY FY
GAO's scenarios 1992 1993 1992 1993
---------------------------- ------ ------ ------ ------
High-case $0.99 $5.2 0.35 1.92
Baseline case $0.60 $4.9 0.21 1.83
Low-case $- $4.0 -0.12 1.47
0.34
------------------------------------------------------------
Note: FY = fiscal year.
Under our low-case economic scenario, which assumes a lower rate of
appreciation in house prices than our baseline, we estimated that the
Fund's economic net worth and capital ratios at the end of fiscal
year 1993 would be lower--$4.0 billion and 1.47 percent,
respectively. Conversely, under our high-case economic scenario,
which assumes a higher rate of appreciation in house prices than our
baseline, we estimated that the Fund's economic net worth and capital
ratios would be greater at the end of fiscal year 1993--$5.2 billion
and 1.92 percent, respectively.
As shown in table 1, we estimated that the economic net worth of the
Fund increased under our baseline scenario by about $4.3 billion
during fiscal year 1993. This increase occurred even though, during
fiscal year 1993, large numbers of FHA borrowers lowered their
interest rates by refinancing their mortgages conventionally, which
resulted in partial refunds of their insurance premiums. The
financial improvement in the Fund is attributable to several economic
and program-related factors working together to (1) increase the
estimated economic net worth of loans endorsed by FHA in fiscal year
1992 and earlier years and (2) result in our estimate of a positive
contribution to economic value made by those loans endorsed by FHA in
fiscal year 1993. Legislative and other changes to the program
contributed to this increase, but favorable prevailing and forecasted
economic conditions in fiscal year 1993 were primarily responsible
for this improvement.
Our analysis of the loans endorsed by FHA in fiscal year 1993 shows
that some of the program-related changes made by the Congress and FHA
in recent years contributed about $1.3 billion, or 26 percent, to the
Fund's economic value. Beginning on July 1, 1991, FHA borrowers were
subject to the higher premium payments mandated by the Omnibus Budget
Reconciliation Act of 1990. We estimated that if FHA borrowers in
fiscal year 1993 had to pay only the premiums that were effective
before the act's passage, the economic net worth of the Fund at the
end of fiscal year 1993 would have been about $4.1 billion, or $0.8
billion (16 percent) less than our baseline estimate of $4.9 billion.
Similarly, we estimated that if FHA had not revised its premium
refund schedule, the economic net worth of the Fund at the end of
fiscal year 1993 would have been about $4.4 billion, or $0.5 billion
(10 percent) less than our baseline estimate of $4.9 billion.
Although the Fund has made a substantial financial improvement
recently, we estimated that it fell about $3 billion short of
achieving the legislative mandate for capital reserves of 1.25
percent of its amortized insurance-in-force by the November 1992
deadline. However, the Fund surpassed the 1992 mandate for capital
reserves by the end of fiscal year 1993 (1.83 percent). Whether the
Fund can sustain this progress; attain the legislative target for
reserves of 2 percent by November 2000, thereby achieving actuarial
soundness under the law; and maintain that ratio thereafter will
depend on many economic and program-related factors that will affect
the financial health of the Fund this year and over the next 6 years.
--------------------
\4 Our estimate of the economic value of the Fund is similar to that
of Price Waterhouse ($4.6 billion). Price Waterhouse has performed
annual actuarial reviews of the Fund for FHA since 1990.
ECONOMETRIC AND CASH FLOW
MODELS WE USED TO FORECAST
ECONOMIC NET WORTH
------------------------------------------------------------ Letter :4
To estimate the economic net worth of FHA's Fund as of September 30,
1992, and September 30, 1993, and its resulting capital ratios under
different economic scenarios, we examined existing studies on the
single-family housing programs of both HUD and the Department of
Veterans Affairs (VA); academic literature on the modeling of
mortgage defaults and prepayments; and previous work performed by
Price Waterhouse, HUD, VA, ourselves, and others on modeling
government mortgage programs. On the basis of this examination, we
developed econometric and cash flow models to prepare our estimates.
For these models, we used data supplied by FHA and DRI/McGraw-Hill, a
private economic forecasting company.
Our econometric analysis estimated the historical relationships
between the probability of loan foreclosure and prepayment and key
explanatory factors such as the borrower's equity and the interest
rate. To estimate these relationships, we used data on the
performance of FHA-insured home mortgage loans--such as foreclosure,
prepayment, and loss rates--originated from fiscal years 1975 through
1993. Also, using our estimates of these relationships and of
economic conditions, we developed a baseline forecast of future loan
performance to estimate the Fund's economic net worth and resulting
capital ratio. We then developed additional estimates that assumed
higher and lower future rates of appreciation in house prices; the
scenario with the lower rate of appreciation of house prices also
assumed higher unemployment.
To estimate the net present value of future cash flows of the Fund,
we constructed a cash flow model to measure the five primary sources
and uses of cash for loans originated in fiscal years 1975 through
1993. The five sources and uses of cash are
income from mortgagees' premiums,
payments associated with claims on foreclosed properties,
net proceeds from the sale of foreclosed properties,
refunds of premiums on mortgages that are prepaid, and
administrative expenses for management of the program.
Our model was constructed to estimate cash flows for each policy year
through the life of a mortgage. An important component of the model
is converting all income and expense streams--regardless of the
period in which they actually occur--into 1993 dollars. In addition
to estimating the economic value of the Fund as a whole, we also
generated approximations of the economic value of the loans
originated in 2 most recent fiscal years. To conduct this analysis,
it was necessary not only to project future cash flows but also to
estimate the level of past cash flows.
To test the validity of our model, we examined how well our model
predicted the actual rates of FHA's loan foreclosures and prepayments
through fiscal year 1993. We found that our predicted rates closely
resembled actual rates. A detailed discussion of our models and
methodology for forecasting the economic net worth of FHA's Fund
appears in appendix I.
AGENCY COMMENTS
------------------------------------------------------------ Letter :5
We discussed the facts in this report with the Acting Housing-FHA
Comptroller; Deputy Assistant Secretary for Single Family Housing;
Acting Director, Management Control Staff; Deputy Director, Office of
Evaluation; Director, Program Evaluation Division; and Deputy
Director, Office of Insured Single Family Housing. These officials
generally agreed with our facts as presented on FHA's single-family
mortgage insurance program and the economic net worth of the Fund.
In addition, the officials told us that our econometric and cash flow
models and methodology for forecasting the economic net worth of
FHA's Fund were credible. The officials told us that they were
considering including several aspects of our models in the models
built by Price Waterhouse. We incorporated, where appropriate,
changes suggested by the officials to clarify certain information
presented. As requested, we did not obtain written agency comments
on a draft of this report.
---------------------------------------------------------- Letter :5.1
We conducted our work between September 1993 and August 1994 in
accordance with generally accepted government auditing standards.
We are sending copies of this report to the appropriate congressional
committees; the Secretary of HUD; and the Director, Office of
Management and Budget. We will also make copies available to others
on request.
Please contact me on (202) 512-7631 if you or your staff have further
questions. Major contributors to this report are listed in appendix
II.
Sincerely yours,
Judy A. England-Joseph
Director, Housing and
Community Development Issues
GAO'S ECONOMETRIC AND CASH FLOW
MODELS USED TO FORECAST FHA'S
ECONOMIC NET WORTH
=========================================================== Appendix I
This appendix describes the econometric and cash flow models that we
built and the analysis we conducted to estimate the economic net
worth of the Federal Housing Administration's (FHA) Mutual Mortgage
Insurance Fund (Fund) as of the end of fiscal years 1992 and 1993.
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 years 1992 and 1993 for each year from
fiscal year 1994 through fiscal year 2022 on the basis of assumptions
stated in this appendix. We estimated equations from data covering
fiscal years 1975 through 1993 that included all 50 states and the
District of Columbia, but excluded U.S. territories.\5
Our forecasting 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.\6
More specifically, our model used logistic equations to estimate the
probability of a claim's payment (or prepayment) in a given year 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.
Cash flows out of the Fund when FHA pays a claim on a foreclosed
mortgage and when a prepaid mortgage results in the partial refund of
a premium. Cash flows into the Fund when FHA sells the foreclosed
property and when borrowers pay the mortgage insurance's premium. We
forecasted the cash flows into and out of the Fund on the basis of
our foreclosure and prepayment models and key economic variables as
determined by DRI/McGraw-Hill, a leading economic forecasting firm.
We then used the forecasted cash flows, including an estimate of
interest that would be earned or foregone, and the Fund's capital
resources to estimate the economic net worth of the Fund.
Separate estimations were obtained for investors' mortgages,
fixed-rate mortgages with terms of 25 years or more, and fixed-rate
mortgages whose terms were less than 25 years. A complete
description of our models, the data we used, and the results we
obtained are discussed in detail in the following sections.
--------------------
\5 We used an analogous approach in estimating the value of the Fund
as of the end of fiscal year 1992. For that analysis, we used data
covering fiscal years 1975 through 1992, so our coefficient estimates
were slightly different from those presented here.
\6 These probabilities are conditional because they are subject to
the condition that the loan has remained active until a given year.
DATA AND SAMPLE SELECTION
--------------------------------------------------------- Appendix I:1
For our analysis, we selected from FHA's computerized files a
10-percent sample of records of mortgages insured by FHA from fiscal
year 1975 through fiscal year 1993 (930,452 loans).\7 From FHA's
records, we obtained information on the initial characteristics of
each loan, such as the year of the loan's origination and state in
which the loan originated; the LTV ratio; the loan's amount; and the
contract's interest rate. We categorized the loans as either
foreclosed, prepaid, or active as of the end of fiscal year 1993.
To describe macroeconomic conditions at the national and local
levels, we obtained data from DRI/McGraw-Hill, by state, on annual
civilian unemployment rates and data from the Economic Report of the
President on the implicit price deflator for personal consumption
expenditures. DRI/McGraw-Hill's data on quarterly interest rates for
30-year mortgages on new and existing housing were used along with
DRI/McGraw-Hill's forecast data, at the state level, on the median
house price and civilian unemployment.
--------------------
\7 FHA's A-43 data base provides current and historical information
on the mortgage loans that FHA insures.
SPECIFICATION FOR MODEL
--------------------------------------------------------- Appendix I:2
People buy homes for consumption and investment purposes. Normally,
people do not plan to default on loans. However, conditions that
lead to defaults occur. Defaults may be triggered by a number of
events: unemployment, divorce, death, etc. These events are not
likely to trigger foreclosure if the owner has positive equity in
his/her home because the sale of the home with realization of a
profit is better than the loss of the home through foreclosure.
However, if the property is worth less than the mortgage, these
events may trigger default.
Prepayments to financial institutions may be triggered by other
events--declining interest rates, which prompt refinancing; rising
house prices, which prompt the take-out of accumulated equity; or the
sale of the residence. Because FHA mortgages are assumable, the sale
of a residence does not automatically trigger prepayment. For
example, if interest rates have risen substantially since the time
the mortgage was originated, a new purchaser may prefer to assume the
seller's mortgage.
We assumed that foreclosure behavior is influenced by the level of
unemployment, size of the loan, value of the home, current interest
rates, contract interest rates, home equity, and region of the
country within which the home is located. We assumed that prepayment
is influenced by 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 an indicator of whether
a given loan was foreclosed in a given year. Each loan-year
observation was weighted by the outstanding mortgage balance,
expressed in inflation-adjusted dollars.
Our claim rates are conditional on whether the loan survives an
additional year. Conditional foreclosures were estimated 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.\8 The dependent variable
(whose value is 1 if foreclosure occurs and zero otherwise) was
regressed on the explanatory variable listed above.
Our second regression model estimated conditional prepayment
probabilities. Current interest rates are the primary determinant of
a mortgage's refinance activity. This independent variable was the
current interest rate relative to the contract rate. The variable
was further separated between ratios above and below 1 to allow for
the possibility of different marginal impacts in higher and lower
ranges.
The variables we used to predict foreclosures and prepayments fall
into two general categories: descriptions of states of the economy
and characteristics of the loan. In choosing explanatory variables,
we relied on the results of our own and others' previous efforts to
model foreclosure and prepayment probabilities and on implications
drawn from economic principles. We included most of the same
variables in both the foreclosure and prepayment regressions.
--------------------
\8 If P1 is the probability that an event will occur in loan-year i,
the "odds ratio" is defined as P1/(1-P1). The logistic
transformation is the natural logarithm of the odds ratio, or
LN[P1/(1-P1)], 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).
EQUITY
------------------------------------------------------- Appendix I:2.1
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.\9
We computed equity as the difference between the value of the
property and the value of the mortgage, expressed as a percentage of
the value of the property. For example, if the value of a property
is $100,000 and the value of the mortgage is $80,000, then equity is
20 percent, or 0.2. To measure equity, we calculated the value of
the mortgage as the present value of the remaining mortgage payments
(up to a maximum of 10 years), evaluated at the current year's
fixed-rate mortgage interest rate, and added the book value of the
mortgage at the end of 10 years, thus assuming a prepayment 10 years
into the future. We calculated the value of the property by
multiplying the value of the property at the time of the loan's
origination by the change in the region's median nominal house price
between the year of origination and the current year.\10 Because the
effects on claims of small changes in equity may differ depending on
whether the level of equity is positive or negative, we used a pair
of equity variables, LAGEQPOS and LAGEQNEG,\11 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 also included LAGEQPOS and LAGEQNEG in our prepayment regression.
We anticipated that higher levels of equity would be associated with
an increased likelihood of prepayment. Borrowers with substantial
equity in their home may be interested in prepaying their existing
mortgage and taking out a larger one to obtain cash for other
purposes. Borrowers with little or no equity may be less likely to
prepay because they may have to take money from other savings to pay
off their loan and cover transaction costs.
For the prepayment regression, equity was defined as book equity
instead of market equity. Book equity was defined as the estimated
property value less the amortized balance of the loan. It is book
value, not market value, that the borrower must pay to retire the
debt. Additionally, the effect of interest rate changes on
prepayment are captured by the relative interest variables.
--------------------
\9 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.
\10 The estimated rate of appreciation in nominal median house
prices, obtained from DRI/McGraw-Hill, 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 DRI/McGraw-Hill's
forecasts.
\11 Essentially, LAGEQPOS takes the value of lagged equity if equity
is positive or zero if equity is negative. LAGEQNEG takes the value
of equity if lagged equity is negative or zero if equity is positive.
LTV RATIO
------------------------------------------------------- Appendix I:2.2
In addition to LAGEQPOS and LAGEQNEG, we included another variable in
our regressions related to equity: the initial LTV ratio. LTV was
entered as a series of dummy variables depending on its size. Loans
fit into eight discrete categories. In some years, FHA measured LTV
as the loan's 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.\12
One minus LTV measures a borrower's initial equity, so we anticipate
that if LTV is an important predictor in an equation that also
includes a variable measuring current equity, it will 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 rate of change for the price of each borrower's house.
Another reason for including LTV and expecting it to have a positive
sign in our foreclosure equation is that it may capture the effects
of income constraints. We are unable to include borrowers' incomes
or payment to income ratios directly because data on borrowers'
incomes are not available.\13 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.
--------------------
\12 For the 1993 regressions, 600 loans with LTV above 106 were
deleted. We assumed that these were the result of coding errors.
\13 We also do not know whether individual borrowers have
subsequently acquired a second mortgage or other obligations that
would affect prepayment or foreclosure probabilities.
UNEMPLOYMENT
------------------------------------------------------- Appendix I:2.3
We used the annual unemployment rates for each state for the period
from fiscal year 1975 through fiscal year 1993 to describe the
condition of the economy in the state where a loan was made. We
anticipated that foreclosures would be higher in years and states
with higher unemployment rates and that prepayments would be lower
because property sales slow down during recessions. The actual
variable we used in our regressions, LAGUNEMP, is defined as the
preceding year's unemployment rate in that state.
INTEREST RATES
------------------------------------------------------- Appendix I:2.4
We included the interest rate on the mortgage as an explanatory
variable in the foreclosure equation. We expected a higher
probability of foreclosure because a higher interest rate causes a
higher monthly payment. However, in explaining the likelihood of
prepayment, our model uses the ratio of current mortgage rates to the
contract rate on the borrower's mortgage. A borrower's incentive to
prepay is high when the interest rate on a loan is greater than the
rate at which money can now be borrowed, and it diminishes as current
interest rates increase. To capture the relative attractiveness of
prepaying, we compared the interest rate on each loan with the
interest rate on 30-year mortgages available in the current year.
In our prepayment regression, we used two relative interest rate
variables RELINTH and RELINTL, so that the effect of changes in
relative interest rates could be different over different ranges.
RELINTH is defined as the ratio of the contract interest rate to the
currently prevailing rate but is never smaller than 1. RELINTL is
also defined as the ratio of the contract rate to the current rate
but is never larger than 1.\14
We created two 0-1 variables, REFIN and REFIN2, that take on a value
of 1 if the borrower had not taken advantage of a refinancing
opportunity in the past and zero 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 points\15 below the rate on the mortgage. REFIN
takes a value of 1 if the borrower has passed up a refinancing
opportunity at least once in the past. REFIN2 takes on a value of 1
if the borrower has 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 in order to avoid the transaction costs
associated with refinancing. In this case, there might be a positive
relationship, with the probability of prepayment if the borrower
fulfilled his/her anticipation and moved, thereby prepaying the loan.
--------------------
\14 For example, if a loan was made at an interest rate of 8 percent
(0.08) and the current mortgage rate is 9 percent (0.09), the loan's
interest rate is "low" relative to the prevailing mortgage rate.
RELINTH is defined as 1 and RELINTL is 8/9.
\15 A basis point equals one one-hundredth of a percentage point.
GEOGRAPHIC REGIONS
------------------------------------------------------- Appendix I:2.5
We created nine 0-1 variables to reflect the geographic distribution
of FHA loans and included them in both regressions. Locational
differences may capture the effects of differences in borrowers'
income, rates of appreciation in house prices, underwriting standards
by lenders, economic conditions not captured by the unemployment
rate, or other factors that may affect foreclosure and prepayment
rates. We assigned each loan to one of the 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.
LOAN SIZE
------------------------------------------------------- Appendix I:2.6
To obtain an insight into the differential effect of relatively
larger loans on mortgage foreclosures and prepayments, we assigned
each loan to one of seven variables (LOAN1-LOAN7). The omitted
category was loans over $100,000, and results on loan size are
relative to those loans over $100,000. All dollar amounts are
inflation adjusted and represent 1991 dollars.
POLICY YEAR
------------------------------------------------------- Appendix I:2.7
Finally, 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-YEAR7 and set them equal to 1 during the
corresponding policy year and zero otherwise.
Table I.1 summarizes the variables we used to predict claims and
prepayments along with their corresponding means. These means are
for fixed-rate mortgages of 25 or more years and less than 25 years
and investor mortgages.
Table I.1
Summary of Predictor Variables
Pr
ed
ic
to
r
va
ri
ab Mean 25 Mean less
le years or than 25 Mean
s more years investor
-- ---------------------------------------- ------------ --------- ------------
Loan size dummy variables
-----------------------------------------------------------------------------------
LO 1 if loan amount is less than $40,000 0.096 0.101 0.093
A
N
1
LO 1 if loan above $40,000 but below 0.114 0.074 0.102
A $50,000
N
2
LO 1 if loan above $50,000 but below 0.151 0.097 0.134
A $60,000
N
3
LO 1 if loan above $60,000 but below 0.166 0.129 0.148
A $70,000
N
4
LO 1 if loan above $70,000 but below 0.151 0.146 0.146
A $80,000
N
5
LO 1 if loan above $80,000 but below 0.213 0.271 0.222
A $100,000
N
6
Economic variables
-----------------------------------------------------------------------------------
IN Contract mortgage interest rate 0.099 0.103 0.104
T
E
R
E
S
T
RE The ratio of the interest rate of the 1.089 1.088 1.121
L loan and the current interest rate if
I the interest rate on the loan is higher
N than current mortgage rates, else 1
T
H
RE The ratio of the interest rate of the 0.923 0.924 0.952
L loan and the current interest rate if
I the interest rate of the loan is lower
N than current mortgage rates, else 1
T
L
RE 1 if, in at least 1 previous year, the 0.088 0.111 0.152
F mortgage interest rates had been at
I least 200 basis points below the
N contract rate and the borrower had not
refinanced, else zero
RE 1 if in at least 2 previous years the 0.055 0.076 0.103
F above situation prevailed, else zero
I
N
2
LI 1 if the property has two living units N/A N/A 0.296
V
U
N
T
2
LI 1 if the property has three or more N/A N/A 0.095
V living units
U
N
T
3
LA The previous year's unemployment rate in 0.066 0.068 0.066
G the state
U
N
E
M
P
L
O
Y
Policy year variables
-----------------------------------------------------------------------------------
YE 1 if in loan's first year, else zero 0.168 0.172 0.166
A
R
1
YE 1 if in loan's second year, else zero 0.152 0.143 0.156
A
R
2
YE 1 if in loan's third year, else zero 0.135 0.121 0.141
A
R
3
YE 1 if in loan's fourth year, else zero 0.114 0.106 0.122
A
R
4
YE 1 if in loan's fifth year, else zero 0.092 0.093 0.103
A
R
5
YE 1 if in loan's sixth year, else zero 0.075 0.080 0.088
A
R
6
YE 1 if in loan's seventh year, else zero 0.061 0.067 0.072
A
R
7
Loan-to-value dummy varriable
-----------------------------------------------------------------------------------
LT 1 if LTV equals zero, assumed missing 0.100 0.120 0.028
V0 data
LT 1 if LTV equals zero and loan was 0.089 0.100 0.025
V written in fiscal year 1983 or earlier,
0 assumed missing data
a
LT 1 if LTV above 0 and less than 60 0.015 0.040 0.008
V1
LT 1 if LTV greater than or equal to 60 but 0.092 0.169 0.244
V2 less than 85
LT 1 if LTV greater than or equal to 85 but 0.089 0.175 0.524
V3 less than 92
LT 1 if LTV greater than or equal to 92 but 0.165 0.248 0.056
V4 less than 96
LT 1 if LTV greater than or equal to 96 but 0.130 0.091 0.037
V5 less than 98
LT 1 if LTV greater than or equal to 98 but 0.179 0.081 0.047
V6 less than 100
LT 1 if LTV greater than or equal to 100 0.157 0.061 0.040
V7 but less than 102
Equity variables
-----------------------------------------------------------------------------------
LA The value of equity, defined as 1 minus -0.006 -0.002 -0.002
G the ratio of the present value of the
E loan balance, evaluated at the current
Q mortgage interest rate, to the current
N estimated house price, if equity is
E less than 0, else 0
G
LA The value of equity, defined as 1 minus 0.230 0.268 0.242
G the ratio of the present value of the
E loan balance, evaluated at the current
Q mortgage interest rate, to the current
P estimated house price, if equity is
O greater than zero, else zero
S
LA The value of equity, defined as 1 minus -0.001 -0.000 -0.000
G the ratio of the amortized loan balance
B to the current estimated house price,
K if equity is less than zero, else zero
N
E
G
LA The value of equity, defined as 1 minus 0.222 0.262 0.259
G the ratio of the amortized loan balance
B to the current estimated house price,
K if equity is greater than zero, else
P zero
O
S
Census division dummy variables
-----------------------------------------------------------------------------------
DV 1 if the loan was in the Mid-Atlantic 0.069 0.063 0.148
/ states (N.Y., Pa., N.J.), else zero
A
DV 1 if the loan was in the East South 0.070 0.062 0.048
/ Central states (Ky., Tenn., Ala.,
E Miss.), else zero
DV 1 if the loan was in the West North 0.089 0.090 0.071
/ Central states (Minn., Mo., Iowa, Neb.,
G Kans., S.D., N.D.), else zero
DV 1 if the loan was in the Mountain states 0.149 0.153 0.155
/ (Colo., Utah, Ariz., N.M., Nev., Idaho,
M Wyo., Mont.), else zero
DV 1 if the loan was in the New England 0.007 0.014 0.024
/ states (Mass., Conn., R.I., N.H.,
N Maine, Vt.) else zero
DV 1 if the loan was in the East North 0.111 0.220 0.169
/ Central states (Ill., Mich., Ohio,
R Indiana, Wisc.), else zero
DV 1 if the loan was in the South Atlantic 0.194 0.111 0.124
/ states (Hawaii, Ga., N.C., S.C., Va.,
S Md., D.C., Del., W.Va.), else zero
DV 1 if the loan was in the West South 0.152 0.167 0.166
/ Central states (Tex., Okla., La.,
W Ark.), else zero
-----------------------------------------------------------------------------------
Note: DV = Division.
N/A = Applicable to investor loans only.
ESTIMATION RESULTS
--------------------------------------------------------- Appendix I:3
As described above, 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
mortgages with terms over 25 years and terms under 25 years and for
investors' loans originated from fiscal year 1975 through fiscal year
1993. We estimated loan activity throughout the life of the loan.
The regressions were weighted by the outstanding loan balance of the
observation.
The logistic regressions estimated the probability of a loan being
prepaid or foreclosed in each year. The standard errors of the
regressions are biased downward because the errors in the regression
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 variable,
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. Both of these effects are
very strong.
As expected, the unemployment rate is positively related to the
probability of foreclosure and negatively related to the probability
of prepayment. Our results also indicate that the probability of
foreclosure is higher when LTV and INTEREST are higher. Tables I.2
and I.3 present the estimated coefficients for all of the predictor
variables for foreclosure and prepayment equations. The overall
goodness of fit was satisfactory: Chi-Square statistics were
significant on all regressions at the 0.01-percent level.
Table I.2 shows that increases in lagged equity were strongly
associated with lower claim probabilities, as long as equity was
greater than zero. Negative equity is not common and is generally
observed in the early years of a loan's duration.
Because the coefficients from a nonlinear regression can be difficult
to interpret, we transformed some of the coefficients for the 30-year
fixed-rate regressions into statements about changes in
probability.\16
Overall conditional foreclosure probabilities are estimated to be
about 1.1 percent. In other words, there is little over a 1-percent
chance for a loan to result in a claim payment in any particular
year.\17
Evaluating all variables from this mean probability, our foreclosure
regression results indicate that a 2.5-percentage-point increase in
the average national unemployment rate will raise the average
conditional claim probability by one-half a percentage point.
Similarly, a 2-percentage-point increase in the mortgage contract
rate will also raise the average conditional claim probability by
one-half a percentage point. This finding is important, in that
average contract rates have been generally declining since 1981, and
our model predicts that conditional foreclosures should also fall,
all else held constant.
Loans in the first policy year are least likely to default compared
with loans held longer than 7 years, and a 20-percentage-point
increase in equity, lagged by 1 year, decreases conditional
foreclosure probabilities by one-half a percentage point.
Table I.2
Foreclosure Equations
Predictor 30-year FRMs Other FRMs Investor
variables coefficient coefficient coefficient
------------------ ------------ ------------ ------------
INTERCEPT -7.0953 -8.5572 -7.5798
Loan size dummy variables
------------------------------------------------------------
LOAN1 0.4242 0.3037 0.1288
LOAN2 0.2762 0.1470 0.0393
LOAN3 0.1377 0.0809 -0.0018
LOAN4 0.0865 -0.2473 -0.0069
LOAN5 0.0589 -0.1748 -0.1207
LOAN6 0.0781 -0.1773 -0.1285
Economic variables
------------------------------------------------------------
INTEREST 21.2515 24.9544 21.5946
REFINANCE 0.2638 0.1644 0.3440
REFINANCE2 0.1041 -0.1130 0.2490
LAGUNEMPLOY 14.5716 13.6482 19.4680
LIVUNIT2 N/A N/A 0.3248
LIVUNIT3 N/A N/A 0.4818
Policy year variables
------------------------------------------------------------
YEAR1 -3.7092 -3.8587 -3.5909
YEAR2 -1.1513 -1.3594 -0.7918
YEAR3 -0.2676 -0.2106 0.0881
YEAR4 -0.0038 0.0288 0.2829
YEAR5 0.1248 0.1235 0.3658
YEAR6 0.1273 0.0986 0.3605
YEAR7 0.0507 0.1287 0.2071
Loan-to-value dummy variables
------------------------------------------------------------
LTV0A -0.5647 -0.2587 -0.3730
LTV0 0.0645 0.1063 -0.4703
LTV1 -0.3872 -2.0065 -0.2345
LTV2 -0.6314 -0.7016 -0.2541
LTV3 -0.5106 -0.2382 0.0569
LTV4 -0.3499 0.1073 -0.0967
LTV5 -0.3017 0.2590 -0.3078
LTV6 -0.1482 0.4050 -0.2066
LTV7 -0.0631 0.3419 -0.0510
Equity variables
------------------------------------------------------------
LAGEQNEG 0.6871 -0.2603 1.3446
LAGEQPOS -2.9437 -1.9388 -2.9875
Census divisions dummy variables
------------------------------------------------------------
DV/A -0.0636 0.4932 -0.8884
DV/E 0.1473 0.6874 0.1660
DV/G 0.3686 0.8296 0.3101
DV/M 0.9188 1.3307 0.9139
DV/N 0.1976 -2.0383 0.1103
DV/R 0.1268 0.6019 -0.3502
DV/S 0.2475 0.5630 0.2445
DV/W 0.8497 1.3850 0.8102
Summary statistics:
------------------------------------------------------------
Concordant 78.1% 81.3% 80.7%
Tied pairs 3.7% 5.4% 2.4%
Number of 4,282,370 259,833 526,816
------------------------------------------------------------
Note: DV = Division.
FRM = Fixed-rate mortgages.
N/A = Applicable to investor loans only.
Table I.3 shows our prepayment regression results. Overall,
conditional prepayment probabilities are estimated to be 8.3 percent.
In any particular year, about 8 percent of the loan dollars
outstanding will be prepaid. Evaluating all variables at the mean
probability, indicate that a 1-percentage-point increase in the
relative interest rate, when the contract rate is greater than the
current market rate, will increase conditional prepayment
probabilities by one-half of a percentage point. A
1.5-percentage-point increase in the unemployment rate will lower the
prepayment probability by one-half of a percentage point. A
7-percentage-point increase in equity will raise the conditional
prepayment probability by one-half of a percentage point.
Table I.3
Prepayment Equations
30-year
FRMs Other FRMs Investor
coefficien coefficien coefficien
Predictor variables t t t
------------------------ ---------- ---------- ----------
INTERCEPT -11.7611 -11.4539 -11.3481
Loan size variables
------------------------------------------------------------
LOAN1 -0.9999 -0.8114 -1.0659
LOAN2 -0.6489 -0.4793 -0.6642
LOAN3 -0.4381 -0.3504 -0.4452
LOAN4 -0.3161 -0.2251 -0.3248
LOAN5 -0.2005 -0.1409 -0.2224
LOAN6 -0.0980 0.0012 -0.0946
Economic variables
------------------------------------------------------------
RELINTL 2.6976 3.3592 3.5573
RELINTH 6.3475 5.6768 5.3891
LIVUNIT2 N/A N/A -0.3615
LIVUNIT3 N/A N/A -0.4521
REFINANCE -0.5837 -0.7497 -0.3477
REFINANCE2 -0.8898 -0.6058 -0.8537
LAGUNEMPLOY -5.2021 -4.1567 -6.1090
Policy year variables
------------------------------------------------------------
YEAR1 -1.8259 -1.6314 -1.5694
YEAR2 -0.3186 -0.2969 -0.2528
YEAR3 0.1947 0.0404 0.0881
YEAR4 0.4187 0.2078 0.2811
YEAR5 0.2768 0.2467 0.2154
YEAR6 0.2036 0.1834 0.1857
YEAR7 0.3381 0.3461 0.4179
Loan-to-value dummy variables
------------------------------------------------------------
LTVOA -1.1735 -0.8832 -0.8332
LTV0 1.4477 0.9036 1.0237
LTV1 0.2292 0.1679 0.3050
LTV2 0.2761 0.0128 0.1863
LTV3 0.2755 0.0642 0.0516
LTV4 0.2728 0.0346 0.2680
LTV5 0.2300 0.0191 0.1168
LTV6 0.1693 -0.0096 0.0679
LTV7 0.1060 -0.0846 -0.0118
Equity variables
------------------------------------------------------------
LAGBOOKNEG -2.3698 -1.1267 -2.4068
LAGBOOKPOS 0.9276 0.3647 0.5980
Census division dummy variables
------------------------------------------------------------
DV/A -0.5202 -0.3468 -0.3303
DV/E -0.3285 -0.0301 -0.1728
DV/G -0.0427 -0.0153 -0.0239
DV/M -0.1909 -0.0166 -0.2152
DV/N -0.2234 0.2769 -0.0666
DV/R -0.0569 0.1093 0.0161
DV/S -0.4345 -0.2077 -0.3741
DV/W -0.5900 -0.5567 -0.4624
Summary statistics:
------------------------------------------------------------
Concordant 80.7% 78.0% 78.7%
Tied pairs 0.6% 0.6% 0.6%
Number of 4,283,370 259,833 526,816
------------------------------------------------------------
Note: DV = Division.
FRM = Fixed-rate mortgages.
N/A = Applicable to investor loans only.
--------------------
\16 To determine the marginal impact of any variable on conditional
foreclosures, we determined F(Z) = EXP(Z)/[1+EXP(Z)], where Z =
i(Xi*Bi), and F(Z) was estimated by the ratio of foreclosed
dollars to total dollars in the sample. We then took the derivative
of F(Z) with respect to a specific variable. 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.
\17 This average is actually for the dollar worth of a loan, not the
number of loans.
FORECAST OF LOAN FORECLOSURES
AND EARLY PAYMENTS
--------------------------------------------------------- Appendix I:4
To test the validity of our model, we examined how well the model
predicted actual patterns of FHA's claim and prepayment rates through
fiscal year 1993. Using a sample of 10 percent of FHA's loans made
from fiscal year 1975 through fiscal year 1993, we found that our
predicted rates closely resembled actual rates.
To predict the probabilities of claim payment and prepayment, we
combined the model's coefficients with the information on a loan's
characteristics and information on economic conditions described by
our predictor variables in each year between a loan's origination and
fiscal year 1993. If our model predicted foreclosure or prepayment,
we determined the loan's balance during that year to indicate the
dollar amount associated with the foreclosure or prepayment. We
estimated cumulative claim and prepayment rates by summing the
predicted claim and prepayment dollar amounts for all loans
originated in each of the fiscal years 1975 through 1993. We
compared these predictions with the actual cumulative (through fiscal
year 1993) claim and prepayment rates for the loans in our sample.
We then forecasted future loan activity (claims and prepayments) on
the basis of the regression results described above and on
DRI/McGraw-Hill's forecasts of the key economic and housing market
variables. DRI/McGraw-Hill forecasts the median sales price of new
and existing housing, by state and year, through fiscal year 1998.
We averaged together DRI/McGraw-Hill's forecasts of new and 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. After 1998, we assumed
that prices would rise at 3 percent per year. For our base case, we
made DRI/McGraw-Hill's forecasts of appreciation rates less
optimistic by subtracting another 1 percentage point per year from
the company's forecasts. DRI/McGraw-Hill also forecast each state's
unemployment rate through fiscal year 2002. For our base case, we
used DRI/McGraw-Hill's forecasts of each state's unemployment rate
and assumed that rates from fiscal year 2003 on would equal the rate
in 2002. We also used DRI/McGraw-Hill's forecasts of interest rates
on 30-year mortgages. Figure I.1 compares predicted and actual
cumulative foreclosure rates, and figure I.2 compares predicted and
actual cumulative prepayment rates.
ESTIMATING ECONOMIC VALUE
------------------------------------------------------- Appendix I:4.1
The economic value of the Fund is defined in the Omnibus Budget
Reconciliation Act of 1990 as the "current cash available to the
Fund, plus the net present value of all future cash inflows and
outflows expected to result from the outstanding mortgages in the
Fund." Information on the capital resources of the Fund as of
September 30, 1992, and September 30, 1993, was obtained from the
audited financial statements for fiscal years 1992 and 1993. Capital
resources were reported to be $9.5 billion and $9.7 billion,
respectively.
Figure I.1: Cumulative
Foreclosure Rates by Book of
Business Through Fiscal Year
1993 for 30-Year, Fixed-Rate,
Noninvestor Loans; Actual and
Predicted
(See figure in printed
edition.)
Figure I.2: Cumulative
Prepayment Rates by Book of
Business Through Fiscal Year
1993, for 30-Year, Fixed-Rate,
Noninvestor Loans; Actual and
Predicted
(See figure in printed
edition.)
To estimate the net present value of future cash flows of the Fund,
we constructed a cash flow model to measure the five primary sources
and uses of cash for fiscal years 1975 through 1993 books of
business. The five sources and uses of cash are
income from mortgagees' premiums,
payments associated with claims on foreclosed properties,
net proceeds from the sale of foreclosed properties,
refunds of premiums on mortgages that are prepaid, and
administrative expenses for management of the program.
In addition to estimating the economic value of the Fund as a whole,
we also generated approximations of the economic value of the two
most recent books of business. To conduct this analysis, it was
necessary not only to project future cash flows but also to estimate
the level of past cash flows.
Our model was constructed to estimate cash flows for each policy year
through the life of a mortgage. An important component of the model
is converting all income and expense streams--regardless of the
period in which they actually occur--into 1993 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 U.S. Treasury securities.\18 As an approximation of
what FHA earned for each book of business, we used a rate of return
comparable to the yield on 7-year U.S. Treasury securities
prevailing when that book was written to discount all cash flows
occurring in the first 7 years of that book's existence. We assumed
that after 7 years the Fund's investment was rolled over into new
Treasury securities at the interest rate prevailing at that time and
used that rate to discount cash flows to the rollover date. For
rollover dates occurring in fiscal year 1994 and beyond, we used 7
percent as the new discount rate. As an example, cash flows
associated with the fiscal year 1992 book of business and occurring
between fiscal years 1992 and 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 discount at
a rate of 7 percent.
Our methodology for estimating each of the five principal cash flows
is described below.
--------------------
\18 Actual rates vary, of course, by the specific date in 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 as the basis for our selection of discount rates.
PREMIUM INCOME
------------------------------------------------------- Appendix I:4.2
Because FHA's premium policy has changed over time, our calculations
of premium income to the Fund changes depending on the date of the
mortgage's origination.
For fiscal years 1975 through 1983:
Premium = annual outstanding principal balance x 0.5%.
For fiscal years 1984 through June 30, 1991:
Premium = original loan amount x mortgage insurance
premium.
The mortgage insurance premium during this period is equal to 3.8
percent for 30-year mortgages and 2.4 percent for 15-year mortgages.
For the purposes of this analysis, mortgages of other lengths of time
are grouped with those they most closely approximate.
Effective July 1, 1991, FHA added an annual premium of 0.5 percent of
the outstanding principal balance to its policy of up-front premiums.
The number of years for which a borrower would be liable for making
premium payments depended on the LTV ratio at the time of
origination. (See table I.4.)
Table I.4
Number of Years of Annual Premium
Payments by Date of Mortgage Origination
and LTV
>=90% -
<90% <=95% >95%
---------------------------------- ---- ------------ ----
4th quarter 1991 5 8 10
FY 1992 5 8 10
FY 1993 7 12 30
------------------------------------------------------------
Notes: FY = Fiscal year.
> = Greater than.
< = Less than.
For the period July 1, 1991, through September 30, 1992:
Premium = (original loan amount x 3.8%) +
(annual outstanding principal balance x 0.5%).
For the period October 1, 1992, through December 31, 1992:
Premium = (original loan amount x 3.0%) +
(annual outstanding principal balance x 0.5%).
For the period January 1, 1993, through September 30, 1993:
30-year mortgages:
Premium = (original loan amount x 3.0%) +
(annual outstanding principal balance x 0.5%).
15-year mortgages:
Premium = (original loan amount x 2.0%) +
(annual outstanding principal balance x 0.5%).
For 15-year mortgages, annual premiums are payable for 8, 4, or 0
years depending on the LTV category of the mortgage at the loan's
origination.
Since some loans originated in the 1990s represent FHA streamline
refinancings--and therefore are not subject to annual premiums-- we
estimated what proportion of the post-Omnibus Budget Reconciliation
Act of 1990 loan originations were actually streamlined refinancings
of business conducted before the act's passage. Since streamline
refinancings do not require an appraisal, we decided that mortgages
coded in FHA's data base with an LTV of zero could reasonably be
assumed to represent streamlined refinancings business conducted
before the act's passage. Since streamlined refinancings do not
require an appraisal, we decided that mortgages coded in FHA's data
base with an LTV of zero could reasonably be assumed to represent
streamlined refinancings. On the basis of this assumption with which
FHA officials concurred, 10 percent of the origination dollars of
loans in the fourth-quarter of fiscal year 1991 were attributable to
streamlined refinancings, 13 percent in fiscal year 1992, and 30
percent in fiscal year 1993.
CLAIMS PAYMENTS
------------------------------------------------------- Appendix I:4.3
Claims Payments = outstanding principal balance
on foreclosed mortgages x acquisition cost ratio.
We define the acquisition cost ratio as being equal to the total
amount paid by FHA to settle a claim and acquire a property (i.e.,
FHA's "acquisition cost" as reported in its data base) 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 1992. (See tables I.5 and I.6.)
Table I.5
Acquisition Cost Ratios by Book of
Business, Fiscal Years 1975 Through 1983
19 19 19 19 19 19 19 19 19
Fiscal year 75 76 77 78 79 80 81 82 83
------------------------ -- -- -- -- -- -- -- -- --
Ratio 1. 1. 1. 1. 1. 1. 1. 1. 1.
39 31 28 23 21 20 21 21 19
------------------------------------------------------------
Table I.6
Acquisition Cost Ratios by Book of
Business, Fiscal Years 1984 Through 1993
19 19 19 19 19 19 19 19 19 19
Fiscal year 84 85 86 87 88 89 90 91 92 93
-------------------- -- -- -- -- -- -- -- -- -- --
Ratio 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
20 18 15 13 14 14 12 11 08 08
------------------------------------------------------------
NET PROCEEDS
------------------------------------------------------- Appendix I:4.4
Net proceeds = (7.8/12) x claims payments from previous
period x (1 - loss ratio) + (4.2/12) x claims payments from
current period x (1 - loss ratio).
We assumed the lag time between the payment of a claim and the
receipt of proceeds from the disposition of the property to be 7.8
months on the basis of the latest available information reported by
Price Waterhouse in its fiscal year 1988 financial audit of FHA. We
define the loss ratio as equal to FHA's reported dollar loss after
the disposition of property divided by the reported acquisition cost.
For forecast periods, we applied a loss rate of 38 percent, which is
the average loss reported by FHA's financial auditors for fiscal year
1993. This is comparable to the weighted average of losses for
fiscal years 1975 through 1989. We also used a loss rate of 38
percent to estimate the value of losses that had already occurred for
fiscal years 1991 through 1993 books of business.
REFUNDED PREMIUMS
------------------------------------------------------- Appendix I:4.5
The amount of premium refunds paid by FHA's Fund depends on the
policy year in which the mortgage is prepaid and the type of
mortgage. For mortgages prepaid between October 1, 1983, and
December 31, 1993, we used the refund rate schedule that FHA
published in the April 1984 edition of Mortgage Banking. In 1993,
FHA changed its refund policy to affect mortgages prepaid on or after
January 1, 1994. The refund rates we used from the new
schedule--which assume prepayment at mid-year--are found in table
I.7.
For loans prepaying through December 31, 1993:
Refunds = original loan amount x refund rate.
For loans prepaying on or after January 1, 1994:
Refunds = up-front mortgage insurance premium x refund rate.
Table I.7
Premium Refund as a Percent of Up-Front
Premium Paid, Assuming Prepayment in the
Sixth Month
Policy year 1 2 3 4 5 6 7
------------------ ---- ---- ---- ---- ---- ---- ----
Percent of premium
refunded 95.0 85.0 70.1 49.4 30.2 15.1 4.2
------------------------------------------------------------
ADMINISTRATIVE EXPENSES
------------------------------------------------------- Appendix I:4.6
Administrative expenses = outstanding principal balance
x 0.1%.
Our estimate of administrative expenses as 0.1 percent of the
outstanding principal balances was based on data in recent years'
financial statements.
SENSITIVITY ANALYSIS
--------------------------------------------------------- Appendix I:5
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 of the appreciation of house prices, we adjusted the
forecasts of unemployment and price appreciation to provide a range
of economic value estimates under alternative economic scenarios.
Our starting points for forecasts of the key economic variables were
forecasts made by DRI/McGraw-Hill.
We used DRI/McGraw-Hill's forecasts of house prices in each state as
the basis for our estimation of future equity. We subtracted 2
percentage points per year from DRI/McGraw-Hill's projected price
increases to adjust for quality improvements over time. This formed
our high case. For our base case, we made DRI/McGraw-Hill's
forecasts of appreciation rates less optimistic by subtracting
another 1 percentage point per year from its forecasts. For our low
case, we subtracted another 1 percentage point per year from our base
case.
DRI/McGraw-Hill also forecast each state's unemployment rate through
2002. For our high case and our base case, we used DRI/McGraw-Hill's
forecasts of each state's unemployment rate and assumed that rates
from 2003 on would equal the rate in 2002. For our low case, we
assumed that each state's 1993 unemployment rate would prevail during
1994 and beyond. Since average unemployment rate forecasts for 1994
to 1998 were lower than the 1993 average, this had the effect of
raising average unemployment through the forecast period.
Table I.8 summarizes the three economic scenarios. The rates of
house price appreciation and unemployment are based on
DRI/McGraw-Hill's forecasts. The numbers in the table are our
weighted averages of DRI/McGraw-Hill's state-level forecasts; each
state's number is weighted by the state's share of FHA's fiscal year
1993 business.
Table I.8
Summary of Forecast Scenarios
Pric Pric Pric
e Unemployme e Unemployme e Unemployme
Year rise nt rate rise nt rate rise nt rate
------ ---- ---------- ---- ---------- ---- ----------
1993 .023 .065 .023 .065 .023 .065
1994 .046 .060 .036 .060 .026 .065
1995 .044 .059 .034 .059 .024 .065
1996 .039 .063 .029 .063 .019 .065
1997 .050 .061 .040 .061 .030 .065
1998 .045 .060 .035 .060 .025 .065
------------------------------------------------------------
To assess the impact of our assumptions of the loss and discount
rates on the economic value of the Fund, we operated our cash flow
model with alternative values for these variables. We found that for
the economic scenario of our base case, a 1-percentage-point increase
in the loss rate (from our assumption of 38 to 39 percent) resulted
in a $200 million decline in our estimate of the economic value of
the Fund. Conversely, each percentage point decrease in the loss
rate below 38 percent resulted in a $200 million 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 (from our assumption of 7 to 8 percent) resulted in a $120
million increase in our estimate of economic value. Conversely, each
percentage point decrease in the discount rate below 7 percent
resulted in a $120 million decrease in our estimate of economic
value.
MAJOR CONTRIBUTORS TO THIS REPORT
========================================================== Appendix II
RESOURCES, COMMUNITY, AND ECONOMIC
DEVELOPMENT DIVISION, WASHINGTON,
D.C.
Jacquelyn L. Williams-Bridgers, Associate Director
Robert S. Procaccini, Assistant Director
Jay R. Cherlow, Assistant Director for Economic Analysis
Patrick L. Valentine, Assignment Manager
DuEwa Kamara, Senior Economist
Austin Kelly, Senior Economist
Bernard Myers, Staff Evaluator