Mortgage Financing: FHA Has Achieved Its Home Mortgage Capital Reserve
Target (Letter Report, 04/12/96, GAO/RCED-96-50).

Pursuant to a congressional request, GAO reviewed the Federal Housing
Administration's (FHA) Mutual Mortgage Insurance Fund, focusing on: (1)
an estimate of the Fund's economic net worth as of the end of fiscal
year 1994; (2) the results of the legislatively prescribed capital
reserve ratio that expresses economic net worth as a percentage of
insurance-in-force; and (3) a comparison between the GAO estimate of the
Fund's economic net worth and an estimate prepared by an accounting
firm.

GAO found that: (1) in 1994, the Fund's economic net worth continued to
improve; (2) as of September 30, 1994, the Fund had $305 billion in
outstanding mortgage loans; (3) using moderate house price appreciation
rates and unemployment rates, the Fund had an economic net worth of
about $6.1 billion and a resulting capital ratio of 2.02 percent; (4)
using low house price appreciation rates and high unemployment rates,
the Fund had an economic net worth of $3 billion; (5) using high house
price appreciation rates and low unemployment rates, the Fund had an
economic net worth of $7.4 billion; (6) during fiscal year 1994, the
Fund's capital ratio of 2.02 percent of the amortized insurance-in-force
exceeded the November 2000 capital ratio goal of 2 percent; (7) the firm
estimated that the Fund had an economic net worth of about $6.68 billion
and a resulting capital ratio of 1.99 percent at the end of fiscal year
1994, which was about the same as GAO estimate; and (8) the Fund's
future economic net worth will depend on a number of economic factors
including the appreciation rates in housing prices and whether FHA is
restructured.

--------------------------- Indexing Terms -----------------------------

 REPORTNUM:  RCED-96-50
     TITLE:  Mortgage Financing: FHA Has Achieved Its Home Mortgage 
             Capital Reserve Target
      DATE:  04/12/96
   SUBJECT:  Economic analysis
             Funds management
             Amortization
             Mortgage programs
             Mortgage protection insurance
             Fair market value
             Insurance cost control
             Insurance losses
             Unemployment rates
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
Opportunity, Committee on Banking and Financial Services, House of
Representatives

April 1996

MORTGAGE FINANCING - FHA HAS
ACHIEVED ITS HOME MORTGAGE CAPITAL
RESERVE TARGET

GAO/RCED-96-50

FHA Mortgage Financing

(385463)


Abbreviations
=============================================================== ABBREV

  ARM - adjustable rate mortgage
  CTM - continuous time estimation routine
  FHA - Federal Housing Administration
  FUND - Mutual Mortgage Insurance Fund
  GAO - General Accounting Office
  HUD - Department of Housing and Urban Development
  LTV - loan-to-value (ratio)
  VA - Department of Veterans Affairs

Letter
=============================================================== LETTER


B-270608

April 12, 1996

The Honorable Rick A.  Lazio
Chairman, Subcommittee on Housing
 and Community Opportunity
Committee on Banking
 and Financial Services
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 insured under HUD's Mutual
Mortgage Insurance Fund.  Borrowers who obtain FHA-insured mortgage
loans pay insurance premiums, which are deposited into the Fund. 
FHA-insured fund mortgages were valued at about $305 billion as of
September 30, 1994.  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 a financially 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, you asked
us to estimate the amount of capital reserves in the Fund. 
Specifically, you asked us to (1) estimate, under different economic
scenarios, the economic net worth of the Fund as of the end of fiscal
year 1994;\1 (2) assess the progress made by the Fund in achieving
the legislatively prescribed capital reserve ratio that expresses
economic net worth as a percentage of insurance-in-force; and (3)
compare our estimate of the Fund's economic net worth with the
estimate prepared for FHA by Price Waterhouse.  We presented
estimates of the Fund's economic net worth and resulting capital
reserve ratios for years prior to fiscal year 1994 in the reports and
testimonies that are listed at the end of this report.  (See "Related
GAO Reports.")


--------------------
\1 That is, the current assets available to the Fund, plus the net
present value of all future cash inflows and outflows expected to
result from mortgages insured under the Fund. 


   RESULTS IN BRIEF
------------------------------------------------------------ Letter :1

Although there is uncertainty associated with any forecast, the
economic net worth of FHA's Fund continued to improve in fiscal year
1994.  As of September 30, 1994, the end of fiscal year 1994, we
estimate, under our conservative baseline scenario, that the Fund's
economic net worth was $6.1 billion.  At that time, the Fund had
capital resources of about $10.7 billion, which were sufficient to
cover the $4.6 billion in expenses that we estimate the Fund will
incur in excess of anticipated revenues over the life of the loans
outstanding at that time.  The remaining $6.1 billion is the Fund's
economic net worth, or capital--an improvement of about $8.8 billion
from the lowest level reached by the Fund at the end of fiscal year
1990.  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 were
primarily responsible for this improvement. 

Our estimate of the Fund's economic net worth represents a capital
reserve ratio of 2.02 percent of the Fund's amortized
insurance-in-force.  Consequently, we estimate that the Fund
surpassed the legislative target for reserves (a 2-percent capital
ratio by Nov.  2000) during fiscal year 1994.  Whether the Fund can
maintain the target ratio at all times will depend on many economic
and program-related factors that will affect the financial health of
the Fund in the future.  While there are some differences in the
economic modeling techniques used and the assumptions made, our
estimate of the economic net worth of the Fund ($6.1 billion) is
similar to that of Price Waterhouse ($6.68 billion). 


   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.  There are two primary sources and three uses of
cash for the Fund.  The two sources of cash are income from
mortgagees' premiums and net proceeds from the sale of foreclosed
properties.  The three uses of cash are (1) payments associated with
claims on foreclosed properties, (2) refunds of premiums on mortgages
that are prepaid, and (3) administrative expenses for management of
the program. 

To cover losses, FHA deposits insurance premiums from participating
borrowers in the Fund.  According to 12 U.S.C.  1711, the Fund must
meet or endeavor to meet statutory capital ratio requirements; that
is, it must contain sufficient reserves and funding to cover
estimated future losses resulting from the payment of claims on
defaulted mortgages and administrative costs.  A determination of
reserves and funding to cover estimated future losses requires the
use of an accrual basis of accounting.\2 The accrual concept is
particularly important for an entity such as FHA (or any insurance
enterprise) because the actual payout or collection of cash may
precede or follow the event that gave rise to the cash transaction by
a substantial time period.  Thus, a favorable cash position, or
positive cash flow, at any given point may not reflect the true
financial position of the entity. 

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

Reforms designed to restore financial stability to the Fund and to
correct problems in loan origination and property disposition were
initiated by the Congress and HUD.  The Omnibus Budget Reconciliation
Act of 1990 (P.L.  101-508), enacted in November 1990, contained
reforms to FHA's single-family mortgage insurance program designed to
place the Fund on a financially sound basis.\3 The legislation, among
other things, required FHA borrowers to pay more in insurance
premiums over the life of the loans by adding a risk-based annual
premium to the one-time, up-front premium.  It effectively raised the
present value of the insurance premium from 3.8 percent of the loan
amount to from 5.5 to 6.8 percent, depending on the amount of the
down payment made.  It accomplished this change via two actions: 
lowering the up-front premium from 3.8 to 2.25 percent of the loan
amount over a 4-year transitional period and, during the same period,
phasing in a new annual premium of 0.5 percent of the loan balances. 
Those borrowers who make higher down payments pay the annual premium
for a shorter period. 

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

The legislation also required the Secretary of HUD to endeavor to
ensure a capital ratio of 2 percent by November 2000 and maintain
that ratio or a higher one at all times thereafter.  The act defined
the capital ratio as the ratio of the Fund's capital, or economic net
worth, to its unamortized insurance-in-force.\4

We and HUD's Inspector General have been reporting on FHA's
management problems since the early 1980s.  We have concluded in
previous testimonies and reports that in addition to economic
factors, poor program management and waste, fraud, and abuse
contributed to the losses sustained by FHA's Fund.  For example, FHA
did not have accounting data and internal controls in place to
reconcile funds from the sales of government-owned properties with
deposits to the U.S.  Treasury.  As a result, private real estate
agents were able to steal millions of dollars by simply retaining the
proceeds from the sale of FHA-owned properties rather than
transferring the funds to the Treasury.\5

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


--------------------
\2 An accrual basis of accounting recognizes revenues when earned and
expenditures when goods or services are received rather than when
cash is actually received or disbursed.  Expenses are recorded in the
same period as related revenues to the extent possible. 

\3 These reforms were also contained in the Cranston-Gonzalez
National Affordable Housing Act (P.L.  101-625).  Both the Affordable
Housing Act and the Reconciliation Act contained a provision stating,
in effect, that the reforms contained in the statute enacted first
would control.  The Reconciliation Act was enacted about 3 weeks
before the Affordable Housing Act. 

\4 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. 

\5 See Impacts of FHA Loan Policy Changes on Its Cash Position
(GAO/T-RCED-90-70, June 6, 1990) and HUD Reforms:  Progress Made
Since the HUD Scandals but Much Work Remains (GAO/RCED-92-46, Jan. 
31, 1992). 


   OUR ESTIMATES OF THE FUND'S
   ECONOMIC NET WORTH
------------------------------------------------------------ Letter :3

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


      ECONOMIC NET WORTH ESTIMATES
      OF FHA'S FUND UNDER THREE
      SCENARIOS
---------------------------------------------------------- Letter :3.1

Table 1 presents our estimates of the economic net worth and
resulting capital ratios for the FHA mortgage loans outstanding as of
September 30, 1994, under each of our three economic scenarios. 
Although future rates of appreciation in house prices are uncertain,
to be conservative, we placed greater reliance on our mid-range
baseline economic scenario because it assumes slightly lower house
price appreciation rates (1 percent annually) than the rates
forecasted by DRI/McGraw-Hill.\6 Under this scenario, we estimate
that the Fund had an economic net worth of about $6.1 billion and
resulting capital ratio of 2.02 percent at the end of fiscal year
1994.  This estimate represents an improvement of about $8.8 billion
from the lowest level reached by the Fund--a negative $2.7 billion
economic net worth estimated by Price Waterhouse at the end of fiscal
year 1990. 

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



                                Table 1
                
                  GAO's Estimates of the Economic Net
                 Worth and Capital Ratios of FHA's Fund
                        as of September 30, 1994

                         (Dollars in billions)

                                Estimated economic   Estimated capital
GAO's scenarios                          net worth     ratio (percent)
------------------------------  ------------------  ------------------
High-case                                     $7.4                2.45
Baseline case                                 $6.1                2.02
Low-case                                      $3.0                0.99
----------------------------------------------------------------------

--------------------
\6 The rates of appreciation in house prices we used were different
for each state.  Table II.10 in app.  II summarizes the aggregate
rates of appreciation and unemployment we used for each of the three
economic scenarios. 


      CHANGES IN THE FUND'S
      ECONOMIC NET WORTH DURING
      FISCAL YEAR 1994
---------------------------------------------------------- Letter :3.2

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


   CAPITAL RATIO TARGET
------------------------------------------------------------ Letter :4

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

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


      ECONOMIC CONDITIONS
---------------------------------------------------------- Letter :4.1

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


      CHANGES TO THE PROGRAM
---------------------------------------------------------- Letter :4.2

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

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


      PERFORMANCE OF REFINANCED
      LOANS
---------------------------------------------------------- Letter :4.3

The substantial refinancing of FHA's loans that occurred during
fiscal years 1992 through 1994 has created a growing class of FHA
borrowers whose future behavior is more difficult to predict than the
typical FHA borrower's.  FHA's streamlined refinanced mortgages\7
accounted for about 40 percent of the loans originated by FHA in
fiscal year 1994.  About 19 percent of FHA's amortized
insurance-in-force at the end of fiscal year 1994 consisted of
streamlined refinanced mortgages for which there is little experience
with the tendency for such loans to be foreclosed and/or prepaid. 
Because FHA insured properties for which mortgages were streamlined
refinanced were not required to be appraised, the initial
loan-to-value ratio of these loans--a key predictor of the
probability of foreclosure--is unknown.\8 The impact of these loans
on the financial health of the Fund is probably positive, since they
represent preexisting FHA business whose risk has been reduced
through lower interest rates and lower monthly payments.  However,
the lack of experience with these loans increases the uncertainty
associated with their expected foreclosure rates. 

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


--------------------
\7 FHA's streamlined refinanced mortgages are those for which an
FHA-insured mortgage loan has been repaid from the proceeds of a new
FHA-insured loan using the same property as security.  Borrowers
often refinance mortgage loans to lower their monthly principal and
interest payments when interest rates decline.  Appraisals and credit
checks are not required by FHA on these loans, and borrowers cannot
obtain cash from the transaction except for minor adjustments not
exceeding $250 at closing. 

\8 Also, FHA's data do not indicate whether there are any existing
second mortgages on these properties. 


      RISKS ASSOCIATED WITH FHA'S
      LOANS
---------------------------------------------------------- Letter :4.4

New developments in the private mortgage insurance market may
increase the average risk of future FHA-insured loans.  Home buyers'
demand for FHA-insured loans depends, in part, on the alternatives
available to them.  Some private mortgage insurers recently began
offering mortgage insurance coverage on conventional mortgages with a
97-percent loan-to-value ratio, which brings their terms closer to
FHA's 97.75-percent loan-to-value ratio on loans for properties
exceeding $50,000 in appraised value.  While potential home buyers
may consider many other factors when financing their mortgages, such
as the fact that FHA will finance the up-front premium as part of the
mortgage loan,\9 this action by private mortgage insurers could
reduce the demand for FHA-insured mortgage loans.  In particular, by
lowering the required down payment, private mortgage insurers may
attract some borrowers who might have otherwise insured their
mortgages with FHA.  If by selectively offering these low down
payment loans, private mortgage insurers are able to attract FHA's
lower-risk borrowers, such as borrowers with better-than-average
credit histories or payment-to-income ratios, new FHA loans may
become more risky on average.  If this effect is substantial, the
economic net worth of the Fund may be adversely affected, and it may
be more difficult for the Fund to maintain a 2-percent capital ratio. 


--------------------
\9 Because FHA will finance the up-front portion of the premium, the
effective loan-to-value ratio on FHA-insured loans can be higher than
100 percent. 


   PRICE WATERHOUSE'S ESTIMATES OF
   THE FUND'S ECONOMIC NET WORTH
------------------------------------------------------------ Letter :5

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

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

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

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


   CONCLUSIONS
------------------------------------------------------------ Letter :6

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


   AGENCY COMMENTS
------------------------------------------------------------ Letter :7

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

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

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

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

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


--------------------
\10 See Mortgage Financing:  Financial Health of FHA's Home Mortgage
Insurance Program Has Improved (GAO/RCED-95-20, Oct.  18, 1994). 


   SCOPE AND METHODOLOGY
------------------------------------------------------------ Letter :8

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

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

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

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

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


---------------------------------------------------------- Letter :8.1

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

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

Sincerely yours,

Judy A.  England-Joseph
Director, Housing and Community
 Development Issues


FACTORS CONTRIBUTING TO THE GROWTH
IN THE MUTUAL MORTGAGE INSURANCE
FUND'S ECONOMIC NET WORTH IN
FISCAL YEAR 1994
=========================================================== Appendix I

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



                               Table I.1
                
                 Factors Contributing to Changes in the
                 Fund's Estimated Baseline Economic Net
                     Worth During Fiscal Year 1994

                         (Dollars in billions)


Contributing factors
------------------------------------------  ------------  ------------
Estimated baseline as of Sept. 30, 1993            $4.90
Value added by additional loans made in             0.26
 fiscal year 1993 but not included in that
 year's estimate
Revised baseline estimate as of Sept. 30,                        $5.16
 1993
Value added by fiscal year 1994 loans               1.40
Changes in value of loans made in fiscal           -0.46
 year 1993 and earlier years
Net increase in baseline estimate during                          0.94
 fiscal year 1994
Baseline estimate as of Sept. 30, 1994                            6.10
----------------------------------------------------------------------
Data provided by FHA last year and used in our September 30, 1993,
economic net worth estimates did not include information on all loan
originations and terminations occurring in fiscal year 1993.  FHA
subsequently updated its records to include the remaining fiscal year
1993 activity.  As shown in table I.1, including this loan activity
increases our estimate of the Fund's economic net worth by about $260
million, resulting in a revised estimate of about $5.16 billion as of
the end of fiscal year 1993.  We also estimate that loans insured by
FHA in fiscal year 1994 contributed about $1.4 billion to the
economic net worth of the Fund.  This represents the third
consecutive year in which the Fund's new loans made a positive
contribution to the Fund's economic net worth.  However, this
increase in economic net worth was reduced by a $460 million decrease
in the economic net worth of loans insured by FHA in fiscal year 1993
and earlier years.  As a result, a net increase of $940 million was
realized in our baseline estimate during fiscal year 1994, bringing
our baseline economic net worth estimate as of September 30, 1994, to
$6.1 billion. 

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



                               Table I.2
                
                 Factors Contributing to Changes in the
                  Economic Net Worth of Loans Made in
                   Fiscal Year 1993 and Earlier Years

                         (Dollars in billions)


Contributing factors
------------------------------------------  ------------  ------------
Net change in value of loans made in               -$.46
 fiscal year 1993 and earlier years
Improvement due to actual loan performance                        $.62
 data in 1994
Interest earned on investments                                     .62
Change due to updated forecasted                                  -.24
 foreclosures and prepayments in 1995 and
 beyond
Modeling changes                                                  -.95
Base year shift                                                   -.27
Other                                                             -.24
----------------------------------------------------------------------
We estimate that the economic net worth of the Fund's loans made in
fiscal year 1993 and earlier years increased by about $620 million
because updated data showed that these loans performed better in
fiscal year 1994 than previously forecasted.  This occurred, in part,
because during fiscal year 1994, house prices increased more rapidly,
and the unemployment rate was lower than in previous economic
forecasts.  Interest earned on investments accounted for an estimated
increase of $618 million. 

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


GAO'S ECONOMETRIC AND CASH FLOW
MODELS USED TO FORECAST FHA'S
ECONOMIC NET WORTH
========================================================== Appendix II

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

Our forecasting models used observations on loan-quarters, that is,
information on the characteristics and status of an insured loan
during each quarter of its life to predict conditional foreclosure
and prepayment probabilities.\1 More specifically, our model used a
continuous time estimation routine, CTM\2 to jointly predict the
probabilities of a loan terminating in a claim or a prepayment at a
given time, as a function of interest and unemployment rates, the
borrower's equity (computed using a house's price and current and
contract interest rates as well as a loan's duration), the
loan-to-value (LTV) ratio, the house price, the geographic location
of the house, and the length of time that the loan has been active. 

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

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


--------------------
\1 These probabilities are conditional because they are subject to
the condition that the loan has remained active until a given
quarter. 

\2 CTM was developed by George Yates, and many others at the
University of Chicago.  Information on CTM is contained in CTM: 
User's Manual, Honore, Walker, Yi 1987.  University of Chicago
National Opinion Research Center. 


   DATA AND SAMPLE SELECTION
-------------------------------------------------------- Appendix II:1

For our analysis, we selected from FHA's computerized files a random
sample of 1.4 million mortgages insured by FHA from fiscal year 1975
through fiscal year 1994.\3 From FHA's records, we obtained
information on the initial characteristics of each loan, such as the
year of the loan's origination and state in which the loan
originated; the LTV ratio; the loan's amount; and the contract's
interest rate.  We categorized the loans as either foreclosed,
prepaid, or active as of the end of fiscal year 1994. 

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


--------------------
\3 FHA's A-43 data base provides current and historical information
on the mortgage loans that FHA insures. 


   SPECIFICATION FOR MODEL
-------------------------------------------------------- Appendix II: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, and so forth.  These events
are not likely to trigger foreclosure if the owner has positive
equity in his/her home because the sale of the home with realization
of a profit is better than the loss of the home through foreclosure. 
However, if the property is worth less than the mortgage, these
events may trigger default. 

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

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

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

Our first set of coefficients estimate conditional mortgage
foreclosure probabilities as a function of a variety of explanatory
variables.  Our second set of coefficients estimate conditional
prepayment probabilities.  The model estimated is a competing risks
hazard model.  The probability of prepaying or terminating with a
loss to the Fund over the course of a quarter is jointly estimated as
a function of time (the baseline hazard) multiplied by a linear
function of the independent variables.  The baseline hazards are
estimated as a Box-Cox transformation of time measured in months.\4

The two equations are estimated jointly and include an estimate of
heterogeneity parameters.  CTM estimates a distribution of points
between zero and 1, and the percentage of the population of mortgages
at each point, referred to as the heterogeneity distribution.  For
each method of termination (claim or prepayment), CTM also estimates
a coefficient by which those points are multiplied, referred to as
the factor loading.  In effect, CTM estimates a distribution of
intercepts for each termination probability.  This incorporates the
assumption that mortgage borrowers differ in their probabilities of
mortgage termination in unobservable ways.  While the different
probabilities are not attached to individual borrowers, the
heterogeneity parameters produce an estimate of the proportions of
borrowers with high or low termination propensities.  The methodology
is analogous to a random effects model for the analysis of panel
data. 

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


--------------------
\4 The Box-Cox transformation is a general class of power
transformation that includes the log transformation and
no-transformation as special cases.  The Box-Cox transformation is Y
= (X - 1)/ when  is not zero, and ln(x)
when =0. 


      EQUITY
------------------------------------------------------ Appendix II: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, (2) property
values can increase or decrease, and (3) prevailing mortgage interest
rates change, while the rate on a fixed-rate mortgage remains
constant.  Equity is a measure of the current value of a property
compared with the current value of the mortgage on that property. 
Previous research strongly indicates that borrowers with small
amounts of equity or even negative equity are more likely than other
borrowers to default.\5

We computed equity as the difference between the value of the
property and the value of the mortgage, expressed as a percentage of
the value of the property.  For example, if the value of a property
is $100,000 and the value of the mortgage is $80,000, then equity is
20 percent, or 0.2.  To measure equity for modeling the foreclosure
behavior of fixed-rate mortgages, we calculated the value of the
mortgage as the present value of the remaining mortgage payments (up
to a maximum of 10 years), evaluated at the current quarter's
fixed-rate mortgage interest rate, and added the book value of the
mortgage at the end of 10 years, thus assuming a prepayment 10 years
into the future.  We calculated the value of the property by
multiplying the value of the property at the time of the loan's
origination by the change in the state's median nominal house price
between the year of origination and the current year.\6

Because the effects on claims of small changes in equity may differ
depending on whether the level of equity is high or low, we used a
pair of equity variables, LAGEQHI and LAGEQLOW,\7 in our foreclosure
regression.  The effect of equity is lagged 1 year, since we are
predicting the time of foreclosure, which usually occurs many months
after a loan first defaults. 

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

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


--------------------
\5 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. 

\6 The estimated rate of appreciation in each state's median existing
house price, which was 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.  For calendar years 1993 and 1994, we made some
adjustments to DRI/McGraw-Hill's forecasts.  Texas homes were
estimated to have fallen in price in calendar year 1994, but others
familiar with the Texas economy claimed that prices had risen during
that year.  We adjusted the forecast for Texas so that Texas home
prices grew at 1 percent during 1994.  Also, the ratio between the
median price of existing housing and the constant quality price
index, reported by DRI/McGraw-Hill for calendar years 1993 and 1994,
was much lower than for other years.  We adjusted price appreciation
rates for calendar years 1993 and 1994 to bring the median-constant
quality ratio more in line with that of other years.  Finally, to
ensure that our estimates were conservative, we subtracted an
additional 1 percent annually from DRI/McGraw-Hill's forecasts. 

\7 LAGEQHI takes the value of lagged equity minus 20 percent if
equity is at least 20 percent.  LAGEQLOW takes the value of equity if
lagged equity is less than 20 percent.  For instance, with 10-percent
equity, LAGEQLOW would be 0.10, and LAGEQHI would be zero.  With
30-percent equity, LAGEQLOW would be 0.20, and LAGEQHI would be 0.10. 
The 20 percent threshold was chosen because loans with equity of 20
percent or more do not require insurance in the private market. 


      DOWN PAYMENT
------------------------------------------------------ Appendix II:2.2

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

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

Another reason for including DOWNPAY and expecting it to have a
negative sign in our foreclosure equation is that it may capture the
effects of income constraints.  We are unable to include borrowers'
incomes or payment-to-income ratios directly because data on
borrowers' incomes were not available for every year in the sample
period.\8 However, it seems likely that borrowers with little or no
down payment are more likely to be financially stretched in meeting
their payments and, therefore, more likely to default.  The
anticipated relationship between DOWNPAY and the probability of
prepayment is uncertain. 


--------------------
\8 Also, FHA's data do not indicate whether individual borrowers have
subsequently acquired a second mortgage or other obligations that
would affect prepayment or foreclosure probabilities. 


      UNEMPLOYMENT
------------------------------------------------------ Appendix II:2.3

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


      INTEREST RATES
------------------------------------------------------ Appendix II:2.4

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

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

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

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

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

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

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

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


      GEOGRAPHIC REGIONS
------------------------------------------------------ Appendix II:2.5

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


      HOUSE PRICE
------------------------------------------------------ Appendix II:2.6

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


      TIME
------------------------------------------------------ Appendix II:2.7

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

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



                                    Table II.1
                     
                       Summary of Predictor Variable Means

                                             30-
                                   30-      year
Predicto                          year     fixed       15-          Invest
r                               fixed-      rate      year  Invest      or
variable                          rate  refinanc    fixed-      or  refina
s                                  new         e      rate     new     nce  ARM
--------  ------------------  --------  --------  --------  ------  ------  ----
House price variables
--------------------------------------------------------------------------------
LOGPRICL  Log of house price      6.34      6.35      6.27    6.36    6.37  6.38
          if < $60,000

LOGPRICM  Log of house price      0.32      0.28      0.27    0.37    0.38  0.39
          > $60,000 but <
          $120,000

LOGPRICH  Log of house price      0.01      0.06      0.02    0.02    0.02  0.01
          > $120,000


Economic Variables
--------------------------------------------------------------------------------
LOGINT    Log of contract        -2.27     -2.29     -2.27   -2.23   -2.28  -
          interest rate                                                     2.59

INTVOL    The volatility of       5.26      3.78      4.78    5.12    3.19  3.69
          mortgage rates,
          defined as the
          standard deviation
          of 30-year fixed
          mortgage rates
          over the prior 12
          months

YIELDCUR  The slope of the        0.13      0.20      0.15    0.14    0.16  0.36
          yield curve,
          defined as the
          difference between
          1-year and 10-
          year Treasury
          interest rates
          minus 250 basis
          points, but not
          less than zero

RELEQLO   The ratio of the        9.44      9.97      9.65    9.64    9.98  N/A
          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       10.42     10.83     10.30   10.54   10.75  N/A
          market value of
          the mortgage to
          the book value if
          the market value
          is above the book
          value, else 1

REFIN     Number of quarters      0.54      0.48      0.49    0.86    0.53  0.06
          that the
          prevailing
          mortgage interest
          rate had been at
          least 150 basis
          points below the
          contract rate and
          the borrower had
          not refinanced, up
          to eight quarters

REFIN2    Number of quarters      0.14      0.13       N/A    0.28    0.03  N/A
          that the above
          situation
          prevailed, beyond
          eight quarters

LAGUNEMP  The logarithm of       -2.76     -2.82     -2.77   -2.76   -2.83  -
          the previous                                                      2.86
          year's
          unemployment rate
          in the state


Time variables
--------------------------------------------------------------------------------
YEAR12    Number of quarters      5.06      3.80      5.00    5.05    3.86  4.58
          since origination,
          up to six

YEAR34    Number of quarters      4.40      1.43      4.24    4.36    1.88  3.02
          since the 6th, up
          to 14


Equity variables
--------------------------------------------------------------------------------
DOWNPAY   The down payment,       0.48      0.19      0.12    0.11    0.10  0.36
          expressed as a
          percentage of the
          purchase price of
          the house. The
          values reported in
          FHA's database
          were adjusted to
          ensure that
          closing costs were
          included in the
          loan amount and
          excluded from the
          house price.

LAGEQLOW  The value of            1.36      0.64      0.16    0.17    0.14  N/A
          equity, defined as
          1 minus the ratio
          of the present
          value of the loan
          balance, evaluated
          at the current
          mortgage interest
          rate, to the
          current estimated
          house price, if
          equity is less
          than 20 percent,
          else 20 percent

LAGEQHI   The value of            0.91      0.09      0.13    0.09    0.10  N/A
          equity, defined as
          1 minus the ratio
          of the present
          value of the loan
          balance, evaluated
          at the current
          mortgage interest
          rate, to the
          current estimated
          house price, minus
          20 percent, but no
          less than zero

LAGBKLOW  The value of            1.34      0.69      1.62    1.67    1.38  1.13
          equity, defined as
          1 minus the ratio
          of the amortized
          loan balance to
          the current
          estimated house
          price, if equity
          is less than 20
          percent, else 20
          percent

LAGBKHI   The value of            0.76      0.10      0.14    0.09    0.15  0.23
          equity, defined as
          1 minus the ratio
          of the amortized
          loan balance to
          the current
          estimated house
          price, minus 20
          percent, but no
          less than zero


Geographic dummy variables
--------------------------------------------------------------------------------
EAST      1, if the loan was      0.07      0.02      0.10    0.15    0.04  0.05
          in the East
          (Conn., Maine,
          Mass., N.H., N.J.,
          N.Y., Pa., R.I.,
          and Vt.), else
          zero

SOUTH     1, if the loan was      0.37      0.31      0.37    0.29    0.23  0.29
          in the South
          (Ala., Ark., D.C.,
          Del., Ga., Ky.,
          La., Md., Miss.,
          N.C., Okla., S.C.,
          Tenn., Tex., Va.,
          and W.Va.), else
          zero

MIDWEST   1, if the loan was      0.21      0.21      0.32    0.20    0.17  0.33
          in the Midwest
          (Ill., Ind., Iowa,
          Kans., Mich.,
          Minn., Mo., Nebr.,
          N.D., Ohio, S.D.,
          and Wis.), else
          zero

JUDICIAL  1, if state             0.37      0.21      0.44    0.43    0.26
          allowed judicial                                                  0.42
          foreclosure (list
          of states varies
          by year)
--------------------------------------------------------------------------------
Notes:  For ARM loans, REFIN is a simple dummy variable that equals 1
for refinancing loans and zero for purchase money loans.  Orders of
magnitude are those used in the regressions. 

Legend

N/A = not applicable. 


   ESTIMATION RESULTS
-------------------------------------------------------- Appendix II:3

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

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

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

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



                                    Table II.2
                     
                              Foreclosure Equations

                                     Refinanc
                                            e
                                New       30-                                15-
Predictor                   30-year      year        New     Refinance      year
variable                      fixed     fixed   investor      investor     fixed
---------------------  ------------  --------  ---------  ------------  --------
INTERCEPT                    17.739    14.106     15.158        14.692    18.662
TIME                          0.564     0.543      0.332         0.061     0.906
EXPONENT                     -1.126    -1.000     -1.522        -2.257    -0.939
YEAR12                       -0.571    -0.297     -0.660        -0.436    -0.638
YEAR34                       -0.155         0     -0.152             0    -0.200
NORTHEAST                    -0.351    -0.734     -0.773        -0.890    -0.164
MIDWEST                      -0.177    -0.132     -0.242        -0.187     0.050
SOUTH                         0.119     0.228      0.322         0.353     0.235
JUDICIAL                     -0.030    -0.241     -0.070        -0.298     0.033
NOAPPRAISAL                  -0.365     0.583     -0.651         0.187    -0.198
REFIN1                        0.081     0.041      0.078        -0.011    -0.112
REFIN2                       -0.028         0     -0.045             0     0.040
LOGPRICLOW                   -0.552     0.478     -0.004         0.784    -0.276
LOGPRICMED                   -0.144     0.424     -0.276         0.684    -0.595
LOGPRICHI                     0.060     1.494      0.792         1.008    -0.943
DOWNPAY                      -0.183     0.097     -0.072         0.577    -0.323
LAGEQHI                      -0.486    -0.481     -0.471        -0.967    -0.342
LAGEQLOW                     -0.236    -0.206     -0.205        -0.380    -0.128
INTVOL                        0.006     0.062      0.003        -0.016     0.041
LAGUNEMP                      0.785     0.689      0.653         0.243     0.706
LOGINT                        3.390     5.856      3.781         7.685     4.289
--------------------------------------------------------------------------------


                                    Table II.3
                     
                               Prepayment Equations

                                     Refinanc
                                            e
                                New       30-                                15-
Predictor                   30-year      year        New     refinance      year
variable                      fixed     fixed   investor      investor     fixed
---------------------  ------------  --------  ---------  ------------  --------
INTERCEPT                   -25.374   -30.372    -23.236       -17.113   -25.331
TIME                          0.256     0.556      0.306         0.227     0.865
EXPONENT                     -0.982    -0.583     -0.762        -0.832    -0.482
YEAR12                       -0.151    -0.368     -0.170        -0.248    -0.377
YEAR34                       -0.046         0     -0.054             0    -0.132
NORTHEAST                    -0.230    -0.859     -0.188        -1.094    -0.340
MIDWEST                       0.180     0.139      0.120         0.052     0.124
SOUTH                        -0.305    -0.466     -0.143        -0.278    -0.279
NOAPPRAISAL                  -0.031     0.431     -0.277        -0.033     0.169
REFIN1                       -0.081    -0.121     -0.071        -0.126     0.338
REFIN2                       -0.081         0     -0.117             0    -0.066
LOGPRICLOW                    1.186     1.632      1.019         0.766     1.172
LOGPRICMED                    0.828     0.913      0.785         0.734     0.763
LOGPRICHI                     0.690    -0.810     -0.090        -0.663     0.093
DOWNPAY                      -0.013    -0.103      0.015        -0.122    -0.056
LAGBKHI                       0.069     0.056      0.058         0.279     0.075
LAGBKLOW                      0.026    -0.055      0.059        -0.089    -0.010
INTVOL                        0.026     0.215      0.035         0.251     0.060
RELEQLOW                      0.444     0.387      0.558        -0.022     0.671
RELEQHI                       1.314     1.454      1.060         1.211     1.382
LAGUNEMP                     -0.211    -1.400     -0.305        -0.466    -0.331
YIELDCURVE                    0.542    -0.769      1.281        -0.847     0.798
Number of loans             334,987   228,307    233,920        46,788   259,328
--------------------------------------------------------------------------------


                               Table II.4
                
                      Heterogeneity Distributions

                                Cumulati              Factor
                                      ve             loading    Factor
                                probabil            foreclos   loading
Type of loan                         ity  Location         e    prepay
------------------------------  --------  --------  --------  --------
New 30-year fixed-rate             0.629         0    -3.179    -7.800
                                   0.877     0.169
                                   0.936     0.389
Refinance 30-year fixed-rate       0.621         0    -3.861     -5.56
                                   0.917     0.352
New investor                       0.879         0    -1.407    -4.124
Refinance investor                 0.846         0    -0.863     -2.38
15-year fixed-rate                 0.511         0     -4.58     -4.94
                                   0.888     0.291
----------------------------------------------------------------------


                               Table II.5
                
                     Adjustable Rate Mortgage Model

Predictor variable                     Foreclosure          Prepayment
------------------------------  ------------------  ------------------
INTERCEPT                                   16.418              -2.404
TIME                                         0.450               0.772
EXPONENT                                    -1.392              -0.583
YEAR12                                      -0.668              -0.396
YEAR34                                      -0.109              -0.127
NORTHEAST                                   -0.037              -0.200
MIDWEST                                     -0.363               0.174
SOUTH                                        0.170              -0.276
JUDICIAL                                    -0.195               0.010
NOAPPRAISAL                                  0.184               0.555
REFIN                                        0.031               0.582
LOGPRICLOW                                  -1.082               0.605
LOGPRICMED                                  -0.335               0.376
LOGPRICHI                                    0.711              -0.611
DOWNPAY                                     -0.118               0.006
LAGBKHI                                     -0.598               0.144
LAGBKLOW                                    -0.284               0.245
CHANGEPOS                                   -0.052              -0.727
CHANGENEG                                   -0.264              -0.117
CAPPEDPOS                                   -0.113              -0.010
CAPPEDNEG                                   -0.030              -0.271
INTRVOLATIL                                  0.115               0.167
LAGUNEMP                                     0.535              -0.282
LOGINT                                       1.530                   0
YIELDCURVE                                       0               0.833
Number of loans                            296,659             296,659
----------------------------------------------------------------------

   FORECAST OF LOAN FORECLOSURES
   AND EARLY PAYMENTS
-------------------------------------------------------- Appendix II: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 1994.  Using a sample of 10 percent of FHA's loans made
from fiscal year 1975 through fiscal year 1994, we found that our
predicted rates closely resembled actual rates. 

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

   Figure II.1:  Cumulative
   Foreclosure Rates by Book of
   Business Through Fiscal Year
   1994 for 30-Year, Fixed-Rate,
   Noninvestor Loans--Actual and
   Predicted

   (See figure in printed
   edition.)

   Figure II.2:  Cumulative
   Prepayment Rates by Book of
   Business Through Fiscal Year
   1994 for 30-Year, Fixed-Rate,
   Noninvestor Loans--Actual and
   Predicted

   (See figure in printed
   edition.)

We then forecasted future loan activity (claims and prepayments) on
the basis of the regression results described above and on
DRI/McGraw-Hill's forecasts of the key economic and housing market
variables.  DRI/McGraw-Hill forecasts the median sales price of
existing housing, by state and year, through fiscal year 1998.  We
subtracted 2 percentage points per year to adjust for improvements in
the quality of housing over time and the depreciation of individual
housing units.  After fiscal year 1998, we assumed that prices would
rise at 3 percent per year.  For our base case, we made
DRI/McGraw-Hill's forecasts of appreciation rates less optimistic by
subtracting another 1 percentage point per year from the company's
forecasts.\9 DRI/McGraw-Hill also forecast each state's unemployment
rate through fiscal year 2002.  For our base case, we used
DRI/McGraw-Hill's forecasts of each state's unemployment rate and
assumed that rates from fiscal year 2003 on would equal the rate in
fiscal year 2002.  We also used DRI/McGraw-Hill's forecasts of
interest rates on 30-year fixed-rate mortgages. 


--------------------
\9 Other adjustments were also made, as indicated previously in
footnote 6. 


      ESTIMATING ECONOMIC VALUE
------------------------------------------------------ Appendix II: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, 1994, was obtained from the audited financial
statements for fiscal year 1994.  Capital resources were reported to
be $10.8 billion. 

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

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

Our model was constructed to estimate cash flows for each policy year
through the life of a mortgage.  An important component of the model
is its ability to convert all income and expense streams--regardless
of the period in which they actually occur--into a 1994 present
value.  We applied discount rates to match as closely as possible the
rate of return that FHA likely earned in the past or would earn in
the future from its investment in U.S.  Treasury securities.\10 As an
approximation of what FHA earned for each book of business,\11 we
used a rate of return comparable to the yield on 7-year U.S. 
Treasury securities prevailing when that book was written to discount
all cash flows occurring in the first 7 years of that book's
existence.  We assumed that after 7 years, the Fund's investment was
rolled over into new Treasury securities at the interest rate
prevailing at that time and used that rate to discount cash flows to
the rollover date.  For rollover dates occurring in fiscal year 1994
and beyond, we used 7 percent as the new discount rate.  As an
example, cash flows associated with the fiscal year 1992 book of
business and occurring from fiscal year 1992 through fiscal year 1998
(i.e, the first 7 policy years) were discounted at the 7-year
Treasury rate prevailing in fiscal year 1992.  Cash flows associated
with the fiscal year 1992 book of business but occurring in fiscal
year 1999 and beyond are discounted at a rate of 7 percent. 

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


--------------------
\10 Actual rates vary 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. 

\11 New mortgage loans insured by FHA in a given fiscal year. 


      PREMIUM INCOME
------------------------------------------------------ Appendix II: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.\12

For fiscal years 1975 through 1983: 

Premium = annual outstanding principal balance x 0.5%. 

For fiscal years 1984 through June 30, 1991: 

Premium = original loan amount x mortgage insurance premium. 

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

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



                               Table II.6
                
                   Number of Years of Annual Premium
                Payments by Date of Mortgage Origination
                                and LTV


                                      <90%  >=90%to<=95%          >95%
----------------------------  ------------  ------------  ------------
4th quarter FY 1991                      5             8            10
FY 1992                                  5             8            10
FY 1993 and 1994                         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 April 17, 1994: 

30-year mortgages:  Premium = (original loan amount x 3.0%) + (annual
outstanding principal balance x 0.5%). 

15-year mortgages:  Premium = (original loan amount x 2.0%) + (annual
outstanding principal balance x 0.25%). 

For the period April 18, 1994, through September 30, 1994: 

30-year mortgages:  Premium = (original loan amount x 2.25%) +
(annual outstanding principal balance x 0.5%). 

15-year mortgages:  Premium = (original loan amount x 2.00%) +
(annual outstanding principal balance x 0.25%). 

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


--------------------
\12 These premium rates also apply to adjustable-rate mortgages
insured since fiscal year 1983. 


      CLAIMS PAYMENTS
------------------------------------------------------ Appendix II: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 database) divided by the
outstanding principal balance on the mortgage at the time of
foreclosure.  For the purpose of our analysis, we calculated an
average acquisition cost ratio for each year's book of business using
actual data for fiscal years 1975 through 1992 and applied that
average to projected claims.  Beginning in fiscal year 1993, FHA's
A43 database no longer contained the information needed to calculate
the acquisition cost ratio.  Therefore, we used the fiscal year 1992
ratio for fiscal years 1993 and 1994.  (See tables II.7 and II.8.)



                               Table II.7
                
                   Acquisition Cost Ratios by Book of
                Business, Fiscal Years 1975 Through 1983


                  1975  1976  1977  1978  1979  1980  1981  1982  1983
----------------  ----  ----  ----  ----  ----  ----  ----  ----  ----
Ratio             1.39  1.31  1.28  1.23  1.21  1.20  1.21  1.21  1.19
----------------------------------------------------------------------


                               Table II.8
                
                   Acquisition Cost Ratios by Book of
                Business, Fiscal Years 1984 Through 1994


                            19  19  19  19  19  19  19  19  19  19  19
                            84  85  86  87  88  89  90  91  92  93  94
--------------------------  --  --  --  --  --  --  --  --  --  --  --
Ratio                       1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.
                            20  18  15  13  14  14  12  11  08  08  08
----------------------------------------------------------------------

      NET PROCEEDS
------------------------------------------------------ Appendix II:4.4

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

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


      REFUNDED PREMIUMS
------------------------------------------------------ Appendix II: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 from October 1, 1983, to December
31, 1993, we used the refund rate schedule that FHA published in the
April 1984 edition of Mortgage Banking.  In 1993, FHA changed its
refund policy to affect mortgages prepaid on or after January 1,
1994.  The refund rates that we used from the new schedule--which
assume prepayment at mid-year--are found in table II.9. 

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

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



                               Table II.9
                
                 Premium Refund as a Percentage of Up-
                Front Premium Paid, Assuming Prepayment
                           in the Sixth Month


                                 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 II: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 II: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 rate of
unemployment and the rate of appreciation of house prices, we
adjusted the forecasts of unemployment and price appreciation to
provide a range of economic value estimates under alternative
economic scenarios.  Our starting points for forecasts of the key
economic variables were forecasts made by DRI/McGraw-Hill. 

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

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

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



                              Table II.10
                
                     Summary of Forecast Scenarios


                  Pric              Pric              Pric
                     e  Unemployme     e  Unemployme     e  Unemployme
Year              rise     nt rate  rise     nt rate  rise     nt rate
----------------  ----  ----------  ----  ----------  ----  ----------
1995              .004        .063  .024        .053  .044        .053
1996              .013        .067  .033        .057  .053        .057
1997              .002        .068  .022        .058  .052        .058
1998              .002        .067  .022        .057  .042        .057
----------------------------------------------------------------------
To assess the impact of our assumptions of the loss and discount
rates on the economic value of the Fund, we operated our cash flow
model with alternative values for these variables.  We found that for
the economic scenario of our base case, a 1-percentage-point increase
in the loss rate (from our assumption of 38 to 39 percent) resulted
in a $201 million decline in our estimate of the economic value of
the Fund.  With respect to the discount rate, we found that for our
base case economic scenario, a 1-percentage-point increase in the
interest rate that was applied to most periods' future cash flow
(from our assumption of 7 to 8 percent) resulted in a $90 million
increase in our estimate of economic value. 


MAJOR CONTRIBUTORS TO THIS REPORT
========================================================= Appendix III

RESOURCES, COMMUNITY, AND ECONOMIC
DEVELOPMENT DIVISION, WASHINGTON,
D.C. 

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
Leslie Black-Plumeau, Senior Evaluator





RELATED GAO PRODUCTS
============================================================ Chapter 0

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

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

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

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

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

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

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

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


*** End of document. ***