Since the housing market collapse the focus of policy makers has shifted from putting borrowers into owner occupied housing to keeping them there.  In a new paper written by Ken Lam, Robert M. Dunsky, and Austin Kelly for the Federal Housing Finance Agency (FHFA) financing to do so are referred to as "sustainable mortgages."

One key variable for limited default risk at the time a mortgage is originated is the downpayment requirement.  While this is not the sole determent of default risk, the authors speculate that the effect of changes in the amount of down payment required for a mortgage may be influenced by how stringent other underwriting requirements are, particularly the borrower's credit score.

The FHFA paper, Impacts of Down Payment Underwriting Standards on Loan Performance - Evidence from the GSEs and FHA portfolios evaluates the extent to which higher down payments produce more sustainable mortgages.  The authors used hazard models to estimate the relationship between the down payment (the loan to value ratio or LTV) requirements and loan performance, controlling for a wide array of borrower and loan characteristics and housing market conditions. 

The study focuses on the market served by the two government sponsored enterprises (GSEs) Freddie Mac and Fannie Mae and by the Federal Housing Administration (FHA) and was limited to 30-year, fixed rate home purchase mortgages.  It does not look at the performance of subprime or Alt-A mortgages.  Loans purchased by the GSEs generally require a 20 percent down payment, mortgage insurance or a second lien.  FHA mortgages may require as little as 3 to 4 percent down.

The study used history of loan performance data from the GSEs for loans originated from 1995 to 2008 and data from FHA's single-family data warehouse for loans originated from 2004 to 2008.  Loan performance was observed through December 2012.  A 17 percent random sample of loans was drawn from the FHA loans and a 5 percent random sample from the GSE analysis universe.  The sample represents 2,200,701 FHA loans and 22,138,803 purchased by the GSEs.

Loan performance data was merged with data from the Bureau of Labor Statistics on state level unemployment rates, Federal Reserve information of Treasury yields, and from Freddie Mac on prevailing mortgage interest rates.  Data for simulating delinquency and foreclosure rates were taken from forecasts of house prices, interest rates and unemployment from Moody Analytics.

The study used two measures of mortgage performance; 90-day delinquency and foreclosure completion which, for GSE loans includes short sales, deeds-in-lieu, third party sales at auction, loans that ever entered the bank owned (REO) inventory, and charge-offs in lieu of foreclosure..  For FHA loans foreclosure completion was measured by claim completion.

For both the FHA and GSE market segments a set of explanatory variables was used across the two measures of performance outcomes.  The variables included:

  • Mortgage age (seasoning).
  • Origination year.
  • FICO score at origination.
  • LTV ratio at origination.
  • Front- and back-end debt-to-income (DTI) ratios at origination.
  • Original loan balance.
  • Interaction of current LTV (on a monthly basis) and FICO score at origination.
  • Spread between loan's contract interest rate and prevailing rate at origination.
  • Interaction of refinance incentives (spread) and burnout factor.
  • Yield curve spread.
  • Geographic variations.
  • State foreclosure laws.
  • State unemployment rate.
  • Source of downpayment funds (FHA only).
  • Presence of junior liens.
  • Number of housing units.
  • Housing structure type.

The authors conducted simulations using regression coefficients and a set of synthetic loan-month records with variations across the variables of interest (especially LTV, FICO score, and front‐end DTI), while other loan and borrower characteristics were held constant throughout. The set of synthetic loan‐month records were constructed with the following loan and borrower characteristics.

  1. Originated in January 2013.
  2. Original mortgage amount of $200,000.
  3. Mortgage rate at origination, 5 percent.
  4. Borrower FICO score at origination varies from 620 to 740 by an increment of 40.
  5. LTV at origination varies from 70 percent to 100 by an increment of 1.
  6. Front‐end debt‐to‐income (DTI) ratio is set at 31 percent and 45 percent.
  7. Back‐end debt‐to‐income (DTI) ratio is set at 45 percent.
  8. Source of down payment is self‐financed (only relevant to the FHA segment).
  9. No second lien.
  10. Structure contains one housing unit and is not a condo.
  11. Located in metropolitan area.
  12. One loan per state (50 states plus the District of Columbia), per loan/borrower characteristic.

This setup generated a total of 12,648 unique synthetic loans. For each loan, the authors then generated monthly records for seven years following origination. This resulted in a total of 1,062,432 loan‐month records.

The outcomes of interest are the predicted seven‐year cumulative foreclosure completion rate and the predicted seven‐year cumulative 90‐day delinquency rate.  The focus however was on the former; findings on the 90-day delinquency rate are covered only briefly in this summary.

The seven-year time span was selected because loan terminations in that time span are more likely due to underwriting variables than other trigger events. It becomes increasingly difficult to tease out other confounding factors in older loans and cumulative rates tend to taper off or flatten beyond 7 years. The measure of delinquency and foreclosure completion used in the study represents the cumulative or lifetime probability of a loan becoming delinquent (or reaching foreclosure completion).

The first finding was that, for both GSE and FHA segments, as the original LTV increases (with borrower FICO and front-end DTI held constant at 620 and 31 respectively), the lifetime foreclosure rate rises monotonically.  For the GSE loans in the table below, for example, as the original LTV increases from 70 to 100, the foreclosure rate climbs progressively from 5.66 percent to 19.77 percent. GSE borrowers appear to have a higher foreclosure rate compared to borrowers in the FHA market segment with the same original LTV but this is an artifact of using different foreclosure measures between the two market segments.

In the second column of each panel foreclosure rate changes are presented in ratio format, where the results are shown relative to the baseline foreclosure rate for loans with 80 percent LTV at loan origination. The Exhibit indicates that, for example, the foreclosure rate is 9.20 percent for a GSE loan with 80 percent LTV. If the same loan was underwritten with 90 percent LTV, the foreclosure rate would be 1.48 times the baseline level.  Apparently the LTV‐ foreclosure rate relationship is nonlinear, especially for the FHA segment. When the original LTV is changed from 80 to 70, the foreclosure rate would be 0.72 times the baseline level. However, if we adjust the original LTV by the same increment in the other direction - from 80 to 90, the foreclosure rate would be 1.62 times the baseline level.  This seems to indicate that foreclosure rates are more sensitive or responsive to LTV changes in the FHA than in the GSE segment of the market.


Exhibit 3 repeats the same analysis, separately, for borrowers with four FICO score levels: 620, 660, 700, and 740 with a constant DTI ration of 31 percent.  By holding LTV constant, borrowers with a lower FICO score are associated with a higher foreclosure rate.  When expressed as a multiple of the baseline rate, the foreclosure rate grows steadily with LTV in each FICO class.  These relationships hold for both GSE and FHA segments.


As a multiple of the baseline rate the rate of foreclosure grows similarly for the four FICO brackets. This nonetheless does not mean that the growth in the foreclosure rate is the same across the four FICO groupings. In fact, the absolute rate of foreclosure rises with LTV much more dramatically for borrowers with lower FICO scores than for borrowers with a higher FICO.


As expected, across all LTV levels, borrowers with a higher DTI had a higher foreclosure rate. This is true across both market segments but the LTV-foreclosure rate relationship has a relatively modest sensitivity to the DTI level.  The dramatic effects of the FICO score impact on the LTV‐foreclosure relationship are not observed here, however and this is true for both segments of the mortgage market.

The authors similarly tested relationships with 90 day delinquencies in the same manner as completed foreclosures.  Overall, they found that the LTV-delinquency rate relationship is very much like the LTV‐ foreclosure rate relationship. As the original LTV rises, the lifetime delinquency rate increases monotonically. This is true for both segments of the market and across FICO levels.  However they found that adjusting the original LTV generates a larger impact on foreclosure than delinquency for both market segments.