## Abstract

How did pricing for mortgage credit risk change during the years prior to the 2008 financial crisis? Using a database from a major American bank that served as trustee for private-label mortgage-backed securitized (PLS) loans, this paper identifies a decline in credit spreads on mortgages conditioned on loan and borrower characteristics. We show that observable risk factors, FICO score and loan-to-value ratio, had less of an impact on mortgage pricing over time. As the volume of PLS mortgages expanded and lending terms eased, risk premiums failed to price the increase in risk.

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## Notes

- 1.
For a history of PLS, see Levitin and Wachter (2011).

- 2.
They also point to the salience of the subprime market in default outcomes.

- 3.
See Justiniano et al. (2017) for further discussion and references on this.

- 4.
PLS are mortgage securitizations, which are not guaranteed by government-sponsored entities (Fannie Mae and Freddie Mac) or the federal government (Ginnie Mae). This bank’s share in the PLS trusteeship market, as measured by total deal dollar volume, was generally in the range of 10% during the years for which data are available (Inside Mortgage Finance 2012). The database is available from the authors and is from one of several major U.S. banks that served as trustees for private-label mortgage-backed securities (PLS).

- 5.
Our analysis collects data from all securitized mortgage pools originated from the same vintage into a single pool by year (vintage pools). Even if mortgage pools are homogeneous in borrower and loan characteristics, the analysis of risk pricing via the coefficients of key variables is unaffected.

- 6.
There are 103 detailed classification of product types. For more information, see Footnote 11.

- 7.
Observations missing FICO score, document type, appraisal value, original balance, origination date, or LTV (almost 40% of the overall data) are dropped from the dataset. Details are provided in the Appendix.

- 8.
To calculate the percentage shares of non-traditional mortgages, we sum up the share of ARM loans with balloon tag “B”, interest-only tag “IO” or negative amortization tag “NegAm” and the share of FRM loans with balloon tag “B” in Table 1.

- 9.
To calculate the percentage share of interest-only (negative amortization) loans, we sum up the share of ARM loans with interest-only tag “IO” (negative amortization tag “NegAm”) in Table 1.

- 10.
2/28 ARMs are adjustable rate mortgages with the initial mortgage rate fixed for the first two years and adjusting for the next 28 years. The interest rate adjustment frequency is every 6 months and over 95% use 6-month London Interbank Offered Rate (LIBOR) as the index rate. The floating mortgage rate is the sum of the index rate and a margin that is specified at the beginning of the mortgage contract.

- 11.
2/6 month ARMs are adjustable rate mortgages with the initial mortgage rate fixed for the first 2 years and adjusting every 6 months later on. 5/1 ARMs are adjustment rate mortgages with the initial mortgage rate fixed for the first 5 years and adjusting every year later on. Detailed mortgage product types provide more information but are only available to a subsample of ARM loans. We follow the coding of the product type in the database. It is possible that the product types are not mutually exclusive. For example, a fraction of “5-year ARMs” may fall in the category of “5/1 ARMs”. There may be characteristics that distinguish those two groups, but they are unobservable to investors or researchers. Given the information provided by the database, we consider the loans within a product type defined by the database as homogeneous.

- 12.
The listed product types cover the vast majority (99%) of loans when data is available on detailed product types. However, we include all 103 variables in our regression results with detailed product types.

- 13.
We also report the frequency and percentage weighted by the original balance with the unweighted counterparts for comparison. The unweighted and weighted rankings generally coincide.

- 14.
We report the trends over time in Figure 1a and b respectively in ARMs by loan purpose and by documentation level. Using quarterly data instead of annual aggregated shares, we show how the shares of refi loans (with and without cash-out) change rapidly within a year.

- 15.
- 16.
There are more than 1400 mortgage pools in the dataset. More than 95% of the pools have either ARMs or FRMs, but not both.

- 17.
We use LTV instead of combined LTV (CLTV), because about 40% of ARM loans do not report CLTV. Levitin and Wachter (2015), using data from INTEX, show that CLTV rose from 80% in 2003 to 89% in 2006.

- 18.
- 19.
Loan performance is recorded for the past 12 months for each loan in the database. A loan that was delinquent in 2006 that was cured and not delinquent in 2007 would not be included as delinquent in this analysis. The database lacks loans that are no longer reported due to foreclosure or prepayment that happened earlier than in the period we observe.

- 20.
We use the following model:

\( delin{q}_j={\gamma}_0+f\left( ag{e}_j\right)+\sum \limits_{t=2002}^{2007}{z}_t\cdot \mathbf{1}\left\{t= orig\_ yea{r}_j\right\}+{\gamma}_1 FIC{O}_j+{\gamma}_2 LT{V}_j+{\mathbf{X}}_j^{\prime }{\varGamma}_3+{e}_j \)

where

*j*indexes the individual mortgage and*t*indexes the origination year with 2001 chosen as the base level.*delinq*_{j}is an indicator of mortgage delinquency in the period.*orig_year*_{j}is the origination year of loan*j*with*z*_{t}to be the corresponding coefficients.*f(age*_{j}*)*includes high-order polynomials of loan age at delinquency if it happened or the loan age at the censoring point (December 2008). The summation term characterizes the vintage effect.**X**_{j}is a collection of the interaction terms of vintage and FICO/LTV and other controls on mortgage characteristics (including loan term, document type, state of origination and loan purpose, IO/NegAm/Balloon indicator), with vector**Γ**_{3}grouping the corresponding coefficients.*e*_{j}is the error term. - 21.
Original interest rate in the data is the initial rate for an ARM that is in effect either for a limited period of a so-called teaser rate or for the full term of the loan.

- 22.
The margin used here, as in prior papers referenced, is thus the gross margin, rather than the net margin, which is reduced by servicing fees and trustee fees, which are relatively constant over time. Mortgage brokers offer these rates to borrowers off the rate sheets that show the available pricing and terms from suppliers of mortgage funds. Mortgage brokers also charge mortgage fees and, if they are able to extract higher rates than the prevailing rates from borrowers, they will gain yield spread premiums. Neither appear to affect mortgage rates investors receive from PLS (Berndt et al. 2014).

- 23.
We include the regression results of original interest rate spread to produce comparable results with the literature. When the sample includes fixed rate mortgages, the studies cited use a risk-free interest rate with similar duration to calculate the risk price (Antinolfi et al. 2016; Justiniano et al. 2017), as we do here.

- 24.
We also analyze purchase money and refinance mortgages separately for comparisons to the studies cited in the literature.

- 25.
Not all loans carry detailed information on product types. About 78% of loans include detailed classification of product types.

- 26.
In general, riskier product types should have higher coefficients, indicating that they are accompanied by a higher credit margin for the higher risk, but the reverse holds in the data. For example, limited information loans have a lower coefficient than fully documented loans and negative amortization loans and IO loans have lower coefficients than fully amortizing loans, indicating they were priced as less risky.

- 27.
We also run a regression of the risk price on mortgage vintage only. The coefficients on the vintage are effectively the average mortgage margin and have the pattern shown in Figure 5.

- 28.
From 2003 to 2007, the coefficients of FICO and LTV of 2/28 ARMs both decreased in absolute value, consistent with the finding in the ARM sample. We report the regression results in Table 9. We also graphically show similar decreasing coefficients of FICO and LTV in absolute value for loans with FICO less than or equal to 660 in the discussion of Demyanyk and Hemert (2011) in Appendix.

- 29.
We don’t include the dummies of balloon, interest-only and negative amortization in Model 3–4 to prevent multicollinearity issues in the regressions. See Table 3 for a list of detailed product types as the additional variables and Footnote 11 for information on the details.

- 30.
If the survival process follows our assumption in the Appendix, we see as much as a 7% downward bias in FICO coefficient and 7% upward bias in LTV coefficient. The scale of the bias is small relative to the time-varying trend of FICO (37% decrease in absolute value from 2001 to 2007) and LTV (more than 50% decrease in absolute value from 2001 to 2004).

- 31.
- 32.
Frame finds securitization itself may not have been the problem to the recent financial crisis, but rather the origination and distribution of observably riskier loans, by both portfolio lenders and PLS investors. This is not inconsistent with our results.

- 33.
Glaeser et al. (2012) show that 20% of the rise in housing prices in this period can be attributed to a decline in mortgage rates over time. However, they use only prime mortgage rates in their analysis.

- 34.
- 35.
For discussions on policies, see Wachter (2018) and Levitin and Wachter (forthcoming).

- 36.
See McCoy and Wachter (2016).

- 37.
As we know, delinquency and foreclosure rates remained low through 2006. See Shiller (2000) on irrational exuberance, and see Levitin and Wachter (2011, forthcoming) on alternative discussion.

- 38.
Credit risk transfer programs (CRTs) implemented by Fannie Mae and Freddie Mac in 2013 are moves toward a market-informing mechanism. See Wachter (2016, 2018, forthcoming) for a discussion of the role.

- 39.
Loans with survival = 0 are off the record due to bankruptcy, decision for foreclosure, loan paid in full, REO.

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## Acknowledgements

We thank Ben Keys, Michael LaCour-Little, Laurie Goodman, and Jing Yang as well as seminar participants at the 2018 AREUEA National Meeting for their helpful comments and discussion. Susan Wachter acknowledges financial support from the Zell Lurie Real Estate Center at the Wharton School of the University of Pennsylvania.

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## Appendix

### Appendix

### Data Cleaning

The data are subject to missing values. There are in total 4,080,770 observations in the cross section of January 2008 and 2,196,117 loans fall in the category of ARM. The origination window, 2001–2007, is selected by the number of observations; we focus on origination years with more than 10,000 observations in ARM loans. Table 14 lists the distribution of missing data on ARM and the operation to produce the clean sample for analysis. 2,576,175 loans meet our criteria, and 1,543,203 of them are ARM. 30% of the data are not usable due to missing values. Figure 13 compares the distribution of observations by origination year, before and after the data cleaning operation, while Fig. 14 compares the quarterly-aggregated margin of ARM loans of the clean sample and the dropped sample. Both figures provide evidence that the sample we work on is representative. Table 15 reports the counts and the shares of missing values by vintage, from 2001 to 2007.

### Robustness Test for Survival Bias

The observations may be subject to survival bias. The earlier the loan origination is, or the riskier a loan is, the less likely a loan will exist in the data we observe. Moreover, loans might be subject to service transfer and disappear in the data. We may overweigh the importance of young and surviving loans. A loan can vanish from the database record either voluntarily or involuntarily. A mortgagor can make payment in full and terminate the contract early or can become delinquent on the loan due to bankruptcy, business failure, illness or death, etc. The lender/servicer will monitor its payment, label any delinquent behavior by 30 days, 60 days or 90+ days past due (dpd), and consider foreclosure of the collateral property. The property is either successfully auctioned or is Real-Estate-Owned (REO) by the lender and ceases to be part of the database.

We use the information on delinquency to test potential survival bias by considering an incidental truncation model. Specifically, we define a binary variable survival in the following way. If a loan in the cross-section carries the delinquency code “no action”, *Survival = 1*. Otherwise, *Survival = 0*.^{Footnote 39} Loans with *Survival = 0* will be removed from or not survive in the next cross-section (let’s call it experimental data). Heckman’s two-step procedure is implemented to test the sample selection problem of the experimental data (Heckman 1976, 1979).

where loan *j* is observable in the experimental data only if *Survival = 0*. Incidental truncation leads to the regression with a correction term

where the first is the selection equation and the second is the outcome equation. *λ* is the inverse Mills ratio and *σ* is the covariance between *e*_{1j} and *e*_{2j} under the assumption of joint normality.

In Table 16, we summarize the test results of survival bias. Three models reported are bias adjustment versions of Model (1) and (5) in Table 7, respectively. To mitigate the concern of violating the joint normality assumption, we use the logarithmic variables instead of their levels to extend the domain from positivity to the entire real line. In addition to FICO and LTV, we include the current loan rate in the selection equation as one driving force of the delinquency decision, especially to ARM loans. We further control loan term, documentation types, loan purpose and mortgage vintage as determinants of sample selection. The coefficients of the inverse Mills ratio using experimental data are statistically significant, providing evidence for survival bias. Since the coefficients of the correction terms are positive, there is an upward bias in estimations without correction. In other words, we tend to bias the marginal effect of FICO downward and bias the marginal effect of LTV upward without a correction procedure. As to the cross-section data we actually observe, there is no way to test how much survival bias our estimates will suffer, but conservatively speaking, our estimates do provide a lower and upper bound for FICO and LTV, respectively. Moreover, if we assume the actual loan survival process is isomorphic to that in the experiment we conduct, we find the selection impact doesn’t drastically change the estimates. Using the experimental data, the coefficient gap (or elasticity gap in the logarithmic setting) between OLS and Heckman estimates in the log margin regression is 0.16 to FICO (7% downward bias) and 0.01 to LTV (7% upward bias).

### Rajan et al. (2015) Revisited

We revisit the benchmark regression results from Rajan et al. (2015) with the model specification

Where *t* is the vintage year and *orig rate* refers to the original interest rate in the data. We look at both FRM and ARM loans originated from 2001 in 2007. For ARM loans, original interest rate refers to the initial rate, while for the FRM loans, it refers to the fixed interest rate. There is no variable in the dataset indicating whether a borrower is a first-time buyer, but we do observe the loan purpose of each observation. We report regression results in Tables 17, 18 and 19 based on loan purposes: primary loan, refinance with cash-out, or refinance without cash-out.

Table 17 is comparable to Table 4 in Rajan et al. (2015) (RSV), and we find consistent results. RSV’s main results focus on the subprime primary purchase loans (both ARM and FRM included); we confirm RSV’s results with the subprime pools (FICO ≤660) but include both prime and subprime shares in our report. For primary purchase loans, the reliance of FICO, measured by the absolute value of the coefficient, is relatively constant, while the reliance of LTV witnesses an increase from 2001 to 2007. The adjusted R-square increases from 0.09 in 2001 to 0.33 in 2006, following a similar trend as RSV quantitatively. Moreover, both FICO and LTV coefficients estimated using our data have similar scales. As to refinance loans with and without cash-out, the reliance on FICO or LTV is increasing over time from 2001 to 2004 and becomes relatively steady from then on. We find that the adjusted R-squares of the refinance pool (with and without cash-out) do not show a similar increasing trend from 2001 to 2006 as the primary purchase pool. Instead, the adjusted R-squares of the refinance pool in 2001 were as high as 0.3 and had ever decreased since 2002. For robustness, we additionally control other loan characteristics similar to the implementation by RSV: whether a loan is ARM and whether it has low documentation. Consistent with their results, we find our previous results on FICO, LTV and R-squares are preserved in the enhanced models. For brevity, they are not reported but available upon request.

To relate our results to RSV’s, we focus on mortgage risk pricing for the ARM sample. Figure 15 compares the trend of R-squares in the mortgage rate regression with the trend in the margin regression by loan purpose, with FICO and LTV as the explanatory variables. Similar to our benchmark results, we cannot find evidence supporting increasing reliance of FICO or LTV from 2001 to 2007 in the margin regressions. In addition, adjusted R-square is relatively flat over time for all loan purposes. The difference in the mortgage rate and margin regressions implies that term structures and other unobserved factors explain the variation in the mortgage rate but not the variation in the risk pricing in terms of gross margin. As year 2001/02 was in the regime of high interest rate, controlling term structures using short- and long-term interest rates (1-year and 7-year constant maturity treasuries) can flatten but cannot reject the increasing trend of R-squares in the mortgage rate regressions within the primary purchase pool. However, part of the increasing trend in R-squares for purchase money loans still remained unexplained due to other unobservable factors.

### Demyanyk and Hemert (2011) Revisited

Demyanyk and Hemert (2011) (DvH) find that securitizers were aware of increasing riskiness of borrowers by examining the determinants of the mortgage rate of subprime 2/28 ARMs. They find the normalized LTV coefficient scaled by the standard deviation has been increasing over time (see DvH Fig. 2). We use our data to confirm and augment the finding. Figure 15 shows the time-varying coefficients on FICO and LTV. The mortgage rate regression with gross margin as one explanatory variable replicates increasing riskiness awareness in DvH’s regression. Alternatively, we consider two alternative variations in specification: one without gross margin and the other with term structures consideration (by controlling 1-year and 7-year constant maturity treasury rates). Similarly, both show more pronounced effects of FICO and LTV over time. To bridge our results with DvH’s, we report the FICO and LTV coefficients in gross margin regression with a sample restricted to subprime 2/28 ARM, defined as loans with FICO scores lower than 660 (Demyanyk and Hemert 2011). Consistent with our benchmark result, we show that there is decreasing reliance on FICO and LTV starting from 2004 (Fig. 16).

### Coefficients on FICO/LTV and Residual Vintage Effect of FRMs

We use the FRM sample in the database and report the time-varying coefficients on FICO and LTV and the residual vintage effect over time. Different from the diminishing impact of hard information in ARMs, we find that the marginal impact of FICO and LTV in FRMs followed an increasing trend. The residual vintage effect of FRMs was relatively constant from 2002 to 2006, compared to a monotonically decreasing trend of ARMs (Fig. 17).

### Justiniano et al. (2017) Revisited and Residuals of Main Regressions

We report the average residuals of the regressions in Table 7. By the Gauss-Markov Theorem, the model errors should be zero in expectation conditional on observable factors. In estimation, the time average of loan-level residuals weighted by the number of loans in each time window, by construction, should be equal to zero. We aggregate the loan-level residuals by taking the monthly average from 2001 to 2007. Figs. 18 and 19 plots the time series of average residuals from Model4 1–4 and Model 5–8, respectively.

Justiniano et al. (2017) (JPT) finds that there was a sudden decrease in mortgage rate and persistently cheaper mortgage credit starting from mid-2003 (the so-called mortgage rate conundrum). JPT shows that the average residuals suddenly plummeted in mid-2003 and stayed low persistently (see JPT Fig. 4.1). Using our ARM samples, we find the average residuals in the original interest rate spread regression did experience a sudden decrease in mid-2003, but the drop was not as persistent as what JPT found. In our margin regression, the average residuals exhibit a less persistent “white noise” pattern, compared to the trend of the average residuals in the original rate spread regressions and in JPT’s models. This suggests that the model controls are able to explain cross-vintage variation of the gross margin, in addition to cross-section variation of the gross margin.

### Additional Tables

We show the number of 2/28 ARMs and the dollar volume by origination year in Table 20.

In Table 21, we report the weighted version of Table 6, using original balance to weigh the observations.

We report hypothesis testing results for Models 1–8 in Table 7 regarding whether the vintage effect and the response to FICO and LTV are statistically different from their counterparts in the previous year. We report the *p*-values from a set of Wald tests, using no time-varying effect in two consecutive years as the null hypothesis in Tables 22, 23 and 24.

### Additional Results on Residual Vintage Effects

We report additional results on decomposition of the residual vintage effects by specific types of non-traditional mortgage product. As shown in Fig. 20, we compare the residual vintage effects for loans including interest-only (IO), negative amortization (NegAm) and balloon mortgages. From 2004 to 2007, the residual vintage dummies are uniformly higher for the affordable products (IO, NegAm, balloon) than their counterparts (non-IO, non-NegAm, non-balloon) and are declining for the more traditional product.

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### Cite this article

Levitin, A.J., Lin, D. & Wachter, S.M. Mortgage Risk Premiums during the Housing Bubble.
*J Real Estate Finan Econ* **60, **421–468 (2020). https://doi.org/10.1007/s11146-018-9682-z

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### Keywords

- Housing bubble
- Risk premium
- Securitization
- Private-label

### JEL

- G01
- G12
- G20
- G21