Mortgage Risk Premiums during the Housing Bubble

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.

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.

Table 14 Operation on raw data, ARM

Table 15 Survival rate by vintage, ARM

Fig. 13

Distribution of observations by origination year, raw data vs. clean sample

Fig. 14

Margin of clean sample (Missing Value = 0) and dropped sample (Missing Value = 1) 2001–2007. Data is aggregated quarterly

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 = 0.³⁹ 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).

$$ {\displaystyle \begin{array}{l} surviva{l}_j=\mathbf{1}\left\{{\mathbf{Z}}_j^{\prime}\gamma +{e}_{1j}>0\right\}\\ {} risk\kern0.17em pric{e}_j={\beta}_0+{\beta}_1 FIC{O}_j+{\beta}_2 LT{V}_j+\sum \limits_{t=2002}^{2007}{d}_t\cdot \mathbf{1}\left\{t= orig\_ yea{r}_j\right\}+{\mathbf{X}}_j^{\prime }{\mathbf{B}}_3+{e}_{2j}\end{array}} $$

(2)

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

$$ {\displaystyle \begin{array}{c} risk\kern0.17em pric{e}_j={\beta}_0+{\beta}_1 FIC{O}_j+{\beta}_2 LT{V}_j+\sum \limits_{t=2002}^{2007}{d}_t\cdot \mathbf{1}\left\{t= orig\_ yea{r}_j\right\}+{\mathbf{X}}_j^{\prime }{\mathbf{B}}_3\\ {}+{\sigma}_{12}\lambda \left({\mathbf{Z}}_j^{\prime}\gamma \right)+{e}_j\end{array}} $$

(3)

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).

Table 16 Test of Survival Bias, Heckman Model vs. OLS

Rajan et al. (2015) Revisited

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

$$ orig\ rat{e}_{jt}={\beta}_{0,t}+{\beta}_{LTV,t} LT{V}_{jt}+{\beta}_{FICO,t} FIC{O}_{jt}+{e}_{jt} $$

(4)

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.

Table 17 Regression Table: Original Interest Rate (Primary Purchase)

Table 18 Regression Table: Original interest rate (Refinance with Cash-out)

Table 19 Regression Table: Original interest rate (Refinance without Cash-out)

Fig. 15

Adjusted R-squares of mortgage rate regression (panel a) and margin regression (panel b) by vintage and loan purposes (primary purchase, refinance with cash-out, refinance without cash-out). The regressions control FICO and LTV. The sample universe in the mortgage rate regression is ARM and FRM loans, while the sample in the margin regression includes ARM loans

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).

Fig. 16

Regression coefficients on FICO (panel a) and LTV (panel b) for subprime section of 2/28 ARM loans (FICO ≤ 660). The dependent variables in percentage points are original interest rate (model 1–3) and the margin (model 4), respectively. Models 1–3 are specifications with margin, without margin, and with term structures in the control variables, respectively. Controlled variables include loan term, documentation types, loan purpose, state dummies, negative amortization flag, interest-only flag and balloon flag. Term structure includes constant maturity treasury rates

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).

Fig. 17

Panel (a): Regression coefficients on FICO (blue) and LTV (orange) from original interest rate spread regression by vintage with FRM sample. Panel (b): Regression coefficients on vintage year from original interest rate spread regression. The dependent variables are measured in percentage points. The dashed bands represent 95% confidence intervals

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.

Fig. 18

Time series of average residuals of Model (1–4) in Table 7 with margin as the dependent variable. Data is aggregated by month

Fig. 19

Time series of average residuals of Model (5–8) in Table 7 with original interest rate spread as the dependent variable. Data is aggregated by month

Additional Tables

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

Table 20 Mortgage Frequency and Dollar Volume of 2/28 ARMs by Origination Year

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

Table 21 Summary statistics: Continuous Variables by Origination Year (Weighted by Original Balance), 2001–2007

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.

Table 22 Wald test of time-varying coefficients, vintage

Table 23 Wald test of time-varying coefficients, FICO

Table 24 Wald test of time-varying coefficients, LTV

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.

Fig. 20

Regression coefficients on vintage year from margin regression (Model 2) in Table 7, decomposed by loan characteristics (interest only, negative amortization, balloon, low documentation). Margin is measured by percentage point. Exclamation mark (!) refers to negation. 2001 is the base level and normalized to 0 for two comparison groups. The dashed bands represent 95% confidence intervals