## Loanto Value Ratio and the Mortgage Rate

The combined LTV ratio rather than the first-lien LTV ratio is believed to be the main determinant of delinquency and foreclosure, because it is the burden of all the debt together that may trigger financial problems for the borrower. In contrast, the first-lien LTV is the more important determinant of the mortgage rate on a first-lien mortgage, because it captures the dollar amount at stake for the first-lien lender.14

In this subsection we try to determine whether lenders were aware that high LTV ratios were increasingly associated with riskier borrowers. Specifically, we test whether the sensitivity of the lender's interest rate to the first-lien LTV ratio changed over time. We perform a cross-sectional OLS regression with the mortgage rate as the dependent variable and loan characteristics, including the first-lien LTV and second-lien LTV (CLTV minus first-lien LTV), as independent variables.15 We perform one such regression for each calendar quarter in our sample period. We can only expect to get accurate results when using relatively homogeneous groups of loans, and therefore consider fully amortizing FRM and 2/28 hybrid loans separately. Together these two contract types account for about half of all mortgage loans in our database. Each cross-sectional regression is based on a minimum of 13,281 observations.

Figure 3 shows the regression coefficient on the first-lien LTV ratio for each quarter from 2001Q1 through 2007Q2.16 We scaled the coefficients by the standard deviation of the first-lien LTV ratio, and

14This is confirmed by our empirical results. To conserve space the results are not reported.

15Specifically, we use the FICO score, first-lien loan-to-value ratio, second-lien loan-to-value ratio, debt-to-income ratio, a dummy for a missing debt-to-income ratio, a cash-out refinancing dummy, a dummy for owner occupation, documentation dummy, prepayment penalty dummy, margin, origination amount, term of the mortgage, and prepayment term as the right-hand-side variables.

16Our data extends to 2007Q3, but due to a near shutdown of the securitized subprime mortgage market we lack statistical power in this quarter.

they can therefore be interpreted as the changes in the mortgage rates when the first-lien LTV ratios are increased by one standard deviation. In the fourth quarter of 2006, a one-standard-deviation increase in the first-lien LTV ratio corresponded to about a 35-basis-point increase in the mortgage rate for both FRMs and 2/28 hybrid mortgages, keeping constant other loan characteristics. In contrast, in the first quarter of 2001, the corresponding rate increase was around 13 basis points. This provides evidence that lenders were to some extent aware of high LTV ratios being increasingly associated with risky borrowers.17 Finally, notice that the effect of a one-standard-deviation increase in the first-lien LTV ratio on the 2/28 mortgage rate increased substantially in the wake of the subprime mortgage crisis: from 34 basis points in 2007Q1 to 47 basis points in 2007Q2.

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