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Article Excerpt
The magnitude of the effect of government-sponsored enterprise purchases on primary mortgage market rates has been a difficult research question with differing data and competing methodologies producing varying results. Here we present a new approach using loan level data and controlling for credit risk differentials between conforming and nonconforming loans. Our method also addresses econometric problems of endogeneity and sample selection bias. We find that conforming loans have yield spreads about 5.5% lower compared to other loans on a risk-adjusted basis. This is lower than previous estimates appearing in the literature.
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Lenders in the primary mortgage market originate a range of contracts, many of which are then sold in the secondary market, either to the government-sponsored enterprises (Fannie Mae and Freddie Mac, hereafter the GSEs (1)) or pooled as collateral for private label mortgage-backed securities. Other loans are retained in portfolio or sold on a whole-loan basis. Loans vary in coupon, size, term, collateral and, of course, credit quality. Based on business strategy and risk preferences, together with information obtained during the underwriting process, and considering rules and price signals from the secondary market, lenders make a hold-versus-sell decision. What factors determine that decision, and what is the overall effect on rates in the primary market?
These questions are among many that are crucial to evaluating the role of the GSEs, whose special status in the economy generates both costs and benefits (Sanders 2002). GSE purchases provide liquidity to primary lenders and perhaps stability to the overall mortgage market (Gonzalez-Rivera 2001, Naranjo and Toevs 2002). In addition, it is widely accepted that GSE activity reduces rates on conforming loans by expanding available funds to lenders (Phillips 1996). But the extent to which the GSEs reduce mortgage rates is controversial. (2) For example, Ambrose, Buttimer and Thibodeau (2001) show the impact of house price volatility on the jumbo/non-jumbo loan rate differential. Their simulations indicate that as much as 20% of the loan rate differential may be due to house price volatility.
On the other hand, GSEs benefit from an implied federal guaranty of their liabilities and are exempt from certain taxes and requirements that other financial intermediaries bear. A number of papers have examined the funding advantage of the GSE, most recently Ambrose and Warga (2002) and Nothaft, Pearce and Sevanovic (2002). The latter identifies seven prior studies, which provide a range of estimates of the funding advantage of between 23 and 72 basis points, depending on data used, comparison instrument and methodology, and the authors provide their own estimate of 27-30 basis points. Ambrose and Warga provide a broader comparison across risk classes and estimate an average funding advantage of 25-29 basis points over "AA"-rated banking sector bonds, 43-47 basis points over "A"-rated banking bonds and 76-80 basis points over "BBB"-rated banking sector bonds.
Our effort here again focuses on the benefit side of the ledger, that is, the rate reduction associated with conforming loan status. In contrast to research that relies on macro-level yield data, we return to the loan level approach as in Hendershott and Shilling (1989). But our data are more recent and include borrower credit score, a key piece of information that allows us to estimate the reduction in mortgage yield spreads attributable to conforming loan status on a risk-adjusted basis. In addition, we can more precisely separate conforming from nonconforming loans, a task that cannot be accomplished with the data used by McKenzie (2002), Ambrose and Buttimer (2004) and Passmore, Sparks and Ingpen (2002). (3) Finally, our approach corrects for two distinct econometric problems: endogeneity and sample selection bias. Endogeneity occurs because the loan-to-value ratio is jointly determined with note rate. Sample selection bias may occur because some loans that could be sold to the GSEs may not be. If the GSEs purchase lower risk loans, then a simple comparison of yields will be confounded by any credit risk differential.
To address this question we develop an ex ante model of yield spreads controlling for credit risk at the loan level. The model incorporates a variety of characteristics including credit score, borrower age and income and loan-to-value ratio (LTV). We also incorporate actual outcomes, that is, whether the loan was, in fact, sold into the secondary mortgage market or retained in portfolio by the originating lender, as well as bond market environmental factors.
The plan for the remainder of the paper is as follows. In the next section, we briefly review relevant literature, drawing analogies to the corporate bond market. In the second section, we sketch out the theory of mortgage valuation and develop our model of mortgage yield spreads. In the third section, we describe the data. The fourth section presents the basic regression model that is comparable to the existing literature. We then refine the model to control for credit risk and address econometric issues. The final section offers conclusions.
Literature Review
A number of studies have examined the conforming-nonconforming rate differential. In most cases rates on jumbo loans are taken as the relevant nonconforming loan category, although the reality is that some conforming loan size loans are, in fact, nonconforming, due to credit or documentation issues (e.g., subprime or low-doc loans). Most previous studies rely on the Federal Housing Finance Board's monthly mortgage interest rate survey (MIRS), which only allows separation into jumbo versus non-jumbo categories and lacks important credit risk measures. McKenzie (2002) provides an excellent discussion of the issues associated with estimating the loan rate differential using the MIRS data. McKenzie also provides a summary of previous empirical estimates. Depending on the period examined and methodology employed, the jumbo/non-jumbo mortgage rate differential has ranged between a high of 60 basis points (Cotterman and Pearce 1996) to a low of 8 basis points (Naranjo and Toevs 2002).
In one of the first studies using MIRS data, Hendershott and Shilling (1989) found that conforming loans had interest rates 24 to 39 basis points lower than nonconforming loans after controlling for loan characteristics. They regressed effective mortgage interest rate against a set of variables to control for jumbo loan status, loan size, loan-to-value ratio, new versus existing home status, as well as dummy variables to capture temporal and regional variations. Subsequent studies (e.g., ICF Inc. 1990, Cotterman and Pearce 1996, Ambrose, Buttimer and Thibodeau 2001, U.S. Congressional Budget Office 2001, McKenzie 2002, Naranjo and Toevs 2002, Passmore, Sparks and Ingpen 2002) have followed a similar methodology with minor variations in data screens designed to isolate the conforming/nonconforming effect as well as geographic differences (e.g., McKenzie 2002, Ambrose and Buttimer 2004). Todd (2001) follows the Hendershott and Shilling methodology adding in the effect of origination costs using Freddie Mac and Federal Reserve aggregate data. Naranjo and Toevs (2002) extend the Hendershott and Shilling methodology to incorporate cointegration to correct for nonstationarity in rates. (4)
Studies of the determinants of yield spreads in the corporate bond literature have focused on credit spreads (see Altman and Saunders 1998 for a review). For mortgages, credit risk has traditionally been viewed as a function of borrower equity or loan-to-value ratio. Early research includes von Furstenberg (1969), von Furstenberg and Green (1974), Campbell and Dietrich (1983) and Cunningham and Capone (1990). Quercia and Stegman (1992) and Vandell (1993) provide surveys focusing on default, while Kau, Keenan and Kim (1994) develop theoretical default given stochastic collateral values. Among recent methodological innovations, Deng, Quigley and Van Order (2000) present a competing risk model of mortgage termination, both default and prepayment, accounting for unobserved borrower heterogeneity. Mortgage default research has also recently begun to incorporate borrower credit score (e.g., Avery et al. 1996). In a related line of research outside of the mortgage literature, Angbazo, Mei and Saunders (1998) examine yield spreads for highly leveraged corporate loans.
Linking the mortgage literature to the broader finance literature, yield spreads on the firm's debt reflect underlying financial risk that depends on firm capital structure, just as default risk in mortgages is related to the borrower's equity. Likewise, we may think of borrower credit score as the analog to firm credit rating and individual borrower demographic characteristics as the analog to firm specific idiosyncratic risk factors.
Theoretical Predications and Model
The general approach to mortgage pricing is now well established. Mortgages are contingent claims contracts in which the mortgage value ([V.sup.M]) depends critically on two stochastic processes, the market interest rate, r(t), and the house value, H(t). For instance, we may specify the interest rate process with a CIR diffusion process:
d(r) = [gamma]([THETA] - r)dt + [[sigma].sub.r][square root of r] d[z.sub.r], (1)
where [THETA] is the steady-state mean rate, [gamma] is the speed of adjustment factor and [[sigma].sub.r] is the volatility of interest rates. (5) Diffusion in collateral value affects mortgage value, too, so we may specify the evolution of house values, H(t), by
[dH]/H = ([alpha] - s)dt + [[sigma].sub.H]d[z.sub.H], (2)
where [alpha] is the instantaneous total return to housing, s is the service flow and [[sigma].sub.H] is the volatility of housing returns. In (1) and (2), d[z.sub.r] and d[z.sub.H] are standard Wiener processes and the correlation between the movements of the two state variables (d[z.sub.H] and d[z.sub.r)]) is [rho].
Kau and Keenan (1995) show that under appropriate assumptions, the value of the mortgage ([V.sup.M]) will satisfy the following partial differential equation (PDE):
[1/2][H.sup.2] [[sigma].sub.H.sup.2] [[[[partial derivative].sup.2][V.sup.M]]/[[partial derivative][H.sup.2]]] + [rho]H [square root of r] [[sigma].sub.H] [[sigma].sub.r] [[[[partial derivative].sup.2][V.sup.M]]/[[partial derivative]H[partial derivative]r]] + [1/2]r[[sigma].sub.r.sup.2] [[[[partial derivative].sup.2][V.sup.M]]/[[partial derivative][r.sup.2]]] + [gamma]([theta] - r)[[[partial derivative][V.sup.M]]/[[partial derivative]r]] + (r - s)H [[[partial derivative][V.sup.M]]/[[partial derivative]H]] + [[[partial derivative][V.sup.M]]/[[partial derivative]t]] - r[V.sup.M] = 0. (3)
Specifying the boundary conditions allows the valuation of the mortgage when the economic variables take on extreme values. With these boundary conditions, (3) can be solved to find the value of the mortgage contract.
We denote the present value of the...
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