Securitization and optimal foreclosure☆
Introduction
In the aftermath of the subprime mortgage crisis, there were more than 14 million U.S. properties with foreclosure filings from 2008 to 2014.1 Particularly, privately securitized mortgages accounted for more than half of these foreclosures. This raises concerns by academics and policymakers over whether securitization has aggravated the crisis by hindering the modification of delinquent mortgages.2 As a response, the U.S. government has developed the Home Affordable Modification Program (HAMP) to incentivise mortgage modification instead of foreclosure.3
However, understanding the foreclosure of securitized mortgages and the effect of such policy interventions in foreclosure has been hindered by the absence of a theoretical framework that allows one to answer some fundamental questions. How might securitization affect banks’ choice of foreclosure policy in equilibrium? Could public interventions in foreclosure carry implications for the origination and the securitization of mortgages?
To answer these questions, we develop a model of asset-backed securitization with endogenous foreclosure. In our model, a risk-neutral bank with liquidity needs, that owns a mortgage pool, first chooses a policy of foreclosing or modifying any fraction of the delinquent mortgages in the future.4 Then, the bank designs and sells a security backed by the cash flow from the mortgage pool to uninformed investors. Foreclosure policy affects the mortgage pool’s cash flow in the following manner: Foreclosing a delinquent mortgage and selling the underlying property returns a safe cash flow, whereas modification delivers a higher (lower) cash flow when the once-defaulted borrower recovers (re-defaults). In the first-best benchmark, the bank sells the entire mortgage pool cash flow to outside investors, and adopts a foreclosure policy that maximizes the mortgage pool cash flow (or, equivalently, minimizes the expected loan losses) by equating the marginal expected cash flow from foreclosure to that from modification.
The main finding of the paper is that, when the bank is more informed about the quality of the mortgage pool than the investors, the bank optimally chooses to foreclose more than in the first-best in order to mitigate the adverse selection problem in securitization, despite reducing the mortgage pool’s expected cash flow. As in DeMarzo (2005), the bank in our model privately observes the mortgage pool’s quality before the mortgage-backed security is sold. The bank with a higher-quality, that is, less default-prone, mortgage pool (the high type) optimally sells a risky debt to uninformed investors and retains the remaining cash flow to deter the low type from mimicking. Debt is optimal because it is least sensitive to the private information held by the bank.56 The new insight of our model is that, when the adverse selection problem is sufficiently severe, foreclosing more than the first-best level further reduces the information sensitivity of a debt security, which in turns allows the high-type bank to raise more liquidity. The optimal foreclosure policy thus trades off the dead-weight loss of a tough foreclosure policy against higher gains from securitization.
Why then does foreclosing more than in the first-best reduce the information sensitivity of the optimal debt security? The reason is as follows. Foreclosure effectively transfers the mortgage pool’s cash flow from the recovery state to the re-default state. If the debt has a face value strictly below the mortgage pool’s cash flow in the recovery state, such a transfer does not affect the debt’s payoff in the no-default or the recovery state but strictly increases its payoff in the re-default state. As a result, the debt derives more of its value from its payoff in the re-default state, and, hence, its overall value becomes less sensitive to the underlying pool’s quality, or, the probability of not defaulting.
Our analysis thus establishes that the equilibrium foreclosure policy, which results in higher expected loan losses, arises optimally to mitigate the information frictions inherent in the securitization process. Regulators who are concerned with the welfare of delinquent households and the potential negative externalities (not modeled) of foreclosures might therefore be interested in foreclosure-prevention policies such as HAMP. We study the implications of such policies by extending the model to endogenise the bank’s ex ante screening choice at origination, and, hence, the equilibrium quality of mortgages.
We show that policies aiming to reduce foreclosure weaken the bank’s incentive to screen mortgages diligently, leading to lower average quality of the mortgage pools. Screening increases the probability of originating a high-quality mortgage pool at a cost. The bank’s expected gains from a high-quality mortgage pool, however, is limited by the extent of the adverse selection in securitization. Since a tougher foreclosure policy alleviates such information friction, foreclosure-prevention policies inadvertently discourage the bank’s screening effort. Our analysis thus suggests that regulators should take into account the equilibrium effects of foreclosure-prevention policies like HAMP on the origination and securitization of mortgages.
Our paper sheds light on various empirical and institutional aspects of the mortgage industry. Our main result yields predictions for observed foreclosure rates of securitized mortgages that are consistent with empirical findings. First, mortgage securitization leads to higher foreclosure rates conditional on delinquency. Piskorski et al. (2010), Agarwal et al. (2011), and Kruger (2018) show that, compared to similar mortgages held in banks’ portfolios, securitized mortgages are more likely to be foreclosed conditional on delinquency.7 Second, our theory predicts that the increase in foreclosure caused by securitization is concentrated among high-quality mortgage pools. Indeed, Piskorski et al. (2010) and Agarwal et al. (2011) highlight the substantial heterogeneity in the effects of securitization on foreclosure rates, with larger effects among higher-quality mortgages. Third, we show that, for securitized mortgages, the marginal foreclosure results in higher expected loan losses relative to modification, with larger effects for mortgages with higher observable quality. Maturana (2017) presents consistent evidence by exploring the effects of an exogenous increase in marginal modification.
In addition, our results can rationalise the apparent biases in the mortgage servicers’ contracts and their lack of modification capacity, which are repeatedly cited as impediments to loss mitigation for delinquent mortgages.89 In practice, mortgage servicers are hired by banks to foreclose or modify delinquent mortgages on their behalf. Our theory can explain when and why banks under-incentivise their servicers to modify mortgages and/or to invest in modification capacity for securitized mortgages, relative to bank-held mortgages.
Our model starts from a discrete cash flow version of models of liquidity-based security design, such as DeMarzo and Duffie (1999), DeMarzo (2005), and Biais and Mariotti (2005). We depart from the literature by allowing the banks to take actions that affect the distribution of the underlying asset’s cash flow. In the context of mortgage securitization, foreclosure policy of delinquent mortgages is one such action. We show that foreclosing more than the first-best could emerge as the optimal policy for banks to mitigate the adverse selection problem in securitization because it further reduces the information sensitivity of the optimal security, namely risky debt.
Several papers have highlighted the incentive problems associated with securitization. In a setting of securitization under adverse selection similar to ours, Chemla and Hennessy (2014) and Vanasco (2017) analyse how liquidity in the MBS market affects ex ante loan originators’ screening effort. Hartman-Glaser et al. (2012) and Malamud et al. (2013) study the optimal design of the originator’s compensation contracts to incentivise screening effort in a dynamic setting. We contribute to this literature by highlighting the effect of the foreclosure policy of the securitized mortgages on the originator’s screening incentives.
Our paper also relates to but differs from the literature on optimal loan modification and foreclosure policy. Wang et al. (2002) and Riddiough and Wyatt (1994) argue that borrowers’ strategic default incentives lead lenders to adopt a tough foreclosure policy in order to deter non-distressed borrowers from opportunistic behavior. However, these papers do not analyze the securitization of the loans and therefore their models based on borrower strategic default do not readily explain the difference in the foreclosure rates between securitized and portfolio loans. Gertner and Scharfstein (1991) focus on the free-riding problem among multiple creditors. Our paper highlights that information asymmetry in securitization can be another important factor that determines foreclosure decisions.
The rest of the paper is organized as follows. Section 2 describes the model setup. Section 3 carries out the main analysis of the equilibrium with endogenous foreclosure policy. Section 4 extends the model to consider the bank’s ex ante screening incentive and to study how it is affected by foreclosure-prevention policies. Section 5 discusses the empirical implications of the model. Section 6 concludes.
Section snippets
Model setup
There are three dates in the baseline model: 2 and 3.10 The model’s participants consist of a bank, which owns a continuum of mortgages, and competitive outside investors. All agents are risk neutral. The bank has a discount factor δ < 1 between and . Outside investors are deep-pocketed and have a discount factor equal to 1. Hence, there are gains from trade between the bank and the investors. This follows the
Securitization and optimal foreclosure
In this section, we analyze the effect of mortgage securitization on foreclosure under information asymmetry. We first present the benchmark case of bank-held mortgage, that is, mortgages whose cash flows are not sold to investors at . We then solve for the optimal foreclosure policy in the baseline model with mortgage securitization.
Foreclosure policy and ex ante screening effort
So far we have treated the prior probability that the mortgage pool is of high quality as exogenous. In this section, we extend the model to incorporate a mortgage-origination stage at which time the bank can endogenously exert costly screening effort to increase the probability that the mortgage pool is of high quality at . We first characterize the bank’s optimal screening effort in equilibrium. We then examine the effect of foreclosure-prevention policies and highlight that an
Empirical implications
In this section, we explore novel empirical predictions of the model on the relationship between foreclosure and loan performance, on the effects of securitization on foreclosure, and on mortgage servicing.
Conclusion
This paper studies the relationship between the securitization and the foreclosure of mortgages. We present a model of mortgage-backed securitization, in which a bank first chooses the foreclosure policy of the mortgage pool and then designs and sells a mortgage-backed security to raise liquidity from uninformed investors. We show that the bank optimally adopts an tougher foreclosure policy than the first-best, in order to mitigate the adverse selection problem in securitization. The optimal
Declaration of Competing Interest
None.
CRediT authorship contribution statement
John Chi-Fong Kuong: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing, Visualization. Jing Zeng: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing, Visualization.
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Cited by (0)
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We are grateful to João Santos (the editor), an anonymous referee, Ulf Axelson, Bruno Biais, Philip Bond, Sonny Biswas, Matthieu Bouvard, Elena Carletti, Gilles Chemla, Amil Dasgupta, James Dow, Daniel Ferreira, John Geanakoplos, Denis Gromb, Barney Hartman-Glaser, Frederic Malherbe, Artem Neklyudov, Enrico Perotti, Guillaume Plantin, Uday Rajan, David Skeie, James Thompson, Andrew Winton and seminar and conference participants at BI Oslo, Cass, ESSEC, Frankfurt School of Finance & Management, HKUST, INSEAD, LSE, McGill, Financial Stability Conference, 8th European Banking Center Network conference, Zurich, ESSFM evening session (Gerzensee), Inaugural Young Scholars Finance Consortium (Texas A&M), Chicago Financial Institutions Conference 2016, Banque de France-TSE “Securitisation: the way forward” Conference, Oxford Financial Intermediation Theory Conference, Finance Theory Group Summer School, CICF, FIRS, and Lisbon Meetings in Game Theory and Applications.