Academic journal article Real Estate Economics

A Dynamic Double-Trigger Model of Multifamily Mortgage Default

Academic journal article Real Estate Economics

A Dynamic Double-Trigger Model of Multifamily Mortgage Default

Article excerpt

Lawrence Goldberg (*)

Charles A. Capone, Jr. (**)

This study advances the commercial mortgage literature by providing theory and methods for incorporating both equity and cash-flow considerations in default models. We use local market conditions to compute a (joint) probability that default is in-the-money, based on both equity and cash-flow considerations. Statistical analysis is performed using data on multifamily mortgages originated in the 1980s and early 1990s. Simulations based on statistical modeling show advantages of the probabilistic double-trigger approach over other measures of equity and cash flow.

The importance of cash flows for commercial mortgage default prediction, in addition to property equity, has been discussed by some authors but never formally developed. We look at how options theory can provide a rationale for including both factors in an empirical default model, and then we expand upon Goldberg and Capone's (1998) use of local market conditions to update equity and cash flow over time. This expansion includes calculation of a joint probability of negative equity and negative cash flow for any given property as the primary default predictor variable. A logistic default model is estimated using cash-window loan purchases by both Fannie Mae and Freddie Mac, from 1983 through 1995. The data set has 13,482 loans, with 89,577 total loan-year observations. While there are a few adjustable rate mortgages in the data set, nearly all of the loans are fixed-rate products that either fully amortize or have balloon terms.

The joint probability specification is tested against a number of alternatives, and its statistical fit of the data is best. Problems with alternative specifications are especially apparent when property financials--equity and cash flow--are not balanced. The joint probability allows us to capture the full market dynamics in a way that is not possible using simple mean rates of LTV and DCR or marginal probability measures alone.

The next section of this article reviews the existing literature on commercial mortgage default modeling, and the third section provides analysis of the relationship between equity and cash flow and default option value. In the fourth section we develop the joint probability variable and in the fifth section, we add other explanatory variables that may influence default behavior. Data sources are reviewed in the sixth section, the statistical model in the seventh section, then estimation results, sensitivity analyses, and conclusions are in the last section.

The Existing Literature

Several authors have introduced models of commercial mortgage default. (1) These are quite diverse methodologically: Researchers use different theoretical frameworks, definitions of default, estimation equations, and observational units. (2) One important issue still to be resolved is how to account for the role of property cash flow in empirical models of commercial mortgage default. All mortgage underwriting hinges on the congruence of both equity and cash flow, as summarized in the loan-to-value (LTV) ratio and, for commercial mortgages, the debt-service-coverage ratio (DCR). (3) Yet the financial options approach to mortgage borrower terminations has downplayed the role of cash flows. Options theory itself recognizes cash flows but, as will be discussed in the next section, the interplay of equity and cash flow for mortgage borrower decisions is not yet well developed, even at the theoretical level.

The issue of equity versus cash flow is related to the debate over the role of so-called trigger events in modeling single-family mortgage defaults, as discussed by Vandell (1995, p. 259). Vandell (1995, p. 260) argues that a commercial mortgage borrower has no incentive to default as long as cash flows are positive, "regardless of how negative his or her equity position is." Abraham (1993b) directly criticizes the options approach to mortgage default modeling for not including cash-flow considerations. …

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