Delinquency and Default in ARMs:
The Effects of Loss Aversion and Protected Equity
Alan Hwee Loon TEO
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Seow Eng ONG
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Key words
Default risk, Bivariate Probit, Loss Aversion
Please direct comments to Alan Hwee Loon TEO at Department of Real Estate, National University of Singapore, 4 Architecture Drive, Singapore 117566, or email:
Extended abstract
Motivation
With the growth of the private residential property markets worldwide, mortgage lending has become an imperative component of the businesses of financial institutions. Consequently, secondary mortgage markets have also been expanding rapidly. Understanding the various types of mortgage risk is thus essential, for both practitioners and academics. Default risk (e.g. Quigley and Van Order, 1990), prepayment risks (e.g. Ong, 2000; and Ambrose and LaCour-Little, 2001) and the competing relationship between them (e.g. Deng, Quigley and van Order, 2000; and Clapp, Deng and An, 2004) are areas of intense study. However, studies on mortgage delinquency or the incorporation of delinquency in overall mortgage risk models are far and few. This can be attributed to a lack of suitable available data (Von Furstenberg and Green, 1974), difficulties in modeling delinquency within the prevailing option-based approach (Quercia and Stegman, 1992), and perception among practitioners that the financial consequences of delinquency is less severe than default (Quercia and Stegman, 1992).
In this paper, we postulate mortgage delinquency as a significant and necessary decision that is taken by the borrower before the default decision. We further propose that motivations of the preceding delinquency decision exert a significant influence on the subsequent motivations of default such that mortgage risk models should incorporate the risk of delinquency.
There is no consensus on the definitions of delinquency and default in past studies. We advocate the set of definitions utilized by practitioners in the US and Singapore, i.e. to differentiate delinquency and default by the number of days the payments have been missed. Delinquency is defined as the nonpayment of a mortgage payment due. Default occurs when a borrower has missed 90 days’ installment and the fourth payment is due. Therefore, delinquency is a necessary precursor to default. Using this terminology, there are two unambiguous decision points i.e. 1) whether to delinquent, and 2) once in delinquency, whether to default. This is useful in differentiating optimal and trigger-event defaulters via different initial motivations of delinquency and default. Optimal defaulters will delinquent to maximize their wealth when their mortgages are in negative equity. They will transit to default unless there are favorable changes in their equity positions. Trigger-event defaulters will delinquent due to some exogenous events and have every intention of reinstating their mortgages. They will avoid default unless the impacts of the trigger-events have seriously affected their financial ability to reinstate. With differing motivations at the two decision points, we propose default to be modeled as a two-step process.
We examine the postulated sequential relationship between delinquency and default, and model default decisions using the bivariate probit model that allows correlation between the two decisions. We test four aspects of delinquency-default behavior of borrowers:
1)the presence of a significant relationship between delinquency incidence and subsequent default decisions;
2)the importance of loss aversion as a behavioral response to borrowers’ default decisions; and
3)the influence of using protected equity, in particular the Central Provident Fund (CPF)[1]retirement savings to fund housing purchases on the likelihood of default.
Model and Tests
The sequential nature of the default decision subsequent to the delinquency decision presents us with the sample selection issue and has to be corrected unless ρ = 0. We expect ρ is not equal to zero, i.e. the default equation and delinquency equation may contain some common unexplained or omitted variables. Using the bivariate probit model, we allow for simultaneous estimation of multiple equations to account for different motivations for each equation and it allows interdependence between the multiple-equations through the covariance matrix, and corrects for selection bias.
This paper postulates that default decisions can be explained by the concept of loss aversion in borrowers. Specifically, we propose a negative relationship between the potential loss that borrowers will suffer if foreclosure occurs and the risk of default. If foreclosure occurs, the borrower faces the potential of losing part or all of his equity. The loss quantum depends on the foreclosure sales proceeds. As the loss quantum increases due to e.g. a declining property market, we expect the loss averse borrower will strive to avoid default.
However, the loss quantum does not increase indefinitely. It is capped by the maximum amount of borrower’s equity. Optimal defaulters will allow foreclosure by exercising the implicit put option to default. Therefore, the value function of the prospect theory (Tversky and Kahneman, 1991) in our case is truncated. This provides unique opportunity to integrate the option theory that is prevalent in mortgage risk studies, and the prospect theory that is quickly finding its way into mainstream finance literature.
We believe that the use of retirement savings like the CPF in Singapore will influence borrowers’ default decisions significantly. We control and examine for three aspects of this. Firstly, the use of CPF to pay for the equity component of the property purchase price enables a lower loan quantum. We expect this to lower the risk of default with the corresponding decrease in the loan-to-value ratios. Secondly, the use of CPF to service the monthly mortgage installments allows borrowers to better withstand trigger-events that may adversely affect their cash flows. We expect the proportion of installment serviced by CPF savings to be negatively correlated with the risk of default. Finally, rulings in Singapore regarding the use of CPF for housing purchases stipulate that in the event of foreclosure, the proceeds from the sale must first be used to repay the entire amount of CPF funds utilized[2]. The lender can only use the reminder to cover the mortgage balance. Therefore, the equity component that is derived from CPF funds is protected or “guaranteed” equity. We expect this feature and a higher proportion of borrower equity being “guaranteed” to encourage default.
Contributions and Implications
A significant correlation between the disturbances of delinquency and that of default will indicate the importance of constructing the effects of delinquency into existing mortgage default and prepayment risk models. Besides the potential of reducing inconsistency in our models, a positive result will suggest that to reduce losses attributed to default or foreclosure, lenders should attempt to minimize the risk of delinquency.
We believe our paper is the first study to examine the presence of loss aversion in borrowers’ behavior. This serves firstly as an induction of the loss aversion concept to mortgage risk studies. We also aim to integrate the traditional option theory and the up and coming behavioral theories.
In the local context, the direction and strength of relationship between the use of CPF savings and the risk of default will likely provide an answer to the potential of the mortgage securitization in Singapore. It is believed that the use of CPF is a major impediment against the development of MBS market locally. Our study looks at the accuracy of such a claim.
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[1] The Central Provident Fund (CPF) is a compulsory retirement savings scheme, which both employer and employee have to contribute a stipulated percentage of the salary to. To encourage homeownership, borrowers are allowed to use their CPF savings to pay for the equity component of the purchase price and also to service the monthly installments of the mortgage loan taken up.
[2] Since October 2002, this ruling has been amended to allow lenders first lien to the foreclosure proceeds. This implies that the CPF component is no longer guaranteed. As before, the cash equity component is similarly reduced when property falls. For the CPF equity component, the borrower will suffer a loss as the property value continues to fall.