Download 1 - American Real Estate and Urban Economics Association

Delinquency and Default in ARMs:
The Effects of Loss Aversion and Protected Equity
Alan Hwee Loon TEO
Email: [email protected]
Seow Eng ONG
Email: [email protected]
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:
[email protected]
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.
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.
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 utilized2. 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.
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.
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.
List of References
Ambrose, B.W. and Buttimer, R.J. (2000). Embedded Options in the Mortgage Contract. Journal of Real
Estate Finance and Economics, 21(2), 95-111.
Ambrose, B.W., Buttimer, R.J. and Capone, C.A. (1997). Pricing Mortgage Default and Foreclosure Delay.
Journal of Money, Credit, and Banking, 29(3), 314-325.
Ambrose, B.W. and Capone, C.A. (1996). Cost-Benefit Analysis of Single-Family Foreclosure
Alternatives. Journal of Real Estate Finance and Economics,13(2), 105-120.
Ambrose, B.W. and Capone, C.A. (1998). Modeling the Conditional Probability of Foreclosure in the
Context of Single-Family Mortgage Default Resolutions. Real Estate Economics, 26(3), 391-429.
Ambrose, B.W. and Capone, C. A. (2000). The Hazard Rates of First and Second Defaults. Journal of Real
Estate Finance and Economics, 20(3), 275-293.
Campbell, Tim, and J. Kimball Dietrich (1983). The Determinants of Default on Insured Conventional
Residential Loans. Journal of Finance, 38(December), 1569-1581.
Canner, G.B., Gabriel S.A. & Woolley J.M. (1991). Race, Default Risk and Mortgage Lending: A Study of
the FHA and Conventional Loan Markets. Southern Economic Journal, 58(1), 249-262.
Clapp, J.M., Deng, Y, and An, X. (2004). Alternative Models for Competing Risks of Mortgage
Termination. Working Paper.
Deng, Y., Quigley, J.M. and van Order, R. (2000). Mortgage Terminations, Heterogeneity and the Exercise
of Mortgage Options. Econometrica, 68(2), 275-307.
Genesove, D. and Mayer, C.J. (2001). Loss Aversion and Seller Behavior: Evidence from the Housing
Market. Quarterly Journal of Economics, 116, 1233-1260.
Greene W.H. (2003). Econometric Analysis. New Jersey: Prentice Hall.
Heckman, J.J. (1979). Sample Selection Bias as a Specification Factor. Econometrica, 47(1), 153-162.
Hunt, G.L. (2000). Alternative Nested Logit Model Structures and the Special Case of Partial Degeneracy.
Journal of Regional Science, 40(1), 89-113.
Ong, S.E. (2000). Prepayment Risk and Holding Period for Residential Mortgages in Singapore. Journal of
Property Investment & Finance, 18(6), 586-601.
Ong, S.E., Ooi, J. and Sing, T.F. (2000). Asset Securitization in Singapore: A Tale of Three Vehicles. Real
Estate Finance, 17(2), 47-56.
Ong, S.E., Maxam, C.L. and Thang, C.L. (2002). Mortgagor Motivations in Prepayments for Adjustable
Rate Mortgages. Review of Urban & Regional Development Studies, 14(2), 97-116.
Phillips, R.A. and VanderHoff, J.H. (2004). The Conditional Probability of Foreclosure: An Empirical
Analysis of Conventional Mortgage Loan Defaults. Real Estate Economics, 32(4), 571-587.
Quercia, R.G. and Stegman, M.A. (1992). Residential Mortgage Default: A Review of the Literature.
Journal of Housing Research, 3(2), 341-379.
Sandor, R. and Sosin, H. (1975). The Determinants of Mortgage Risk Premiums: A Case Study of the
Portfolio of a Savings and Loan Association. The Journal of Business, 48(1), 27-38.
Tversky, A. and Kahneman, D. (1991). Loss Aversion in Riskless Choice: A Reference Dependent Model.
Quarterly Journal of Economics, 106(4), 1039-1061.
Von Furstenberg, G.M. & Green, R.J. (1974). Home Mortgage Delinquencies: A Cohort Analysis. The
Journal of Finance, 29(3), 1545-1548.