Delinquency and default in ARMS the effects of protected equity

Chapter One Introduction 1.1 Background Mortgage Lending is an imperative component of the businesses of financial institutions worldwide. This is accelerated by the growth of the private residential property markets in the respective countries. In the US, almost half of the mortgages are securitized as Mortgage-backed Securities (MBS) (Deng, Quigley and van Order, 2000). Similar trends can be found in Singapore. With Singapore’s de facto central bank, Monetary Authority of Singapore recommending the securitization of real estate (Sing and Ong, 2004) and the provision of favorable tax treatment for such issues (Ong, Ooi and Sing, 2000), there is enormous potential for the secondary mortgage market to take off in Singapore. In accordance to these trends, the roles and abilities of mortgage servicers in controlling default outcomes become increasingly crucial. Understanding the various types of mortgage risk is thus essential, for both practitioners and academics. For practitioners, the credit risk management functions of financial institutions are essentially geared towards assessing the credit or default risk of customers i.e. the possibility of a borrower not being able to service a loan. On the other hand, to mitigate prepayment risk and share interest rate risk with borrowers, lenders are increasing moving towards issuing adjustable-rate mortgages (ARMs). In academia, default risk (e.g. Quigley and Van Order, 1990), prepayment risks (e.g. Ong, 2000; Lee 1 and Ong, 2006) and the competing relationship between them (e.g. Deng, et al., 2000; and Clapp, Deng and An, 2004) are areas of intense study. However, studies on mortgage delinquency and 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, et al., 1992). Understanding delinquency risk will also help practitioners better determine the default risk of their portfolio. In this paper, we deem mortgage delinquency as a significant and necessary decision that is taken by the borrower prior to the default decision. Accordingly, we propose that the motivations for delinquency exert a significant influence on the subsequent motivations for default such that default risk models should incorporate the risk of delinquency. Among the factors affecting the risk of default and delinquency, the extent of the borrower equity is considered one of the most important variables (Kau, et al., 1993 and 1994, and Lambrecht et al., 1997). In Singapore, the use of CPF savings (a compulsory retirement savings scheme) to pay for the initial housing downpayment and the repayment of the mortgage loan is prevalent. Before September 2002, the CPF Act guarantees the CPF savings utilized such that when the house is subsequently sold either for foreclosure or relocation, the sale proceeds must be used to repay the CPF savings 2 first before being utilized to repay the mortgage balance with the financial institution. Interests foregone must also be returned to the retirement accounts. Thus, the portion of borrower equity financed by CPF savings is “protected”. We postulate that the impacts of “protected equity” on the risks of default and delinquency performances are different from conventional measures of borrower equity financed by cash savings. This provides a natural experiment for us to investigate the role of government policy and the role of borrower equity in affecting mortgage risks. 1.2 Definition of Mortgage Delinquency & Default It is crucial to define and differentiate delinquency and default at this early stage. There is a lack of consensus on this aspect. Earlier scholarly works (von Furstenberg and Green, 1974; Campbell and Dietrich, 1983; and Zorn and Lea, 1989) differentiate them according to the eventual outcome. Loans with missed payments that are eventually repaid are defined as delinquent while loans that are eventually foreclosed are defined as default. These papers focus on studying the latter and assume that default is synonymous with foreclosure. This differentiation is only possible with hindsight and is not useful for lenders and servicers, as they cannot differentiate between the two at the time when missing the first mortgage and thus undertake suitable strategies. These studies also do not differentiate between different motivations of defaulters – those who miss payments with the intention of giving up their properties and do eventually foreclose, and those who miss payments with the intention of reinstating their mortgages but were eventually unable to prevent foreclosure. 3 The second group of studies, developed by Vandell (1993) and later in the works of Ambrose, Buttimer and Capone (1997), Ambrose and Capone (1996, 1998 and 2000), Ambrose and Buttimer (2000), Deng (1997) Deng, et al. (2000) and Phillips and VanderHoff (2004) included the distinction between default and foreclosure in their models. Foreclosure is regarded as one of the possible paths a defaulted loan can take. However, this group of papers classifies loans as default once a scheduled payment is missed. Therefore, no distinction is made between delinquency and defaults. On the other hand, practitioners in the US and Singapore1 differentiate delinquency and default by the number of days of missed installments. Delinquency is defined as the nonpayment of a mortgage payment due (e.g. Ambrose and Buttimer, 2000; and Holmes, 2003). Default occurs when a borrower has missed 90 days’ installment and the fourth payment is due (Ambrose and Capone, 2000; and Chen and Deng, 2005). This is also sometimes termed serious delinquency. Therefore, delinquency is a necessary precursor to default. During delinquency, the lender usually sends reminders to the borrower to make up the missed payments. Although the lender has the right to foreclose the property as missing an installment is tantamount to a breach of contract, he would usually refrain until default. Thus, the borrower has the option to repay the missed installments and reinstate the mortgage. Once the loan transited to default, the lender will issue a formal legal letter to the borrower indicating the lender’s right to proceed with foreclosure 1 This definition is supported by Section 25 of the Conveyancing and Law of Property Act in Singapore, which states that "A mortgagee shall not exercise the power of sale conferred by this Act unless - notice requiring payment of the mortgage money has been served on the mortgagor or one of several mortgagors, and default has been made in payment of the mortgage money or part thereof for 3 months after the service…” 4 proceedings any time from then on. The commencement of foreclosure proceedings is significant because borrowers are generally not able to reinstate their delinquent loans once the foreclosure sale occurs (except for some states). Thus, the borrower faces real danger of losing his home with the transition 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. We adopt this set of definitions in our paper. Besides the significance of the crossover from delinquency to default, this definition is also useful in differentiating optimal and trigger-event defaulters via different initial motivations of delinquency and default. Optimal defaulters refer to borrowers who delinquent to maximize their wealth when their mortgages are in negative equity positions. They will transit to default unless there are favorable changes in their equity positions2. Trigger-event defaulters refer to borrowers who 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. The differing motivations of the two categories of defaulters are elucidated by the practitioners’ definition as shown in Exhibit 1. 2 This follows from Ambrose and Capone (1998), which offers similar arguments for the transition from default to foreclosure. 5 Exhibit 1 Differing Motivations of Delinquency and Default Optimal Trigger-event Delinquency Time Default Financial difficulties in paying installments due to exogenous events Financial position not improved sufficiently to enable reinstatement Wealth maximizing to delinquent due to negative equity position No favorable changes in net equity position to support reinstatement 1.3 Research Problems & Objectives The unique feature of the mortgage market in Singapore is the use of borrowers’ retirement funds or CPF savings to finance the purchase of residential properties. With protection being conferred by regulations to the CPF portion of borrower equity, this provides a natural experiment to investigate the role of government and the role of protected borrower equity in controlling mortgage risk. As mentioned, borrower equity is found to be an important variable of default decisions in past mortgage literature. Furthermore, the effect of protected borrower equity on mortgage risk is likely to be different from the conventional borrower equity, which can be lost if foreclosure occurs. However, this disparity has not been addressed by past mortgage studies. Therefore, the first research question of our paper aims to examine the impact of protected equity from different angles and perspectives. 6 From the academia point of view, providing insights into a different variant of borrower equity is significant towards contributing to the overall knowledge of borrower behavior and the influence of equity on mortgage risks. It also shows how government policy and regulation can manipulate the default and delinquency performances of mortgages and their securities. More practically, understanding the effects of protected equity is significant to policymakers and advocates of pension fund reforms. As pension funds are being liberalized or reformed, the use of such funds to finance the purchase of housing may become a possibility. This will probably be advocated to improve the accessibility and affordability of homeownership. The Singapore experience, where pension funds are allowed to finance home purchases and to service the monthly mortgage installments, provides an opportunity to investigate the potential impacts of such a policy on mortgage risk. Equally important to local context, the direction and strength of the relationship between the use of CPF savings and the risk of default will likely provide an answer to whether the policy of allowing CPF funds to partially furnish the mortgage is a bane for mortgage securitization in Singapore. Despite tax incentives and regulatory liberalizations, Singapore has yet to see its first MBS. It is generally believed that the use of CPF savings is holding up securitization of mortgages. The main reason is the regulation that stipulates the CPF Board as having first lien on the properties. This implies that private lenders will then have secondary claims on the properties3. However this preconception has not been tested as yet. A better understanding of the effects of the protection conferred to the 3 However, this has recently been amended in September 2002. 7 retirement funds used will provide support for further development of Singapore’s securitization market. Therefore, the study’s first contribution is the understanding of the role of government policy and of protected equity in controlling default and delinquency risks. Based on the definitions adopted in this paper, there is a seemingly obvious relationship between delinquency and default. Firstly, the essential preceding step of a defaulting mortgage is delinquency. Secondly, as iterated in Exhibit 1, the motivation for default is essentially originated from the motivation for delinquency. For instance, Waller (1989) found that lengthy delinquency period might cause borrowers to accumulate so much back payments that default becomes unavoidable. Thus, the relevant observed and unobserved variables for delinquency and default are likely to be related. As a result, Quercia, et al. (1992) advocated the study of default decision within a framework that incorporates the delinquency decision. However, no studies have tested or taken into account the potentially influential relationship between default and delinquency4. Thus, the second research question of our paper contends with the presence and significance of such a relationship. The importance of the research question is derived from the absence of the delinquency decision in existing default models. If a significant relationship can be proven to exist between the two decisions, such default models can be deemed to be mis-specified and 4 Except for a recent working paper by Chen and Deng (2005) that recognized the transition from delinquency to default. 8 inefficient. It would also be necessary to incorporate the delinquency option to mortgagepricing models. By examining whether such a relationship exists, our paper aims to expand the existing knowledge of borrower behavior. More practically, lenders and servicers often ignore delinquency and focus their attention on controlling default risks. As delinquency is the essential preceding step of default and the effects of their determinants may be different, it may be more efficient to engage different risk mitigation tactics in different stages, i.e. whether they are in delinquency or have transited to default. Lenders and servicers will thus be able to alter borrower behavior in delinquency through the appropriate loss mitigation programs. In addition, it may be necessary to predict the delinquency and default performance of mortgage pools in order to effectively price them and determine the appropriate subsequent actions. Thus, the second and third contributions of this paper are to verify the presence of a significant relationship between mortgage delinquency and default, and to identify whether the sequential nature of delinquency and default does exert a significant impact on default decision modeling. Provided that the relationship between delinquency and default is found to be significant, the obvious next step would be to examine the default/reinstatement behavior of borrowers after taking into account the effects of delinquency. Previous studies mostly focus on the post-default outcomes, i.e. the conditional risk of foreclosure given default (e.g. Ambrose and Buttimer, 2000), rather than the default behavior itself. These studies 9 also ignore pre-default influences e.g. the potential influence of delinquency on default behavior. Therefore, we intend to examine this pre-default influence in our study. More critically, no past research has focused specifically on reinstatement behaviors. Although reinstatement after delinquency is the direct opposite of default, placing emphasis on the former allows us to view the issue from a different, and perhaps more interesting point of view. Therefore, the third research question relates to the determinants that influence whether a borrower reinstates or transits to default after taking into account the predefault influence of delinquency. By examining the reinstatement question, we are essentially looking at the default question from another angle or point of view. This is expected to provide insights to borrower behaviors, adding on to our existing knowledge. Furthermore, this research question is significant to lenders and servicers. When a loan missed a first payment, it is important to lenders and servicers to assess its likelihood of reinstatement. Subsequently, they can identify and focus their efforts toward loans that are more likely to transit to be reinstated. This enables a more efficient allocation of resources and also mitigates the risk of foreclosure by increasing the probability of reinstatement. In addition, the income earned by servicers is the spread between payments collected and funds paid to MBS investors. With insights to the characteristics of delinquent loans that are more in risk of delaying payment for a longer period of time by transiting to default, servicers can better predict their income and also act on these riskier loans. 10 Thus, the fourth contribution is to provide pioneering insights to the reinstatement behavior in a conditional probability of reinstatement framework that assumes a significant relationship between default and delinquency. The impact of repeat delinquency or default is under-researched in existing mortgage literature. Ambrose and Capone (2000) is the first paper to examine the issue of whether the default risk of mortgages that have avoided foreclosure on an initial default (or reinstated) is similar to those that have not previously been defaulted. The paper found that the prediction of default risk for the two groups is different. Essentially, the probability of default for the former is higher, especially during the first two years after the initial reinstatement from default. After the two-year period, the default rates for the two groups are similar but the volatility of repeat defaulters is higher. In addition, economic variables are more influential in predicting default in the former group. Following Ambrose and Capone (2000), the third research problem of our paper examines the postulation that the risk of default and delinquency is different between first time delinquents and repeat delinquents who have reinstated from previous delinquencies. To test this hypothesis, we include a dummy variable to indicate loans that has previous delinquency experiences. The relative riskiness of repeat delinquents compared to first-time delinquents enables a more detailed understanding of borrower behavior. Taking into account their heterogeneity, mortgage risk modeling can be further improved. Furthermore, lenders and servicers are concerned about whether previous delinquency experiences are indications 11 of greater riskiness of subsequent defaults. They may want to focus their resources on first-time delinquents or have different strategies for different groups to try to reduce the transition to default. Ambrose and Capone (2000) also suggested important implications of their research to the riskiness of MBS, the income of mortgage servicers, and the success of the loss mitigation program of the FHA. Similarly, these implications are also applicable to our study of repeated delinquencies. The fifth contribution of our study is the verification of the presence of a differing risk profile and behavior for a first time delinquent and a repeat delinquent. In responding to the research questions, we test five aspects of the borrower delinquencydefault behavior: 1. the role of the government and the role of borrower equity in affecting the risk of delinquency and of default; 2. the presence of a significant relationship between delinquency incidence and subsequent default decisions; 3. the disparity in the expected behavior of borrowers in a model that takes into account the relationship between delinquency & default as compared with a model that assumes no such relationship exists; 4. the borrowers’ decision to reinstate or to allow transition to default given delinquency; and 5. the probability of default for reinstated/repeat-delinquent borrowers as compared to first time delinquents. 12 To preview our findings, we found that: 1. the use of protected borrower equity to help finance housing purchases is shown to increase the risk of default when its use at origination increases, but the risk of default is decreased as the protected equity is accumulated over time; 2. the relationship between delinquency and default is highly significant and should be included in subsequent default risk modeling; 3. variables like the probability of negative equity, mortgage term, tenure and land area of the property, and the number of co-borrowers have inverse relationships with regards for a model that takes into account the relationship as compared to a model that does not; 4. the borrowers’ decision to reinstate a delinquent mortgage depends on a number of variables like the initial loan-to-value ratio, whether borrowers can service the mortgage entirely via the retirement fund contributions and occupation, and the influential determinants can sometimes be different from the unconditional default behavior; and 5. the risk profile of borrowers with previous experiences of delinquency is found to be different and riskier than borrowers who are first-time delinquents. 13 1.4 Organization of Report Chapter Two provides a review of related literature, followed by a brief introduction to the CPF Scheme in Singapore in Chapter Three. The next chapter describes the research methodology and data for the intended analyses. Chapter Five examines the relationship between delinquency and default, and the impact of repeated delinquency on subsequent default behavior. In addition, the chapter also examines the effects of protected borrower equity Chapter Six investigates the conditional risk of reinstatement given delinquency. Finally, Chapter Seven concludes the study. 14 Chapter Two Literature Review 2.1 Introduction It is necessary to note that most literature on mortgage risks was originated from the US, where Fixed Rate Mortgages (FRMs) are prevalent (Ong, 2000). Conversely, all mortgages originated in Singapore are ARMs (Khor and Ong, 1998). The exogeneous and endogeneous factors affecting both forms of mortgages may thus diverge. For instance, the prepayment risk for Singapore mortgages is very low (Ong, Maxam and Thang, 2002) while the prepayment risk for ARMs in US may be higher resulting from potential switches to FRMs to take advantage of interest rate movements (Ambrose and LaCour-Little, 2001). However, Campbell, et al. (1983) found that most determinants that affect default decisions influence delinquency in the same way. Therefore, the methods and factors used in the literature to rationalize mortgage risks in FRMs serve as a platform for our analysis. 2.2 Methodologies of Mortgage Risk Studies Mortgage risk studies essentially started in the early 1960s and the main methodologies used included regression (von Furstenberg and Green, 1974; Morton, 1975; and Campbell, et al., 1983), logit (Vandell and Thibodeau, 1985), and multinomial logit (Zorn, et al., 1989; and Cunningham and Capone, 1990). Such models often suffer from a 15 lack of theoretical basis for the borrower behaviors. This led to the development of the Borrower Payment Model and the Option-based Model. Mortgage risk studies that utilize the options-based theories to explain default and prepayment behaviors focus on the net equity position i.e. the house price movement and the term structure. These two factors are postulated to be the main determinants of such behaviors (Kau, Keenan, Muller and Epperson, 1992; Kau, Muller and Epperson, 1993; Kau, Keenan and Kim, 1993 & 1994; Ambrose, Buttimer and Capone, 1997; Ambrose and Buttimer, 2000). However, earlier options-based studies failed to take into account the competing nature of foreclosure and prepayment. Thus, more recent studies utilize the competing risk model employed by Deng, et al. (2000) to incorporate a wider range of default factors like borrower characteristics (Ambrose and Capone, 2000; Ong, et al., 2002; Lambrecht, et al., 2003), macroeconomic characteristics (Ambrose and Capone, 2000; Ambrose and LaCour-Little, 2001; Ong, et al., 2002) and loan factors (Ambrose and LaCour-Little, 2001; Ong, et al., 2002). These mostly utilize the Cox proportional hazards model. This model is similarly utilized in a more recent paper (Chen and Deng, 2005). In addition, Ambrose and Capone (1998) and Phillips, et al. (2004) use a multinomial logit model to test the influence of borrower, mortgage and macroeconomic variables on the conditional probability of foreclosure. The former relied upon the options-based 16 approach to identify the independent variables while the latter included the variables that they believe to be significant. 2.3 Variables of Delinquency and Default Decisions 2.3.1 Determinants of Mortgage Delinquency Ambrose and Capone (1996, 1998) and Waller (1988) described the aim of delinquency is either to put the funds, originally intended to pay the installments, to other uses due to financial difficulties, or to exercise the implicit put option to abandon the property. A third cause of delinquency noted by Waller (1988) is the economic incentive borrowers can gain from living in the house rent-free before foreclosure takes place. Only a handful of studies are conducted to examine the determinants of delinquency. Von Furstenberg, et al. (1974) found that the equity-value ratio possesses a significant negative relationship with delinquency while the age of mortgages has a positive relationship. For instance, as the loan-to-value ratio increases from 80 to 90 per cent, the delinquency rate escalates by about two-thirds, and when the ratio further increases to 95 per cent, delinquency rate would increase by another 70 per cent. In addition, mortgages of existing houses are more prone to delinquency than those taken on new houses. Herzog and Earley (1970) and Morton (1975) also found income, occupation and the number of children to be influential determinants. In particular, von 17 Furstenberg and Green (1974) discovered that when household family increased from US$5000 to US$10,000, the delinquency rate declines by 31 per cent. Zorn, et al. (1989) argued that delinquency can be regarded as a form of borrowing from the lender at the mortgage contract rate. Therefore, when interest rate increases, delinquency rate will correspondingly rise as people “borrow” at the relatively cheaper source of fund to finance other uses. Canner et al. (1991) found that the receipt of government assistance, headed by a minority, and martial status have positive influences. On a more somber note, Canner et al. (1991) pointed out that delinquency prediction consists of a large unexplained random component as credit problems can arise from events that are difficult to foresee. Thus, the use of ex-ante data has the ability to capture components that systematically affect delinquency and are observable to the lender at loan origination but ignores the more unpredictable ex-post components. Campbell, et al. (1983) did a comparison between the determinants of delinquency and default rates and verified that household income and interest rate are more influential than equity measures because they represent the availability and opportunity costs of funds used to repay the mortgage installments. They also expected the loan-to-value ratio to be less important than for default incidence because delinquency is without potential termination of ownership of the property, although their results differ. 18 2.3.2 Determinants of Mortgage Default Mortgage Loan Specific Characteristics Literature on mortgage loan specific characteristics traditionally focuses on the equity position of the borrower, which has generally been found to be significant. This is coherent with earlier studies where the borrower is assumed to default once negative equity position is reached whereby the value of the property falls below the mortgage value. Transaction costs and other costs associated with default/ foreclosure were ignored in these studies. Several proxies of the equity position of borrowers were used. Herzog and Earley (1960) and von Furstenberg (1969) were among the first studies to use the loan-to-value ratio at origination and to endorse its dominance. Other studies that use the loan-to-value ratio include Von Furstenberg and Green (1974), Vandell (1978), Schwartz and Torous (1993), Kau, et al. (1993, 1994) and Lambrecht et al. (1997). Campbell and Dietrich (1983) attributed its significance to the high correlation between the initial and subsequent loanto-value ratio, and to it acting as a proxy for borrowers’ non-housing wealth. Several studies employ the current loan-to-value ratio as a measure of equity including Follain and Struyk (1977), Campbell and Dietrich (1983), Vandell and Thibodeau (1985), Anderson and Weinrobe (1986), Cunningham and Capone (1990), and Capozza et al. (1997). A study to compare the relative importance of the initial and current loan-to-value 19 ratio was undertaken by Waller (1989). It was found that although the latter ratio had a greater influence on foreclosure decision, the two ratios are significantly correlated. Other proxies used include the value-to-total debt ratio (Waller, 1988; Zorn and Lea, 1989; Springer and Waller, 1993) and book value (Giliberto and Houston, 1989; Hendershott and Schultz, 1993). Specifically, Springer and Waller (1993) adopted three measures of equity namely, property value-to-total borrower debt ratio, property value-tomortgage value ratio, and property value-to mortgage balance ratio. It was found that the first measure using total borrower debt was more effective in explaining the default rate than the other two. Most studies found that equity measures are positively significant in explaining the default/ foreclosure rate. In contrast, Foster and Van Order (1984), Zorn and Lea (1989) and Lambrecht et al. (1997) found that equity measure is negatively correlated with default/foreclosure rate with a low level of significance. The first two studies attributed these to reluctance among the borrowers to default even under negative equity situations. It is interesting to note that the latter two studies utilize ARMs data from outside the US, i.e. Canada and the UK, respectively. Von Furstenberg (1969 and 1974), who was among the first to use the age of mortgage as a determinant, found it to be significant and that foreclosure rates peaked three to four years after origination and will decline until they become negligible when about half the mortgage term expired. This is similar with Waller (1989), Schwartz and Torous (1993) 20 and Kau et al. (1994) whereas Campbell and Dietrich (1983) discovered a peak at 6.7 years. Vandell (1978) found the peak of foreclosure for ARMs to be between the 2-5 years. With regards to the signs of influence, contradictory results are obtained. Furstenberg (1969), Vandell (1978) and Campbell and Dietrich (1983) using log age and Cunningham and Capone (1990) using quadratic function of age found a negative correlation. Springer and Waller (1993) attributed this to the higher level of principal repayment and equity build-up as more payments are made. On the other hand, studies that use age directly as a variable mostly found a positive relationship (Furstenberg, 1969; Vandell, 1978; Campbell and Dietrich, 1983; Cunningham and Capone, 1990 and Capozza et al., 1997). This is attributed to a close correlation between age and other determinants of foreclosure determinants. Mortgage term is found to have a significant direct relationship with the default/ foreclosure rate (Furstenberg, 1969; Herzog and Earley, 1970; Bervokec et al., 1994). Specifically, Furstenberg (1969) attributed the positive correlation to the faster equity build-up in shorter-term mortgages. With regards to the effect of mortgage rate, consistent results were lacking in the literature. The relationship between an ARM mortgage rate and the corresponding default/ foreclosure risk is found to have a low negative elasticity (Zorn and Lea, 1989). In contrast, Vandell, et al. (1993) and Ambrose and Capone (1996 and 2000) discovered 21 a low positive relationship. Riddiough and Thompson (1993) found that the impact of interest rate is minimal when compared with other factors like property and mortgage contract. Property Specific Characteristics Property related factors examined include the returns from property, the price volatility of the property, age and the neighborhood quality. Returns from property are often divided into capital appreciation and rental yield. Capital appreciation as estimated by the difference between the current property price and the purchase price, is found to have a positive significant relationship (Waller, 1989; Vandell, 1992; Schwartz and Torous, 1993; Kau et al., 1994; Case and Shiller, 1996). However, Lea and Zorn (1986) using the ratio of property price index to the consumer price index, found it to be insignificant. Capozza et al. (1997 and 1998) uses the rent-to-price ratio to evaluate the influence of rental yield. Both studies found a significant negative relationship but suggested the limited economic impact. Capozza et al. (1998) highlighted that there are two offsetting effects relating to a higher rental rate. A higher rent implies a lower capital appreciation, which increases the probability of reaching the default boundary. On the other hand, a higher rental rate makes the existing mortgage on the property financially more attractive relative to renting. 22 In addition to the returns from property, the volatility of property price is also an important factor of default/ foreclosure rate. In a comparison study, Schwartz and Torous (1993) found that when measured up against the cumulative housing index returns, volatility of the index is more significant in explaining the rate of default. This is attributed to the fact that a property price index captures the average prices whereas default depends on the lower tail of the distribution. However, the literature does not have consistent findings on the influence on default/ foreclosure rate. Capozza et al. (1997) measured the volatility using the standard deviation of the time series of the percentage price changes. Consistent with other studies (Schwartz and Torous, 1993; Capozza et al., 1998; Ambrose and Capone, 2000), they found a positive relationship. In contrast, Kau and Kim (1994) pointed out that when the volatility of house price increases, the probability of default in the next period will decrease. This is because the expected house price changes make waiting more valuable. On a similar note, Clauretie (1987), Zorn and Lea (1989), Canner et al. (1991), Gabriel and Rosenthal (1991) and Kau et al. (1994) also found a negative relationship with the rate of foreclosure. Capozza et al. (1998) found that the effect of house price volatility interact with the level of current loan-to-value ratio such that when the ratio is low, there is a positive relationship, and when the ratio is high, the impact is negative and high. Kau et al. (1994) 23 discovered that even with significant house price volatility, the probability of default becomes negligible very quickly when transaction costs increases. Vandell et al. (1993) found that the type of property is a significant determinant and that hotel, office and apartment properties possess the highest default/ foreclosure rates while retail and industrial properties have the lowest risks. Bervokec, Canner, Gabriel and Hannan (1994) found that condominium properties were most risky among the various residential property categories. Hakim and Haddad (1999) suggested a higher default risk occurring for borrowers of new condominiums. Mortgages on new houses were discovered to have higher rates of default than that on existing houses (Furstenberg, 1969, Campbell and Dietrich, 1983). Similarly, the age of the property is found to have a negative relationship with default rate (Canner et al., 1991 and Hakim and Haddad, 1999). However, Vandell and Thibodeau (1985) demonstrated the insignificance of this variable. Neighborhood quality is basically adopted to reflect the price variability of a location. Canner et al. (1991) use residential vacancy rate and median age of housing stock as measures for neighborhood quality while Carroll, Clauretie and Neil (1997) use the location zip codes. Similar with these studies, Vandell and Thibodeau (1985) showed that neighborhood quality is influential in explaining the default rate in a negative relationship. 24 Borrower Specific Characteristics Previous studies generally found borrower related characteristics influential in explaining the default/ foreclosure rate. However, there is no uniformity in the set of variables that are statistically significant. Ambrose and Capone (1998) further argued that there exist different categories of defaulters with differing motivations to default and thus, different probabilities. Some of the variables used include ability to pay measures, household income, previous history of delinquency or default, number of years of tenure of the job and occupation. Borrower’s ability to meet the periodic mortgage payments is a prevalent factor that has been widely researched. The payment-to-income ratio is a popular measure but yields inconsistent results. Vandell (1978) and Campbell and Dietrich (1983) found a positive relationship while other studies found a negative relationship (Vandell and Thibodeau, 1985, Springer and Waller, 1993, Cunningham and Capone, 1990). Age of the owner has also produced ambiguous findings regarding the extent and direction of its influence. Furstenberg (1969), using the age of the principle mortgagor, discovered a negative non-linear relationship with the default rate. Capozza et al. (1997) found age to be a major determinant of default. Canner and Luckett (1990), whose study included both consumer and mortgage loans, again used the age of the household head and found it significant. 25 Campbell and Dietrich (1983) attributed this significant relationship to the strong correlation between age and other determinants of default (including the current loan-tovalue ratio and payment-to-income ratio). On a similar note, Furstenberg (1969) ascribed the relationship more to the financing characteristics of the mortgage whereby younger borrowers are required to pay a higher downpayment. Besides these studies, the work by Anderson and VanderHoff (1989), Zorn and Lea (1989) and Canner et al. (1991) have found that the variable possesses a negative relationship. In contrast, Cunningham and Capone (1990) found that the older the borrower, the greater the probability of default. Other studies including Waller (1988), Springer and Waller (1993), Bervokec et al. (1994) and Hakim and Haddad (1999) found age to be insignificant towards explaining default/ foreclosure. The overall wealth and household income are useful factors by which to explain the likelihood of default/ foreclosure. Vandell and Thibodeau (1985) indicated that higher wealth individuals have a source of funds to fall back on and will thus delay default, suggesting a negative relationship. This is in accordance to other studies by Gabriel and Rosenthal (1991) and Canner et al. (1991). In contrast, Cunningham and Capone (1990) found that the net worth of the borrower has a positive effect on default rates. This suggests that instead of using the higher net worth to defer default, borrowers use it as a source to pay for moving costs when house prices fall. Anderson and VanderHoff (1989) used education and income to proxy wealth and found no significant relationship. 26 Other studies focus on the impact of total household income. Earlier studies by Furstenberg (1969), Vandell (1978) and Bervokec et al. (1994) found that the higher the income of the borrower, the lower will the probability of default be. In addition, Bervokec et al. (1994) also found that the intensity of the negative relationship decreases as the level of income rises. Lambrecht et al. (1997) uses the total income of the household at the time of origination in natural logarithmic form and similarly observed a negative relationship with default rate. This is supported by Canner et al. (1991). Amborse and Capone (2000) discovered that borrowers, who have defaulted but reinstated their mortgage before foreclosure, have a higher but declining likelihood of defaulting again in the next two years. Furstenberg (1970b) used seasoning, i.e. the number of years since origination, as a proxy for attachment to the property and experience for successful mortgage installment payments. The number of years of job tenure and the history of employment on the current job serve as a useful proxy for security of future income. Vandell and Thibodeau (1985) established an inverse relationship in the earlier case while other studies (Waller, 1988; Cunningham and Capone, 1990; Hakim and Haddad, 1999) found no significant relationship. With regards to the latter case, Cunningham and Capone (1990) found that borrowers with a longer period of employment in their current line of work are less likely to foreclose. 27 Occupation as a determinant, especially the impact of sales-related job, does not present a set of consistent findings from past works. Vandell and Thibodeau (1985) suggest that borrowers who are self-employed or hold jobs that are commission-based have a higher probability of foreclosure. Waller (1988) commented that borrowers with occupation in the categories of sales, self-employment and unskilled labor generally have a higher risk of default. However, when he classified borrowers’ occupation into either sales or nonsales, he ascertained that borrowers in a sales occupation are far less likely to default than other occupations. Waller (1993) attributed it to the potential loss of credit, which salespersons with less stable income rely on, if default occurs, and that salespersons have a lower selling costs as they can sell the property themselves. Cunningham and Capone (1990) and Hakim and Haddad (1999) found that investors of properties are more likely to foreclose than owner-occupiers. This is likely due the fact that the funds used to repay the periodic mortgage payments for investors coming from rentals received, which are more uncertain. However, Berkovec et al. (1994) found an insignificant relationship. Macroeconomic Variables Exogenous factors include demographic or macroeconomic factors (Dickinson and Hueson, 1994). Most past researches focused on trigger events like that of retrenchment and divorce. 28 Unemployment refers to both the actual loss of job and it being a proxy of the security on future income or financial ability. It can also be a measure of the vitality of the economy. Campbell and Dietrich (1983) discovered a significant positive relationship between the regional unemployment rate and default incidence. This also indicates the importance of geographic diversification in mortgage default risk. Additionally, Springer and Waller (1993) found the influence of unemployment rate of local area is more important than national unemployment statistics. Other studies with similar results include that by Lea and Zorn (1986), Gabriel and Rosenthal (1991), Case and Shiller (1996) and Capozza et al. (1997). Cunningham and Capone (1990) discovered a negative relationship. Foster and Van Order (1984,1985) showed that even if unemployment rate increased, as long as the equity is positive, borrowers should not default, thus discounting its significance as a variable. This is in accordance to the works of Vandell (1985), Clauretie (1987), Canner et al. (1991) and Berkovec et al. (1994). 2.4 Studies Incorporating the Delinquency-Default Relationship To the best of our knowledge, this paper is the first to investigate the relationship between delinquency and default but several past studies do deal with post-delinquency outcomes without reference to the subsequent default decision. Herzog and Earley (1970) examined the factors affecting the conditional risk of foreclosure given delinquency and also the unconditional risk of foreclosure. The results 29 show that after taking into account the effect of delinquency, although the signs of the variables remain the same, factors like the loan-to-value ratio, number of dependents, borrower age, and occupation became insignificant. This constitutes preliminary evidence of the importance of taking into account the conditional effect of delinquency. Ambrose and Buttimer (2000) postulated to study lenders’ ability to influence borrower behavior in post-delinquency situations through the use of deficiency judgments. It defined “delinquency” as having missed one mortgage installment and studied the probability of foreclosure, reinstatement and prepayment, conditional on delinquency. Ambrose and Buttimer (1998) examined the conditional probability of foreclosure given default. Holmes (2003) examined commercial mortgage borrower actions after delinquency occurs using a game-theoretic model. It postulates that post-delinquency action is either reinstatement or foreclosure. The paper thus investigates the probability of foreclosure and the probability of reinstatement given delinquency. The paper also utilized a multinomial logit specification in two sets of tests. In a recent working paper, Chen and Deng (2005) recognized the transition from delinquency to default as they examine the special service workouts for commercial mortgages. These mortgages are transferred to special servicers when events like delinquency, imminent default, borrower bankruptcy, litigation, and borrower forebearance requests occur. The transition is thus from delinquency to special service, 30 and then to default. However, the focus is on the factors influencing loan defaults when they are being special serviced. Most of these papers do not consider the transition from delinquency to default, and the extent of their relationships, which are the main postulations of our study. In addition, our paper utilizes the bivariate probit model instead of the multinomial logit model as we propose a sequential decision-making framework for borrowers. 31 Chapter Three CPF Scheme in Singapore 3.1 Background of the Central Provident Fund (CPF) Scheme The Central Provident Fund or CPF was first introduced in 1 July 1955 as the national funded pension scheme in Singapore by the colonial British government at that time. The primary objective of the scheme is to pool contributions from people who are economic active and redistribute to the pensioners. Under the requirements of the scheme, the employee had to save a certain percentage of his income to the account. The employer also had to contribute a certain percentage of the salary to the employee’s account. The rate of contribution has steadily increased over the years until it reached 20 per cent for both employee and employer in 1995. From then on, the rate of contribution has changed according to the economic growth of the country. This allows the government to control the labor costs (Chua, 1997) and make economy attractive to foreign investors. The CPF scheme has expanded over years to have three accounts for every member. This expansion also represents the growth in the range of functions that the CPF plays. The savings in the Ordinary Account can be used to buy a home, pay for CPF insurance, investment and education. The savings in the Special Account is to ensure sufficient amount is available to support a member in his old age. In addition, it can also be used for contingency purposes and investment in retirement-related financial products. Finally, the 32 Medisave Account consists of savings that can only be used for hospitalization expenses and approved medical insurance. Exhibit 2 presents the variations of the contribution rates from 1955 to 2004 with the relative contributions to the different accounts. Exhibit 2 CPF Rate of Contributions (Proportion of Income Earned) (1955 – 2004) Year 1955-1967 1968-1969 1970 1971 1972 1973 1974-1976 1977 1978 1979 1980 1981 1982 1983 Account Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary 35 years & Below 35-45 0.1 0.13 0.16 0.2 0.24 0.26 0.3 0.3 0.01 0 0.31 0.3 0.03 0 0.33 0.3 0.07 0 0.37 0.32 0.065 0 0.385 0.385 0.04 0 0.425 0.4 0.05 0 0.45 0.4 45-55 55-60 60-65 above 65 33 1984-1985 1986 1987 1988 1989 1990 1991 1992 1993 1994-1998 1999 Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave Total Ordinary Special Medisave 0.06 0 0.46 0.4 0.04 0.06 0.5 0.29 0 0.06 0.35 0.29 0 0.06 0.35 0.3 0 0.06 0.36 0.3 0.02 0.06 0.38 0.3 0.035 0.06 0.395 0.3 0.04 0.06 0.4 0.3 0.04 0.06 0.4 0.3 0.04 0.06 0.4 0.3 0.04 0.06 0.4 0.24 0.3 0 0.06 0.36 0.3 0.02 0.06 0.38 0.3 0.035 0.06 0.395 0.3 0.04 0.06 0.4 0.29 0.04 0.07 0.4 0.29 0.04 0.07 0.4 0.29 0.04 0.07 0.4 0.23 0.3 0 0.06 0.36 0.3 0.02 0.06 0.38 0.3 0.035 0.06 0.395 0.3 0.04 0.06 0.4 0.29 0.04 0.07 0.4 0.28 0.04 0.08 0.4 0.28 0.04 0.08 0.4 0.22 0.06 0.07 0.08 0.25 0 0.06 0.31 0.22 0.22 0 0.06 0.28 0.15 0.2 0 0.06 0.26 0.11 0.06 0.28 0.19 0.06 0.21 0.09 0.06 0.17 0.04 0.06 0.25 0.19 0.06 0.15 0.09 0.06 0.1 0.04 0.06 0.25 0.18 0.06 0.15 0.08 0.06 0.1 0.03 0.07 0.25 0.12 0.07 0.15 0.07 0.07 0.1 0.02 0.08 0.2 0.12 0.08 0.15 0.07 0.08 0.1 0.02 0.08 0.2 0.085 0.08 0.15 0.015 0.08 0.1 0.08 0.08 0.07 34 2000 2001 2003Sep 2003Oct 2003Dec 2004 Total Ordinary Special Medisave Total 0.3 0.24 0.02 0.06 0.32 0.3 0.23 0.02 0.07 0.32 0.3 0.22 0.02 0.08 0.32 0.165 0.09 0.095 0.02 0.07 0.08 0.17 0.08 0.1 0.075 0.075 Ordinary Special Medisave Total 0.26 0.04 0.06 0.36 0.23 0.06 0.07 0.36 0.22 0.06 0.08 0.36 0.105 0 0.08 0.185 0.025 0.085 0.11 0.085 0.085 Ordinary Special Medisave Total Ordinary Special Medisave Total 0.22 0.05 0.06 0.33 0.22 0.05 0.06 0.33 0.2 0.06 0.07 0.33 0.2 0.06 0.07 0.33 0.18 0.07 0.08 0.33 0.18 0.07 0.08 0.33 0.105 0 0.08 0.185 0.105 0 0.08 0.185 0.025 0 0.085 0.11 0.025 0 0.085 0.11 0 0 0.085 0.085 0 0 0.085 0.085 Source: The CPF Board The CPF account earns interest for its members. The interest rate is market-determined, being a weighted average of the 12-month fixed deposit and month-end savings rates of the major local banks. The CPF Act stipulates a minimum interest of 2.5% per annum when the calculated interest rate yields a lower rate. The Special Account (introduced in July 1977) and Retirement Account (introduced in January 1987) earns 1.25% higher than the normal interest rate from 1 July 1995 and 1.5% higher than the normal CPF interest rate from 1 July 1998. The Medisave Account (introduced in April 1984) also earns 1.5% higher from 1 October 2001. The CPF rates are revised quarterly from 1 July 1999. Currently, as the formula yields a rate lower than the stipulated minimum, the CPF rate is 2.5% for the Ordinary Account and 4% for the Special, Retirement and Medisave Accounts. Exhibit 3 shows the fluctuation of the interest rates of the Ordinary Account over the years. 35 Exhibit 3 CPF Ordinary Account Interest Rates (1955 – 2004) CPF Ordinary Account Interest Rates 7 6.5 6 Interest Rate (%) 5.5 5 4.5 4 3.5 3 2.5 19 55 19 Q1 57 19 Q2 59 19 Q3 61 19 Q4 64 19 Q1 66 19 Q2 68 19 Q3 70 19 Q4 73 19 Q1 75 19 Q2 77 19 Q3 80 19 Q4 83 19 Q1 85 19 Q2 87 19 Q3 89 19 Q4 92 19 Q1 94 19 Q2 96 19 Q3 98 20 Q4 01 20 Q1 03 Q 2 2 Year/Quarter Source: The CPF Board As mentioned, the functions of the CPF have expanded since it was started to include funding for property purchases, medical expenses, and financial investments. Given the nature of our study, we shall focus on its role in financing property purchases. 36 3.2 CPF and its Role in Financing Home Purchases Property buyers in Singapore tend to utilize their CPF savings to partially pay for the purchase price of their property before borrowing the reminder from a financial institution. In addition, the CPF savings can also be used to service the monthly mortgage installments. As a result, the CPF plays an important role in the housing finance system in Singapore. However, the CPF has not always been a major force in housing finance. Between 1968 and 1981, the CPF could only be used for paying the downpayment, stamp duties and mortgage payments of public housing under the Approved Housing Scheme (AHS). These flats include those built by the Housing and Development Board (HDB), Ministry of Defense (Mindef), Jurong Town Corporation (JTC) and now defunct Housing and Urban Development Company (HUDC). In 1981, the Approved Residential Properties Scheme (APRS) was passed to allow buyers to utilize up to 90 per cent of their CPF savings to pay for the mortgage payments of a private housing. In addition, the CPF savings can be used to pay a lump sum amount to reduce the mortgage amount required and also to pay for the monthly mortgage installments. In 1982, members were allowed to purchase private housing whether completed or under construction. The scheme was further expanded in 1984 when members were allowed to reuse CPF savings for a second private housing investment and in 1985, up to 100 per cent of their CPF savings and monthly contributions can be used to purchase new properties. 37 In October 1993, the Available Housing Withdrawal Limit (AHWL) was included to allow members to use more than 100 per cent of the price of the housing through their CPF savings. Specifically, members were allowed to draw down further the ordinary account savings after the Valuation Limit (VL) is reached and loan balance is still outstanding. The VL is the lower of the purchase price or the value of the property at the time of purchase. The AHWL is subject to a maximum of 80 per cent of the gross CPF savings after setting aside a stipulated minimum sum. The main effect of the AHWL is that CPF savings can be used to cover the interest cost of the mortgages. The CPF contributions withdrawn for housing purchases have traditionally been high. As at 2001, the figure stood at a high of around 20 per cent. Thus, housing is tying up a high proportion of Singaporeans’ retirement funds. The CPF Act requires the repayment of all CPF funds utilized (including the foregone interests according to the CPF rates) to the members’ CPF account when the property is sold under foreclosure or for relocation purposes. This implies that financial institutions issuing the mortgages only have a second lien while the CPF Board has the first claim. Effectively, this transfers additional costs of foreclosure to the lenders and away from the borrowers. However, the use of CPF savings for housing purchases is not totally free. In particular, the cost of the CPF equity is the foregone saving interest, which would otherwise have been earned (Ambrose, Chu, Sa-Aadu, and Sing, 2004). 38 However, with effect from September 2002, several changes have been made related to the use of CPF savings for housing purchases. 3.3 Recent Development and Liberalization The Economic Review Committee or ERC as established in October 2001 to review fundamentally Singapore’s development strategy and formulate a blueprint to restructure the economy. Restructuring the CPF and its role is one of the seven terms of references. The ERC submitted its proposal on the usage of CPF related to housing purchases on July 2002. There are effectively two key changes to be applied to the CPF policies. Firstly, from September 2002, private property buyers need only pay half the initial 20 per cent downpayment in cash. They can use their CPF savings to pay for the other half. This improves the accessibility of potential housing purchasers as it makes it easier to own a house. Secondly, the other change is the restriction on the use of CPF savings for servicing of the home mortgages to 150 per cent of the property price and the limit will be lowered at 6 per cent per annum to 120 per cent eventually after 5 years. This restricts the amount of retirement savings that can be used for servicing the mortgage loans. If the limits are reached, the borrowers will need to pay cash for the rest of the mortgage life. This change adversely affects the affordability of home purchases, but is aimed towards reducing an individual’s exposure of his retirement funds to housing. 39 Perhaps more significantly is the announcement that financial institutions that issued the mortgages are to be given first lien ahead of the CPF Board. This is expected to increase lenders’ confidence of issuing mortgages to riskier borrowers. Furthermore, this removes a major impediment towards the issuing to MBS. 40 Chapter Four The Model 4.1 Research Methodology and Theory We motivate our model with the conventional options-pricing theory for pricing mortgages and the subsequent competing risk methodology. In line with the objectives of the paper, we develop and argue for a bivariate probit model for the delinquency-default decisions that allows for correlated disturbances. Subsequently, we also require a probit and logit model to assess the conditional probability of reinstatement given delinquency. Competing Risk Methodology Initially, studies using option models focus on modeling either default (Foster and Van Order, 1984; Quigley and Van Order, 1995) or prepayment (Schwartz, et al., 1989; Quigley and Van Order, 1990) independent of the other. These studies focus on the role of stochastic processes of house price (H) and interest rates (r) on borrower decisions. However, the importance of the joint relationship between default and prepayment is increasingly underscored by Kau and Keenan (1996), Kau, et al. (1992, 1995), and Schwartz, et al. (1993). According to Deng, et al. (2000), the proportional hazard model originated by Cox and Oakes (1984) provides a convenient framework for analyzing the exercise of options. In addition, Han and Hausman (1990), Sueyoshi (1992) and McCall (1996) provided a 41 maximum likelihood estimation approach to model competing risks simultaneously. Thus, the competing risks of the prepayment and default options, the joint survivor function conditional on η p , η d , r, H, Y, and X can be expressed in the following form: ( S t p , t d r , H , Y , X , η p ,η d ) tp  ' − η  p ∑ exp γ pk + g pk (r , H , Y ) + β p X k =1 = exp  td  ' − η d ∑ exp γ dk + g dk (r , H , Y ) + β d X k =1  ( (  ) )     (1) where Y is a vector of option-related variables other than r and H that will be used to estimate the market values of the options empirically, X is a vector of other non-optionrelated variables to account for other effects on the function. γ jk are parameters of the baseline function while η p and η d are the unobserved heterogeneities associated with the hazard functions for prepayment and default respectively. Based on the joint survival function, the explanatory variables are expanded to include a proxy for the put option to default, a proxy for the call option to prepay, a control for information asymmetry or self-selection, and proxies for transaction costs and triggerevents. The call-option for each loan can be defined as Call _ Optioni , k = Vi , m − Vi *,r Vi , m where V * i ,r = TM i − k i Pi ∑ (1 + r ) S =1 i S and Vi , m = TM i − k i Pi ∑ (1 + m ) τ S =1 S i +ki (2),(3),(4) 42 and ri is the mortgage note rate, TM i is the mortgage term, k i is the mortgage duration after origination at time τ i , mτ i + k i is the market interest rate, and Pi is the monthly mortgage payment. It shows the fraction of the difference between the present values of the mortgage balance payment stream at the mortgage rate and the market interest rate. However, since we are working on ARMs, we expect ri = mτ i + k i . The call-option value, and thus the risk of prepayment can be argued to be effectively zero. The put-option for each loan or the probability of negative equity can be defined as  (log Vi , m − log M i , k )   Put_ Option i , k = Φ  2 ω   where Φ (.) is cumulative standard normal distribution function, M i , k value of the property and (5) is the market ω2 is the estimated variance. Deng, et al. (2000) described the presence of asymmetric information where the borrowers know more about their own house price volatility than the lenders. Thus, risky houses will be financed with higher initial loan-to-value ratios (LVR). The paper uses the initial equity-to-value ratio (EVR) as a variable in an attempt to control for asymmetric information. At the same time, self-selection theory predicts such risky borrowers will self-select themselves into the group with high LVR (Hendershott, LaFayett, Haurin, 1997). In addition to initial EVR, we propose whether a loan has previous experiences of delinquencies, the number of co-borrowers and mortgage term as proxies for asymmetric information and self-selection. 43 The contingent claims approach utilized in pricing of mortgages requires the assumption of perfect capital markets and borrowers act in an impersonal way on maximizing their financial positions (Kau, et al., 1993). Thus, pure options-theoretic default models postulate default to occur once the value of the property falls below the value of the mortgage (Kau, et al., 1992, 1995). However, it is well established that borrowers do not default straight away when their mortgages are in negative equity due to transaction costs like default penalty, deficiency judgment, cost of moving, etc. As a result, the frequency of actual defaults is under-predicted by pure option-theoretic default models (Foster et al., 1984, 1985; Cunningham, et al., 1984). In addition, the extent of this transaction costs can be more logically treated as differing from individual to individual. Given a portfolio of mortgages with largely similar characteristics, some borrowers will default once the mortgages falls into negative equity (“pure” rational default) while other borrowers will not default even when their mortgages are deep in negative equity due to the presence of “personalized” transaction costs (Kau and Keenan, 1995). Therefore, Stanton (1995) and Green and LaCour-Little (1999) modeled transaction costs as varying across borrowers. We postulate to motivate the use of observable personalized factors like borrower, property and mortgage characteristics to proxy transaction costs in modeling delinquency/ default decisions. Deng and Gabriel (2002) and Clapp et al. (2004) included 44 these variables without directly motivating them but also found them to be influential in estimating mortgage termination risks. In addition, the presence of a “trigger-event” may be necessary to force the borrower to default on the mortgage. Since trigger-events are exogenous, we should incorporate macro level variables to proxy for them. As the responses of these events are differentiated among individuals, this is additional motivation to include the personalized factors. Despite of the inclusion of proxies for transaction cost and trigger-events, estimations may not be perfect due to unobserved/ unmeasured heterogeneity among borrowers as described by the unobserved error terms, η p and η d . These include borrower tastes or abilities, and property-specific factors such as unexpected depreciation or appreciation. Our paper focuses on the correlation of these unobserved factors. A strong correlation between the unexplained tendency to delinquent and the unexplained tendency to default would substantiate the inclusion of delinquency decision into existing default models. 4.2 Empirical Model The Sample Selection Problem Past studies that utilize the proportional hazard model (e.g. Deng, et al., 1996 and 2000) multinomial logit methodology (e.g. Vandell and Thibodeau, 1985; Zorn, et al., 1989; 45 and Ambrose and Capone, 1998) assumes that the borrower decides on the course of action at a single point in time. However, it is likely that the borrower makes his decisions on a sequential basis. The sequential nature of the borrower decisions is illustrated in Exhibit 4. Exhibit 4 Borrowers’ Sequential Decision-Making Framework Borrower Decisions Continue Payment 1 Delinquency Reinstatement Reinstatement 2 Default 3 Termination As can be seen, the sequential nature of borrower decisions presents us with the sample selection or incidental truncation issue. The loans that are in default must have gone through delinquency as a preceding step, i.e. the dependent variable of the default equation yields a value only if the loan is delinquent. If we do not incorporate the influential variables of the delinquency decision into the subsequent default decision, the 46 latter will produce biased result (unless the correlation between the two decisions is found to be zero). Inconsistency in the parameters estimated will make any inferences dubious. As mentioned, when ρ is not equal to zero, the default equation and delinquency equation may contain some common unexplained or omitted variables. In our research question, we expect the variables that increase the probability of delinquency to increase the risk of default. We also expect the unobserved factors of the two decisions to be positively correlated. The presence of such unobserved similarities between the two decisions will make a one-level decision-making framework like multinomial logit or conditional logit inappropriate. Other reasons that Ditto for independent probit or logit models. The delinquency decision and the subsequent default decision process constitute a bivariate discrete dependent variable model that exhibits the selection bias. The multivariate probit model (MVP) allows 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. We can correct for the selection bias by applying a concept initially developed by Heckman (1979) for continuous variable. Wynand and Bernard (1981) further the concept by applying it to discrete dependent variable analysis. Utilizing a joint approach, the bivariate probit model (BVP) with selection accounts for the potential correlation between the two decisions, and corrects for selection bias. 47 In addition, another advantage of utilizing the BVP over single-level models is that independence from irrelevant alternatives (IIA) need not be assumed. IIA, which follows from the assumption of independence of random errors, implies that the odds ratio does not depend on other choices. However, studies on consumer behavior require the relaxation of the IIA assumption (Greene, 2003) due to the presence of close substitutes for the choices. The nested logit model (NL) is often presented as an alternative to the BVP for relaxing the IIA assumption across clusters of choices. However, choices within a cluster have to maintain the IIA, i.e. the individual unobserved disturbances at any given level and across levels of the decision framework within a cluster are to be independently distributed (Hunt, 2000). Consequently, as delinquency and default decisions belong to the same cluster (see Exhibit 4), the NL does not allow for disturbance correlation between them5. Since we are interested in the significance of including delinquency in existing default models, we should adopt a model that allows correlation rather than assume zero correlation between their disturbances. In addition, although the decision structure in Exhibit 4 looks like a nesting structure, it does not assume a simultaneous decision- making process as is required by NL (Knapp, White and Clark, 2001). The structure is intended to represent a sequential decision-making process. 5 It does, however, allow the composite disturbances that share an upper-level to be positively correlated [i.e. Cov (ε1, ε2‫׀‬ε1) > 0]. 48 The Bivariate Probit (BVP) Model To examine the relationship between the probability of delinquency and the conditional probability of default given delinquency, our empirical model requires an assumption of a delinquency probability function and a default probability function where the ith borrower maximizes a linear indirect utility function V ij* over j outcomes Vij* = α j + β j X i + δ jW i + φ j Z i + ε ij , i = 1, ….., N, j = 1, ….., J (6) where Xi is a vector of option-related characteristics, Wi is a vector of individual borrower, property and mortgage characteristics and Zi is a vector of macroeconomic variables other than house price and interest rate to proxy trigger events. Utilizing the utility theory or rational choice perspective on behavior as developed by McFadden (1973), and using subscript 1 and 2 to represent steps 1 and 2 of the default decision-making framework, the BVP specification for (6) would be Vi1* = x'i1 βi1 + ε1 , yi1 = 1 if Vi1* > 0, 0 otherwise, (7) Vi *2 = x'i2 βi2 + ε2 , yi2 = 1 if Vi1* > 0, 0 otherwise, (8) E [ε1 | x1, x2] = E [ε2 | x1, x2] = 0 (9) Var [ε1 | x1, x2] = Var [ε2 | x1, x2] = 1 (10) Cov [ε1, ε2| x1, x2] = ρ. (11) 49 where Vij represents the unobservable indirect utility developed above, y1 is the observable actual decision for default incidence in the second step decision, y2 is the observable actual decision for delinquency incidence in the first step decision, and x1, x2 represents the vector of independent variables affecting y1 and y2 respectively. The relationship between delinquency and default decisions is examined by testing the covariance of their disturbances, ρ. The bivariate normal CDF is P ( X 1 p x1 , X 2 p x 2 ) = ∫ x2 −∞ ∫ φ (z , z x1 1 −∞ 2 , ρ )dz1 dz 2 (12) which we denote as Φ 2 ( x1 , x 2 , ρ ) where φ (.) is a notation for standard normal distribution and the subscript 2 indicates its bivariate nature. The density is φ 2 ( x1 , x 2 , ρ ) = e ( 2 )(x − 1 2 2 1 + x 2 − 2 ρx1 x 2 ( 2π 1 − ρ 2 ) )/ (1− ρ ) 1 2 (13) 2 Due to the selection bias, there are three types of observations in our sample: a) Continue Payment (CP) (y2 = 0) : P ( y 2 = 0) = 1 − Φ ( x 2 β 2 ) (14) b) Delinquent but Reinstated (DR) (y2 = 1, y1 = 0) : P( y 2 = 1, y1 = 0 ) = Φ ( x 2 β 2 ) − Φ 2 ( x 2 β 2 , x1 β 1 , ρ ) , (15) 50 c) Delinquent and Default (DD) (y2 = 1, y1 = 1) : P( y 2 = 1, y1 = 1) = Φ 2 ( x 2 β 2 , x1 β 1 , ρ ) . (16) The likelihood function is L = ∏ P(CP ) × ∏ P ( DR) × ∏ P( DD) CP n DR ( =∏PV [...]... delinquencydefault behavior: 1 the role of the government and the role of borrower equity in affecting the risk of delinquency and of default; 2 the presence of a significant relationship between delinquency incidence and subsequent default decisions; 3 the disparity in the expected behavior of borrowers in a model that takes into account the relationship between delinquency & default as compared with a... Chapter Five examines the relationship between delinquency and default, and the impact of repeated delinquency on subsequent default behavior In addition, the chapter also examines the effects of protected borrower equity Chapter Six investigates the conditional risk of reinstatement given delinquency Finally, Chapter Seven concludes the study 14 Chapter Two Literature Review 2.1 Introduction It is... period, the default rates for the two groups are similar but the volatility of repeat defaulters is higher In addition, economic variables are more influential in predicting default in the former group Following Ambrose and Capone (2000), the third research problem of our paper examines the postulation that the risk of default and delinquency is different between first time delinquents and repeat delinquents... and the success of the loss mitigation program of the FHA Similarly, these implications are also applicable to our study of repeated delinquencies The fifth contribution of our study is the verification of the presence of a differing risk profile and behavior for a first time delinquent and a repeat delinquent In responding to the research questions, we test five aspects of the borrower delinquencydefault... delinquency and default but several past studies do deal with post -delinquency outcomes without reference to the subsequent default decision Herzog and Earley (1970) examined the factors affecting the conditional risk of foreclosure given delinquency and also the unconditional risk of foreclosure The results 29 show that after taking into account the effect of delinquency, although the signs of the. .. events like delinquency, imminent default, borrower bankruptcy, litigation, and borrower forebearance requests occur The transition is thus from delinquency to special service, 30 and then to default However, the focus is on the factors influencing loan defaults when they are being special serviced Most of these papers do not consider the transition from delinquency to default, and the extent of their relationships,... relationship (Vandell and Thibodeau, 1985, Springer and Waller, 1993, Cunningham and Capone, 1990) Age of the owner has also produced ambiguous findings regarding the extent and direction of its influence Furstenberg (1969), using the age of the principle mortgagor, discovered a negative non-linear relationship with the default rate Capozza et al (1997) found age to be a major determinant of default Canner and. .. but declining likelihood of defaulting again in the next two years Furstenberg (1970b) used seasoning, i.e the number of years since origination, as a proxy for attachment to the property and experience for successful mortgage installment payments The number of years of job tenure and the history of employment on the current job serve as a useful proxy for security of future income Vandell and Thibodeau... origination increases, but the risk of default is decreased as the protected equity is accumulated over time; 2 the relationship between delinquency and default is highly significant and should be included in subsequent default risk modeling; 3 variables like the probability of negative equity, mortgage term, tenure and land area of the property, and the number of co-borrowers have inverse relationships... either reinstatement or foreclosure The paper thus investigates the probability of foreclosure and the probability of reinstatement given delinquency The paper also utilized a multinomial logit specification in two sets of tests In a recent working paper, Chen and Deng (2005) recognized the transition from delinquency to default as they examine the special service workouts for commercial mortgages These ... government and the role of borrower equity in affecting the risk of delinquency and of default; the presence of a significant relationship between delinquency incidence and subsequent default decisions;... risk models should incorporate the risk of delinquency Among the factors affecting the risk of default and delinquency, the extent of the borrower equity is considered one of the most important... Five examines the relationship between delinquency and default, and the impact of repeated delinquency on subsequent default behavior In addition, the chapter also examines the effects of protected