Journal of Credit Risk

Risk.net

The impact of loan-to-value on the default rate of residential mortgage-backed securities

Luis Otero González, Pablo Durán Santomil, Milagros Vivel Búa and Rubén Lado Sestayo

  • The relation between the probability of default and LTV seems to be nonlinear.
  • A sharp increase is seen for values greater than 80%.
  • The findings confirm the adequacy of the new Basel III proposal.

ABSTRACT

This paper analyzes the validity of using the loan-to-value (LTV) ratio to explain the behavior of mortgage borrowers at an empirical level. To perform this analysis we use data for mortgage loan portfolios securitized in Spain during the period 2005-8. In the regression models developed, we find that higher initial LTV ratios are associated with greater default risk. The relation between the probability of default and LTV seems to be nonlinear, and a sharp increase is seen for values greater than 80%. Our findings confirm the adequacy of the new Basel III proposal that sets nonlinear capital requirement levels for banks holding residential mortgage loans at different LTV ratios. However, the significance shown in the regression models estimated with the "seasoning" variable could be considered in order to improve the models used to measure capital requirements.

Predicting the default rate is one of the main elements of the credit risk management process. In the particular case of mortgages, the probability of default is related to the loan-to-value (LTV), among other factors. The relationship between the two variables could be explained by the equity theory of default (Deng et al 2000), where borrowers base their default decisions on a rational comparison between returns and costs related to continuing to make mortgage payments. Under this theory, the borrowers have a put option with a strike equal to the value of the loan, and they will exercise it when the asset value drops below the value of the loan. The relation between the probability of default and LTV seems to be nonlinear and there is a sharp increase for an LTV greater than 80% (Campbell and Cocco 2015).

These aspects were still under discussion at the time of writing, during the implementation of the Basel III capital standards, with a proposal to set nonlinear capital requirement levels for banks holding residential mortgage loans at different LTV ratios. Regulatory capital requirements are designed to guarantee that banks have a sufficient quantity of capital to absorb losses during financial crises. In the rollout of Basel II, capital requirements for mortgage exposures were harmonized across the European Union at a 35% risk weight (RW). However, under Directive 2006/48/EC, competent authorities may tighten the capital requirements of these mortgage exposures by setting a higher RW (European Parliament 2006, Annex VI, Paragraph 9.1). Some European countries use LTV as a means of establishing RW, so mortgages above a certain LTV ratio must have an additional capital charge. The Basel Committee on Banking Supervision (BCBS) is aware that a 35% RW approach lacks risk sensitivity, so in recent a consultative document (Basel Committee on Banking Supervision 2015) it proposed to introduce a table of RWs ranging from 25% to 100%, based on the LTV ratio, because it believes that the LTV ratio is the most appropriate risk driver.

In this regard, it seems important to analyze the performance of the LTV approach empirically. To perform this analysis we use the data for mortgage loan portfolios securitized in Spain between 2004 and 2008. The Spanish securitization market was one of the most important in Europe during this period. According to data published by the European Securitisation Forum,11See http://afme.eu/divisions/securitisation.aspx. the volume of Spanish residential mortgage-backed securities (RMBSs) issues accounted for 14.88% of the total volume of European RMBSs issues in 2006, 18.49% in 2007, 10.43% in 2008 and 14.48% in 2009. Taking into account the outstanding balance of mortgage-backed securities at the end of the third quarter of 2009, Spain was in third place with a total of €167.1 billion (14.48% of the total), behind the United Kingdom (with €458 billion and 39.67% of the total) and Holland (with €202.4 billion and 17.53% of the total). Moreover, during that period, based on data provided by the INE (Spanish Statistical Office), prices at the end of 2010 accounted for a 13% drop.22See http://www.ine.es. This is an ideal scenario setup for the analysis of equity default theory. Moreover, in Spain most of the mortgage loans do not limit the liability of the debtor to the value of their home. In case of default, the mortgage is foreclosed, and if the proceeds are not equivalent to the value of the debt, the lender may proceed against the remaining assets of the debtor. In the Spanish case this implies that the option is on all the debtor’s assets, not just on the value of the home, which could affect the performance of the equity default theory.

The aim of this paper is to provide empirical evidence on default behavior for the Spanish RMBS market. This work contributes to the existing literature by presenting new evidence of the relation between LTV and RMBS default rate. Note that, despite the importance of the issue, as far as we are aware there are few empirical studies in the literature and most of them do not refer to this particular subject. Our results will be useful for regulators, as they provide further insight into the amount of capital that banks should hold against residential mortgage portfolios with different LTV profiles. We also believe the analysis can be used by the research and investor communities to assess the risk of default caused by negative equity.

The paper is structured as follows. Section 2 reviews prior research. Section 3 details the empirical analysis. Finally, Section 4 presents the conclusions of the study.

2 Literature Review

In many studies on mortgage default risk, the LTV ratio is highlighted as the most important variable in determining the likelihood of mortgage loan default (Otero et al 2015). Under the equity theory of default, borrowers base their default decisions on a rational comparison of returns and costs related with ongoing mortgage payments. From the perspective of option pricing (Archer et al 2002), the mortgage borrower is considered to have a property sale option equivalent to the value of the mortgage principal. Therefore, the greater the LTV, the higher the intrinsic value of the option, the more likely it is to be exercised and the greater the incentive to incur default. Under this theory, the LTV ratio is considered to be the most important factor in default decisions (Wong et al 2004). As shown by Wong et al, the default probability is a nonlinear function of the independent variables, where LTV is included. According to the model proposed by Deng et al (2000), the option to default is exercised when the value of the property drops below the strike (value of the loan) by some specific amount. The default is not automatic when the equity value becomes negative because borrowers prefer to wait until default is irreversible (Foster and Van Order 1985). In this regard, Kau et al (1994) show that it may be optimal to wait to default until the house price is as much as 15% below the mortgage value. In addition, Deng and Quigley (2012) point out that higher initial LTV ratios are associated with greater default risk, since borrowers who have less wealth available for a down payment are more likely to be constrained. This relationship has been verified empirically by Vandell (1978), Campbell and Dietrich (1983), Schwartz and Torous (2003) and Mayer et al (2009). The model proposed by Campbell and Cocco (2015) also establishes that a small down payment reduces the incentive of borrowers to continue meeting their payments. The relation obtained between the probability of default and LTV in the model seems to be nonlinear, and the probability increases excessively for values greater than 90%. Although this model is characteristic of the US market, where in many states the mortgage is backed purely by the value of the collateral as there is no universal recourse to the borrower’s other assets, in the Spanish market there is also a direct relationship between the likelihood of default and the LTV. This is because the value of the property has a direct effect on the borrower’s willingness to pay off the mortgage, which drops as the value of the property decreases.

Despite the importance of LTV in default decisions, another important factor is related to the economic capacity of the borrower to pay the mortgage. In addition, there are other economic and social factors for avoiding default, such as: switching the costs of a new home; the legal environment; the mobility of those not considered in the call option view. The ability-to-pay hypothesis of default (the cashflow approach) states that mortgagors will always try to pay off the loan if their income flows are sufficient to meet the periodic payment without undue financial burden. Deng et al (2000), Fisher (2005) and Foote et al (2008) support the ability-to-pay theory. Finally, as Campbell and Cocco (2015) state, “regulators should think about combinations of LTV and LTI [loan-to-income], and should not try to control these parameters in isolation”.

3 Empirical Analysis

We analyzed empirically the impact of LTV on the probability of default of the Spanish market RMBSs. To this end, we created a database of the characteristic elements of each of the securitization issues in Spain from 2005 to 2008. With this analysis, comprised of 138 outstanding issues, we considered 97.9% of the mortgage-backed securities market.33According to the volume of outstanding securitizations in Spain published by the European Securitisation Forum. The information sources consulted were the prospectuses of these issues and presale reports published by the respective rating agencies. We also used Bloomberg to obtain a series of related data on the evolution of the transaction, such as date of issue or level of default of the loan portfolio, as well as another series of variables. Based on this information, we analyze the importance of the equity theory of default in explaining the default rate in the Spanish RMBS market. We also believe that it is necessary to include information on the average scoring of the credits included in the portfolio (although this data is not available from our database) in order to test the ability-to-pay theory, and therefore the effect of income and the interaction between both variables.

3.1 Dependent variable

As the dependent variable we use the default rate of each securitization at the end of 2010, provided by Bloomberg. As can be seen in Figures 1 and 2, there is a relation between the rate of default and the LTV calculated at the origination date of each issue. Furthermore, this relation seems to be nonlinear and, with some exceptions, there is a sharp increase for levels of between 80% and 100%.

Loan-to-value and default rate for the overall sample
Figure 1: Loan-to-value and default rate for the overall sample. Source: Bloomberg and compilation by the author. The initial weighted average LTV of each securitization is plotted on the horizontal axis, and the final default rate calculated at the end of 2010 is shown on the vertical axis. The higher the initial weighted LTV, the greater the default rate.
Loan-to-value and default rate by year
Figure 2: Loan-to-value and default rate by year. Source: Bloomberg and compilation by the author.

This relation holds even if we differentiate by year. The dispersion around a certain level of LTV is explained by other characteristics related to the debtors’ ability and inherent willingness to pay. Obviously, the ability of banks to select better customers could be reflected in the level of default given a certain LTV. Figures 1 and 2 also show that there is lot of dispersion, especially around WALTV=0.7. This is possibly due to other characteristics that affect the probability of default (size, volume, credit score, etc), many of which will be controlled for later.

3.2 Hypothesis and variables

Table 1: Variables and hypotheses considered in the study.
Determinants Variable Prediction Definition Hypothesis
LTV

Weighted average LTV (WALTV)

+

Initial weighted average LTV

The higher the initial weighted LTV, the greater the credit risk

         
Seasoning

Average age (WASeasoning)

-

Average age of loans included in the portfolio (in months)

The greater the age of the portfolio, the lower the likelihood of default, and therefore the lower the likelihood of being classified in the subprime group

         
Diversification

Initial securitized volume (Volinitial)

-

Total securitized volume

The larger the securitized volume, the greater the diversification of the loan portfolio, and therefore the lower the risk

         
Loan size

Average loan value (Loanaverage)

+

Average amount of securitized loan portfolio

The larger the amount, the higher the default rate

The explanatory variable is the weighted average LTV of each securitization at the moment of issue, defined as the initial weighted average LTV (WALTV), and we establish the following hypotheses for the relation between LTV and the probability of default based on the previous theoretical analysis.

Hypothesis 1:

a higher LTV is considered to have a positive effect on the default rate of mortgage-backed securities.

Hypothesis 2:

the relation between LTV and default rate is nonlinear.

In addition, we have included some control variables that could affect the default rate. In this sense, we include the age in months (or months-on-books (MOB)) of the mortgage loans included in the securitization transactions at issue (WASeasoning). Seasoned loans are considered less likely to default because the borrowers have demonstrated their ability to pay (DBRS 2011). Glennon and Nigro (2011) showed that seasoning is a key factor in making accurate forecasts of losses in mortgage portfolios. There is also evidence of a negative impact on performance in portfolios with a high credit concentration (Rossi et al 2009). Thus, diversification seems to be an important determinant of default rate. In this sense, we include the initial securitized amount of each securitization (Volinitial) as a proxy for the diversification effect associated with the size of the securitization. In addition, larger loan mortgages, defined as the average amount of securitized loan portfolio (Loanaverage), have higher default rates because expensive properties are more illiquid and take longer to sell during a market downturn (Qi and Yang 2009).

3.3 Descriptive analysis

Table 2: Descriptive statistics of continuous independent variables. [This table presents summary statistics for the variables used in the analysis. The sample includes 138 outstanding issues, representing 97.9% of the outstanding balance of mortgage-backed securities at the end of 2009. The data sources consulted were the prospectuses of these issues and presale reports published by the respective rating agencies. We also used Bloomberg to obtain a series of related data on the evolution of the transaction, such as date of issue or level of default of the loan portfolio, as well as another series of variables. “WASeasoning” is the average age of the loans. “Loanaverage” is the average size of the loans included in the portfolio. “Loaninitialvol” is the log of the value of the securitization.]
      Standard    
  Observations Mean deviation Minimum Maximum
WALTV 138 0.6997 0.1135 0.4616 0.9533
WASeasoning 138 22.31 8.65 7.8 57
Loanaverage 137 133 628 37 426.01 22 177 222 576
Loaninitialvol 138 20.73 0.79 18.24 22.86

Table 2 shows the main descriptive statistics of the variables used in the empirical multivariable analysis. Our sample is composed of 138 issues by the Spanish RMBS market from 2005 to 2008, representing almost the entire volume issued during the period under review. Thus, the securitization transactions in the sample have an average loan of €133 628 and the weighted average age is 22.31 months. Finally, the WALTV of the securitization transactions is 69.97%; 23.05% of the loans have LTV levels over 80%; and 0.54% of the loans have LTV levels over 100% on average.

Table 3: Description of the securitization sample.
Year Initial   Average
of securitized Average seasoning
issue volume (€m) LTV (%) (months)
2005 29 164 66.33 20.16
2006 38 929 69.00 20.59
2007 62 055 73.64 21.44
2008 62 593 70.41 25.16
Table 4: Table of correlations. [Table shows Pearson’s correlation coefficients for variables.]
  Default        
  rate WALTV WASeasoning Loanaverage Loaninitialvol
Default rate 1        
WALTV -0.4012 1      
WASeasoning -0.4285 -0.1645 1    
Loanaverage -0.3541 -0.5474 -0.4385 1  
Loaninitialvol -0.0328 -0.1022 -0.1469 0.0296 1

Table 3 shows a more detailed description of the total sample regarding initial LTV levels and seasoning according to the year of the transaction origination.

Table 4 shows the correlation matrix of the independent variables used in the empirical analysis. As can be seen, there are significant correlations between the expected sign and the dependent variable for a large number of independent variables. The highest correlations are between WALTV and default rate (with a value of 0.40) and between WALTV and the average loan amount (with a value of 0.54), both with a positive sign.

3.4 Explanatory models of default rate

Our goal was to create a model to explain the empirical relation between WALTV and the rate of default. In addition, we check the importance of LTV in predicting subprime securitizations. We create a multiple regression model in which the dependent variable is determined by the default rate logarithm, while the main explanatory variable is the loan-to-value:

  log(PD)i=ci+β1iWALTV+j=1kβj+1,iCj+εi,  

where log(PD)i is the natural logarithm of default rate estimated for each regression i (years 2006, 2007, 2008 and period 2005–8), ci is the constant term for each regression, WALTV is the explanatory variable, Cj are the control variables (Loaninitialvol, WASeasoning and Loanaverage), β is a matrix of parameters to be estimated (four parameters for each regression) and εi is the error term of each regression.

Table 5: Multiple regression estimates of Spanish RMBS default. [This table includes the regression that estimates the relation between the default rate logarithm and the independent variables mentioned. * and ** denote statistical significance at the 5% and 1% confidence levels, respectively. For each model in turn, we checked the lack of multicollinearity between the variables by calculating the variance increase factor (VIF): to ensure that the models have no multicollinearity problems, they should have a VIF below 10. We also include White test data for heteroscedasticity.]
  Model Model Model Overall model
  2006 2007 2008 (2005–8)
WALTV 5.617** 4.460** 1.528* 4.139**
Loaninitialvol -0.174 0.089 -0.223 -0.025
WASeasoning -0.081** -0.063** -0.075** -0.006**
Loanaverage -0.884 -0.782 0.051 -0.211
C 8.036 20.323 0.567 -2.473
Observations 32 42 42 137
R2 0.475 0.4344 0.563 0.401
F-statistic 7.600** 8.940** 13.110** 24.460**
White test 10.250** 14.870** 10.960** 22.150**
VIF 1.71 1.77 1.50 1.36

The estimated models have a good fit to the data (Table 5), with an average R2 around 0.45. In addition, the most important explanatory factor is the WALTV, and the relation is nonlinear; this supports both hypotheses tested in our study. In any case, we consider that the incorporation of the LTI or the borrower scoring would considerably increase the explanatory power of the model. Moreover, the F-statistic is very significant, indicating the validity of the proposed models. The validity of the model presented is also based on the absence of heteroscedasticity problems, contrasted by the White test, which is highly significant in all cases. Finally, the value of VIF shows no problems of multicollinearity between the variables analyzed. The fact that the models estimated for each year and for the entire period exceed the test discussed above justifies their validity for checking the hypotheses.

Table 6: Level of fit measured by R-squared.
    LTV and
Model LTV model seasoning models
2006 0.2013 0.4485
2007 0.3039 0.3995
2008 0.1949 0.5319
(2005–2008) 0.2104 0.3923

Table 6 shows the R-squared value of the estimated models that exclusively consider LTV as the explanatory variable and subsequently incorporate the effect of the “seasoning” variable. As we can see, the first models show the LTV is a very important determinant of default risk. However, the explanatory power greatly improves when seasoning is incorporated. This means that regulation of capital requirements based on the LTV must be complemented by other factors, such as seasoning or LTI.

Default estimations of default rate based on LTV estimated models
Figure 3: Default estimations of default rate based on LTV estimated models.
Default projections of default rate based on LTV and seasoning
Figure 4: Default projections of default rate based on LTV and seasoning.

Regarding the results obtained in our regression models, we first highlight that the WALTV ratio was significant, with a high level of confidence in most models, and it has a positive sign, producing the expected effect that a higher LTV ratio would increase the default probability of Spanish mortgagors (see Figures 3 and 4). These results support those of Schwartz and Torous (2003), Deng and Quigley (2012) and Campbell and Cocco (2015) and are consistent with the equity value theory; they show the sensitivity of Spanish debtors’ housing values relative to their debt. Undoubtedly, falling housing prices in Spain affected the default rates recorded in 2010; these have since soared to unprecedented levels. The projection of the default rate from the regression models, using only the LTV as an explanatory variable, shows how the relationship is clearly nonlinear, and the default rate soars from an LTV of around 80%. The results are confirmed for the models fitted for each year and for the global model, although for 2006 and 2007 we can observe a higher gradient, associated with further relaxation of standards when granting loans. Our findings are also consistent with those made by Campbell and Cocco (2015) and in line with the BCBS’s proposal explained in Section 1.

The estimations of default rates adding the seasoning shows a moderating effect that is greater with higher levels of seasoning. This result supports the need to combine LTV with other variables, in particular seasoning, LTI or credit scoring. Although LTI and credit scoring were unavailable in our database, Deng et al (2000) and Foote et al (2008) support the ability to pay as an important determinant of default probability.

4 Conclusions

This paper analyzed the validity of the loan-to-value ratio to explain the behavior of mortgage borrowers in Spain and to establish capital requirements. Using the regression models developed, we showed that a higher LTV ratio increases the default probability of Spanish mortgagors. The results are confirmed for the models fitted for each year and for the global model, although for the 2006 and 2007 observed a higher gradient, associated with a greater relaxation of standards when granting loans. Our results support those of Schwartz and Torous (2003), Deng and Quigley (2012) and Campbell and Cocco (2015), who found that higher initial LTV ratios are associated with greater default risk. The projection of the default rate from the regression models showed how the relationship is clearly nonlinear and the default rate soars from an LTV around 80%. Our findings are also consistent with those made by Campbell and Cocco (2015) and confirm the adequacy of the reform proposed in Basel III establishing nonlinear capital requirements that depend on the LTV of the portfolio. However, the significance of other variables, eg, seasoning or LTI, could be considered in order to refine the models used to estimate the probability of default and to determine capital requirements. In addition, our findings are consistent with the equity default theory and show the sensitivity of Spanish debtors’ housing values to debt. This result confirms the validity of default equity theory for countries with full recourse mortgage loans. In our view, the reason there are no major differences is because debtors with high LTVs are the most vulnerable and have little to lose in the case of default.

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

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