Residential Mortgage Delinquency Risk and Real Estate Prices:

(1)

Residential Mortgage Delinquency Risk and Real Estate

Prices:

An empirical study of the relationship between Delinquency on Dutch

residential mortgages and residential property values.

By: Rense Remmelts 1

S1671928

Master Thesis University of Groningen Faculty of Economics and Business MSc Business Administration, Finance

Supervisor: Dr. P.P.M. Smid

Abstract:

This paper aims to provide evidence that a relationship between delinquency and Dutch residential real-estate property value exists. If such a relation exists, it might indicate that a derivative based on real-estate value could function as a hedging instrument to reduce delinquency risk. The main results show that when Dutch residential property value is lagged by one month, delinquency in excess of 90 days is significantly influenced. As the question remains whether this relation is substantial enough to serve as a hedging instrument, further study is warranted.

Keywords: delinquency, hedging, real estate value, homeowner risk JEL classification: G11 E24

1

(2)

1. Introduction

Spending on a mortgage has traditionally been a significant part of an average income. This varies in Western Europe from 25 to 35 percent (Englund, Hang and Quigley, 2002). However, among young people this percentage is even higher (Flavin & Yamashita, 1998). Unfortunately owning a home equity is also liable to various elements of risk. An important risk associated with high levels of debt (mortgages) is the interest rate risk. This is widely recognized as many homeowners choose for a fixed interest on their mortgage when interest rates are low.

The second risk that an individual homeowner faces is the depreciating of the price of the property. This price risk in real estate is negligible when aggregate prices are increasing rapidly, but becomes substantial when aggregate prices level off for a few years, and becomes severe when aggregate prices fall. Furthermore, this price risk seems to be closely related to the probability of default in mortgages (see e.g. Mayer, Pence, and Sherlund, 2009; Case, Shiller, and Weiss, 1996). This value decline is far greater than the risk of any physical disaster to real estate. Furthermore, research has shown that foreclosure rates or default on the mortgages is closely related to declines or interruptions in real estate prices (Case, Shiller, and Weiss, 1996). The large group of individual mortgage holders would therefore undoubtedly benefit if hedging or risk reduction using derivatives were offered. Yet, there is no way for an average Dutch household to insure against a drop in home value. Although some researchers like Case, Shiller, and Weiss (1996) recognize this problem, not many studies research the possibility of a derivative market that can potentially limit this homeownership risk from an individual mortgage holder’s perspective. This study will therefore focus on this particular group and describes the relationship between the risk of homeownership and Dutch residential real-estate property prices.

The probability of default is widely used to define risk in a mortgage from a

mortgagor’s perspective, whereas I prefer to use delinquency rates to define the risk of

(4)

risk for their entire mortgage lending operation. Moreover, focusing on default may be too late in preventing foreclosure, making delinquency rates a more suitable proxy for homeowner risk. The goal of this paper is to research the relation of delinquency risk and Dutch real-estate property value. This will provide a deeper understanding on whether a derivative based on real estate property value is a potential suitable hedging instrument that could limit the risk for individual homeowners. There is however currently no successful market that trades these derivatives, although there were numerous attempts to create one. The London Futures and Options Exchange was the first to introduce a futures market in real estate in 1991, they however traded at very low volumes and the market was closed after a scandal caused by traders to boost the volume (so called wash-trading).

In 2001, City Index launched a spread betting market with an underlying index in single-family homes. The IG Index quickly followed this in 2002. Both markets were shut down in 2004. Goldman Sachs opened a market in 2003 for covered warrants on UK property price indices. While this index was moderately successful, it did not cover residential mortgages. In 2004, Hedgesteet.com created betting instruments based on price increases or decreases of single-family homes. While this was initially meant for betting purposes, the founder of Hedgestreet.com believed that his “instrument” could be used for hedging the economic risk of owning a house. The site was however no success and was soon closed down.

(5)

goes short in a future in an upward market (the prices rise), then the house-owner would experience a realized loss, while his wealth would be the same. Nevertheless, the experience that he must pay for this risk management weighs more than an equally sized gain if he went long in the futures contract. Another theory that could explain the unwillingness to hedge is the Lack-of-Hedging-Demand Theory; if the homeowner did nothing he would not have experienced the loss (or gain), if his wealth would decrease (or increase) he would not actively experience it until he sold the commodity. While the US has some limited and small residential real-estate future markets available, the European market does not. If such a market would exist, a strategy could be formed to hedge against the risk of delinquency in homeownership with these futures.

Overall, the purpose of this paper is to answer the following main empirical question. Is there a relationship between delinquency risk and Dutch residential real-estate property values? Since delinquency can also be influenced by other (economic) factors, it is also interesting to study other variables that influence the risk of homeownership. The second empirical (sub) question is therefore: Which other economic factors influence the delinquency risk? A generalized autoregressive conditional heteroskedasticity (GARCH, Bollerslev (1986)) model will analyze the monthly time series data, from the period February 2003 until August 2010.

(6)

responsible for distributing the pool's cash flow is called the Trustee. The final party is the Underwriter that usually takes the risk by reselling the security to investors..

The delinquency rates are obtained from performance reports made by various servicers monitoring these securities. Access to these reports is provided by Lewtan technologies and gives an insight in the delinquency level of Dutch residential mortgages in the period from 2000 to 2010. This period will provide a most interesting period to study the various factors of homeowner risk, as various aspects of economic downturn and a decrease in real estate prices meet.

(7)

2. Literature review

One of the first important studies that study the risk in mortgages was by Williams, Beranek and Kenkel (1974). They explored the reasons of default using 18 different variables in the period 1962 to 1972. They tried to provide a further insight into what social, economic and demographic factors affect default risk in mortgage lending in metropolitan areas. Williams, Beranek, and Kenkel find the variables: Loan to value, payment to income and age of property among the significant variables.

Case, Karl, and Shiller made their first debate in 1988 to allow a derivative market based on residential property values. Case, Shiller, and Weiss (1993) proposed later a market in futures contracts tied to regional house-price indexes, allowing households to hedge by taking a short position in these contracts.

(8)

2.1 Delinquency

While Williams, Beranek, and Kenkel (1974), Kau, Keenan, and Kim (1994), Case, Shiller and Weis (1996) defined a default event as a foreclosure, it could also be defined as a delinquency of a single mortgage payment. Delinquency on mortgages has not been given as much as consideration as default/foreclosure on mortgages. Von Furstenberg and Green (1974) attributed this to the lack of suitable data. Kendall (1964) wrote the first paper to study the determinants of delinquency based on survey results, followed by Herzog and Earley (1970). While the Herzog and Earley (1970) study was based on a discriminant analysis, it however did not allow standard significance tests to be applied. As a result, no coefficients and significance levels could be obtained. However, the study by Von Furstenberg and Green (1974) did perform a standard significance test to analyze various variables causing delinquencies in US mortgages. Von Furstenberg and Green performed the analysis on a limited set of variables, they did find significant results for the age of a house, the location of a house, the age of a mortgage and the loan to value ratio for explaining the delinquency on US mortgages.

(9)

Teo (2004) uses a hazard function to explain delinquency in mortgages. The hazard function can be defined as the rate of incidence, on the mortgage having survived delinquency until that time. Teo (2004) tries to analyze the rate of delinquency in Singapore using a non-parametric model. A second parametric duration model provides a deeper insight in explaining delinquency. This model uses 19 determinants in explaining delinquency. A notable part of this study is that the author also has property and borrower specific characteristics as explanatory variables. Interesting is that Von Furstenberg and Green (1974) and Campbell and Dietrich (1983) find the loan to value ratio to be significant in explaining delinquency, while Teo (2004) did not. However, Campbell and Dietrich (1983) did note that this ratio is less significant in explaining delinquency than in a foreclosure event. Teo (2004) found Central Providence Fund (a type of pension plan in Singapore) to Price ratio, changes in mortgage rate, changes in Straits Times Index (STI), the premium of mortgage rate over investment returns and changes in Residential Property Price Index (RPPI) to be significant. Property specific characteristics and borrower specific characteristics were not significant. The author notes that this is interesting because lenders traditionally focus on lending criteria and on borrower-specific criteria, but these seem to be not significant in explaining delinquency on mortgages. Teo (2004) concludes that lenders should reassess their lending criteria based on borrower specifics because delinquency in mortgages seems to be more closely related to macro-economic factors. The second conclusion the author draws is that underwriters of MBS typically try to enhance lower quality securities by including higher quality borrowers based on borrower specific characteristics when constructing a MBS. This could be a trivial task because delinquency risk seems to be largely depending on systematic macroeconomic factors, which are not known at the beginning of the collateralization.

(10)

Campbell and Dietrich (1983) also used data provided by a large financial institution and focus on the period from 1960 to 1980 in a dataset composed of 2.5 million mortgages. Campbell and Dietrich tested three dependent variables, namely: prepayment, delinquency and default of the mortgage. This multinomial logit regression used 11 independent variables, from which the variable age was omitted due to strong collinearity with other variables. The variables payment to income, old or new estate, current to original mortgage rate and various dummy variables exhibiting various ratios of loan to value percentages were significant. The variable loan to value was also significant, but had a wrong sign. Contrary to Teo (2004), Campbell and Ditrich also find unemployment especially significant in explaining delinquency. Furthermore, Campbell and Dietrich note that unemployment rates are especially important and show significant differences when taken regionally, illustrating the need of geographic diversification in mortgages default risk. Campbell and Ditrich note that it remains difficult to explain the decision to delay payments/delinquency in mortgages. Like Teo in 2004, Campbell and Ditrich conclude that most economic variables have a relation between delinquency incidences.

(11)

Like Teo (2004), Webb found borrower characteristics of the household were generally not significant in determining the probability of potential delinquency. However, some evidence was found that race and age are of some significance in explaining potential delinquency under PLAM or CPF-VRM loans. Other loans did not show any significance with age and race. Occupational difference like income trend, asset to family income, wife work status and variability were found to be very important in determining the probability of potential delinquency. In all the various AMI loans were these variables very significant in explaining the potential delinquency.

(12)

Table I

Empirical finding on delinquency of previous researchers

This table contains empirical findings by authors that conducted research on delinquency rates.

***significant at the 0.01 level; ** significant at the 0.05 level.

2_{Danis and Pennington-Cross (2005) supply no significance levels.}

Authors Research subject

Period Method Significant results

Herzog and Earley (1970)

Residential mortgage delinquency and default in the US.

1950-1969 Data obtained from interviews and analyzed using OLS regression

Loan/Value ratio *** Payment/Income ratio** borrowing for refinancing *** presence of junior financing *** Von Furstenberg and Green (1974) Residential mortgage delinquencies in Pittsburgh

1961-1972 Panel study using OLS regression New vs. Existing*** Age of Mortgage*** Loan to Value*** Mortgagor Income*** Morton (1975) Residential mortgage delinquency in Connecticut

1973 Logit regression Existence of junior financing**

Three-family property** Loan to Value** Job classification** Webb (1982) Potential residential mortgage delinquency in the US. 1968-1975 Tobit regression (censored regression model). Income volatility**

Low income trend***

Asset to family income***

Wife work status ***

Campbell and Dietrich (1983) Residential mortgage delinquency and default in insured mortgage loans

1960-1980 Logit model Payment/income ***

Loan/value***

Unemployment rate*** Age***

Current to original mortgage rate ***

Teo (2004) Adjustable rate mortgage delinquencies in Singapore

1980- 1999 Duration model using a hazard ratio

CPF to Price***

Premium of mortgage rate over investment rate **

Changes in Straits Times Index*** Danis and Pennington-Cross (2005) The determinants of the performance of subprime mortgages

1996-2003 Logit regression Change in House Price Index2 Loan/value

(13)

2.2 The determinants of mortgage delinquency

The main variable that is considered potentially significant in determining the delinquency of an individual residential homeowner is the residential real estate property value. The only noticeable study on this variable in relation to mortgage payment is from Case, Shiller and Weiss (1996). While the researchers study incidence of default, Case, Shiller and Weiss note that default will tend to be determined by a sort of distributed lag on past real estate value changes. The regression shows high significant relations of default and real estate prices lagged by one, four and five quarters. I also expect a lag to be present in the relation of real estate property values and delinquency, but to a lesser extent than in the case of default. I therefore set the lag of the residential real estate property values to one, three and six months.

However, it is clear that many other economic variables could also influence delinquency levels. It is therefore important to control for these influences. Campbell and Ditrich (1983), Teo (2004), and Diaz-Serrano (2005) conclude that (macro) economic and socio-economic variables are likely to be the most significant in determining delinquency in residential mortgages. I therefore focus on including these (macro) economic and socio-economic variables by including the national unemployment rate of the Netherlands. Unemployment will affect the borrower’s ability to continue with the mortgage payment and is therefore expected to have a positive association with the probability of delinquency. Another variable to be considered as potential significant is the change in the AEX. Market sentiments are a proxy of returns on other investments. When the market sentiment is good, funds will be directed away from mortgage payment to other more attractive investments (Teo, 2004). Moreover, poor sentiments imply a lack of good investments therefore stimulating the incentive to pay the mortgage and prevent possible late payment penalties. Ong (2000) and Ong et al. (2002) use a similar argument, although they researched prepayment. Note that, while changes in house prices also reflect fluctuations in sentiment, it does so by a lag to currents market sentiments (Ong, 2000 and Ong, Maxam and Thang, 2002). I therefore use the Amsterdam Exchange Index (AEX) as a proxy for the investor sentiment.

(14)

mortgage rate as a variable. This is possible because Campbell and Dietrich have access to records of individual mortgages insured by the Mortgage Guaranty Insurance Corporation (MGIC). Whereas Teo (2004) obtains data from servicer reports, he uses the premium of mortgage rate over investment returns to proxy this effect. Because the same kind of data is used in this paper, I also include the premium of mortgage rate over investment returns as a possible determinant of delinquency. Like Teo, I use the risk free rates as a proxy for investment returns. The expected sign of the coefficient is more difficult to predict. If the premium decreases, there could be an increasing incentive for the borrower to reallocate funds from mortgage payments to other alternative investments. This occurs only if an increase in investment returns is dominant. On the other hand, if the decrease in the premium is due to a decrease in mortgage rate, the consequent effect may become similar to that of the change in mortgage rate (Teo, 2004). A further analysis of the development of this premium is therefore required. Table II summarizes these variables and gives the expected signs.

Table II

List of independent variables in the regression and expected sign

This table contains the main variable and various macro-economic control variables used in this study.

Variable Code Expected sign

Main variable House prices

(lagged by one, three and six months)

Hp -

Control variables

Unemployment Unpl +

AEX AEX +

Premium of mortgage rate over investment rate

Premium +/-

Hourly wages Hw -

To answer the empirical research questions in the previous section, I present the following hypothesis:

H0: There is no significant relationship between delinquency and a change in Dutch

residential real estate value lagged by one, two or three months.

H1: There is a significant relationship between delinquency and a change in Dutch

(15)

3 Methodology and model

3.1 General model

Table I illustrates the various methods used by previous authors researching the determinants of delinquency. The authors generally used two kinds of data of the explanatory variable namely; binary depended data (Morton, 1975; Webb, 1982; Campbell and Dietrich, 1983) or continuous data (Herzog and Earley, 1970; Von Furstenberg and Green, 1974). Because the data is obtained from performance reports issued by Servicers of a MBS, it is on a continuous level. Like Campbell and Dietrich (1983), I take logarithms of the monthly mortgage delinquency rates 3 and the independent variables. The general model is of the form:

(1)

Where, is a constant, , is the logarithm delinquency rate at level d in month t, reflects the Dutch residential property value in month t lagged by one, three and six months (q), reflects the unemployment rates in month t, reflects the AEX index in month t, reflects the premium of mortgage rate over investment rate in month t, reflects the hourly wages in month t and is the error term in month t.

3.2 Model specification

Of course, one can estimate equation (1) with an OLS regression. However, I expect a certain amount of volatility clustering in the delinquency rates during the financial crisis. Therefore, I shall first test for the presence of heteroskedasticity in the residuals. Autoregressive Conditional Heteroskedasticity (ARCH, Engle 1982) effects are a special kind of heteroskedasticity where the residuals vary over time and where the series exhibit volatility clustering (Brooks, 2008). If ARCH effects were present in a linear model, any implication about the standard errors would be wrong. Table AI in appendix A displays

(16)

the various heteroskedasticity test statistics. The ARCH LM test is performed on the regression’s residuals, with the null hypothesis that there is no ARCH up to lag-order q. For the 90 and 120-day delinquency rates, the null hypothesis of no ARCH effects is highly significantly rejected for q=3 and q= 5. While the 30, 60 and total- day delinquency rates do not possess ARCH effect, they do however contain heteroskedasticity in the residuals (see column three, White test). Another important requirement for the OLS regression is that the relationship between variables should be linear. The BDS test (Brock, Dechert and Scheinkman, 1987) is a powerful tool for detecting serial dependence in time series. It tests the null hypothesis of independent and identically distributed (I.I.D.) against an unspecified alternative. Table AI in appendix A illustrates that the majority contain non- linearly dependent time series. For these reasons, I use the non-linear GARCH model4 (Bollerslev and Taylor, 1986) that provides a good description of these two important characteristics of the time series: volatility clustering (ARCH) and non-linearity.

The basic specification of the mean without ARCH effects may be written as:

(2)

where zt is a random variable drawn from a Gaussian distribution centered at 0 with

standard deviation equal to 1, Yt is the 60, 90, 120, total delinquency rates and the house price at t = 0, Xt the exogenous variable and εt the error term (white noise).

(17)

2.3 Generalized ARCH (p, q) model

The generalized ARCH model (GARCH) (p, q) model assumes a linear function where the moving average of past variances in included present conditional variances, where, p is the order of the autoregressive GARCH term and q is the order of the moving average ARCH term. The specification of the mean, here as a function of an exogenous variable with an error term, may be written as:

(2)

The conditional variance can be modeled using ARCH models.

Where α0 is the constant term, ε2t-1 is the ARCH term, σ2t-1 is last period’s fitted variance (the GARCH term). Note that the conditional variance coefficients must satisfy

and to maintain stationarity and positive conditional variance GARCH is a basic model based and uses the maximum likelihood to estimate the model. It does not model asymmetric variance and is limited by a non-negativity constraint on the conditional variance (Patterson, 2000).

3 Data

3.1 Data description

Delinquency

(18)

MBS deal has a different start date; this severely limits the number of variables in a single month. For example, on July 2001 only two servicers reported delinquency rates on their MBS deals. To keep the power of the statistical test sufficient, I start the time series analysis on February 2003, with a minimum of 25 and a maximum of 89 per month, resulting in 91 monthly periods. The data represents the dollar amount of loans currently N-days delinquent as a percent of the ending pool balance of a particular month.

The dataset contains information on five separate delinquency levels namely; a 30-day, 60-day, 90-day, 120-day and total delinquency. These various day delinquency rates can be interpreted as the severity of the delinquency. The 30-day delinquency indicates that the loan is 30-59 days delinquent in the given month (t), 60-day delinquency indicates that the loan is 60-89 days delinquent in the given month, 90-day delinquency indicates that the loan is 90-119 days delinquent in the given month (t), 120-day delinquency indicates that the loan is over 120 120-days delinquent in the given month(t) , finally the total-delinquency indicates the loan is over 30 day delinquent in the given month (t).

(19)

Figure I

Various delinquency series and trend line

This figure illustrates the balance amount of loans currently 30, 60, 90, 120 and total-days delinquent as a percent of the ending pool balance from February 2003 until August 2010, and a linear trend line is fitted

(20)

Figure II (continued)

Various delinquency series and trend line

House price

To determine if a hedging strategy based on real estate property value is possible in the Netherlands the relationship between delinquency and price changes in real estate must be described. The necessary real-estate price data is obtained from a price index maintained by the Dutch Central Bureau of Statistics (CBS). The price index tracks property values of current residential real estate which are designated for permanent occupation and is based on the Dutch statute on property values (WOZ, Waardering

Onroerende Zaken). The index provides data from 1995 to the present on a monthly basis.

(21)

Unemployment

The uncertainty of future income and the threat of retrenchments are measured by the change in average unemployment rate in the Netherlands of people from 25 to 65. The data is obtained from the CBS. The log-first difference (change) has been used to reduce the chance of non-stationarity in the data (see Appendix B, table BI).

AEX

I use the change of the Amsterdam Exchange (AEX) index to determine the market sentiment in the Netherlands. The index is composed of a maximum of 25 of the most actively traded securities and therefore providing a good indication of the sentiment in the market. Continuously compounded returns are calculated from monthly closing prices of the AEX. No non-stationarity is detected in this series.

Premium

In this study, the monthly one-year mortgage rates are used. The average 12-month Euribor rate is used as a proxy for the average return of investments. Data is obtained from DataStream. The log-first difference of premium of one-year mortgage rate over the twelve-month Euribor rate is used to reduce the chance of non-stationary in the data (see Appendix B, table BI).

Hourly wages

(22)

3.2 Descriptive statistics

Table III displays the descriptive statistics of the variables used in this study. The Jarque-Bera test (used for testing for non-normality, Brooks 2008) illustrates variables that could cause potential problems in the analyses when using a model that requires normality. The positive excess kurtosis5 of the first difference 60, 120, total-day delinquency rates, hourly wage, premium and unemployment rates indicate a leptokurtic distribution. The positive skewness and excess kurtosis indicate a higher probability of extreme values due to fatter tales in the distribution than assumed in a normal distribution. Whereas the 30 and 90-day delinquency has a negative excess kurtosis, which results in a wider peak around the mean and thinner tails, indicating a platykurtic distribution (Patterson, 2000). Hence, the probability of values around the mean is higher and the probability of extreme values is lower than a normal distribution assumes. The AEX and house prices are negatively skewed, with positive excess kurtosis, indicating fatter tails with a majority of the values more negatively distributed. A more detailed test for non-normality will be conducted in the next section and see if the residual poses a problem when a model is chosen.

5

(23)

Table III Summary statistics

This table contains summary statistics of time series variables used in the analysis. MBS is the value of the Mortgage Backed Securities presented in euro’s, the 30, 60, 90,120 and total-day delinquency rates are presented as a delinquency percentage of the total MBS portfolio value in a specific month, Real estate property value is given as an euro amount, Change in hourly wage is the percentage change of the wage

index, Premium is the one-year mortgage rate over the twelve-month Euribor rate and is presented as a percentage, Unemployment is presented as an absolute figure and AEX is presented as a percentage of the

continuously compounded return. The variables are obtained from a sample of 91 observations.

Mean Median Max Min Std. dev. Skewness Kurtos

is JB MBS (x1000) 1,677,446 975,250 11,846,100 68,000 1,941,261 2.34 9.40 382.16* 30-day delinquency rate 0. 5700 0.5302 0.8959 0.3515 0.1286 0.55 2.31 6.41** 60-day delinquency rate 0.2060 0.2093 0.3150 0.1227 0.0471 0.13 2.06 3.58 90-day delinquency rate 0.1280 0.1217 0.2283 0.0588 0.0430 0.59 2.50 6.19** 120-day delinquency rate 0.0874 0.0825 0.1819 0.0335 0.0301 0.46 2.95 3.25*** Total delinquency rate 1.0582 1.0450 1.6770 0.5434 0.3089 0.24 1.91 5.35*** Real estate property value 231,915 235,361 261,948 199,880 17,096 -0.23 1.93 5.19* Change in Hourly wage 0.0110 -0.0620 0. 8572 -0.2333 0.2092 2.25 8.35 185.52*** Premium 0.0088 0.0053 -0.5180 -0.3510 0.1461 0.59 4.54 14.20*** Unemployment 305,846 306,000 407,000 191,000 53.8331 -0.19 2.03 4.15 AEX _0.0774 _1.0758 _12.8535 -21.9583 6.057 -1.20 5.62 47.81***

***significant at the 0.01 level; ** significant at the 0.05 level; * significant at the 0.10 level

3.3 Stationarity and multicolinearity

(24)

data will lead to inconsistency in the descriptive statistics, will strongly influence the behavior of a series and will lead to spurious regressions (Brooks, 2008 and Patterson, 2000). We therefore test our variables for the presents of non-stationarity using the augmented Dickey-Fuller (ADF) unit root test (Dickey and Fuller, 1979 and Said and Dickey, 1984), the Phillips–Perron (PP) test (Phillips and Perron, 1988) and the KPSS test (Kwiatkowski et al.,1992). Since every variable used in model 1 shows signs of non-stationarity, I use first differences. The unit root tests in Table BI (Appendix B) shows statistics on the first difference of the dependent and independent variables.

In Table IV, a correlation matrix is presented. Correlation between independent variables is important because it can cause significance tests to draw inappropriate conclusions, raise and lead to high standard errors and make the regression sensitive to small changes in the specification (Brooks, 2008). The variables are not correlated high enough for any issues of multicolinearity to arise.

Table IV

Pearson’s correlations matrix

This table contains Pearson correlation coefficients and significance levels using Pearson’s table of the independent variables used in this study, N=91.

***significant at the 0.01 level; ** significant at the 0.05 level; *significant at the 0.10 level.

Hourly wage Unemployment Premium AEX Real estate property value

(lagged, t-1)

Hourly wage 1

Unemployment -0.017 1

Premium -0.059 0.177* 1

AEX -0.072 0.114 -0.093 1

Real estate property

(25)

4 Results

(26)

Table V

Results of the GARCH model

Period: 2003:02-2010:08 Monthly

Dependent Variable: (n)-DRt (First difference log of the nth -delinquency level in the Netherlands) Independent variables: PVt-q (First difference log of theReal estate property value lagged by q months)

AEX (Monthly continuously compounded return, calculated from closing prices) Unplt (First difference log of the average unemployment rate)

Hwt (First difference log of the hourly wage)

Pmt (First difference log of premium of one-year mortgage rate over the twelve- month Euribor rate)

In the parentheses below each estimation is the z-statistic. The models are estimated with heteroskedasticity consistent covariance (Bollerslev-Wooldridge) and autoregressive terms AR (1) and AR (2) to remove serial correlation in the residuals. The Ljung-Box Q-statistics for high-order serial correlation is used to fit the appropriate terms.

Variable 30-DRt 60-DRt 90-DRt 120-DRt Total-DRt Constant <0.0001 (0.0956) <0,0001 (0,8925) <0,0001 (0,8702) <0,0001 (0,0381) 0,0002 (2,2941)** Pvt-1 -0.0024 (-0.2956) -0.0055 (-1.8918)* -0.0083 (-2.8676)*** -0.0066 (-2.7893)*** -0.0408 (-3.2120)*** Pvt-3 0.0021 (0.2109) -0.0016 (-0.3162) 0.0003 (0.1149) -0.0052 (-2.8395)*** -0.0105 (-0.5489) Pvt-6 -0.0012 (-0.1364) 0.0018 (0.5888) -0.0026 (-0.9569) 0.0041 (2.0028)** -0.0147 (-1.0138) AEXt 0.0006 (1.0309) -0.0006 (-1.8145)* -0.0005 (-2.4690)** -0.0001 (-0.2328) -0.0031 (-2.2652)** Unplt 0.0016 (1.7169)* 0.0004 (1.1590) 0.0004 (1.6814)* 0.0001 (0.2632) 0.0014 (0.8923) Hwt -0.0937 (-5.0609)*** -0.0209 (-2.4251)** -0.0213 (-4.2814)*** -0.0025 (-0.3776) -0.0867 (-2.2540)** Pmt -0.0212 (-0.9588) -0.0048 (-0.4524) -0.0047 (-0.6231) 0.0041 (0.5231) -0.0514 (-1.2288) ARCH 0.9869 (1.9692)** -0.1117 (-2.9763)*** 0.9754 (3.7474)*** -0.0661 (-1.0116) -0.0694 (-0.7132) GARCH -0.0121 (-0.2491) 1.0631 (17.0655)*** 0.0016 (0.1262) 1.0396 (10.8143)*** 1.0968 (6.8588)*** R-squared6 0.1539 0.1960 0.0823 0.2392 0.218 Durbin-Watson stat 1.1588 1.7774 1.5748 1.8655 1.3848 Log likelihood 512.0742 600.2287 617.6754 633.4148 464.5104

***significant at the 0.01 level; ** significant at the 0.05 level;* significant at the 0.10 level.

(27)

The results for the growth rate7 of different delinquency levels vary broadly. When the growth of the Dutch residential real estate value is lagged by one-month, a one percent growth of real estate value will significantly decrease the 90 to 119-day (90-DRt) growth in delinquency by 0.008 % (p<0.01) . For residents that are more than 120 days in arrear this decrease is 0.007%, and shows a decrease of 0.041% in the total delinquency series (p<0.01). If the growth of the Dutch residential real estate value is lagged by three-months, a one-percent increase in growth of the real estate value decreases the growth in delinquency for resident that are more than 120 days in arrears by 0.005 % (p<0.01). The six-month lag in real estate value shows no significant result with an appropriate sign.

Notice however, that the coefficients of the ARCH (1) and GARCH (1) terms (variance equation) of the first four delinquency models are between the 0.95 and 0.99, suggesting traditional slow reducing variance process and mean reverting variance process. However, the total-day delinquency model has an ARCH (1) and GARCH (1) term higher than one, indicating that the variance increases as no mean reversion is present, suggesting an unstable GARCH model. As robustness check, I therefore include an OLS regression (Appendix C). This regression illustrates that house prices influence the delinquency levels at a lower significance level than in the GARCH (1, 1) model. This could be caused by ARCH effects that are present in the error, or by the non-linearity of the model (Table BI, Appendix B). However, the results do show a similar trend when comparing it with the GARCH (1, 1) model. Case, Shiller, and Weiss (1996) find similar results in an OLS regression based on national delinquency data, varying from –0.017 if real estate value is lagged by one quarter to –0.023 if real estate value is lagged by two quarters. They do find a much higher coefficient when running the regression per individual state. The coefficient is as high as -3.605 for the state Massachusetts, if the real estate value is lagged by two quarters.

Like Danis and Pennington-Cross (2005), I find the most significant relation of house prices and delinquency levels after a long period of delinquency. However, while Danis and Pennington-Cross also find a strong relationship in the 30 and 60 delinquency levels, no high significant relationship is found in the shortest delinquency periods.

(28)

The various macroeconomic variables are significant on a lower delinquency period. Unemployment has a positive sign as expected, but is only significant at the 0.10 level for the 30 and 90-days delinquency. This is in accordance to previous studies like Teo (2004), who did not find unemployment significant at explaining delinquency. Note that the OLS (Appendix C) does not find any significant relationship for unemployment in explaining delinquency.

The growth in hourly wages corrected for inflation is much better at explaining the start of the delinquency period. When the growth of the hourly wages decreases by one percent, the 30 to 59 day (30-DRt) growth in delinquency will significantly decrease by 0.094% followed by a drop of 0.021 % in the growth of 60-89 (60-DRt) and 90-119 day (90-DRt) delinquency. The OLS regression shows similar results (see Appendix C, table CI). This is in accordance with previous studies like Webb (1982), Herzog and Earley (1970), Campbell and Dietrich (1983), Von Furstenberg and Green (1974).

Unlike Teo (2004), I do not find the relation of the return of the AEX and delinquency levels extremely significant. While there are some low significance (at 0.1 and 0.05 level), the return of the AEX seems to influence delinquency levels at the 60, 90 and total-day delinquency period. Whereas Teo also finds an unexpected positive significant impact of the premium of mortgage rate over investment rate, I do not find it an important variable in explaining delinquency. Although the sign is negative, as expected, none of the premiums are significant in relation to any of the delinquency periods.

4.1 Mortgage crisis

(29)

the time series is divided, but since there are still some significant ARCH effects left in the 120-DRt, a GARCH regression is used. Results are presented in appendix D.

Pre-crisis

During the period of February 2003 until December 2007, only when the growth of real-estate value is lagged by three-month, a significant decrease of the 120-day delinquency level is found. A one percent growth of real estate value will significantly decrease the growth in delinquency by 0.022 percent of residents that are in excess of 120-days in delinquency. For the other economic variables only the growth of unemployment significantly increases the growth of the 30 to 59 days (30DRt) and the 90 to 119 days (90DRt) delinquency by respectively 0.005 and 0.001 percent.

During-crisis

(30)

5 Conclusion

This paper determines if there is a relation between delinquency risk and Dutch residential real-estate property value. To accomplish this I analyze various delinquency rates obtained from performance reports from large mortgage backed security deals in the Netherlands. A GARCH (1,1) model is used to determine the relationship between delinquency levels, house prices and various macroeconomic variables.

The results show that a lag of one month of the change in real-estate property value yields most significant results for Dutch homeowners who are in excess of 90 days in arrears. During the mortgage crisis however, the Dutch real estate prices seems to have a more profound influence at the beginning of the delinquency period. Furthermore, the coefficients are also significantly higher. When regarding the entire delinquency period (Total-DRt, in excess of 30-days in arrears), a one percent increase of the change in real-estate value decreases the change of total-day delinquency by 0.106 percent in times of the mortgage crisis, while there is only a 0.041 percent decrease before the crisis. Of the macroeconomic variables, only the change in hourly wage corrected for inflation seems to significantly decrease the change in delinquency for Dutch homeowners that are not more than 89 days in arrears. Hourly wages influence delinquency levels more than real estate property value since the coefficient is noticeably higher.

I therefore conclude that the hypothesis can be rejected when the change in real estate property value is lagged by one month on Dutch homeowners that are above 90 days in arrears on their mortgage. However, this changes when dividing the time series in a pre- and during-mortgage crisis period. Pre-crisis, the hypothesis can only be rejected when the change in real-estate property value is lagged by three months and only when Dutch homeowners are above 90 days in arrears. During the crisis, the hypothesis can be rejected when the change in real-estate value is lagged by one month and when Dutch homeowners are 30 to 89 days in arrears. Although with an unexpected sign, the hypothesis can also be rejected when the change in real-estate value is lagged by six-months and the Dutch homeowner is in arrears in excess of 120 days.

(31)

during the mortgage crisis at the total-day delinquency period and yields: -0.106. This means that if there was a market that trades a futures derivative based on real-estate property value, a homeowner must short the futures contract 10 times for the value of his real estate value to perfectly hedge his delinquency risk (holding all else constant). A perfect hedge would therefore be unrealistic since the large investment needed. Another approach would be to invest in put options based on these futures contracts. While limiting the size of the investment, an option requires premium to be paid and can therefore be a costly hedging instrument. Therefore, a hedging instruments based on Dutch real estate property value for individual homeowners appears to be too costly to implement successfully.

(32)

6 Bibliography

Brock, W., Dechert, W., & Scheinkman, J. (1987). A Test for Independence Based on the Correlation Dimension. Working Paper, University of Wisconsin at Madison, 1-39. Brooks, C. (2008). Introductory Econometrics for Finance. Cambridge: Cambridge

University press.

Campbell, T. S., & Dietrich, K. J. (1983). The Determinants of Default on Insured Conventional Residential Mortgage Loans. The Journal of Finance, 1569-1581. Case, K., & Shiller, R. J. (1988). Prices of Single Family Homes Since 1970: The

Experiences of Four Cities. New England Economic Review, 1-12.

Case, K., Shiller, R. J., & Weiss, A. (1993). Index-Based Futures and Options Markets in Real Estate. Journal of Portfolio Management, 83-92.

Case, K., Shiller, R. J., & Weiss, A. N. (1996). Mortgage Default Risk and Real Estate Prices: The Use of Index-Based Futures and Options in Real Estate. Journal of

Housing Research, 243-258.

Danis, M. A., & Pennington-Cross, A. (2005). The Delinquency of Subprime Mortgages.

Working Paper , 1-39.

Diaz-Serrano, L. (2005). Income volatility and residential mortgage delinquency across the EU. Journal of housing economics, 153-177.

Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation. Econometrica, 987-1008.

Engle, R. (2001). GARCH 101: The Use of ARCH/GARCH Models in Applied Economics. Journal of Economic Perspectives, 157–168.

Englund, P., Hawang, M., & Quigley, J. M. (2002). Hedging Housing Risk. Journal of

Real Estate Finance and Economics, 167-200.

Flavin, M., & Yamashita, T. (1998). Owner-occupied Housing and the Composition of the Houshold Portfolio over the Live Cycle. Working paper No. 6389, 1-55. Group, C. (2010). CMEG Exchange Volume Report. Chicago : CME Group.

Herzog, J. P., & Earley, J. S. (1970). Home Mortgage Delinquency and Foreclosure. New York: Columbia University Press.

Kau, J. B., Keenan, D. C., & Kim, T. (1994). Default Probabilities for Mortgages. Urban

(33)

Kendall, L. T. (1964). Anatomy of the Residential Mortgage. U.S. Savings and Loan

League.

Mann, H. (1945). Nonparametric test against trend. Econometrica , 245-259. Morton, G. T. (1975). A Discriminant Function Analysis of Residential Mortgage

Delinquency and Foreclosure. Journal of the American Real Estate and Urban

Economics Association, 73-90.

Patterson, K. (2000). An Introduction to Applied Econometrics. London: Macmillan. Perron, P., & Phillips, P. (1988). Testing for a Unit Root in Time Series Regression.

Biometrika, 335–346.

Quantitative Micro Software, LLC. (2010). EViews 7 User’s Guide II. Irvine CA.

Shiller, R. J. (2008). Derivatives Markets for Home Prices. NBER working paper, 17-33. Shiller, R. J. (2008). The Subprime Solution: How Today’s Global Financial Crisis

Happened, and What to Do about It. Princeton: Princeton University Press.

Shiller, R. J., & Weiss, A. N. (1999). Home Equity Insurance. Journal of Real Estate

Finance and Economics, 21-47.

Teo, A. H. (2004). Delinquency Risk in Residential ARMs: A Hazard Function Approach.

Journal of Real Estate Portfolio Management, 243–258.

Von Furstenberg, G. M., & Green, J. R. (1974). Home Mortgage Delinquencies: A Cohort Analysis. Journal of Finance, 1545-1548.

Webb, B. G. (1982). Borrower Risk Under Alternative Mortgage Instruments. The

Journal of Finance, 169-183.

West, K., & Newey, W. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 703-708.

(34)

Appendix A: Heteroskedasticity and functional form statistics

Table AI

This table contains the statistics of the ARCH LM test with a lag structure (q) set to three and five, the F-statistics of the White test are included cross terms, the Z-F-statistics of the BDS test (for non-linearity) with dimensional vectors (m) set to three and five. The ARCH and White statistical tests are established with an

OLS regression model using the following independent variables: .

The BDS test for independence is used on the dependent variables individually. Only the one regression with a residential property value lagged by one month is included in the table to conserve space, the results

however do not vary significantly. ARCH LM (q=3) ARCH LM (q=5) White BDS (m =3) BDS (m=5) D30,t 11.676*** 8.047*** 0.9758 0.004 0.996 D60,t 1.111 1.545 1.0489 2.406*** 2.914*** D90,t 17.466*** 10.268*** 0.9247 6.183*** 9.074*** D120,t 8.308*** 5.519*** 0.5095 4.722*** 6.694*** Dtotal,t 4.470*** 5.117*** 1.0185 1.299 3.211***

(35)

Appendix B: Unit root tests on first difference variables

Table BI

MK refers to the Mann-Kendall test, ADF refers to the Augmented Dickey–Fuller test and shows the t-statistic. PP to the Philips-Perron test, the adjusted t statistic is given. KPSS to the Kwiatkowski-Phillips-Schmidt-Shin test with the LM statistic. The lag structure in the ADF test is selected automatically on the

basis of the Scharz Information Criterion (SIC). In the case of the PP and KPSS tests, the bandwidth parameter is selected automatically according to the Newey and West (1994) approach. d indicates the first

difference of the variable.

ADF PP KPSS d(30-day delinquency) -10.715*** -14.088*** 0.147 d(60-day delinquency) -16.242*** -20.021*** 0.100 d(90-day delinquency) -4.113*** -32.038*** 0.067 d(120-day delinquency) -22.187*** -27.149*** 0.091 d(Total delinquency) -2.264 -24.720*** 0.067

d(Real estate property value) -2.023 -7.938*** 0.699**

d(Wage) -0.770 -10.117*** 0.276

d(Unemployment) -4.196*** -6.266*** 0.245

d(Premium) -7,733*** -7.826*** 0.280

AEX -7.642*** -7.592*** 0.175

(36)

Appendix C: Ordinary Least Square regression

Table CI

Period: 2003:02-2010:08 Monthly

Method: Ordinary least squares with HAC standard errors and covariance ( Bartlett kernel, Newey-West fixed bandwidth = 4)

Dependent Variable: (n)-DRt (First difference log of the n th

-delinquency level in the Netherlands) Independent variables: PVt-q (First difference log of theReal estate property value lagged by q months)

This table contains the results of the OLS regression. In the parentheses below each estimation is the t-statistic. Variable 30-DRt 60-DRt 90-DRt 120-DRt Total-DRt Constant <0,0001 (-0,3423) <0,0001 (0,5006) <0,0001 (1,0769) <0,0001 (1,2714) 0,0002 (2,5620)** Pvt-1 -0.0044 (-0.3183) -0.0071 (-1.6115) -0.0408 (-2.3342)** -0.0041 (-1.2507) -0.0343 (-1.8362)* Pvt-3 0.0102 (0.7452) -0.0012 (-0.2303) -0.0012 (-0.3227) -0.0046 (-1.1933) -0.0155 (-0.4848) Pvt-6 -0.0008 (-0.0663) -0.0001 (-0.0170) -0.0043 (-1.3826) 0.0041 (1.8582)* -0.0120 (-0.7546) AEXt -0.0006 (-0.5885) -0.0008 (-1.5003) 0.0006 (0.5519) 0.0001 (0.3034) -0.0024 (-1.8584)* Unplt 0.0008 (0.4370) 0.0002 (0.4701) 0.0002 (0.1066) 0.0004 1.0432 0.0004 0.1887 Hwt -0.0911 (-2.8167)*** -0.0218 (-1.8482)* -0.0405 (-1.8226)* -0.0051 (-0.5660) -0.0913 (-2.0252)** Pmt -0.0682 (-1.6528)* -0.0086 (-0.6550) -0.0013 (-0.0213) 0.0032 (0.3572) -0.0652 (-1.1692) R-squared 0.1626 0.2187 0.1238 0.0668 0.1854 Durbin-Watson stat 2.5696 2.6972 2.8443 2.8352 2.667903 Log likelihood 514.0704 587.8030 605.6282 582.4639 466.8063

(37)

Appendix D: Mortgage crisis

Table DI

Periods: 2003:02-2007:12 Monthly (pre-crisis, 59 observations) and 2008:01-2010:10 monthly (during crisis, 32 observations)

Method: GARCH (1,1) regression with autoregressive AR (1) AR (2) terms when appropriate. Dependent Variable: (n)-DRt (First difference log of the nth -delinquency level in the Netherlands) Independent variables: PVt-q (First difference log of theReal estate property value lagged by q months)

This table contains the results of the GARCH regression with the appropriate AR(1) AR(2) structure for the period February 2003 to December 2007 (pre-crisis, 59 observations) and January 2008 to August 2010

(during crisis, 32 observations). In the parentheses below each estimation is the z-statistic. Pre-crisis (2003:02-2007:12) Variable 30-DRt 60-DRt 90-DRt 120-DRt Total-DRt Constant 0.0001 (0.7781) 0.0001 (1.6929)* 0.0001 (1.1240) 0.0001 (0.7114) 0.0002 1.0700 Pvt-1 -0.0399 (-0.7473) -0.0182 (-1.4617) -0.0018 (-0.8248) -0.0096 (-1.0333) -0.0449 (-1.3082) Pvt-3 0.0521 (1.6404) -0.0032 (-0.3662) 0.0133 (6.3482)*** -0.0222 (-9.6711)*** 0.0368 (0.8363) Pvt-6 0.0321 (0.9545) 0.0074 (1.0075) -0.0019 (-0.8845) 0.0059 (1.2534) 0.0470 (1.9767) AEXt 0.0006 (0.2264) -0.0013 (-1.5701) -0.0006 (-1.7882)* 0.0009 (1.9261)* -0.0040 (-0.9633) Unplt 0.0052 (2.2675)** 0.0008 (1.4280) 0.0009 (3.4281)*** 0.0003 (0.8483) 0.0012 (0.3343) Hwt -0.0473 (-0.6694) -0.0290 (-1.9003)* -0.0163 (-1.9339)* -0.0004 (-0.0319) -0.1343 (-1.7795)* Pmt -0.0219 (-0.1831) -0.0092 (-0.2715) -0.0173 (-1.0950) 0.0038 (0.2049) 0.1998 (1.3870) ARCH 0.3784 (1.4086) 0.163507 (1.3686) 0.2787 (1.2267) -0.0905 (-1.5091) -0.1308 (-2.6827)*** GARCH 0.3700 (1.0997) 0.3903 (0.8774) -0.4008 (-1.1612) 0.4015 (0.5065) 0.5965 (2.6924)*** R-squared8 0.1137 0.2261 0.296081 0.0436 0.2577 Durbin-Watson stat 2.4895 1.7290 1.6847 1.8972 1.5460 Log likelihood 339.0478 388.9772 402.1019 397.2851 310.4190

***significant at the 0.01 level; ** significant at the 0.05 level; * significant at the 0.10 level.

8

(38)

Table DI (continued) During crisis (2008:01-2010:10) Variable 30-DRt 60-DRt 90-DRt 120-DRt Total-DRt Constant 0.0001 (0.2078) 0.0001 (0.1103) 0.0001 (1.9727)* -0.0001 (-0.4147) 0.0002 (1.3279) Pvt-1 -0.0662 (-2.8038)** -0.0191 (-2.1021)** -0.0177 (-1.3794) -0.0113 (-2.5475)** -0.1058 (-3.0539)*** Pvt-3 0.0383 (1.3134) 0.0080 (1.0210) 0.0069 (0.5992) 0.0056 (1.7410)* 0.0210 (0.3368) Pvt-6 0.0495 (1.4500) 0.0066 (0.4730) 0.0095 (1.5070) 0.0121 (5.1227)*** 0.0275 (1.3660) AEXt -0.0011 (-0.7715) -0.0009 (-2.1995)** -0.0002 (-0.4203) -0.0002 (-0.9614) -0.0016 (-1.6211) Unplt -0.0075 (-1.2388) -0.0024 (-2.1095)** -0.0022 (-1.4591) -0.0006 (-0.8621) -0.0137 (-3.7196)*** Hwt -0.1070 (-3.8734)*** 0.0130 (0.9745) -0.0179 (-0.8500) 0.0071 (1.0448) 0.0091 (0.3162) Pmt -0.0554 (-1.1552) 0.0078 (0.6001) -0.0165 (-1.0087) 0.0144 (1.5641) -0.0171 (-0.3448) ARCH -0.2941 (-3.3447)*** -0.1776 (-0.8946) 0.1401 (0.6844) -0.0640 (-0.1910) -0.3921 (-4.4053)*** GARCH 0.6171 (2.2184)*** 0.4811 (1.0123) 0.3944 (0.4719) 1.2264 (3.3684)*** 0.6844 (5.2216)*** R-squared9 0.15747 0.2480 0.2598 0.1317 0.2656 Durbin-Watson stat 1.6605 1.9521 1.8292 2.1075 1.4643 Log likelihood 191.6299 217.0777 219.9441 236.9624 170.9087

***significant at the 0.01 level; ** significant at the 0.05 level; * significant at the 0.10 level.

9

Residential Mortgage Delinquency Risk and Real Estate Prices: