How To Find Out If A Loan Is Safe

Transcription

1 THE JOURNAL OF REAL ESTATE RESEARCH 1 Borrower Risk Signaling Using Loan-to-Value Ratios Donald R. Epley* Kartono Liano* Richard Haney** Abstract. This paper evaluates the signaling capability of the borrower s selected loan-tovalue ratio, and finds the equity proportion of housing capital to be a good indicator of the loan s riskiness. It also compares residential mortgage bundles among the commonly used statistical models of multiple discriminant analysis, probit and logit. Classification accuracy and significance are contrasted among the bundles using loan-to-value ratios of 80%, 90% and 95%. The results show major differences in significance and sign changes among loan-to-value ratio levels and the choice of model. All models were highly significant, but classified different variables with substantial differences in the significance levels. Introduction Interest in evaluating the underwriting collateral requirements of a residential mortgage has grown in the 1990s with the increase in competition among lenders originating loans and the concurrent need to avoid discrimination in mortgage terms. One aspect of this interest is a concern that the traditional loan-to-value ratio requirement may not be transmitting the correct default signals to the lender. Recent research by Bester (1985), Milde and Riley (1987), and Chan and Kanatas (1985) has suggested that other variables such as the loan size or borrower s income could signal loan and potential default better than the traditional initial equity requirement that is measured by the loan-to-value ratio. Savings and loan failures in the last decade have been blamed partially on inadequate credit screening of real estate loans. A recent study by Jameson, Shilling and Sirmans (1990) demonstrated that the sign on the loanto-value variable can change through time. Continual evaluation and analysis of signaling given by this highly important loan-to-value ratio is critical for the protection of lender collateral value because of its widespread use by originators and investors to judge creditworthiness and loan risk. The major purpose of this article is to evaluate the current underwriting loan-to-value rules that are used by primary mortgage market lenders to qualify applicants for residential first loans. The major requirement examined is the traditional 80% rule that has been enforced by secondary market investors. This rule functions as an initial gatekeeper to eliminate potential borrowers who do not possess the minimum downpayment. Further, it divides the remaining successful applicants into two default *Department of Finance and Economics, Mississippi State University, PO Box 9580, Mississippi State, Mississippi **Department of Finance, College of Business Administration, Texas A&M University, College Station, Texas Date Revised May 1995; Accepted August

2 72 THE JOURNAL OF REAL ESTATE RESEARCH risk classes that depend on the amount of initial collateral available. The results show that the traditional loan-to-value underwriting rule that allows the borrower to signal risk is working well in that the explanatory risk variables are almost identical with slight differences in significance. The second purpose of this paper is to compare multiple discriminant analysis (MDA), probit and logit models as the appropriate tool of analysis when a qualitative dependent variable is used in a large sample. This is important to any study of loan-to-value ratios as they tend to classify themselves into groups such as 80% and 90% that reflect the investor requirements in the secondary mortgage market. Also, the sale to the borrower of private mortgage insurance is quoted in ordinal terms such as greater that 80% and less-than-or-equal-to 80%. The results show that substantial differences occur between MDA and the more traditional probit and logit analytical tools in evaluating the importance of individual variables and their statistical significance. The remainder of this article is divided into four sections. The second examines relevant previous studies, the third presents the model and data, the fourth contains the results, and the fifth, the conclusions. Previous Studies Two areas of research are important. The first covers the theoretical concept and the relatively small number of empirical studies on the ability of the initial collateral requirement 1 to signal the applicant s default risk to the lender. The second area covers the correct identification of those mortgage terms that may be classified as discriminatory among classes of applicants. One of the first theoretical papers on borrower signaling collateral selection is by Bester (1985) who explains collateral requirements in debt contracts as a response by the lender to imperfect market information and imperfect signaling of default risk. Banks are unable to distinguish borrowers of different risk directly, and they attempt to do so by offering different credit contracts that enable borrowers to self-select on the basis of risk. This theoretical model concludes that banks compete by offering a combination of initial collateral requirements and the rate of interest simultaneously so that applicants may, in effect, screen their own riskiness. Borrowers with a higher probability of default elect a contract with a higher interest rate and a lower collateral requirement than borrowers with a lower probability of default. Two papers have examined the need for additional initial screening devices for the high quality loan applicant to convey information on loan quality. Chan and Kanatas (1985) suggested that the high quality appplicant must make the first move by offering personal assets as collateral. Each loan applicant first selects the loan requirements and then presents the case for funding to a primary lender. Milde and Riley (1987) constructed a model where banks separate loan risks by offering larger loans at higher interest rates. The loan size reflects the applicant s desire for risk. Stiglitz and Weiss (1981) and Williamson (1986) argued that lenders may apply more stringent credit constraints to loan applicants based on uncertainty about their ability to repay a loan as scheduled, or because of market conditions that may adversely affect the collateral value of the property. These may be rejection, higher loan-to-value ratios, shorter maturities, or higher interest rates. One potential outcome is that the borrower may seek or be encouraged to use a government-related program such as FHA-insurance or a VA-guarantee, which greatly reduces the lender s risk of payment default. VOLUME 11, NUMBER 1, 1996

3 BORROWER RISK SIGNALING 73 This paper examines the typical underwriting guidelines that longer maturity, higher debt, higher monthly payment, and high-risk employment typically should be positively related to higher risk of default. The customer signals this risk by electing to commit only a small amount of capital as a downpayment. The lender examines the other explanatory variables and approves or rejects the mortgage terms. Peterson (1981) argued that these lender adjustments to perceived default risk would be systematic. Relatively poor credit risks receive unfavorable terms because the credit officer receives a better management review in comparison to the terms received by borrowers who signal a good credit risk. The second area of research covers those empirical studies that examine the mortgage terms that serve to discriminate among potential borrowers who are more likely to default on a loan. Following Peterson (1981), these terms may be called prejudicial discrimination or non-prejudicial discrimination. 2 The former uses one or more of the Equal Credit Opportunity Act-covered classes to assess risk which has illegal implications. The latter uses the economic variables of employment stability, potential income, and credit history to divide mortgage bundles into favorable and unfavorable terms. Favorable bundles contain terms that are similar to others that have been given to applicants with similar signaling characteristics and represent the average or norm with the highest frequency of all bundles offered in the market. An unfavorable bundle contains a collection of terms in a mortgage that has been approved, but has terms that are outliers to the norm as the buyer has signaled a higher potential for default. Examples could be a higher loan rate, shorter maturity, higher discount points, larger downpayment, or a combination. The term or collection of terms used is dependent on the applicant and the local market conditions. Shear and Yezer (1983) used national data in a regression analysis of FHA and conventional new loans in their study of favorable and unfavorable mortgage terms. Their results revealed that the different loan requirements shifted potential buyers among the government and private mortgage sectors, but had no significant market level impact. Further, they showed that location was not a factor. Jud and Epley (1991) also used national data in a regression analysis as they examined differences in regional mortgage rates and mortgage bundles. They found that differences still exist in rates that are caused by expected differences in loan risk by region, but the interest-rate differentials have been minimized since deregulation. The empirical model used in this paper is an expanded version of the bivariate logit analysis used by Canner, Gabriel and Woolley (1991) in their study of loan delinquency on borrower-selected FHA or conventional mortgages. It incorporates the results of Campbell and Dietrich (1983) and Vandell and Thibodeau (1985) who found that default rates increase with the loan-to-value ratio. Our paper is one of the first empirical examinations of the ability of the loan-to-value ratio to signal risk in residential mortgage markets. In previous studies, it was used as one of several explanatory variables. In this one, the loan-to-value variable serves as a classification instrument to signal initial collateral available for the loan, while the traditional underwriting risk measures serve as explanatory variables. Further, this paper uses approved mortgages only. We are interested in the loans that have passed successfully through the underwriting process. The emphasis here is on the ability of the potential borrower to signal default through the loan-to-value ratio and the ability of traditional classification techniques to accurately capture the resulting mortgage bundle. The results in this paper substantiate the probit analysis of mostly

4 74 THE JOURNAL OF REAL ESTATE RESEARCH accepted bank loans by Black, Schweitzer and Mandell (1978) but expand the analysis to residential mortgages and the use of logit and multiple discriminant analysis. The Model and Data The Model The appropriate multivariate test is a classification model as the mortgage borrower is classified into one of two groups that depends on the size of the downpayment. The first group has a loan-to-value ratio that is greater than 80% of the price or value of the property, and the second group has a ratio that is less than or equal to 80%. 3 Although the borrower can select the proportion of personal assets to use as a downpayment, the typical family most likely will maximize the downpayment to minimize the monthly payment. The underwriting function has forced an initial self-selection and classification by the borrower. The default risk information signaled by a loan-to-value ratio above 80% has been considered historically to be high risk as the borrower has less collateral and, supposedly, less commitment in repaying the loan. The lender will require these applicants to purchase private mortgage insurance (PMI), FHA insurance, or use a VA guarantee. 4 Default insurance is designed to equalize the risk of default to the lender from the two groups. The risk of default by those borrowers who pay a low downpayment and purchase default insurance or obtain a guarantee should equal the risk by those borrowers who pay a larger downpayment and are not required to purchase default insurance. If the risk of default to the lender is identical between the two groups, the mortgage terms offered to individual borrowers in each group should be approximately the same. Any significant differences between the two groups should reflect discrimination or unfavorable terms. This paper expands the analysis on the high-risk group further by examining mortgage bundles with a loan-to-value ratio of (a) greater than 90% compared to 90% or less, and (b) greater than 95% compared to 95% or less. The null hypothesis tested is that all statistical classification models should produce the same signs on the coefficients and the same level of statistical significance. After the borrower has selected an initial loan-to-value ratio, the next step in the underwriting loan process is to approve the borrower s income-to-debt ratios as an indication of the ability to repay. If these are not satisfied, the loan is rejected regardless of the loan-to-value ratio. These ratios should not be significant in this paper s empirical section as the study and data cover approved loans only on conventional, FHA and VA mortgages. 5 The analytical problem is to isolate those explanatory variables contained in the approved loan packages in such a manner that discriminatory, favorable and unfavorable terms can be identified. The null hypothesis tested is, H o: x 0 = x 1, where x 0 is a vector of favorable mortgage terms for each borrower in low-risk group 0, and x 1 is a similar vector of favorable mortgage terms for high-risk borrowers in group 1. VOLUME 11, NUMBER 1, 1996

5 BORROWER RISK SIGNALING 75 The explanatory variables in the high-risk and low-risk groups and the level of statistical significance should not reveal any differences as the risk levels of the two groups should be equal. Any variables that are significant in one group that are not significant in the other, or substantial differences in the overall level of statistical significance, reveals the presence of risk that has not been adequately covered under the PMI, FHA insurance or VA guarantee. The risk should have been equalized between the two classes by the initial screening of applicants and the requirement for default insurance or guarantee on the higher risk loans. The model used is, L/V f (I,L,M), where I represents the individual applicant risk factors such as age, income and employment status, L represents risk that might be associated with location of the property in the city, or in different regions of the country, and M covers market risk factors that arise from the interest on competing investments such as Treasury bonds. The estimating model becomes, (L/V ) i a o + a i X i + e, where, (L/V ) i 1 if the ratio for loan i is in the high-risk group or 0 if it is in the low-risk group, X i vector of explanatory mortgage terms for loan i that are outlined in Exhibit 1, and e error term. Doyle (1977) recommends three methods of analysis that have been used in cases of qualitative dependent variables: multiple-discriminate (MDA), probit, and logit analysis. Following Ingram and Frazier (1982) in their study of discrimination in mortgage loan applications, all three were used and compared in this analysis. The models should reveal the same mortgage bundles and the same level of statistical significance, if the signaling is accurate. Probit analysis may be appropriate when loan-to-value is dichotomous. The regression is interpreted as describing the maximum likelihood that a loan bundle will equal that value given the other mortgage terms. A common characteristic of this equation is that the variance of the error term is heteroscedastic, or non-normal; however, the coefficients may still be unbiased and consistent. Additive logit analysis classifies the data into one of two outcomes, and gives the natural log value of the odds in favor of a positive response, or more risk that the independent variable will be found in the higher loan-to-value group. A key difference between the two is the underlying population. In probit, a normal distribution is assumed for large samples, and in logit, a logistic distribution. Berkson (1950) and Press and Wilson (1978) hold that the choice between the two is a matter of individual preference as (a) the results from one can be transformed into the other, and (b) very large datasets may be necessary to obtain significant differences, although the exact size is unknown. The third choice is multiple discriminant analysis. It assigns data to one or more distinct groups, and is appropriate when (a) the groups under examination are discrete

6 76 THE JOURNAL OF REAL ESTATE RESEARCH and identifiable, (b) each member of the group can be profiled by a set of predictor variables, and (c) the explanatory variables have a normal distribution. No clear-cut theoretical or empirical basis exists for selecting one approach over the others when a limited dependent variable model is used (Ingram and Frazier, 1982). Therefore, a comparison of probit, logit, and multiple discriminant analysis is undertaken to determine whether meaningfully different outcomes could be generated in a given empirical problem. The Data The sample from the National Association of Realtors Home Finance Annual Survey includes approved conventional, FHA and VA residential first mortgages from all types of lenders in the U.S. from 1985 through There are 1741 loans representing responses that do not have any missing observations for any explanatory or classification variable. The dependent and explanatory variables, along with the specification for each variable, are shown in Exhibit 1, and the descriptive statistics for the variables are shown in Exhibit 2. Because the dependent variable is coded zero for the lower risk loans and 1 for the higher risk loans, a positive coefficient implies that the dependent variable approaches one as the value of the explanatory variable approaches one, or becomes more risky, which suggests a positive relationship. As the value of this independent variable increases, the probability increases that it will be found in a higher loan-to-value loan. As the value of an explanatory variable declines, the probability of it existing in a high ratio loan declines, suggesting a negative coefficient and less risk. An explanation of the variables and their expected signs follows: L/V ratio The dependent variable, the loan-to-value ratio, is calculated as the ratio of the amount of the first mortgage to the sales price of the property. 6 Traditionally used as one of the key underwriting variables, it has been shown to have a positive relationship to default risk when used as an independent variable (Jameson, Shilling and Sirmans, 1990; Jud and Epley, 1991). MATURITY The number of years to maturity of the first mortgage is reported in + the survey. Borrowers who select a longer maturity opt for a lower monthly payment and represent a higher risk class due to a presumed lower ability to repay, given their income level. Also, a shorter loan is subject to less uncertainty (Ingram and Frazier, 1982; Black, Schweitzer and Mandell, 1978). LOANRATE The effective interest rate is calculated as the contract rate on the + first mortgage plus the ten-year amortized points paid by the buyer and seller. 7 This rate is reflective of the lender s yield requirement and is expected to vary directly with the mortgage risk level after controlling for changes in market rates (Ostas, 1977). MONTHPAY The monthly payment is calculated for the terms reported on the first + mortgage. A positive sign is expected as a higher monthly payment is associated with a higher risk of default, given the borrower s income level. VOLUME 11, NUMBER 1, 1996

7 BORROWER RISK SIGNALING 77 Exhibit 1 Variables and Specification Variable Specification Terms of loan, I : L/ V (dependent variable) Amount of first mortgage divided by sales price MATURITY Years to maturity of first mortgage, years LOANRATE Effective interest rate* MONTHPAY Calculated monthly payment for the approved loan terms DINSUR 1 PMI, 0 others INCOME Midpoints of household income from $22,500 in increments of $5,000 DNETWOR 1 first-time homebuyer, 0 others DSTATUS 1 single borrower, 0 others EMPLOYED Number of adult wage earners in borrower household DEBT Number of dependents in borrower household AGE Age of borrower, years** Location, L: DLOC HOMEAGE 1 central city, 0 others Age of house, years Market Conditions, M: TBOND DREG1 DREG2 DREG3 Rate for month loan was approved 1 Northeast, 0 others 1 Northcentral, 0 others 1 South, 0 others*** *Effective interest is the contract rate plus the ten-year amortized points paid by the buyer and seller on the first mortgage. **Age was inserted once as the midpoints of age brackets, and a second time as a code from 1 8 with 1 less than 25 and 8 over 65 with increments of five years in each bracket. The results were not significantly different. ***The fourth region, the West, is included in the intercept. DINSUR A loan in a high risk group with default insurance 1, 0 others. A + larger L /V ratio will increase the likelihood of default and the likelihood of purchasing default insurance. INCOME The survey results report income by category. For example, category 1 represents income less than $25,000, 2 represents income $25,000 29,999, etc. The midpoints were used in this study. Category 1 was represented by $22,500, 2 was represented by $27,500, etc. The higher income families will most likely be in the lower risk group as they can afford a larger downpayment. DNETWOR 1 first-time homebuyer, 0 others, is a dummy proxy for net worth. + First-time homebuyers are not expected to possess substantial equity for a sizeable downpayment and represent a higher default risk.

8 78 THE JOURNAL OF REAL ESTATE RESEARCH Exhibit 2 Descriptive Statistics Total L/V.80 L/V.80 (N 1741) (N 749) (N 992) Variable Mean Std Dev. Mean Std Dev. Mean Std Dev. L/ V ratio MATURITY LOANRATE (in %) MONTHPAY (in 000s) DINSUR HOMEAGE DNETWOR DSTATUS DEBT INCOME (in 000s) EMPLOYED AGE DLOC TBOND (in %) DREG DREG DREG Total L/V.90 L/V.90 (N 1741) (N 1103) (N 638) Variable Mean Std Dev. Mean Std Dev. Mean Std Dev. L/ V ratio MATURITY LOANRATE (in %) MONTHPAY (in 000s) DINSUR HOMEAGE DNETWOR DSTATUS DEBT INCOME (in 000s) EMPLOYED AGE DLOC TBOND (in %) DREG DREG DREG VOLUME 11, NUMBER 1, 1996

9 BORROWER RISK SIGNALING 79 Exhibit 2 (continued) Total L/V.95 L/V.95 (N 1741) (N 1256) (N 485) Variable Mean Std Dev. Mean Std Dev. Mean Std Dev. L /V ratio MATURITY LOANRATE (in %) MONTHPAY (in 000s) DINSUR HOMEAGE DNETWOR DSTATUS DEBT INCOME (in 000s) EMPLOYED AGE DLOC TBOND (in %) DREG DREG DREG DSTATUS 1 single borrower, 0 others, reflects the familial status of the borrower. + Single borrowers may not be expected to possess substantial net worth and thus, may represent a higher risk. EMPLOYED The number of adult wage earners reflects the amount of collateral available for a downpayment and the ability to repay the loan. A larger number of wage earners should have a larger amount of downpayment and income and represent a lower risk. DEBT The number of the borrower s dependents captures the amount of + household debt. A higher number of dependents will most likely mean additional debt that most likely places the borrowers in the high-risk group. AGE The age of the borrower was entered to determine if this Equal Credit Opportunity Act-covered class was being used as a risk variable. A negative relationship was expected as older buyers should possess more income and collateral and present a smaller default risk. DLOC 1 central city, 0 others, was used to estimate any capital shortages in + the inner areas of the city that might be from higher risk due to crime rates or deteriorating neighborhoods. This variable was expected to have a positive sign meaning that a central city location would carry a higher default risk.

10 80 THE JOURNAL OF REAL ESTATE RESEARCH HOMEAGE The age of the property was used to capture condition of collateral. An + older home typically exhibits a greater need for depreciation which reflects a higher risk. TBOND The ten-year rate that was in effect when the loan was approved was + entered to capture the current financial market conditions and the lender s position on the yield curve. A higher bond rate is associated with a higher mortgage rate which means that the borrower would apply for a smaller loan. DREG1, 1 Northeast, 0 others DREG2, 1 Northcentral, 0 others DREG3 1 South, 0 others Census regions were entered as dummy variables to capture regional risk factors. The West is included in the intercept, and the coefficients are interpreted relative to the West. During the period, all regions were expected to show a negative sign relative to the West due to a higher priced market and unstable economy in the western states. The probit and logit models were run with and without the regional dummies to use as a comparison. Results The use of the loan-to-value ratio with default insurance as a signal to the lender of default risk appears to be working well. The results reveal the same mortgage underwriting bundle with almost the same level of significance using probit and logit with regional dummies. Our analysis shows that the correct method of evaluating this variable and capturing its interrelationships in the mortgage bundle is to divide the applicants into risk classes as determined by the size of the ratio as signaled by the borrower s initial selection. The choice of model with a large sample should be either probit or logit with regional variables. The hypothesis that the initial loan-to-value ratio will correctly signal the mortgage insurance, FHA insurance, and the VA guarantee are working well in equating the risk classes of applicants after the loan-to-value ratio has been accepted. Although Bester s model (1985) of borrower signaling with other loan variables has not been tested directly, our conclusions provide further justification for the continual use of the loan-to-value ratio as an initial tool of borrower creditworthiness. The loan-to-value ratio of 80% produced a set of significant variables and signs that were not the same as the two higher loan-to-value ratios examined. Those borrowers who elect to pay a smaller amount down on the loan are more sensitive to other factors such as the contract loan rate and the general level of interest rates. Our results substantiate the changing sign conclusions found by Jameson, Shilling and Sirmans (1990), but the same interrelationships between this ratio and the other mortgage terms can be captured in a probit and logit analysis rather than a simultaneous equation model. VOLUME 11, NUMBER 1, 1996

11 BORROWER RISK SIGNALING 81 Exhibit 3 Summary of Statistical Models (dependent variable is 0 for L/V.80 and 1 for L/V.80) Probit Logit without without MDA Regional Regional Variables F-statistic a Probit b Logit b Dummies b Dummies b Coefficients: Intercept *.982* 1.752* MATURITY ***.025***.042***.023***.038*** LOANRATE MONTHPAY *** DINSUR *** 1.204*** 2.128*** 1.170*** 2.035*** HOMEAGE ***.004**.007** DNETWOR ***.712*** 1.196***.681*** 1.133*** DSTATUS DEBT *** *.098* INCOME ***.019***.033***.020***.034*** EMPLOYED ***.274***.461***.279***.469*** AGE ***.031***.051***.027***.044*** DLOC 9.458*** TBOND *.193* DREG ***.473***.832*** DREG ** DREG ***.376***.655*** N Goodness of Fit: R c 68.5 c.692 Significance of Model: Log likelihood *** *** *** *** F 48.00*** Classifying Accuracy: 75.35% 75.93% 76.05% 74.73% 74.61% ***significant at the.01 level; **significant at the.05 level; *significant at the.10 level a These figures were generated using SAS. b These figures were generated using LIMDEP. 2 (log likelihood) c The pseudo-r 2 =. N + log likelihood One of the most interesting results is shown in a comparison of the mortgage bundle selected by those borrowers with the lower loan-to-value ratio shown in Exhibit 3 with the bundles selected by the higher ratio loans shown in Exhibits 4 and 5. For example, the contract mortgage rate (LOANRATE) is insignificant in the 80% model, but is highly significant in the two higher ratio models. Also, the TBOND rate is significant only at 10% or not at all in the 80% model, but becomes highly significant in the probit and logit models at 90% and 95% loan-to-value ratios. Sign changes occurred among models in the intercept, MONTHPAY, DINSUR, DEBT, and DREG2. The variables in Exhibits 4 and 5 that are classified as important under logit and probit with identical signs are MATURITY, LOANRATE, DINSUR, HOMEAGE, DNETWOR,

12 82 THE JOURNAL OF REAL ESTATE RESEARCH Exhibit 4 Summary of Statistical Models (dependent variable is 0 for L/V.90 and 1 for L/V.90) Probit Logit without without MDA Regional Regional Variables F-statistic a Probit b Logit b Dummies b Dummies b Coefficients: Intercept MATURITY ***.047***.088***.043***.082*** LOANRATE ***.190***.335***.189***.332*** MONTHPAY ***.140*.264* DINSUR ***.344***.665***.339***.644*** HOMEAGE ***.004**.008** DNETWOR ***.565***.923***.539***.868*** DSTATUS DEBT 8.520*** INCOME ***.022***.040***.023***.041*** EMPLOYED ***.305***.573***.298***.547*** AGE ***.024***.042***.020***.036*** DLOC 7.778*** TBOND ***.444***.228***.414*** DREG ***.239**.442** DREG * DREG ***.591*** 1.008*** N Goodness of Fit: R c 68.2 c.728 Significance of Model: Log likelihood *** *** *** *** F 40.18*** Classifying Accuracy: 75.23% 76.11% 76.11% 75.47% 75.36% ***significant at the.01 level; **significant at the.05 level; *significant at the.10 level a These figures were generated using SAS. b These figures were generated using LIMDEP. 2 (log likelihood) c The pseudo-r 2 =. N + log likelihood INCOME, EMPLOYED, AGE, TBOND, DREG1, and DREG3. These results are further justification that the traditional L/V ratios combined with default insurance are working well to accurately signal and classify risk in mortgage bundles. According to probit and logit without regions, HOMEAGE and MONTHPAY are not significant in any of the results. This means that region variables are necessary to capture regional market conditions. Also, the significant MDA mortgage bundle in comparison to the significant bundles from probit and logit with regions is more inclusive. The probit and logit models produce almost all of the expected signs. The unexpected negative sign on age of the home (HOMEAGE) for the 80% loans and positive sign for VOLUME 11, NUMBER 1, 1996

13 BORROWER RISK SIGNALING 83 Exhibit 5 Summary of Statistical Models (dependent variable is 0 for L/V.95 and 1 for L/V.95) Probit Logit without without MDA Regional Regional Variables F-statistic a Probit b Logit b Dummies b Dummies b Coefficients: Intercept 1.768*** 3.065** 1.407* 2.752** MATURITY ***.062***.121***.056***.119*** LOANRATE ***.203***.337***.202***.338*** MONTHPAY *** DINSUR *** 1.475*** 2.806*** 1.422*** 2.746*** HOMEAGE ***.006***.010*** DNETWOR ***.508***.845***.479***.795*** DSTATUS 4.098** DEBT *** INCOME ***.022***.040***.023***.039*** EMPLOYED ***.362***.641***.344***.609*** AGE ***.022***.039***.019***.033*** DLOC *** *.297* TBOND ***.373***.187***.343*** DREG ***.293**.506** DREG *.281 DREG ***.598***.987*** N Goodness of Fit: R c 60.7 c.727 Significance of Model: Log likelihood *** *** *** *** F 40.54*** Classifying Accuracy: 77.09% 80.24% 80.36% 79.04% 79.44% ***significant at the.01 level; **significant at the.05 level; *significant at the.10 level a These figures were generated using SAS. b These figures were generated using LIMDEP. 2 (log likelihood) c The pseudo-r 2 =. N + log likelihood the number of adult wage earners in the household (EMPLOYED) could reflect an underlying structural change. Buyers may be using larger downpayments on older homes. As the number of wage earners per household increases, the risk of default may be increasing from a large mortgage. AGE of the borrower is highly significant in all models and shows a negative sign that could reflect a violation of the Equal Credit Opportunity Act. The sign indicates that older age is associated with less risk, but the variable should not be statistically significant at any level. Further research is needed to determine its role to the mortgage bundle. DLOC has a positive sign and is significant in all of the MDA models and two of the probit and logit models without regions. This means that the central city location still

14 84 THE JOURNAL OF REAL ESTATE RESEARCH contains high risk which could restrict the flow of mortgage funds to an area of high need and demand. A second hypothesis is that the classification accuracy of MDA, probit, and logit is identical, making each of them appropriate tools of analysis when using a large sample. We find that the choice of statistical models will cause a significant difference between the results for MDA and those using probit and logit. A great deal of similarity exists between the estimates from probit and logit analysis. The results shown in Exhibits 3, 4 and 5 are similar to those found by Ingram and Frazier (1982) in that the three models show small differences in classifying accuracy, but substantial differences in the accuracy and significance of the individual variables. Obviously, additional theoretical work is needed on the best tool of analysis to use with financial models that have qualitative dependent variables and a large dataset, as the choice of model will determine the results. Eisenbeis and Altman (1978) and Karson and Martell (1980) correctly outlined the problems of assessing the importance of individual variables in MDA applications in financial analysis. Exhibits 3, 4 and 5 show that variables such as monthly payment (MONTHPAY), DEBT, and location (DLOC) are highly significant in MDA, but are not significant at all or significant at 10% in either probit or logit analysis. The characteristics of the mortgage bundles vary significantly among the five models tested. In particular, note the following points: All five models are significant at the.01 level for each loan-to-value ratio. The classifying accuracy of probit and logit, when using regional dummy variables, is better than MDA, but not by a substantial amount. The classifying accuracy of probit and logit with regions is higher than if the regions are omitted, but only by a small amount. The significance of the independent variables varies among the five classifying models, but is the largest between MDA and the other four. Our results show the diversity in the significance of the individual variables between MDA and the other models. MONTHPAY, DEBT and location (DLOC), are significant in MDA, but are not significant or significiant only at the 10% level in probit and logit. MDA is more sensitive as it includes more variables. Notes 1 The loan-to-price ratio was used as a proxy for the loan-to-value ratio in this paper as the loan amount and purchase price were included in the survey. The amount of the first mortgage was divided by the gross reported price. 2 The concepts of prejudicial and non-prejudicial discrimination were used by Peterson (1981) in his description of examples that were used in congressional testimony to support the passage of the Equal Credit Opportunity Act of An 80%, 90%, or 95% loan-to-value ratio has become the self-selection dividing line between high-risk and low-risk loans that is used by virtually all regulatory agencies and secondary market purchasers such as Fannie Mae and Freddie Mac and other investors that follow their lead. It is used by lenders who want to portfolio their loans and not sell into the secondary market as it has become a universal policy that is easily understood and enforced. Further, an L/V ratio has been made a part of state law in those states that have made a legal requirement that a private mortgage insurer may not sell a default policy of more than 20% of the loan amount. VOLUME 11, NUMBER 1, 1996

15 BORROWER RISK SIGNALING 85 4 The default coverage to the lender is not the same among PMI, FHA insurance, and the VA guarantee. PMI covers only the portion of the 20% requirement that is not paid in cash as a down payment by the borrower. Hence, it gradually expires as the loan is repaid. FHA insurance covers the whole loan approved by the FHA-approved lender. The VA guarantee covers only the top part of the loan up to a maximum of the veteran s guarantee entitlement. This study lumps them together as the lender will view all of these indifferently relative to default risk, ceteris paribus. 5 Discrimination studies historically examine the application characteristics of the rejected applicants compared to those revealed by the accepted applicants (see Black, Schweitzer and Mandell, 1978; Ingram and Frazier, 1982). This study classifies mortgage terms approved once the lender has self-selected the desired bundle similar to Shear and Yezer (1983) in their study of applicants who selected FHA loans. Although the Black, Schweitzer and Mandell (1978) analysis of bank loans used a probit model of loans that had been rejected and accepted, the results are very close to those on accepted loans only as the number of rejected loans was less than 10% of the total sample. 6 This variable is actually continuous but becomes discrete when the borrower selects a loan size by announcing the magnitude of the downpayment. 7 The effective interest rate was used as it approximates the lender s return. Another alternative is to include both the nominal mortgage rate and total loan costs in the model to observe their interaction. This analysis used the effective rate as the lender is more likely to offer an effective rate in combination with mortgage terms that have been adjusted for specific risks. References Aldrich, J. and F. Nelson, Linear Probability, Logit, and Probit Models, Beverly Hills, Calif.: Sage Publications, Berkson, J., Why I Prefer Logits to Probits, Biometrika, April 1950, Bester, H., Screening vs. Rationing in Credit Markets with Imperfect Information, American Economic Review, September 1985, 75, Black, H., R. L. Schweitzer and L. Mandell, Discrimination in Mortgage Lending, American Economic Review, May 1978, 68, Campbell, T. and J. Dietrich, The Determinants of Default on Insured Conventional Residential Mortgage Loans, Journal of Finance, December 1983, 38, Canner, G., S. Gabriel and J. Woolley, Race, Default Risk and Mortgage Lending: A Study of the FHA and Conventional Loan Markets, Southern Economic Journal, July 1991, 58, Chan, Y. and G. Kanatas, Asymmetric Valuations and the Role of Collateral in Loan Agreements, Journal of Money, Credit, and Banking, February 1985, 17, Doyle, P., The Application of Probit, Logit, and Tobit in Marketing: A Review, Journal of Business Research, September 1977, 5, Eisenbeis, R. and E. Altman, Financial Application of Discriminant Analysis: A Clarification, Journal of Financial and Quantitative Analysis, March 1978, 13, Hair, J., R. Anderson and R. Tatham, Multivariate Data Analysis with Readings, New York: Macmillan, second edition 1987, ch. 3. Ingram, J. and E. Frazier, Alternative Multivariate Tests in Limited Dependent Variable Models: An Empirical Assessment, Journal of Financial and Quantitative Analysis, June 1982, 17, Jameson, M., J. Shilling and C. Sirmans, Regional Variation of Mortgage Yields and Simultaneity Bias, Journal of Financial Research, Fall 1990, 13, Jud, G. D. and D. R. Epley, Regional Differences in Mortgage Rates: An Updated Examination, Journal of Housing Economics, 1991, 1, Karson, M. and T. Martell, On the Interpretation of Individual Variables in Multiple Discriminant Analysis, Journal of Financial and Quantitative Analysis, March 1980, 15,

16 86 THE JOURNAL OF REAL ESTATE RESEARCH Milde, H. and J. Riley, Signalling in Credit Markets, Quarterly Journal of Economics, February 1987, 103, Ostas, J., Regional Differences in Mortgage Financing Costs: A Reexamination, Journal of Finance, December 1977, 32, Peterson, R., An Investigation of Sex Discrimination in Commercial Banks, Bell Journal of Economics, Autumn 1981, 12, Press, J. and S. Wilson, Choosing Between Logistic Regression and Discriminant Analysis, Journal of the American Statistical Association, December 1978, 73, Shear, W. and A. Yezer, An Indirect Test for Differential Treatment of Borrowers in Mortgage Markets, AREUEA Journal, Winter 1983, 10, Stiglitz, J. and A. Weiss, Credit Rationing in Markets with Imperfect Information, American Economic Review, June 1981, 71, Vandell, K. and T. Thibodeau, Estimation of Mortgage Defaults Using Disaggregate Loan History Data, AREUEA Journal, Fall 1985, 12, Williamson, S., Costly Monitoring, Financial Intermediation and Equilibrium Credit Rationing, Journal of Monetary Economics, September 1986, 20, This paper is a revised version of an earlier edition that was presented to the American Real Estate Society meetings in Santa Barbara, California, in April The authors have benefitted from comments by participants in the Housing Finance session. The results may not be quoted without permission from the authors. VOLUME 11, NUMBER 1, 1996