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Three essays in commercial mortgages Holmes, Cynthia 2005

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Three Essays in Commercial Mortgages by Cynthia Holmes  B . S c , M c G i l l University, 1989 M B A , Concordia University, 1995  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF D O C T O R OF PHILOSOPHY in T H E F A C U L T Y OF G R A D U A T E STUDIES (BUSINESS ADMINISTRATION)  The University of British Columbia April 2005  © Cynthia Holmes, 2005  ABSTRACT  This dissertation consists of three essays on the topic of commercial mortgages. The first paper contributes to the commercial mortgage literature and the multiple factor asset-pricing literature by creating a model for commercial mortgage returns. The result of an initial analysis using the five Fama and French (1993) factors is that the sensitivities of commercial mortgage returns and corporate bond returns to all factors are statistically indistinguishable.  However, further analysis was  performed using factors associated with real estate returns, and the result is that unlike corporate bonds, commercial mortgage returns are sensitive to the factor that measures growth in personal consumption.  In the second paper, I investigate the two potential outcomes that can eventually arise when a commercial mortgage borrower fails to make a scheduled payment. Either the borrower reinstates the loan and resumes payment or the lender forecloses on the property. The following question arises: under which situation does each outcome occ.ur? I investigate this using a game-theoretic model and multinomial logit empirical tests on a disaggregate dataset. M y key finding is that the outcome is based on the relative values of variables that include the borrower's equity in the secured property and the rate of property appreciation. Empirical tests confirm that the characteristics of real estate loans across delinquency outcomes are distinguishable.  The third paper investigates the role of commercial mortgage guarantees in default. Childs, Ott and Riddiough (1996) use an options-based theoretical model to show that recourse should reduce the likelihood of default. This paper tests that prediction empirically using a database from a Canadian lender. The advantage of using a Canadian dataset is the prevalence of recourse lending not seen in the U.S. I find a negative relationship between default and the presence of a guarantee, supporting the Childs, Ott and Riddiough (1996) prediction.  ii  T A B L E OF CONTENTS  Abstract  ii  Table of Contents  iii  List of Tables  iv  List of Figures  vi  Acknowledgements Chapter 1  A Multiple Factor Asset Pricing Model for Commercial Mortgages  Chapter 2  Commercial Mortgage Delinquency, Foreclosure and  Chapter 3 Bibliography  vii 1  Reinstatement: A n Empirical Investigation  35  Commercial Mortgage Guarantees  94 125  in  LIST OF T A B L E S  1. List of factors  22  2. Descriptive statistics  23  3. Correlations  24  4. Estimation results  25  5. Test for equality of coefficients  26  6a. Estimation results for stock portfolios (Fama-French specification)  27  6b. Estimation results for stock portfolios (Ling Naranjo specification)  28  6c. Estimation results for stock portfolios (six factor specification)  29  7. Estimation results for bond series  30  8. Estimation results for unsmoothed real estate series  31  9. Estimation results for REITs for additional timelines  32  10. Estimation results for credit losses for commercial mortgages  33  11. Portfolio allocations  34  12. Regional and property type distributions across outcomes  82  13. Loan outcome by loan-to-value ratio  83  14. Descriptive statistics  84  15. Correlations  85  16. Results of logit estimations (foreclosure)  86  17. Results of logit estimations (delinquency)  87  18. Results of logit estimations (reinstatement)  88  19. Results of multinomial logit estimations (all loans)  89  20. Results of multinomial logit estimations (all delinquent loans only)  90  21. Predict foreclosed loans from all delinquent loans  91  iv  LIST OF T A B L E S Continued  22. Predict reinstated loans from all delinquent loans  92  23. Results of probit models with selection  93  24. Population by metropolitan area, 1996  114  25. Descriptive statistics relating to guarantee  115  26. Model to predict the presence of a guarantee  116  27. Model for the contract rate  117  28. Descriptive statistics relating to default  118  29. Model to predict default (30-days delinquent)  119  30. Model to predict default (90-days delinquent)  120  31. Model to predict default (foreclosure)  121  32. Multinomial logit model - role of guarantee across default definitions  122  33. Effect of guarantees by region  123  34. Probit model by region  124  v  LIST OF FIGURES  1. Commercial Mortgage Returns and B A A Corporate Bonds  20  2. Smoothed and Unsmoothed Appraised Real Estate Return Series  21  3. Game Tree  71  4. Single Period Typical case for P > M  72  5. Single Period Typical case for P < M  73  6. Multiple Periods  74  7. Multiple Periods Typical case P < M l + M 2 and M l < M 2  75  8. Multiple Periods Typical case P < M l + M 2 and M l > M 2  76  9. Multiple Periods Typical case P > M l + M 2  77  10. Number of loans with their first delinquency by month  78  11. Number and percentage of delinquent loans  79  12. Number of new loans / average contract rate on new loans  80  13. Portfolio rate and market rate  81  vi  ACKNOWLEDGEMENTS  I am very grateful to my research supervisor, Tsur Somerville and my committee members, Adlai Fisher and Stan Hamilton, for their advice and comments. I thank Kenneth French for making his portfolio returns and factors available to all researchers on his data library website, Yuming Fu for providing de-lagged N C R E I F returns, an anonymous lender who allowed me access to their complete loan database, and Michael Giliberto for supplying the values of the Giliberto-Levy Commercial Mortgage Return Index.  In addition, funding from the Real Estate Research Institute is gratefully acknowledged. Thank you to audiences and discussants at the 2003 RERI Conference, 2003 A R E U E A Annual Conference, 2005 A R E U E A Annual Conference, University of British Columbia and Florida State University for helpful feedback and suggestions. Thank you, Peter. Any errors or omissions are mine.  vu  CHAPTER 1 A Multiple Factor Asset Pricing Model for Commercial Mortgages  Introduction  Commercial mortgages are a large asset class. The size of the U.S. market was about $1.2 trillion at 1  the end of 2000, about a quarter of the size of the market for corporate bonds. But despite the large size of the market, the size of the body of academic literature about commercial mortgages is small. This is most likely due to the difficulty in obtaining access to data , since most commercial mortgages 2  are held by the originating lender and are not traded on any secondary market. However, as the secondary market grows through the issuance of commercial mortgage backed securities, so does the need for research that addresses questions about this asset class . 3  Commercial mortgages have term structure risk, like corporate bonds. But while the source of cash flow to service corporate bonds is from the general operation of the firm, the source of cash flow for commercial mortgages is the rental income of the specific property secured by the mortgage. Therefore, the structure of default risk is different. This is an important factor that distinguishes the two asset classes. In addition, commercial mortgages are less liquid and less divisible than corporate bonds, and have a different payment structure. Commercial mortgages typically have amortizing payments of interest and principal, while corporate bonds typically have only interest coupons. In this paper, I examine how the differences in the asset classes are manifested in the returns using multiple factor asset pricing models.  Federal Reserve Board, Flow of Funds Accounts of the United States, September 18, 2001. In this paper, I overcome this problem by using an index created by Giliberto-Levy Inc. Further details are in the data description in section 4. The amount of CMBS issued grew from less than $10 billion in 1990 to over $90 billion in 2001. (Source: John B. Levy, The Ground Floor, Barron's, January 1991 and January 2001). 1  2  3  1  The development and testing of asset pricing models is one of the central research areas in finance dating back to the 1960s with the work of Sharpe (1964) and Lintner (1965) on the capital asset pricing model. But most of research attention is turned to stock market returns, with little attention to bonds and real estate, and none at all on commercial mortgages.  In this paper, I test the five-factor asset-pricing model of Fama and French (1993) on a broad set of assets that includes stocks, bonds, real estate and commercial mortgages. This allows me to compare 4  the sensitivity of different assets to the factors. The result is that the Fama and French five factors describe stock, real estate investment trust (REIT), bond and commercial mortgage returns. In fact, the sensitivity of bonds and commercial mortgages to each of the five factors is statistically indistinguishable. That specification, however, does not include the factor that measures growth in personal consumption.  The second specification, developed in the real estate literature by Ling and Naranjo (1997), describes whole, appraised real estate returns and includes the consumption factor. There is a strong theoretical justification for including consumption as a factor to describe asset returns dating back to the formulation of the consumption capital asset pricing model of Breeden (1979). But the empirical evidence linking stock and bond returns to consumption has been mixed.  5  The empirical test based on a multiple factor model from the real estate literature demonstrates that commercial mortgage returns are sensitive to the factor that measures growth in personal  Real estate returns are measured two ways in this paper. The first is an index of real estate investment trusts (REIT) and the second is based on appraisals of whole real estate. More detail is in the data description in section 4. For example, Mankiw and Shapiro (1986) find that the CAPM performs better than a consumption-based model, while Breeden, Gibbons and Litzenberger (1989) find that the performance of the CAPM and a consumption-based model are similar. More recently, Cochrane (1996) finds that the CAPM outperforms a consumption model and Lettau and Ludvigson (2001) have shown that a conditional consumption CAPM works just as well as the Fama-French three-factor model in explaining stock returns. 4  5  2  consumption, while the stock and bond returns are not. This finding is one of the key contributions of this paper, because it distinguishes the underlying factors driving commercial mortgages and corporate bonds. This finding justifies the examination of commercial mortgages as an asset class distinct from corporate bonds, because it shows that the returns have different characteristics. And in particular, the characteristic distinguishing commercial mortgages from corporate bonds is the same one that links commercial mortgages and appraised real estate, since appraised real estate is also sensitive to the factor growth in personal consumption.  Based on the results from the first two estimations, I create a third specification that consists of the five Fama and French factors along with the consumption factor. The consumption factor is still significant for commercial mortgages and insignificant for corporate bonds. In fact, this six-factor specification is the best model (in terms of adjusted R and the root mean squared error) for 2  commercial mortgages.  The main conclusions are that commercial mortgage returns and whole real estate returns are sensitive to the factor that measures the growth in personal consumption, while stock returns and REIT returns are not. To confirm this finding, several additional estimations are performed with the following modifications to the return series:  whole real estate returns were "unsmoothed" using  several different techniques, REIT returns were divided to sub-periods, and the default losses for commercial mortgages were isolated. These changes had no effect on the key conclusions.  Given the evidence in the academic literature that whole real estate returns are sensitive to the consumption factor, the commercial mortgage results are not surprising. If changes in the growth of personal consumption affect real estate, then debt secured on real estate should also be affected. The key result is also interesting because it distinguishes commercial mortgage returns from corporate bond returns.  3  To demonstrate and reinforce this difference between the asset classes, the optimal allocations for a multiple asset portfolio that includes both corporate bonds and commercial mortgages is performed. For example, i f the potential assets are corporate bonds, commercial mortgages, T-bills and stocks, commercial mortgages will have a positive allocation for moderate risk levels. This fact further distinguishes commercial mortgages as a distinct asset class from corporate bonds.  Commercial Mortgages  Commercial mortgages are distinguished from residential mortgages by the nature of the underlying security as well as regulatory and institutional factors.  Commercial mortgages are secured by a  specific commercial property, such as an office building, retail property or apartment complex, as opposed to a residential mortgage which is secured by a single-family home. There is no mortgage insurer for commercial mortgages as there is for residential mortgages, so default risk falls to the lender, not any government agencies. As a consequence of this, the maximum loan-to-value ratios for commercial mortgages are usually lower than those for residential mortgages. There is less interest rate risk for investors due to the presence (usually) of a yield maintenance prepayment penalty. So the incidence of prepayment is lower for commercial mortgages relative to residential mortgages. (See Clauretie and Sirmans (1999), page 399, for a textbook description of the characteristics of commercial mortgages.)  Commercial mortgages and corporate bonds are similar in that they both have term structure risk and default risk. But the default risk for mortgages is based on the value of the underlying real estate asset, while for corporate bonds, it is based on the value of the firm. Another key difference between commercial mortgages and corporate bond investments is that commercial mortgages are less liquid and less divisible.  4  Commercial mortgages require specialized knowledge by investors, who perform underwriting based on property appraisals of the real estate that forms the collateral. Along with the lack of liquidity and the indivisibility, this implies that the potential investor pool is largely limited to major financial institutions. The cash flow structure of a commercial mortgage is comparable to a corporate bond in that they are usually fixed-rate, although for commercial mortgages, interest and principal is paid on an amortizing basis.  Literature Review  Ciochetti and Vandell (1999) investigate the characteristics of the returns from investment in commercial mortgage loans. Ciochetti and Vandell's data comes from a single insurance firm, which they use to construct a return series for the period 1974 to 1990. They compare the mean and variance of their return series with those of various stock and bond indices, and find that commercial mortgages are quite similar to bonds. The returns on commercial mortgages were found to have an important positive correlation of 0.95 with bond series, a small positive correlation of 0.30 with stocks and a small negative correlation of -0.27 with real estate series. Other work investigating the returns of commercial mortgages includes Snyderman (1990) and Giliberto (1996), both of whom create a performance index based on American Council of Life Insurance submissions by life insurers who are commercial mortgage lenders.  While my paper contributes to the small literature on commercial mortgage returns, it also contributes to the asset pricing literature by applying the existing multiple factor models to a new asset return series.  5  A n early paper about the empirical testing of multiple factor asset-pricing models is Chen, Roll and Ross (1986).  Motivated by the Arbitrage Pricing Theory of Ross (1976), they identify a set of  macroeconomic factors and create a model to describe stock market returns. The five factors that are identified and tested are the term spread between long and short interest rates, the default spread between high and low risk bonds, growth in industrial production, change in expected inflation and unexpected inflation. In addition, Chen, Roll and Ross use a value-weighted stock market index.  Fama and French (1993) (FF) differ from Chen, Roll and Ross in two ways relevant to my work. First, they expand the set of asset returns to include corporate and government bonds, which I will expand further to include commercial mortgages and real estate. Second, they employ a time-series regression approach that originated with Black, Jensen and Scholes (1972).  The equation being  estimated is K  t, ~  r  r ft  = a, + X P F ik  kt  +e  (1)  u  where F , are various macroeconomic factors at time t and the dependent variable is an excess return k  (r is the return for asset / at time t and rf, is the risk-free rate of return at time r). it  FF designated three factors as stock market-related: an overall market factor, a factor related to firm size and a factor related to the ratio of book equity to market equity . Two factors were designated 6  bond market factors: the term spread and the default spread.  Several papers have used the multiple factor model framework to examine real estate returns (although none have yet considered commercial mortgage returns). Chan, Hendershott and Sanders (1990) analyze real estate returns using the method and factors from by Chen, Roll and Ross. A difficulty in analyzing real estate is that there are two potential sources of return information, REIT 6  See Table 1 for more detail about the factors.  6  returns and appraisal-based returns, neither which is believed to be a perfect measure of the true nature of real estate volatility, as discussed in Corgel and deRoos (1999) and others . Although Chan, 7  Hendershott and Sanders appreciate that REIT data may be "too" volatile, they prefer this to appraisal-based returns because they feel that REIT returns are more representative of transaction prices. Thirty-eight REITs are combined to create portfolios, and excess returns are used in the estimations. Their key finding is that REITs are consistently sensitive to the term spread and the default spread.  While Chan, Hendershott and Sanders use the factors and methods of Chen, Roll and Ross, Peterson and Hsieh (1997) use those of FF. Peterson and Hsieh explore REIT returns (both equity REITs and mortgage REITs) using the time-series approach and factors identified by FF. They found significant relationships between equity REIT returns and the market factors.  Ling and Naranjo (1997) use both REITs and appraisal-based returns to generate real-estate portfolios. They applied nonlinear seemingly unrelated regression techniques in their estimation and identified a set of economic factors relevant to real estate. Their factors are the real t-bill return, the growth in personal consumption and unexpected inflation, along with the term spread.  While there is evidence that the consumption factor is related to real estate returns, researchers (for example, Cochrane (1996), Mankiw and Shapiro (1989)) have failed to find strong empirical evidence that the consumption factor plays an important role in describing stock and bond returns. This raises the important question of whether commercial mortgage returns, which are positively correlated to corporate bond returns, but are linked to appraised real estate (since it is the underlying security for  The explanation for this phenomenon, where the volatility of real estate returns is understated, is usually attributed to the systematic behavior of property appraisers during the valuation process. Several methods have been developed to adjust the returns to account for this smoothing process. Appendix 1 provides details about how the appraisal-based returns used in this paper were unsmoothed. 7  7  the commercial mortgage cash flow), will be sensitive to the consumption factor. The finding is that commercial mortgage returns are sensitive to the bond factors and to the consumption factor.  Data  In order to test the multiple factor asset pricing models, I use an index of commercial mortgage returns prepared by Giliberto-Levy Inc (GLI) . This index is the only commercial mortgage index in 8  existence, and is widely used as a benchmark by industry practitioners.  The index is created by constructing a model portfolio that mimics the holdings of life insurance companies that hold commercial mortgages. Using data provided by the life insurers to the American Council of Life Insurers (ACLI), the model portfolio has mortgages added to it every quarter based 9  on the characteristics of the new loans done by the life insurers. Loans that terminate, either through maturation or foreclosure, are removed from the index. The cash flows in quarter t, CF,, are the interest and principal payments plus recoveries from foreclosures. The market value in quarter t, MV,, is the present value of all future contracted cash flows, discounted using the current market mortgage rate. The returns for quarter t, r,, are then:  MV -MV _ CF t  '"  t  ]+  t  MV _ (  ( 2 ) X  This return calculation in (2) is analogous to the one used for bond indices. However, for bonds, MV, is usually based on the price observed in the market, and CF, are the coupon payments. The specific instruments that are included in bond indices are selected based on criteria such as the size and the rating. Periodically, the set of bonds included in the index are re-determined.  This implies, for  Giliberto (1997) and www.jblevyco.com/giliberto.html describe the methods of constructing the index in detail. Giliberto (1997) estimates that the included lenders represent more than two-thirds of the total industry commercial mortgage assets. 8  9  8  example, that any A A A bonds with ratings downgrades will be removed from the A A A index. So a key difference between the ratings-based bond indices used in this paper and the G L I is that the GLI bears the costs of default and foreclosure, while the bond indices may not i f there are ratings downgrades. But this difference is consistent with the experience of investors. Since corporate bonds are liquid, then i f there is a ratings downgrade, then the investor can divest of his holdings. Since commercial mortgages are not liquid, when a loan goes into default, the investor must bear the losses resulting from foreclosure.  One limitation of the GLI index is that the returns are only available quarterly, as opposed to stock and bond return data that is observed more frequently. For this reason, all the return series used in this paper will be on a quarterly basis.  The G L I incorporates several (reasonable) assumptions, making it an imperfect proxy for the true commercial mortgage returns. First, only fixed rate and fixed term mortgages are included in this index , there are no development loans and all loans are assumed to be non-recourse and closed to 10  prepayment. In addition, assumptions are made about the lag between the commitment and funding dates, the amortization period length, the periodicity of payments (monthly) and credit losses.  The credit loss model used in the generation of the G L I warrants further explanation. A C L I data gives the proportion of the lenders' portfolio (based on book value) that is delinquent and that has been foreclosed. GLI allocates this percentage across its model portfolio based on an algorithm that takes into account the current loan-to-value ratio of each model loan. A range of loan to value ratios will exist in the model portfolio since as loans age, principal is repaid and the underlying real estate appreciates (or depreciates).  Once the algorithm has selected which of the model loans to make  This assumption excludes less than 10% of all the life insurer's submissions. Giliberto (1997) also reports that most lending done outside the life insurance industry is also based on afixed-rate,fixed-termstructure. 10  9  delinquent and which to foreclose upon, it generates a cash loss. Based on evidence from Ciochetti (1997), the G L I charges a loss equal to 30% of the loan's book value on average (with variation across property type) for foreclosed loans. For delinquent loans, the loss is assessed as 0.5% of the book value per month. This figure is based on evidence from Snyderman (1991).  To derive the excess returns, the return on a 1-month T-bill is deducted from the GLI. The resulting excess commercial mortgage series is plotted in Figure 1, against the excess returns on a BAA-rated, intermediate-term corporate bond. Note that the duration for the commercial mortgage series varies between 3.5 and 7.0 years (based on the true holdings of the A C L I submitting lenders), so it is comparable to an intermediate term bond in terms of duration.  The macroeconomic variables used in the multiple factor model estimation are summarized in Table 1. The factors correspond to the factors used by FF and Ling and Naranjo (1997). The size factor and the book equity to market equity factor were obtained from Kenneth French's online data library, along with the returns on 25 stock portfolios, sorted by size and book-to-market equity . Bond return 11  series were obtained through DataStream from Lehman Brothers. These 8 series include indices for different ratings classes of corporate bonds ( A A A , A A , A and B A A ) and for two maturity lengths, long and intermediate. The REIT return series is an index compiled by the National Association of Real Estate Trusts. These returns are based on the traded value of REIT units, not on the values of the properties held by the REIT. A n important consideration is that many of the REIT properties are held with a commercial mortgage, so the REIT returns are essentially levered. This is analogous to  " The French website elaborates on the construction of the 25 portfolios: "The portfolios, which are constructed at the end of each June, are the intersections of 5 portfolios formed on size (market equity) and 5 portfolios formed on the ratio of book equity to market equity. The size breakpoints for year t are the NYSE market equity quintiles at the end of June of t. Book-equity to market-equity for June of year t is the book equity for the lastfiscalyear end in t-1 divided by the market equity for December of t-1. The ratio book-equity to market-equity breakpoints are NYSE quintiles. The portfolios for July of year t to June of year t+1 include all NYSE, AMEX and NASDAQ stocks for which we have market equity data for December of t-1 and June of t, and positive book equity data for t-1."  10  stock market returns on firms that hold debt, and it is not possible to separate the returns for this effect.  The index for whole, appraised real estate is from the National Council of Real Estate  Investment Fiduciaries.  Table 2 lists the descriptive statistics (quarterly) for selected return series, unsmoothed real estate return series and all the factors. All return series shown are the excess form, where the one-month tbill rate (quarterly) has been subtracted from the raw returns. The highest quarterly excess return of 4.40% is for the stock portfolio shown, which is the 13 FF portfolio, which is of medium size and th  medium book equity to market equity. The lowest return of 0.47% is for the appraised real estate series.  Note that this series, being appraisal based, is smooth and autocorrelated.  Problems with the  measurement of real estate returns arise because of the nature of property appraisals. There is a behavioral aspect to the valuation that reduces variation, a process known as appraisal smoothing.  For this reason, real estate researchers have developed methods to recover unsmoothed returns. The most common method is to model the effects of prior observations on current returns as N  i=\ where r*, is the smooth return for time /, and r*,_,are lagged smooth returns. Further, if the error term is modeled as e, = r,w, where r, is the unsmoothed return and vv is a smoothing factor, then 1  w  11  What remains is to determine w and the lag structure. In this paper, two unsmoothing methods are applied.  In the first, called the variance method, vv is set so that the standard deviation of the  unsmoothed series is equal to one half of the standard deviation of stocks. In the second, called the mean method, w is set so that the mean of the unsmoothed series is equal to the mean of the smoothed series. Both methods are described in Fisher, Geltner and Webb (1994). In both the variance method and the mean method, the lag structure is an AR(1,4) with no constant.  W  The lag model is estimated only on the observed capital return, and the resulting unsmoothed capital return is added to the observed income return to generate the total unsmoothed return.  The result is that 6, = 0.5207 (p<0.01) and 6 = 0.4099 (p<0.01). The smoothing factor vv is 0.2416 4  for method 1 and 0.6937 for method 2.  Fu (2003) estimates the lagging error using a dynamic state-space model, and then removes it from the returns. His method takes into account the seasonality evident in appraisals. The unsmoothed NCREIF data used in my paper was obtained directly from the author of Fu (2003).  The descriptive statistics for the unsmoothed real estate return series are shown in Table 2, and graphs are in Figure 2.  The commercial mortgage returns are higher than the B A A corporate bond returns (0.98% versus 0.64%) but the standard deviation is also higher (3.32% versus 3.04%). Figure 1 plots the excess commercial mortgage and B A A corporate bond returns.  12  Table 3 shows the correlations across selected return series and factors.  Commercial mortgage  returns have the highest correlation with B A A corporate bond returns at 0.63 and the lowest correlation with appraised real estate at 0.08. It may be considered counter-intuitive that commercial mortgage returns and whole real estate have such a low correlation, because commercial mortgages are linked to the performance of real estate through the property securing the commercial mortgage debt. REITs and stocks have the highest correlation shown, at 0.76. This is consistent with the prior results in the real estate literature that identifies the shared characteristics of stock and REIT returns, for example Ling and Naranjo (1999).  Results  The testing of the multiple factor models is done using the time-series approach originated by Black, Jensen and Scholes and employed by FF, based on equation (1). This method is used to facilitate comparison to the FF results. The alternative method used by Chen, Roll and Ross (1986) and Ling and Naranjo (1997) is the two-stage cross-sectional approach originated by Fama and MacBeth (1972). In this method, the first stage is a series of rolling time-series regressions to generate a series of time-variant factor sensitivities. In the second stage, a regression is performed for every time period where the dependent variable is the returns across the portfolios and the independent variables are the coefficients from the first stage. The results from the second stage are the risk premiums, which do not vary across assets.  There are several reasons why this cross-sectional method is not appropriate for my study. First, I am not able to separate my single commercial mortgage return series into a set of portfolios due to data limitations. In any case, it is not logical to sort commercial mortgage returns on a size factor and a book-equity to market-equity factor since these factors have no meaning for commercial mortgages. This is the reason that FF used the time-series method when examining bond returns. Second, since N  13  is only 83 (since the data is quarterly), there are simply not enough observations to create a meaningful set of rolling factor coefficients. Third, the purpose of my study is to compare a model for commercial mortgages against other assets, especially corporate bonds. The second stage results from a cross-sectional approach, the risk premiums, do not vary across assets, and so do not provide information to distinguish assets. For these reasons, the time-series method is preferable.  The results from the regressions of the excess returns of the selected return series on factor variables are in Table 4. Standard errors are adjusted based on the Huber-White method for robustness. Three specifications are shown, where the first one is based on the FF factors and the second on the LingNaranjo real estate factors. The third specification is the FF factors with the addition of the factor of growth in personal consumption.  In the first specification, where the FF factors are used, I confirm that the 3 factors, stock market return, size factor and book-to-market equity factor describe returns on the selected stock portfolio very well. A l l three factors are significant at 1% and the R is 88%. In addition, I confirm FF's 2  findings for corporate bonds, where the two factors, term spread and default spread are significant. REITs are also well described by the FF factors, but appraised real estate is not (R is only 5% and 2  only the term spread is significant).  Since commercial mortgages have similar coefficients to corporate bonds on all factors under this specification, a test is performed to determine whether the sensitivity of commercial mortgage returns and corporate bond returns are statistically different. A dummy variable is created and is set to 0 i f the returns are corporate bonds and 1 i f commercial mortgages. To create a fully interacted model, each factor is multiplied by this dummy variable. The estimation is performed with the returns (both commercial mortgage and corporate bonds) on the factors and the dummy-interacted factors. The coefficients on the factors will be identical to those obtained for corporate bonds alone, and the  14  coefficients on the dummy-interacted factors will be equal to the difference between the corporate bond sensitivity and the commercial mortgage sensitivity.  So i f the coefficient on the dummy-  interacted factor is significant, then the sensitivity of commercial mortgages and corporate bonds to that factor is significantly different. Under the FF specification, none of the dummy-interacted terms are significant, indicating that the sensitivities of commercial mortgages and corporate bonds are indistinguishable. At this point, one is tempted to conclude that commercial mortgages are simply corporate bonds renamed, and that the real estate underlying the commercial mortgages plays no role in the movement of returns. In order to investigate this, I test commercial mortgage returns against a set of factors identified by Ling and Naranjo (1997) to explain real estate.  Using the real estate factors improves the performance of the model for appraised real estate as shown in the middle panel of Table 4. The new factors are the real T-bill return, unexpected inflation and growth in consumption, while the term spread is retained from the FF set of factors. But while this specification works better for appraised real estate, it is not as good at describing corporate bond, REIT or stock returns. Interestingly, this set of factors is approximately equally good at describing commercial mortgage returns, with the adjusted R of 74% for both specifications. The factors that 2  are significant for commercial mortgages in this second specification are the term spread and the growth in personal consumption.  The final specification is the five FF factors plus the growth in personal consumption. The result is that for commercial mortgages, the consumption factor is still significant, and the term spread, default spread and stock market return from the FF specification remain significant. The new, six-factor specification increases the adjusted R from 74% to 76% and improves the root mean squared error 2  from 1.643% to 1.575% for commercial mortgages. In addition, the tests for equality across coefficients in Table 5 show that the sensitivity of commercial mortgages and corporate bonds to the factor growth in personal consumption is significantly different.  15  In the six factor specification, the term spread is significant for 4 of the 5 series, while the default spread, the stock market return, the size factor and the book-to-market equity factor are significant for 3 series. The growth in consumption is significant for only 2 series, commercial mortgages and appraised real estate.  Table 4 reports the results across only selected return series. For stocks, the medium size and medium book-to-market equity portfolio are shown. The results of the estimations across all 25 size and book-equity to market-equity sorted portfolios are shown in Table 6a, 6b and 6c. Similarly, Table 7 has the estimation results for the 8 bond series. The key findings are unchanged. Stocks are consistently sensitive to the FF stock-market factors and bonds are consistently sensitive to the FF bond market factors.  The key findings of this paper are that commercial mortgage returns, like whole real estate returns, are sensitive to the consumption factor, and that stocks, bonds and REITs are not. To confirm these findings, three additional studies are performed.  First, the appraised real estate series was unsmoothed three different ways as described in Appendix 1. Numerous academic studies, such as Fu (2003), have confirmed that there are issues with the measurement of whole real estate returns. In Table 8, the results show that all the unsmoothed series are still sensitive to the consumption factor.  Second, since REIT volumes have increased dramatically during the 1980-2000 timeframe, estimations were repeated for more recent sub-periods. Table 9 shows the results for three timeframes: the original 1980-2000 and the 1986-2000 and 1992-2000 sub-periods. REIT returns were not found to be sensitive to consumption at the 5% level of significance. However, in the six-  16  factor specification, the coefficients on the consumption factor were marginally negative and significant. This is not the predicted sign, since whole real estate returns and commercial mortgage returns are positively related to the consumption factor.  Third, the commercial mortgage returns are modified to exclude the credit losses, to determine whether the sensitivity to the consumption factor is maintained. The result, presented in Table 10, is that commercial mortgage returns excluding credit losses are also sensitive to the consumption factor. In addition, the credit loss series itself (which has a negative mean) has a positive and significant coefficient on the consumption factor.  This paper demonstrates that commercial mortgages are distinct from corporate bonds since their return series are driven by different macroeconomic factors. In addition, optimal portfolio allocation calculations reinforce the fact that commercial mortgages are distinct from corporate bonds. Since commercial mortgages have a favorable risk-return relationship, positive allocations occur at moderate risk levels. Table 11 shows the results of optimal portfolio allocation calculations.  The mean-variance efficient frontier is the set of portfolio allocations that minimize variance at all return levels. The return of a portfolio is calculated as a weighted average of the asset returns, and the portfolio risk is determined based on the weights, the standard deviation of each asset, and the correlations between the assets. Five mean-variance efficient portfolios are displayed in Table 11 for each set of possible assets. The portfolio labeled number 1 has the maximum return at the lowest possible risk level. Number 5 has the maximum return at the highest possible risk level. Portfolios number 2, 3 and 4 have the maximum return at equally-sized risk level intervals. These moderate risk level portfolios consistently have positive allocations to commercial mortgages.  17  When commercial mortgages are added to a portfolio that includes BAA-rated intermediate corporate bonds and t-bills, positive allocations to commercial mortgages are observed at all risk levels. Note that other corporate bonds were included in the choice set, but had a 0% allocation. At the lowest risk levels, a relatively larger share of the allocation is to treasury bills, with relatively smaller allocations to commercial mortgages. As the risk level increases, the allocation to commercial mortgages increases, to a 100% allocation at the highest risk level. With this asset choice set, commercial mortgages have essentially displaced corporate bonds, since commercial mortgages have a more favorable risk-return relationship and are highly correlated with corporate bonds.  When the set of potential assets is expanded to include stocks, commercial mortgages, corporate bonds and treasury bills, the allocation to stocks is positive at all levels, and increases with the risk level. The Treasury bill allocation decreases as risk increases, and the corporate bond allocation is never higher than 1%. Commercial mortgages have a positive allocation at moderate risk levels, reaching 50.8% at the medium level. At the highest risk level, stocks dominate with 100% of the allocation, which displaces any allocation to commercial mortgages.  The final set of potential assets also includes REITS, but the results are largely unchanged. Since REITS are highly correlated with stocks, only a small proportion of the allocation is directed into REITs. Commercial mortgages retain their positive allocation for moderate risk levels, attaining 49.9% at the medium level.  The general conclusion from these allocation calculations is that commercial mortgages have a favorable risk/return relationship profile and play an important role in a multiple asset portfolio. Commercial mortgage should be considered as distinct from corporate bonds, based on the different structure of their returns, and based on the results of the optimal portfolio optimization calculations.  18  Conclusion  This paper contributes to the commercial mortgage literature and the asset pricing literature by creating a multiple factor model to price commercial mortgages. Commercial mortgage returns are measured using the ACLI-based Giliberto-Levy Index. In order to compare results across different types of assets, I also include 25 size and book-equity to market-equity ratio sorted stock portfolios, 8 corporate bond return series and 4 real estate return series. The real estate series are REITs, appraised real estate, appraised real estate unsmoothed using the variance method and appraised real estate unsmoothed using the mean method.  Three specifications of a multiple factor asset-pricing model are tested using the time-series method. The first is the Fama and French (1993) specification, which includes the term, spread, the default spread, the size factor and the book-equity to market-equity factor.  The main finding is that  commercial mortgage returns and corporate bond returns are identically sensitive to these factors.  Using a specification derived from the real estate literature, I find that commercial mortgages are also sensitive to the factor that measures growth in personal consumption. When a six-factor specification is tested, using the five FF factors with the growth in personal consumption factor, I find that commercial mortgages are still sensitive to the consumption factor.  Commercial mortgages and  corporate bonds are not identically sensitive to the consumption factor.  The implication is that while commercial mortgages are highly correlated to corporate bonds and share the same risk factors, there is more to commercial mortgages. The sensitivity to the growth in personal consumption is a characteristic shared with appraised real estate, which underlies commercial mortgages as security. In addition, commercial mortgages play an important role in a mixed asset portfolio, due to their favorable risk-return tradeoff and the low correlation with stocks.  19  Figure 1 Commercial Mortgage Returns and BAA Corporate Bonds Quarterly 1980 Q2 to 2000 Q4  <b  N  <fc> #  &  4>  <§>  <£> cfi  BAA Corp Bonds  o>  &  eft  o>  Comm Mtg  eft  eft  eft  eft  c£  Figure 2 - Smoothed and Unsmoothed Appraised Real Estate Return Series Raw Appraised Real Estate  Unsmoothed Real Estate (Var Method)  Unsmoothed Real Estate (Mean Method)  Unsmoothed Real Estate (Fu Method)  21  Table 1 - List of Factors Variable  Description  Source  Stock market return  Total return on the S&P 500 composite index (dividends reinvested), converted to the quarterly return  Ibbotson & Associates SBBI Yearbook 2001  Term spread  The difference between the long-term government bond return and the onemonth treasury bill ratefromthe previous month  Calculated using data from Ibbotson & Associates SBBI Yearbook 2001  Default spread  The difference between the long-term corporate bond return and the long-term government bond return  Calculated using data from Ibbotson & Associates SBBI Yearbook 2001  Unexpected inflation  The residualsfroman inflation model with 3 lags, quarter dummies and  Constructed based on inflation data from Ibbotson & Associates SBBI Yearbook 2001  ARCH(2), where inflation is the percentage change in the Consumer Price Index  2  Consumption  Growth in personal consumption expenditures (consumer spending and retail) (constant 1985 dollars)  Bureau of Economic Analysis  Real T-bill  The difference between the one-month treasury bill return and inflation, where inflation is the percentage change in the Consumer Price Index  Constructed based on inflation data and treasury bill returns from Ibbotson & Associates SBBI Yearbook 2001  Firm size factor  The difference in the excess returns between small-stock portfolios and bigstock portfolios  Kenneth French's data library: http://mba.tuck.dVtmouth.edu/pages/faculty/ken.french/dat a_library.html  Book equity to market equity  The difference in the excess returns between high book equity to market equity portfolios and low book equity to market equity portfolios  Kenneth French's data library: http://mba.tuck. (lartmouth.edu/pages/faculty/ken.french/dat a_library.html  1  Since the commercial mortgage return series was only available quarterly, all data series were convertedfrommonthly to quarterly. The exception is the factor growth in consumption which was obtained as a quarterly series.  2  The model for inflation is It = -0.003*** + 0.476*** Li + 0.089 L + 0.207*** L + 0.009*** Q l + 0.004*** Q2 + 0.005*** Q3 + (? 2  varfo) = 5.00 x 10 ** + 1.075*** e 6  to to  2  3  - 0.080** e . 2  M  t 2  where I is inflation in quarter t, Q l to Q3 are quarter dummies and *** ** * represent significance at the 1%, 5%, 10% level, ;  ;  Table 2 - Descriptive Statistics Min  Max  Sharpe  4.61 1.92 2.69 2.05 2.97  -22.14% -7.03% -12.25% -17.66% -5.51%  20.63% 10.27% 9.59% 19.05% 3.32%  0.506 0.211 0.296 0.225 0.326  3.94% 1.57% 2.89%  10.30 3.03 0.92  -10.18% -4.32% -7.68%  14.32% 4.36% 8.89%  1.131 0.333 0.101  5.70% 1.69% 7.56% 5.59% 7.05% 0.61% 0.49% 0.65%  1.59 (0.59) 2.72 0.70 0.99 10.51 (0.62) 11.48  -14.62% -7.78% -26.99% -11.16% -28.48% -0.54% -1.81% -2.30%  16.10% 3.24% 18.29% 19.56% 20.73% 2.34% 1.54% 2.06%  Mean  Std. Dev.  Return Series Stock portfolio (Medium size, medium book equity to market equity) BAA-rated Corporate Bond (Intermediate term) Commercial Mortgage Giliberto-Levy Return Index REIT Appraised real estate  4.40% 0.64% 0.98% 1.50% 0.47%  8.70% 3.04% 3.32% 6.68% 1.45%  Unsmoothed Real Estate Series Variance-matching method Mean-matching method Fu de-lagging method  4.46% 0.52% 0.29%  1.00% -0.11% 2.26% 0.43% 0.76% 0.70% -0.03% 0.82%  Variable  Factors Term spread Default spread Stock market return Firm size Book-to-market equity Real T-bill Unexpected inflation Growth in consumption  t-test  Notes: 1. A l l returns series are quarterly, excess (the one month Tbill rate has been subtracted) and log form. 2. A l l factors are quarterly and log form. 2. The t-test is based on the hypothesis that the mean return=0. The formula for the test is r divided by the square root of the variance divided by N , where N is the number of observations. 3. The Sharpe ratio is the mean excess return divided by the standard deviation and can be interpreted as a reward for volatility.  Table 3 - Correlations  Return Series  Stock portfolio BAA-rated Corporate (Medium size, medium Bond (Intermediate term) equity)  Commercial Mortgage  Real estate (var method)  REIT  BAA-rated Corporate Bond (Intermediate term)  0.38  1.00  Commercial Mortgage  0.42  0.63  1.00  REIT  0.76  0.44  0.46  1.00  Real estate (var method)  0.04  (0.22)  0.00  0.01  1.00  Real estate (Fu method)  0.15  (0.12)  0.08  0.19  0.49  Term spread  Default spread  Stock market return  Firm size  Book-equity to market-equity  Real T-bill  Unexpected inflation  Factors  (0.62)  1.00  0:27  (0.03)  1.00  Firm size  (0.09)  0.15  0.35  Book-equity to market-equity  (0.08)  0.04  (0.52)  (0.23)  1.00  0.37  (0.16)  0.06  (0.12)  0.05  1.00  Unexpected inflation  (0.38)  0.19  (0.15)  (0.05)  (0.06)  (0.58)  1.00  Growth in consumption  (0.26)  0.24  (0.01)  0.19  0.03  (0.05)  0.07  Default spread Stock market return  Real T-bill  1.00 '  Table 4 - Estimation Results Fama-French Specification  R-squared  Adjusted R- Root meansquared squared error  Stock portfolio (medium size, medium equity)  88.1%  87.5%  3.046%  BAA-rated corporate bond (intermediate term)  49.3%  46.6%  2.106%  Commercial mortgage  75.4%  74.1%  1.643%  REIT  63.2%  61.3%  4.177%  5.4%  0.5%  5.440%  Appraised real estate  Ling-Naranjo Specification  R-squared  Adjusted R- Root meansquared squared error  Stock portfolio (medium size, medium equity)  10.6%  7.0%  8.314%  BAA-rated corporate bond (intermediate term)  32.3%  29.6%  2.352%  Commercial mortgage  74.9%  73.9%  1.657%  REIT  18.6%  15.4%  6.226%  Appraised real estate  21.3%  18.2%  1.317%  Six factor specification  R-squared  Adjusted R- Root meansquared squared error  Stock portfolio (medium size, medium equity)  88.2%  87.4%  3.056%  BAA-rated corporate bond (intermediate term)  50.0%  46.7%  2.105%  Commercial mortgage  77.7%  76.2%  1.575%  REIT  63.4%  60.9%  4.196%  Appraised real estate  24.9%  20.0%  1.314%  Default spread  Term spread 0.1432 * (1.77) 0.3996 " * (7.06) 0.5301 *** (8.64) 0.2843 *** (2.88) -0.0763 *** (3.00)  Term spread  Real Tbill  0.4559 * " (2.72) 0.2838 *** (5.04) 0.4916 * " (9.08) 0.4061 *** (3.07) -0.0117 (0.52)  Term spread 0.1351 (1.66) 0.3916 (6.77) 0.5462 (8.96) 0.2757 (2.80) -0.0551 (2.01)  -O.2082 (0.85) 0.6455 * " (4.49) 0.3997 " (2.30) -0.0132 (0.05) -0.1321 (1.50)  -1.0071 (0.68) 0.0125 (0.02) 0.1629 (0.33) -1.8397 (1.16) 0.3203 (1.31)  Default spread  "* *" "* "  •0.1929 (0.76) 0.6606 " * (4.51) 0.3694 ** (2.35) 0.0031 (0.01) -0.1723 * (1.92)  Stock market return 0.9021 * " (15.88) 0.0404 (1.31) 0.0536 " (2.23) 0.5290 * " (6.63) 0.0346 (1.39) Unexpected Inflation -2.3323 (1.00) -0.1374 (0.21) -0.6399 (1.11) -3.8766 " (2.06) -0.0469 (0.17) Stock market return 0.9023 * " (16.07) 0.0406 (1.30) 0.0533 " (2.03) 0.5292 *** (6.68) 0.0342 (1.39)  Size factor 0.7832 * " (11.91) 0.1322 " (2.60) 0.0657 (1.53) 0.5637 * " (5.72) -0.0243 (0.61) Growth in consumption 1.5077 (0.79) 0.0484 (0.08) 1.1501 " * (2.74) 0.8474 (0.53) 1.1418 " * (3.24)  Size factor 0.7913 * " (11.79) 0.1402 **' (2.79) 0.0496 (1.22) 0.5722 " * (5.58) -0.0456 (1.33)  Equity factor 0.4404 * " (5.94) 0.0608 * (1.76) 0.0152 (0.58) 0.4167 *** (4.55) 0.0108 (0.42)  Constant 0.0186 " * (4.86) 0.0008 (0.31) 0.0027 (1.30) -0.0023 (0.51) 0.0046 *** (2.74)  Constant 0.0287 (1.19) 0.0024 (0.33) -0.0078 * (1.70) 0.0132 (0.57) -0.0076 * (1.98)  Equity factor 0.4423 * " (5.97) 0.0627 * (1.86) 0.0114 (0.45) 0.4188 * " (4.59) 0.0057 (0.26)  Growth in consumption -0.4710 (0.90) -0.4638 (0.92) 0.9316 " (2.45) -0.4991 (0.58) 1.2332 * " (3.32)  Constant 0.0227 *** (4.32) 0.0048 (0.98) -O.0054 (1.25) 0.0020 • (0.22) -O.0062 (1.55)  Note 1. Adjusted R-squared is 1 - (1-R2)(N-1)/(N-k) where k is the number of factors. 2. The t-statistic is in parenthesis below the coefficient. 3. * " , " , * indicates significance at the 1%, 5% and 10% level. 4. There are 83 quarters in the sample, so N is 82 if the term spread is used (since one observation is lost in its construction) and N is 80 if unexpected inflation is used (since three lags are used in the inflation model).  Table 5 - Test for Equality of Coefficients between BAA Intermediate Term Corporate Bonds and Commercial Mortgages Ling-Naranjo F F Specification Term spread  0.3996 * " (7.06)  Specification  S i x factor S p e c i f i c a t i o n  0.2838 ***  0.3916 ***  (5.04)  (6.77)  Default s p r e a d  0.6455 *** (4.49)  (4.51)  S t o c k m a r k e t return  0.0404  0.0406  S i z e factor  0.1322 **  B o o k to m a r k e t factor  0.0608 *  0.6606 ***  (1.30)  (1.31)  0.1402 ***  (2.60)  (2.79) 0.0627 *  (1.76)  (1.86)  G r o w t h in c o n s u m p t i o n  0.0484  -0.4638  (0.08)  (0.92)  R e a l T-bill  0.0125 (0.02)  U n e x p e c t e d inflation  -0.1374 (0.21)  Constant Term spread * Dummy Default s p r e a d * D u m m y S t o c k m a r k e t return * D u m m y  0.0008  0.0024  (0.31)  (0.33)  0.0048 (0.98)  0.1305  0.2078 '  0.1545  (1.56)  (2.66)  (1.84) -0.2912  -0.2458 (1.09)  (1.36)  0.0132  0.0127  (0.34)  (0.31)  S i z e factor * D u m m y  -0.0666  -0.0906  (1.00)  (1.40)  B o o k to m a r k e t factor * D u m m y  -0.0455  -0.0513 (1.22)  (1.05) G r o w t h in c o n s u m p t i o n * D u m m y  1.1017  1.3954  (1.44)  (2.20)  R e a l T-bill * D u m m y  0.1504 (0.18)  U n e x p e c t e d inflation * D u m m y  -0.5025 (0.58)  Dummy  R  2  N F-test  0.0019  -0.01 Q2  -0.0102  (0.60)  (1.18)  (1.56)  63.9% 164 0.0047  56.7%  65.5%  164 0.0394 '  164 0.0002  ( A L L d u m m y - i n t e r a c t e d t e r m s are 0)  Notes: D u m m y = 1 if c o m m e r c i a l m o r t g a g e return, 0 if c o r p o r a t e b o n d return. E a c h factor in the s p e c i f i c a t i o n i s multiplied b y the d u m m y v a r i a b l e to c r e a t e a fully i n t e r a c t e d m o d e l . T h e c o e f f i c i e n t s o n the f a c t o r s will b e e q u a l to t h o s e o b t a i n e d o n the r e g r e s s i o n for t h e B A A Intermediate T e r m c o r p o r a t e b o n d r e t u r n s o n their o w n , a n d the coefficient o n the d u m m y - i n t e r a c t e d f a c t o r s will b e e q u a l tothe difference b e t w e e n the coefficient o n the B A A i n t e r m e d i a t e t e r m c o r p o r a t e b o n d return r e g r e s s i o n a n d the c o m m e r c i a l m o r t g a g e return r e g r e s s i o n . S o if the coefficient o n the d u m m y - i n t e r a c t e d factor is insignificant, t h e n the s e n s i t i v i t i e s a r e i n d i s t i n g u i s h a b l e .  26  ' Table 6a - Estimation results for Stock Portfolios (Fama-French Specification) Size BE/ME ranking ranking  R-sq  Term spread  1  1 93.8%  1  2 93.9%  1  3 94.6%  1  4 93.2%  1  5 92.6%  2  1 95.9%  2  2 93.5%  2  3 91.1%  2  4 89.1%  2  5 93.2%  3  1 92.8%  3  2 89.9%  3  3 88.1%  3  4 83.2%  3  5 86.1%  4  1 92.9%  4  2 85.2%  4  3 83.7%  4  4 81.5%  4  5 78.2%  5  1 94.0%  5  2 87.9%  5  3 80.8%  5  4 77.1%  5  5 76.5%  -0.0609 (0.860) 0.0130 (0.230) 0.0575 (0.970) -0.0416 (0.760) -0.0411 (0.670) 0.0211 (0.260) 0.0821 (1.320) 0.1880 ** (2.440) 0.1491 ** (2.400) 0.1118 ** (2.200) 0.1546 (1.660) 0.1399 * (1.740) 0.1432 * (1.770) 0.1793 " (2.530) 0.1442 * (1.910) 0.0531 (0.510) -0.0011 (0.010) 0.1568 ** (2.010) 0.2564 *** (4.030) 0.2819 *** (3.450) 0.0220 (0.330) -0.0150 (0.210) 0.0189 (0.290) 0.1428 * (1.960) 0.0653 (0.660)  Default spread -0.3568 (1.100) -0.0425 (0.190) -0.1467 (0.560) -0.4408 (1.280) -0.1516 (0.500) -0.0223 (0.080) -0.1625 (0.890) 0.1319 (0.620) -0.1075 (0.480) -0.1903 (0.890) 0.4883 (1.150) 0.0077 (0.030) -0.2082 (0.850) 0.0012 (0.010) -0.2062 (0.750) -0.0065 (0.020) -0.3986 (1.590) -0.2816 (0.910) -0.2401 (0.710) -0.0063 (0.030) 0.1085 (0.520) -0.2298 (0.860) -0.0202 (0.080) 0.2684 (0.970) 0.0080 (0.030)  Stock market Size factor Equity factor 0.9106 (13.230) 0.8434 (16.660) 0.8212 (17.450) 0.8513 (15.620) 0.9459 (17.250) 0.9837 (12.380) 0.9325 (18.820) 0.8978 (18.290) 0.8769 (16.450) 0.9647 (25.170) 0.9681 (12.480) 0.9259 (14.740) 0.9021 (15.880) 0.8898 (16.050) 0.9258 (16.030) 0.8615 (10.440) 0.9925 (14.950) 0.9368 (16.150) 0.8158 (13.660) 0.8460 (13.830) 0.9995 (26.110) 1.0711 (17.570) 0.9916 (16.390) 0.9716 (16.210) 0.9298 (14.670)  *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***  1.6172 "* (16.830) 1.5271 *** (22.580) 1.4205 *" (16.960) 1.3412 *** (15.500) 1.4228 *** (13.920) 1.1548 *** (14.710) 1.2108 *** (15.980) 0.9606 *** (15.360) 0.9441 *** (12.510) 1.0790 *** (14.320) 0.8668 *** (8.770) 0.9241 *** (12.620) 0.7832 *** (11.910) 0.7258 *** (9.130) 0.7336 *** (9.690) 0.6501 *** (7.530) 0.5893 *** (8.150) 0.6373 *** (7.760) 0.4310 *** (5.310) 0.5325 *** (6.740) -0.1219 * (1.990) 0.0047 (0.070) -0.0991 (1.190) 0.0257 (0.330) 0.1351 (1.380)  -0.6912 *** (6.570) -0.1548 (1.220) 0.0814 (1.420) 0.2611 *** (3.740) 0.4844 *** (6.140) -0.5280 *" (7.710) 0.0567 (0.970) 0.2603 *** (3.930) 0.4956 *** (7.660) 0.6556 *** (12.850) -0.5118 *** (6.080) 0.1258 * (1.800) 0.4404 "* (5.940) 0.5551 "* (7.420) 0.6497 *** (8.140) -0.6434 *** (5.490) 0.2084 ** (2.450) 0.3677 *** (4.310) 0.3283 *** (3.990) 0.4959 *** (4.270) -0.3799 *** (5.860) 0.0770 (1.220) 0.1768 ** (2.570) 0.5190 *" (7.350) 0.7068 *** (9.460)  Constant -0.0002 (0.040) 0.0229 *** (5.390) 0.0261 *** (8.390) 0.0291 *** (8.220) 0.0261 *" (7.000) 0.0091 " (2.440) 0.0177 *** (5.450) 0.0250 *** (6.970) 0.0257 *** (6.990) 0.0201 *** (6.470) 0.0146 *** (3.080) 0.0215 *** (5.550) 0.0186 *** (4.860) 0.0209 *** (5.120) 0.0267 *** (6.820) 0.0265 *" (5.860) 0.0166 *** (3.820) 0.0164 *** (3.770) 0.0230 *** (5.640) 0.0235 *** (4.900) 0.0240 *** (8.260) 0.0179 *** (4.830) 0.0154 *** (3.480) 0.0162 *** (3.750) 0.0208 *** (4.490)  Table 6b - Estimation results for Stock Portfolios (Ling Naranjo Specification) Size  BE/ME  ranking  Ranking 1  1 1 1 1 2 2  Unexpected R-sq 1 2 3 4 5 1 2  5.2% 5.1% 5.8% 5.6% 7.6% 3.3% 5.7%  Term spread  R e a l tbill  3  7.7%  4  7.6%  -4.3253  -3.4710  4.5347  -0.0039  (1.340)  (0.830)  (1.150)  (0.080)  0.3217  -2.9196  -3.4059  3.7059  0.0220  (1.260)  (1.170)  (0.940)  (1.130)  (0.540)  0.3188  -2.8118  -3.8245  2.8631  0.0338  (1.310)  (1.200)  (1.120)  (0.910)  (0.860)  0.2883  -2.6133  -3.1722  3.0645  0.0360  (1.270)  (1.150)  (1.010)  (1.070)  (1.010)  0.2597  -3.7355  -4.5865  3.8127  0.0379  (1.180)  (1.630)  (1.330)  (1.240)  (0.960)  0.4035  -2.0090  -2.2430  1.5479  0.0188  (1.470)  (0.720)  (0.590)  (0.460)  (0.430)  -1.5315  -2.4127  2.3470  0.0217  (0.700)  (0.750)  (0.840)  (0.620)  -0.7630  -2.2577  1.5572  0.0324  (0.440)  (0.810)  (0.660)  (1.060)  -0.8633  -2.2527  1.7200  0.0338  (0.550)  (0.910)  (0.830)  (1.240)  -2.0148  -3.8370  1.7028  0.0394  (1.090)  (1.350)  (0.640)  (1.140)  -0.9938  -1.9769  0.5383  0.0270  (0.410)  (0.610)  (0.180)  (0.700)  -1.1791  -2.2842  1.2110  0.0343  (0.670)  (0.810)  (0.490)  (1.080)  -1.0071  -2.3323  1.5077  0.0287  (0.680)  (1.000)  (0.790)  (1.190)  -0.9232  -2.5116  0.7938  0.0389  (0.630)  (1.120)  (0.400)  (1.470)  -0.7385  -2.6143  1.5447  0.0387  (0.460)  (1.200)  (0.790)  (1.420)  -1.4299  -0.6785  0.9307  0.0360  (0.640)  (0.230)  (0.350)  (1.100)  -1.9690  -2.1025  1.5548  0.0319  (1.210)  (0.850)  (0.720)  (1.170)  -1.6952  -1.6074  1.1011  0.0355  (1.180)  (0.650)  (0.530)  (1.300)  -0.6948  -1.6186  0.1890  0.0425 *  (0.550)  (0.910)  (0.110)  (1.910)  0 . 4 9 3 5 ***  0.3668  -1.5322  1.6199  0.0246  (3.030)  (0.250)  (0.790)  (0.940)  (1.090)  0 . 3 8 0 0 **  0.6434  -0.1159  -0.7585  0.0384  (2.060)  (0.330)  (0.050)  (0.370)  (1.370)  -0.2559  -1.2704  0.1320  0.0348  (0.180)  (0.600)  (0.070)  (1.440)  -1.0781  -0.3288  1.0436  0.0290  (0.870)  (0.180)  (0.760)  (1.630)  0 . 3 6 8 6 **  0.1883  -1.3173  0.2756  0.0328  (2.560)  (0.150)  (0.750)  (0.180)  (1.600)  -0.1361  -2.6631  0.8610  0.0348  (0.080)  (1.270)  (0.540)  (1.560)  0.4173 * 0.4149  "  0 . 3 8 6 2 ** (2.120)  2  5  7.8%  0.3620 * (1.920)  3  1  4.0%  0.4093 *  •  (1.690) 3  2  6.3%  0.4077  "  (2.060) 3  3  10.6%  0 . 4 5 5 9 *** (2.720)  3  4  8.5%  0 . 3 8 0 6 ** (2.240)  3  5  9.1%  0 . 3 8 4 3 ** (2.360)  4  1  3.7%  0.4351 * (1.830)  4  2  8.1%  0 . 4 4 7 6 ** (2.520)  4  3  11.0%  0 . 5 3 7 6 *** (3.190)  4  4  15.0%  0 . 5 0 1 3 *** (3.430)  4 5 5  5 1 2  14.7% 6.9% 8.8%  0 . 4 0 9 8 ** (2.610)  5  3  9.6%  0 . 4 5 8 3 *** (2.700)  5 5  4 5  10.0% 9.7%  Constant  0.4480  (2.170) 2  Consumption  (1.350)  (1.930) 2  Inflation  0.2862 * (1.770)  28  Table 6c - Estimation results for Stock Portfolios (Six Factor Specification) Size BE/ME ranking Ranking  R-sq  Term spread  Default spread  94.1%  -0.0348 (0.500) 0.0245 (0.390) 0.0578 (0.980) -0.0358 (0.650) -0.0276 (0.450) 0.0042 (0.060) 0.0772 (1.250) 0.1749 ** (2.260) 0.1418 ** (2.300) 0.0987 ** (2.020) 0.1249 (1.430) 0.1224 (1.560) 0.1351 (1.660) 0.1603 ** (2.360) 0.1385 * (1.760) 0.0397 (0.390) -0.0021 (0.030) 0.1441 * (1.860) 0.2367 *** (3.630) 0.2831 *** (3.330) -0.0020 (0.030) -0.0265 (0.380) 0.0271 (0.410) 0.1308 * (1.790) 0.0634 (0.630)  -0.4062 (1.390) -0.0642 (0.300) -0.1473 (0.550) -0.4517 (1.300) -0.1772 (0.590) 0.0098 (0.040) -0.1532 (0.830) 0.1567 (0.810) -0.0936 (0.410) -0.1656 (0.740) 0.5446 (1.360) 0.0408 (0.140) -0.1929 (0.760) 0.0374 (0.190) -0.1955 (0.690) 0.0190 (0.060) -0.3966 (1.540) -0.2575 (0.790) -0.2029 (0.560) -0.0087 (0.040) 0.1540 (0.810) -0.2081 (0.770) -0.0356 (0.130) 0.2910 (1.060) 0.0117 (0.040)  1  1  1  2 94.0%  1  3 94.6%  1  4 93.3%  1  5 92.7%  2  1 96.0%  2  2 93.5%  2  3 91.3%  2  4 89.2%  2  5 93.4%  3  1  3  2 90.2%  3  3 88.2%  3  4 83.7%  3  5 86.2%  4  1 93.0%  4  2 85.2%  4  3 83.9%  4  4 82.1%  4  5 78.2%  5  1 94.6%  5  2 88.0%  5  3 80.9%  5  4 77.3%  5  5 76.5%  93.4%  Stock market Size factor 0.9101 *** (13.520) 0.8432 *** (16.460) 0.8212 *** (17.320) 0.8512 *** (15.590) 0.9456 *** (17.010) 0.9841 *** (12.890) 0.9326 *** (19.080) 0.8981 *** (17.990) 0.8771 *" (16.450) 0.9650 "* (25.670) 0.9687 *** (13.510) 0.9263 *** (15.570) 0.9023 *** (16.070) 0.8902 *** (16.630) 0.9259 *** (15.690) 0.8618 *** (10.760) 0.9925 "* (14.880) 0.9370 *** (16.200) 0.8162 *** (13.770) 0.8459 *** (13.770) 1.0000 *** (28.250) 1.0714 *** (18.520) 0.9915 *** (15.820) 0.9719 *** (16.440) 0.9299 *** (14.600)  Equity factor Consumption  1.5911 *** -0.6974 *** (6.950) (16.770) 1.5156 *** -0.1576 (21.870) (1.250) 1 4202 * " 0.0813 (16.460) (1.390) 1.3354 *** 0.2597 *** (16.210) (3.710) 1.4093 *** 0.4811 *** (13.650) (6.240) 1.1717 *** -0.5239 *** (16.110) (7.710) 1.2157 *** 0.0579 (15.680) (0.990) 0.9737 *** 0.2634 *** (16.650) (3.920) 0.9515 *** 0.4973 *** (7.600) (12.730) 1.0921 *** 0.6587 "* (14.330) (12.230) 0.8966 *** -0.5046 *** (10.250) (6.230) 0.9417 *** 0.1300 * (12.670) (1.940) 0.7913 *" 0.4423 *" (11.790) (5.970) 0.7449 *** 0.5597 *** (9.890) (7.370) 0.7393 *** 0.6510 *** (10.120) (7.940) 0.6636 *** -0.6401 "* (7.870) (5.310) 0.5903 *** 0.2087 ** (8.110) (2.440) 0.6501 *** 0.3707 *** (7.950) (4.300) 0.4506 *** 0.3331 *** (5.960) (3.780) 0.5313 *** 0.4956 *** (6.610) (4.210) -0.0978 * -0.3741 *** (1.850) (6.050) 0.0162 0.0798 (0.260) (1.300) -0.1073 0.1748 ** (1.230) (2.470) 0.0376 0.5219 *** (0.470) (7.480) 0.1370 0.7073 *** (1.410) (9.450)  Constant  1.5172 " -0.0134 * (2.060) (1.820) 0.6678 0.0170 *** (1.170) (3.070) 0.0174 0.0260 *** (0.030) (4.050) 0.3374 0.0261 *** (0.580) (5.560) 0.7848 0.0193 *** (1.000) (2.690) -0.9833 * 0.0177 *** (1.800) (3.100) -0.2867 0.0202 *** (0.430) (2.980) -0.7641 * 0.0317 "* (1.740) (6.380) -0.4253 0.0294 *** (0.860) (5.960) -0.7588 0.0267 *** (1.100) (4.020) -1.7298 ** 0.0297 "* (4.470) (2.470) -1.0182 0.0304 *** (1.570) (4.800) -0.4710 0.0227 *** (0.900) (4.320) -1.1105 ** 0.0306 *** (2.090) (5.230) -0.3305 0.0296 *** (0.550) (5.330) -0.7845 0.0333 *" (1.360) (5.550) -0.0588 0.0171 *** (0.100) (2.870) -0.7393 0.0228 *** (1.190) (3.800) -1.1434 * 0.0330 *" (1.740) (6.180) 0.0730 0.0228 *** (3.560) (0.110) -1.3990 *** 0.0362 *** (3.080) (7.840) -0.6684 0.0237 *** (1.170) (4.160) 0.4740 0.0112 (1.650) (0.740) -0.6948 0.0223 *** (1.160) (3.680) -0.1139 0.0218 *** (0.190) (3.240)  29  Table 7 - Estimation results for Bond Series Rating |Teim  | R-sq |  AAA  Intermediate 52.3%  AA  Intermediate 52.7%  A  Intermediate 51.9%  BAA  Intermediate 49.3%  AAA  Long  60.7%  AA  Long  59.9%  A  Long  57.9%  BAA  Long  57.5%  Rating |Term  R-sq |  AAA  Intermediate 39.2%  AA  Intermediate 37.9%  A  Intermediate 36.8%  BAA  Intermediate 32.3%  AAA  Long  50.0%  AA  Long  48.5%  A  Long  45.6%  BAA  Long  41.3%  Rating |Term  R-sq |  AAA  Intermediate 54.1%  AA  Intermediate 54.2%  A  Intermediate 53.2%  BAA  Intermediate 50.0%  AAA  Long  61.0%  AA  Long  60.2%  A  Long  58.3%  BAA  Long  57.6%  Term spread | 0.4138 (8.100) 0.4183 *** (8.190) 0.4186 *** (8.030) 0.3996 *** (7.060) 0.7368 (8.740) 0.7162 *** (8.510) 0.6961 — (7.910) 0.6819 — (8.280) Term spread | 0.2767 (5.420) 0.2880 *** (5.470) 0.2890 — (5.360) 0.2838 *" (5.040) 0.5932 "* (6.800) 0.5676 *** (6.790) 0.5538 *** (6.320) 0.5339 *" (5.870) Term spread  |  0.4016 *" (7.770) 0.4068 *" (7.820) 0.4081 (7.670) 0.3916 (6.770) 0.7280 *" (8.370) 0.7079 "* (8.090) 0.6867 "* (7.570) 0.6760 *** (8.020)  Default spread  |  0.5993 (4.290) 0.6022 "* (4.410) 0.6321 *** (4.560) 0.6455 *" (4490) 0.7579 " (2.640) 0.7886 (2.850) 0.7756 *" (2.930) 0.8920 • " (3.620) Real tbill  I  0.0207 (0.660) 0.0287(0.840) 0.0290 (0.860) 0.0404 (1.310) 0.0868 * (1.710) 0.0701 (1.490) 0.0773 (1.610) 0.0874 * (1.790) Unexp infl -0.1608 (0.280) -0.1289 (0.210) -0.1240 (0.200) -0.1374 (0.210) -0.3073 (0.290) -0.0632 (0.060) -0.0225 (0.020) -0.0186 (0.020)  0.1846 (0.280) 0.0709 (0.110) 0.1205 (0.180) 0.0125 (0.020) 0.1144 (0.110) 0.2153 (0.210) 0.1628 (0.160) 0.1765 (0.170) Default spread  Stock market  |  Stock market  0.6225 *" (4.330) 0.6239629 *" (4.440) 0.6519 "* (4.570) 0.6606 *** (4.510) 0.7746 *" (2.630) 0.8044 *** (2.840) 0.7934 *" (2.940) 0.9031 *" (3.630)  0.0210 (0.650) 0.028973 (0.820) 0.0292 (0.840) 0.0406 (1.300) 0.0870 • (1.690) 0.0703 (1.490) 0.0775 (1.600) 0.0875 * (1.770)  Size factor  |  0.0814 • (1.740) 0.0970 " (2.030) 0.1095 " (2.220) 0.1322 " (2.600) 0.1343 * (1.700) 0.1393 * (1.820) 0.1601 " (2.040) 0.1956 " (2.450) Consumption  0.0310 (1.020) 0.0401 (1.250) 0.0429 (1.300) 0.0608 * (1.760) 0.0655 (1.330) 0.0536 (1.130) 0.0603 (1.250) 0.0540 (1.100) |  -0.3483 (0.570) -0.2683 (0.450) -0.1657 (0.280) 0.0484 (0.080) 0.0530 (0.060) 0.0791 (0.090) 0.0592 (0.070) 0.3509 (0.360) Size factor  Equity factor  Constant -0.0011 (0.510) -0.0010 (0.460) -0.0006 (0.250) 0.0008 (0.310) -0.0045 (1.280) -0.0035 (1.020) -0.0026 (0.750) . -0.0008 (0.240)  Constant 0.0024 (0.410) 0.0028 (0.460) 0.0019 (0.310) 0.0024 (0.330) -0.0022 (0.240) -0.0026 (0.280) -0.0010 (0.100) -0.0020 (0.190)  |  Equity factor  Consumption  0.0937 * (1.930) 0.1084535 " (2.240) 0.1200 " (2.420) 0.1402 "* (2.790) 0.1432 • (1.830) 0.1476 * (1.970) 0.1695 " (2.190) 0.2015 " (2.530)  0.0339 (1.180) 0.0429106 (1.400) 0.0454 (1.430) 0.0627 • (1.860) 0.0676 (1.400) 0.0556 (1.200) 0.0625 (1.320) 0.0554 (1.140)  -0.7124 (1.260) -0.6682622 (1.300) -0.6084 (1.210) -0.4638 (0.920) -0.5135 (0.690) -0.4850 (0.700) -0.5469 (0.760) -0.3408 (0.440)  Constant 0.0048 (0.930) 0.004724 (0.950) 0.0048 (0.980) -0.0001 (0.010) 0.0007 (0.110) 0.0022 (0.310) 0.0021 (0.280) ?????  30  Table 8 - Estimation results for Unsmoothed real estate series Series  Smoothed  R-sq  5.4%  Unsmoo (var)  12.9%  Unsmoo (mean)  10.0%  Unsmoo (Fu)  Series  5.9%  R-sq  Smoothed  21.3%  Unsmoo (var)  23.0%  Unsmoo (mean)  34.9%  Unsmoo (Fu)  18.4%  Series  R-sq  Smoothed  24.9%  Unsmoo (var)  22.4%  Unsmoo (mean)  21.0%  Unsmoo (Fu)  20.9%  Term spread  -0.0763 *** (3.00) -0.2038 *** (2.79) -0.0712 * (1.99) -0.0768 (0.88) Term spread  -0.0117 (0.52) -0.0260 (0.36) 0.0074 (0.27) 0.0432 (0.63) Term spread  -0.0551 ** (2.01) -0.1546 * (1.95) -0.0501 (1.35) -0.0399 (0.47)  Default spread  -0.1321 (1.50) -0.2346 (0.83) -0.0688 (0.58) -0.0722 (0.32) Real tbill  0.3203 (1.31) -2.1501 ** (2.54) -1.3919 *** (4.67) -0.3131 (0.44) Default spread  -0.1723 * (1.92) -0.2985 (0.94) -0.0962 (0.75) -0.1423 (0.60)  Stock market  0.0346 (1.39) 0.0943 (1.60) 0.0409 (1.64) 0.0706 (1.10) Unexp infl  -0.0469 (0.17) -1.2580 (1.39) -0.9157 *** (2.67) 0.3936 (0.51) Stock market  0.0342 (1.39) 0.0933 (1.53) 0.0404 (1.54) 0.0698 (0.95)  Size factor  -0.0243 (0.61) 0.1476 (1.49) 0.0510 (1.28) 0.0697 (0.83) Consumption  1.1418 *** (3.24) 2.6181 ** (2.62) 1.1164 *** (3.32) 2.2380 *** (3.55) Size factor  -0.0456 (1.33) 0.0961 (1.04) 0.0289 (0.80) 0.0327 (0.47)  Equity factor  0.0108 (0.42) 0.1629 ** (2.13) 0.0500 (1.63) 0.0366 (0.61)  Constant  0.0046 *** (2.74) 0.0441 *** (10.39) 0.0050 *** (2.72) 0.0020 (0.55)  Constant  -0.0076 * (1.98) 0.0378 *** (3.13) 0.0054 (1.31) -0.0146 * (1.69) Equity factor  0.0057 (0.26) 0.1475 ** (2.01) 0.0434 (1.44) 0.0277 (0.47)  Consumption  1.2332 *** (3.32) 2.3239 ** (2.44) 0.9975 *** (2.78) 2.1512 *** (3.24)  Constant  -0.0062 (1.55) 0.0236 ** (2.34) -0.0038 (0.99) -0.0167 ** (2.19)  Table 9- Estimation Results for R E I T s for additional timelines  Fama-French Specificatior R-squared  N  Adjusted R- Root meansquared squared error  REIT (Full)  63.2% 82  61.3%  4.177%  REIT (1986-2000)  63.9% 60  61.3%  4.227%  REIT (1992-2000)  47.1% 36  40.3%  4.708%  Ling-Naranjo Specificatior R-squared  N  Adjusted R- Root meansquared squared error  REIT (Full)  18.6% 80  15.4%  6.226%  REIT (1986-2000)  20.5% 60  16.3%  6.215%  REIT (1992-2000)  12.4% 36  4.2%  6.404%  Six factor specification  R-squared  N  Adjusted R- Root meansquared squared error  REIT (Full)  63.4% 82  60.9%  4.196%  REIT (1986-2000)  66.1% 60  62.9%  4.138%  REIT (1992-2000)  52.4% 36  44.5%  4.879%  Term spread 0.2843 *** (2.88) 0.4310 * " (2.77) 0.2213 (0.95)  Term spread 0.4061 * " (3.07) 0.3345 * (1.88) 0.3180 (1.39)  Term spread 0.2757 * " (2.80) 0.3050 * (1.88) 0.0415 (0.16)  Note 1. Adjusted R-squared is 1 - (1-R2)(N-1 )/(N-k) where k is the number of factors. • 2. The t-statistic is in parenthesis below the coefficient. 3. ***, **, * indicates significance at the 1%, 5% and 10% level.  to  Default spread -0.0132 (0.05) 0.1509 (0.37) -0.4488 (0.64)  Real Tbill  Stock market return 0.5290 *** (6.63) 0.5069 * " (6.57) 0.4887 " (2.63)  Unexpected Inflation  Size factor 0.5637 *** (5.72) 0.5451 * " (4.24) 0.4450 " * (2.81)  Growth in consumption  -1.8397 (1.16) -4.8340 ** (2.20) -3.0013 (1.01)  -3.8766 ** (2.06) -7.5558 ** (2.58) -2.5137 (0.47)  0.8474 (0.53) -0.9285 (0.45) -3.4506 (0.99)  Default spread  Stock market return  Size factor  0.0031 (0.01) -0.0696 (0.16) -0.8032 (1.07)  0.5292 *** (6.68) 0.4949 *** (6.47) 0.4633 " (2.60)  0.5722 *** (5.58) 0.5969 *** (4.88) 0.5604 *** (3.86)  Equity factor 0.4167 *** (4.55) 0.5062 *** (4.58) 0.5276 * " (3.48)  Constant -0.0023 (0.51) -0.0026 (0.44) -0.0013 (0.13)  Constant 0.0132 (0.57) 0.0387 (1.50) 0.0586 (1.45)  Equity factor 0.4188 *** (4.59) 0.5267 *** (4.44) 0.4828 *** (3.42)  Growth in consumption -0.4991 (0.58) -2.1881 * (1.84) -5.2095 * (1.90)  Constant 0.0020 (0.22) 0.0169 (1.37) 0.0509 * (1.72)  Table 10 - Estimation Results for Credit Losses for Commercial Mortgages  Fama-French Specification  R-squared  Adjusted R squared  N  Root meansquared error  Including Credit Losses  75.4%  82  74.1%  1.643%  Excluding Credit Losses  75.5%  82  74.2%  16.730%  Credit Loss Amount  12.1%  82  7.5%  0.205%  Adjusted R squared  Root meansquared error  Ling-Naranjo Specification  R-squared  N  Including Credit Losses  74.9%  80  73.9%  1.657%  Excluding Credit Losses  73.8%  80  72.8%  1.727%  Credit Loss Amount  34.3%  80  31.7%  0.177%  Six factor specification  R-squared  Adjusted R squared  N  Root meansquared error  Including Credit Losses  77.7%  82  76.2%  1.575%  Excluding Credit Losses  77.3%  82  75.8%  1.622%  Credit Loss Amount,  17.7%  82  12.2%  0.200%  Note 1. Adjusted R-squared is 1 - (1-R2)(N-1 )/(N-k) where k is the number of factors. 2. The t-statistic is in parenthesis below the coefficient. 3. ***, **, * indicates significance at the 1%, 5% and 10% level.  Term spread 0.5301 *** (8.64) 0.5447 *** (8.63) -0.0146 *** (3.34)  Term spread 0.4916 *** (9.08) 0.5015 *** (8.83) -0.0099 " (2.25)  Term spread 0.5462 *** (8.96) 0.5591 *** (8.87) -0.0129 *** (2.73)  Default spread 0.3997 ** (2.30) 0.4273 " (2.43) -0.0275 ** (2.27)  Real Tbill  Stock market return 0.0536 " (2.23) 0.0545 ** (2.21) -0.0009 (0.31)  Unexpected Inflation  Size factor  Equity factor  0.0657 (1.53) 0.0697 (1.61) -0.0040 (0.84)  0.0152 (0.58) 0.0195 (0.74) -0.0043 (1.08)  Growth in consumption  Constant  0.0027 (1.30) 0.0052 " (2.39) -0.0025 *** (10.02)  -0.0078 * (1.70) -0.0031 (0.65) -0.0047 *** (9.96)  0.1629 (0.33) -0.0571 (0.11) 0.2200 *** (5.10)  -0.6399 (1.11) -0.8074 (1.33) 0.1675 *** (3.61)  Default spread  Stock market return  Size factor  Equity factor  0.0533 " (2.03) 0.0542 " (2.02) -0.0010 (0.35)  0.0496 (1.22) 0.0553 (1.34) -0.0057 (1.22)  0.0114 (0.45) 0.0160 (0.62) -0.0047 (1.25)  0.3694 ** (2.35) 0.4000 " (2.49) -0.0307 ** (2.61)  1.1501 *** (2.74) 1.0773 ** (2.45) 0.0728 ** (2.28)  Constant  Growth in consumption 0.9316 ** (2.45) 0.8359 " (2.18) 0.0957 * " (3.04)  Constant -0.0054 (1.25) -0.0021 (0.48) -0.0033 *** (7.98)  T a b l e 11 - P o r t f o l i o A l l o c a t i o n s Portfolio  |  1 2 3 4 5  Portfolio  |  1 2 3 4 5  Portfolio  |  1 2 3 4 5  Portfolio  |  1 2 3 4 ' 5  Portfolio  |  1 2 3 4 5  Portfolio 1 2 3 4 5  |  Risk  Return  BAA  0.69% 1.36% 2.43% 3.63% ' 5.15%  1.66% 1.91% 2.17% 2.43% 2.69%  0.0% 36.8% 73.5% 78.2% 0.0%  Risk  Return  Comm Mtg  0.69% 1.09% 1.83% 2.63% 3.47%  1.66% 1.93% 2.19% 2.45% 2.71%  0 8% 24 6% 47 0% 69 4% 100 0%  Risk  Return  0.68% 1.92% 3.64% 5.45% 7.60%  1.69% 2.33% 2.98% 3.62% 4.26%  0.0% 18.7% 39.2% 33.7% 0.0%  Risk  Return  Comm Mtg  0.68% 1.78% 3.36% 5.14% 7.60%  1.69% 2.33% 2.98% 3.62% 4.26%  0 0% 25 4% 50 8% 41 5% 0 0%  Risk  Return  0.67% 1.42% 2.59% 3.96% 6.85%  1.68% 2.12% 2.55% 2.98% 3.42%  Risk  Return  0.67% 1.73% 3.25% 5.06% 7.58%  1.70% 2.34% 2.98% 3.62% 4.26%  BAA  (inter) |  Weights BAA (long) | 0.0% 0.0% 0.0% 21.8% 100.0%  1.1% 28.2% 54.6% 61.6% 0,0%  Comm Mtg. | 0.8% 25.6% 49.9% 39.0% 0.0%  100.0% 63.3% 26.5% 0.0% 0.0%  Weights (inter) | BAA  BAA  0.0% 1,5% 5.1% 8.7% 0.0%  (inter) | BAA  Comm Mtg. |  T-bill  T-bill  0.0% 0.0% 0.0% 0.0% 0.0%  99.2% 73.9% 47.9% 21.9% 0.0%  Weights (long) | T-bill  Stocks  0.0% 0.0% 0.0% 0.0% 0.0%  BAA  (long) |  Weights BAA (long) |  (inter)  0.0% 0.0% 0.0% 0.0% 0.0%  0.0% 0.0% 0.7% 0.0% 0.0%  REIT  Weights | T-Bills  1.0% 8.1% 15.2% 38.4% 100.0%  REIT 0.1% 0.8% 1.2% 4.3% 0.0%  1.4% 21.0% 40.2% 66.3% 100.0%  98.6% 60.3% 20.7% 0.0% 0.0%  |  Weights Stocks 1.5% 14.4% 27.2% 56.7% 100.0%  Stocks  98.6% 58.9% 18.6% 0.0% 0.0%  1.4% 15.8% 29.9% 58.5% 100.0%  BAA  (inter)  0.0% 2.8% 7.1% 0.0% 0.0%  98.0% 60.9% 23.1% 0.0% 0.0%  |  T-bill  |  T-Bills 97.8% 55.3% 12.2% 0.0% 0.0%  Notes 1. All the other corporate bonds AAA to A were also included in the calculation but had a 0% allocation 2. Returns expressed quarterly.  |  BAA (inter) 0.0% 4.0% 9.4% 0.0% 0.0%  CHAPTER 2  Commercial Mortgage Delinquency, Foreclosure and Reinstatement: A n Empirical Investigation  Introduction Commercial mortgages are loans secured by income-producing property, such as apartment buildings and retail malls. The primary source of funds to service the mortgage is generated through the rental income. In contrast, the source of funds to pay residential mortgages is the income generated by members of the household, and the secured property is a single-family dwelling. For lenders or investors in residential mortgages, prepayment is a primary source of risk.  Since penalties are  relatively low, families refinance their mortgage when interest rates decline.  For commercial  mortgages, penalties are high enough so that i f it occurs, it does not reduce the yield to the lender. Therefore, in the commercial mortgage context, prepayment risk is mitigated.  Another difference between residential and commercial mortgages is the presence of mortgage insurance. In some circumstances, a residential mortgage lender may require that the borrower purchase mortgage insurance in order to reduce the loss associated with default and foreclosure. In commercial mortgages, there is no mortgage insurance, so the investor has to absorb any losses associated with default. Therefore, at the time of loan initiation, there has to be a careful evaluation of the likelihood of future default.  Since commercial mortgages have large prepayment penalties and no mortgage insurance, prepayment risk is mitigated and the primary source of risk is through default. The default risk of commercial mortgages is a particularly timely topic, as the issuance of commercial mortgage-backed securities grows and a broader set of investors become involved. These investors require information that specifies the nature and structure of commercial mortgage default risk. Additional work is  35  needed to improve the pricing and monitoring of commercial mortgage loan portfolios, since so few academic studies exist.  In this paper, one particular unstudied aspect of commercial mortgage risk is investigated: reinstatement of delinquent loans. In this paper, the usual definition of delinquency is applied, which is that 90 days have elapsed since the last mortgage payment was made. Reinstatement is one possible outcome of delinquency, which occurs when the bonower resumes their mortgage payments and makes up any existing shortfall. The other possible outcome of delinquency is foreclosure, where the lender assumes ownership of the secured commercial property in exchange for release of the mortgage contract.  Delinquency with reinstatement is a common and costly problem for lenders and investors. In the database used for the empirical estimations, 214 of the total 1637 loans (13%) were delinquent at least once during the period November 1996 to May 2001. Several loans were delinquent multiple times, so there were a total of 297 delinquency instances observed. O f these, 187, or 63%, were eventually reinstated. For a lender, a delinquent and reinstated loan is costly because of the interruption of the cash flow and because of the extra costs associated with servicing the loan.  To examine delinquency behavior, a game-theoretic model is created in which the commercial mortgage borrower and lender interact strategically over two time periods. At time 1, the borrower either pays the mortgage amount (terminating the game) or becomes delinquent. In the event of a delinquency, the game can end either through foreclosure or reinstatement. The lender plays a role in determining the outcome by having the ability to defer the foreclosure process in order to allow the borrower time to reinstate the mortgage. Between time 1 and time 2, the property can appreciate or depreciate. This is a realistic feature since foreclosure does not occur simultaneously with the first failure to make a scheduled mortgage payment.  Another unique feature of the model is that a  36  borrower has a reward for delinquency since the unpaid amount earns a return when it's invested in an alternate use. The most interesting result of the model is that reinstatement occurs under both positive and negative equity positions.  For example, a positive equity borrower can enter  delinquency in order to divert the payment amount to an alternate use, intending to eventually reinstate the loan. In this situation, the lender is deterred from foreclosing because of the foreclosure costs, and reinstatement is the ultimate outcome. In addition, my model demonstrates that loans with negative equity at time 1 don't always end in foreclosure. For example, a borrower with negative equity may enter delinquency, but then experience positive price appreciation, which creates an incentive for the borrower to reinstate the loan.  This model is then extended to multiple periods. One advantage of a multiple period model is that the effects of changing market interest rates can be investigated. When market rates increase, this creates a disincentive for the borrower to default. Essentially, there is a cost to giving up a low rate mortgage that encourages continuing payment on the part of the borrower. Another advantage of extending the model to multiple periods is that more realistic payment schedules can be modeled. In the single period model, the entire mortgage was repaid in one lump sum. In a multiple period model, the effect of uneven repayments can be studied.  This is particularly relevant in the commercial mortgage  context since balloon mortgages are common. The model shows that a balloon type mortgage affects both the likelihood and the timing of default. When the final payments are relatively smaller, there is less default at the end of the loan term.  The contribution of this paper on the theoretical side is the novel approach to modeling default behavior. Instead of the usual options-based approach, I employ a game-theoretic approach. The key advantages to this approach are:  37  1.  Since the model is strategic, both the borrower and the lender are involved in determining the outcome of the loan. This is in opposition to the options approach that provides no facility for the lender to participate.  2.  In my model, time elapses between initial default and foreclosure, which allows movement in property values and market rates to affect the outcome of the loan. This is a realistic feature of the true default process that is neglected in the standard option-based models.  3. Delinquency and reinstatement can occur for both positive and negative equity loans in this model, since there is an incentive for a borrower to be temporarily default in order to divert funds to an alternative use. Lenders will not foreclose in many cases because foreclosure costs are high. This strategic default is observed empirically, but is not well-modeled using the options approach.  For the empirical component of the paper, tests to study the outcome of delinquency are performed using data supplied by a large Canadian commercial mortgage lender. The database includes the payment status per month, so the movement in and out of delinquency can be tracked for each loan. Foreclosure status is also known. A n interesting feature of the database is that the lender periodically re-appraises the secured properties; so good measures of the borrower's equity are available. The key results are that the outcome of a loan (to either never-delinquent, delinquent and reinstatement, or delinquent and foreclosure) is related to the characteristics of the loan, consistent with the predictions from the game-theoretic model. The dominant empirical contribution is that delinquent loans that eventually reinstate can be distinguished from those that do not, and end up in foreclosure. The implication for lenders is that an empirical model can created to predict which of the current loans in the portfolio are most likely to become delinquent and reinstated and which would likely end in foreclosure. This can improve lender's portfolio management strategies. And even further, a model can be created for use at the moment that a loan enters delinquency to predict the eventual outcome.  38  The remainder of this paper is structured as follows. The associated literature is reviewed, then the game theory model is presented. After this, the database used for empirical tests is described, the results are presented and a brief section concludes.  Literature Review  The options-based model for the value of a mortgage is based on the two sources of uncertainty, term structure risk and default risk. Foster and Van Order (1984,1985) modeled the default aspect of a mortgage as a put option, where the underlying asset is the secured property. Property value growth is modeled as  dV — = (a-c)dt + a dz , y  (1)  v  where V is the property value, a is the instantaneous gross rate-of-return from the property, c is the instantaneous cash payout rate, dt is the time interval, cr is the growth rate volatility parameter and v  dz is the Weiner process (standard normal random variable). The model for term structure risk is the y  standard mean-reverting interest rate process from Cox, Ingersoll and Ross (1985):  dr = y (0 - r)dt + <J sfrdz , r  (2)  r  where r is the interest rate, #is the instantaneous mean, y is the speed of the reversion to the mean, a  r  is a constant and dz is the Weiner process. r  Based on these state variables V and r, option-pricing techniques derive the partial differential equation for the value of the derivative asset X as:  1 dx /- d x i dx . dx . . dx ax - r c r — - + p4rV + -V al + y(0-r) — + (r-c)V + 2 dr drdV 2 dV dr dV dt 2  2  2  2  T / 2  2  2  T/  2  T  r  2  v  v  A  „  N  rX = 0, (3)  2  where p is the correlation coefficient between interest rate variations and property value movements.  39  This equation is valid for any asset with the state variables V and r.  In order to distinguish  commercial mortgages, and in order to solve the model, boundary conditions must be specified. The boundary conditions for default for commercial mortgages, from Kau et. al (1987, 1990) are:  _  c 0,  whenL < V  ) L T - Vj  otherwise,  T  T  (4) and  {  when MV, - V,  M  y  » ' -  F  ~ < -  D  » <  +  P  <  V  ,  otherwise,  where D, is the value of the default option at time t, Tis the terminal month of the mortgage, L \s the T  final payment on the mortgage, P is the mortgage payment amount per period, MV, is the market value of the mortgage at time t, and r is the per period discount rate. The call option F, is the value of e  the right to prepay the mortgage.  In situations where prepayment is forbidden by the mortgage  contract, F, is zero.  Goldberg and Capone (2002) modified the boundary conditions to take into account the debt coverage ratio, their reasoning being that when equity is negative, the default decision is based on whether the property is generating a cash flow larger than the debt payments.  Their new formulation of the boundary condition is D  '  + l  when  MV, - V, when  NOF>P  or  NOP < P  and  M  V  '^ ~ ~  MV  -F  (i  ' «  D  '  + l  -D  +O  +p<y  '  +1  + P > V.  (6)  where NOI, is the net operating income from the property at time t.  40  The earliest empirical testing of the determinants of commercial mortgage default using disaggregate data was Vandell et al. (1993). The dataset in this study consists of multiple commercial property types originated by a single lender. They use the proportional hazards methodology, where failure is defined as the time when the mortgage is foreclosed. They find that the contemporaneous loan-tovalue ratio and the interest rate were positive and significant.  The debt coverage ratio is not  significant, but the value at loan origination is used, not the contemporary value. The property type and the borrower type also have significant effects.  There has been a recent explosion in work on the empirical estimation of commercial mortgage default, including Ciochetti et al (2002), Ciochetti et al (2003), Ambrose and Sanders (2003), Archer et al. (2002), Chen and Deng (2002) and Goldberg and Capone (2002). These studies differ in their data sources, estimation technologies, set of independent variables and definition of default. For example, with regards to data sources, my study uses data from a single large commercial mortgage lender, as does Ciochetti et al. (2002), although they use a different, American firm. Other studies use commercial mortgage backed securities data (Ambrose and Sanders (2003) and Chen and Deng (2002) ) or multifamily mortgages (Archer et al. (2002) and Goldberg and Capone (2002)).  As for independent variables, the critical measurement suggested by option theory is a measurement of the borrower's equity, the loan-to-value ratio. Goldberg and Capone's (2002) findings suggest that cash flow considerations, measured as the debt coverage ratio, also play a role in default. Archer et al. (2002) and Ambrose and Sanders (2003) both confirm the lack of a relationship between initial loan-to-value ratio and default, while Ciochetti et al. (2002) find that contemporaneous loan-to-value ratio and debt coverage ratio are significantly positive and negative, respectively. Ciochetti et al. (2003) correct for originator bias, which arises since lenders have different underwriting standards. Deng, Quigley and Sanders (2005) find that there is regional variation associated with default. Other  41  variables used as independent variables in these studies include borrower characteristics, property location and market conditions. The estimations in my paper take into account these findings.  In most of these studies, a mortgage is considered to be in default at the time when the loan terminates through foreclosure.  12  But work by Ambrose and co-authors explicitly recognize that  default and foreclosure are not synonymous.  Ambrose and Capone (1996) address the question of the outcome of a residential delinquent mortgage loan using simulations from a parameterized model.  Possible loan outcomes are reinstatement,  foreclosure or a foreclosure alternative (such as deed-in-lieu).  Specifically, they calculate under  which conditions it is worthwhile for a lender to incur the costs necessary to offer a foreclosure alternative to the borrower. Their parameters are set based on information from industry sources. For example, for a house value of $100,000, the legal cost of deed-in-lieu was set equal to $750. Once the model is fully parameterized, they calculate the break-even success probabilities for each alternative, and find that under a variety of conditions, it is worthwhile for a lender to offer a foreclosure alternative.  Ambrose and Buttimer (2000) modify the standard residential mortgage-pricing model to include reinstatement. In the standard residential model, the borrower can exercise their prepayment option, make their scheduled payment or exercise their default option to terminate the loan. In their modified model, the borrower can choose to enter delinquency by missing a scheduled payment. This does not terminate the loan immediately. Instead, it generates a new set of alternatives for the borrower: they can prepay, allow foreclosure to occur or reinstate the loan. The primary pricing implication of these modifications is that incorporating the reinstatement option increases the incidence of delinquency.  An exception is Archer et al. (2002) who define default as 90-days delinquent.  42  Like my paper, this work explicitly addresses the issue that delinquency is not synonymous with foreclosure. One difference between this paper and mine is that they used the option theory as a basis for modeling, while I use game theory. With my method, I'm able to capture the strategic interaction between the borrower and the lender. In their model, the borrower can essentially force a foreclosure, whereas in mine, the lender can delay the foreclosure i f they find it to be strategically advantageous. Another difference between this paper and mine is that they are operating in the residential context. Therefore, they include prepayment, which is less relevant in the commercial context.  Ambrose and Capone (1998) also make the distinction between delinquency and foreclosure in this primarily empirical paper motivated by the standard option-theory based model. Their goal is to determine under which borrower characteristics, mortgage terms and economic conditions foreclosure is more likely to result. Therefore, their work is similar to mine in that they are also concerned with the outcome of delinquent loans.  However, in addition to the different modeling techniques  employed, the different institutional context (residential versus commercial mortgages) implies a different set of driving forces. For example, in the residential context, where prepayment is open and commonly observed, the relative difference between the market interest rate and the contract interest rate is an important variable in predicting the outcome.  Gardner and Mills (1989) and Springer and Waller (1993) are other papers that recognize and study the distinction between delinquency and foreclosure. Chun and Deng (2002) examine the workout strategy decisions of commercial mortgage backed securities special servicers on loans that are 60days delinquent. They find that cash flow considerations are relevant.  Riddiough and Wyatt (1994) use a game theoretic approach to study negotiated workout solutions for delinquent commercial mortgage loans. In their game, a borrower's decision to default is a function of the property value and the amount outstanding on the mortgage loan. The magnitude of the  43  foreclosure costs is also relevant, since in the second stage of their game, the lender decides whether to foreclose (and incur the associated costs) or to negotiate a workout solution. They find that, conditional on default taking place, there is always a workout solution that will dominate the foreclosure alternative, as long as foreclosure costs are positive. This paper is similar to mine in that a game theoretic framework is used to study default. The additional contribution of my paper is that I provide a framework for the borrower to reinstate the loan. This is the critical point of my paper: many delinquent loans are reinstated when the lender strategically provides the opportunity. Therefore, my model contributes to the literature by elaborating on the mechanism and motivation for reinstatement to occur.  Theory  The goal of the theory in this paper is to create a model with commercial mortgage loan outcomes of full repayment, reinstatement or foreclosure. As seen in the previous section, the standard optionsbased model does not allow for reinstatement.  In that model, delinquency and foreclosure are  synonymous, so that when a borrower exercises their default option, foreclosure is implicitly assumed to be instantaneous, so there is no opportunity for a borrower to reinstate the mortgage.  Ambrose and Buttimer (2000) modify this standard model to incorporate prepayment  and  reinstatement in the residential mortgage context. In their model, the borrower would be motivated to reinstate their delinquent mortgage i f there is favorable property value appreciation during the delinquency period.  However, there is another motivation for delinquency and reinstatement  behavior that is not included in their model. A borrower may decide to temporarily halt their mortgage payments in order to divert cash to another use. For example, a borrower might direct funds to operations or invest in inventory. Therefore, the delinquent borrower has a reward from engaging in this strategic behavior.  44  Another issue with the both the standard default option model and the Ambrose-Buttimer model is that there is no role for the lender to influence the outcome of the loan. Realistically, lenders have various techniques that they can employ to encourage reinstatement behavior. For example, a lender may defer the commencement of the foreclosure process in order to provide an opportunity for the borrower to reinstate.  In this section, I construct a simple game-theoretic model that has full payment, reinstatement and foreclosure as outcomes. Reinstatement behavior is driven by two incentives: the borrower earns a return on the unpaid mortgage payment amount, and the secured property can experience positive appreciation. This element of earning a return on the unpaid mortgage amount is unique to my model. In addition, my model has the lender involved in the determination of the loan outcome as the second player in the game.  This simple model can be solved analytically, instead of using the  numerical methods seen in both the standard default option model and the Ambrose-Buttimer model. The structure of the model makes it easy to incorporate other variables, such as late fees or payment structure, while still retaining tractability and clarity. Another advantage of the game-theoretic model is that the solution has the unique feature that reinstatement exists under both positive and negative equity situations. This is not a feature of the standard default option model or the Ambrose-Buttimer model.  It would be possible to create a model with strategic exercise of options. The borrower and the lender would strategically exercise options. But this approach is not implemented here since a simple gametheoretic approach satisfies the research goal of modeling the multiple loan outcomes.  The game-theoretic model includes two payoff-maximizing players, the borrower and the lender. At time 0, the loan is initiated. At time 1, the borrower chooses whether to pay the mortgage or to  45  become delinquent. In this model, the entire mortgage loan is due as a lump sum at time 1. Also at time 1, the lender has the alternative to foreclose on a delinquent loan immediately, or to wait. If the lender chooses to foreclose at time 1, then the game terminates. If the lender waits, then the borrower has the choice of paying the mortgage or remaining in default. If the borrower defaults, then the game ends with a foreclosure in time 2. If, instead, the borrower makes the payment, then the game ends with a reinstatement at time 2. Figure 3 displays the game tree.  The payoff to player i under outcome j is  n;.  =f(P,M,F,L,K,r,a)  where P is the property value at time 1, M is the mortgage repayment amount that is due at time 1, F is the foreclosure costs, L is the late fee, r is the discount rate and a is the property appreciation multiplier. K is the reward from delinquency for the borrower, which can be thought of as the return earned on the unpaid mortgage amount. The range of possible values for all variables is (0, +oo). The player indicator i can be B for borrower or L for lender. The possible outcomes j are pay at time 1 ( P I ) , foreclosure at time 1 (Fl), foreclosure at time 2 (F2) or reinstatement at time 2 (R2).  At time 2, the property value P has appreciated (or depreciated) to Pa and the borrower has earned K by investing the unpaid mortgage amount. If the borrower repays the mortgage at time 2, then a late fee L is incurred, and the amount due is M+L. The borrower has both an incentive to default (K) and a cost (L). If the game terminates at time 1, then the payoffs are multiplied by (1+r) to calculate the future value at time 2. This step makes the payoffs at the different time periods equivalent. A l l outcomes are shown in Figure 3.  46  Based on the payoff structure in Figure 3 and using backward induction, the borrower will pay at time 2 if  Pa-M-L  + K>0  If equation (7) holds, then the lender will choose to wait i f T1  >n  L  i  M + L>(P-F)(\  Assuming P-F>0,  r<\  + r)  then  fM +L  (8)  P-F  If (7) does not hold, then the borrower will choose to default at time 2. In this situation, the lender's decision is based on whether  Pa-F a >1+  >(P-F)(l P-F  + r)  (9)  Equation (7) considers the borrower's decision at time 2 while equations (8) and (9) consider the lender's decision at time 1. A l l that remains is to consider the borrower's decision at time 1.  47  If the borrower w i l l pay at time 2 and the lender w i l l wait at time 1, then (7) holds and (8) holds. The borrower evaluates: s- i i ^ j  lip,  ( P - M ) ( l + r)>  a<  P +  L-K  •+  Pa-M-L  +K  P-M  (10)  If (7) does not hold and (9) holds, the borrower's decision is based on:  rr  Hp,  > ri ir  ^  F  2  ( P - M ) ( l + r) > 0  P>M  (11)  In addition, i f the lender would foreclose at time 1, then the borrower's decision at time 1 is: lip,  s>  11^, ,  w h i c h reduces to P > M, equivalent to (11).  Equations (7) through (11) determine the outcome o f the game. The results are presented graphically in Figures 4 and 5 under two typical cases, one with positive equity and one with negative equity. A l l outcomes are possible i n this model, depending on the relative values o f the parameters. W h e n there is positive equity, meaning P>M, then the outcomes can be reinstatement or payment at time 1. W h e n there is negative equity, then the outcomes can be reinstatement or foreclosure. Therefore, this model demonstrates that reinstatement is a strategic borrower behavior that can occur under both positive and negative equity situations.  48  For example, consider the case where P = 115, M= 100,Z= \0,F=30,K=5,r  = 5% and a = 107%.  The outcome here would be reinstatement, which maximizes the borrower's payoff, since they receive 18.05 under reinstatement and only 15.08 i f they pay at time 1. Both of these outcomes provide a higher payoff than foreclosure, which is 0.  For this case, the lender's payoff is also  maximized under reinstatement, at 110 compared to 105 i f the borrower pays at time 1. The lender's payoff under foreclosure is 89.25 or 93.05 (depending on whether it takes place at time 1 or time 2), which is smaller than under reinstatement or payment at time 1. The reason why foreclosure is not optimal here is that the costs are relatively high. In positive equity situations, this model predicts that foreclosure never takes place, since the lender is only motivated to foreclose when P exceeds M by a large enough margin to offset the foreclosure cost, and the in those situations, a borrower would pay at time 1.  If a was 100% instead of 107%, then the outcome would be payment instead of reinstatement, since the borrower's return under the reinstatement outcome is reduced to 10, which is less than the 15.8 payoff from paying at time 1.  Figure 4 shows a diagram representing the regions of a and r where reinstatement would occur for a representative positive equity case. The region is where equation (8) holds and equation (10) does not hold. The a intercept for line (10) is ^  +  ^ — — and the r intercept for line (8) is ^  +  ^ - 1 . Using  the values of P, M, F, L and K above, the a intercept is 104.4% and the r intercept is 29.4%. When r = 29.4%, the value of a is 108.2% at the intersection of lines (8) and (10).  When the value of r is much larger than 29.4%, then the lender's payoff to foreclosing at time 1 becomes large, and the borrower pays at time 1 to avoid the 0 payoff they would receive under foreclosure. When a is depreciating and r is very small, then the lender would choose to wait at time  49  1, but the borrower would pay at time 1 to maximize their payoff. When K is larger, then the line (10) moves down, and reinstatement occurs for lower values of a. When F is larger, then the line (8) moves to the right, and reinstatement occurs for larger values of r.  In the case of negative equity, the only possible outcomes are reinstatement, foreclosure at time 1 and foreclosure at time 2. Payment at time 1 never occurs because that would cause a loss for the borrower, and foreclosure (with a 0 payoff) would always be preferred.  Consider the case where P = 90, M = 100, L = 10, F = 30, K = 5, r = 5% and a = 120%. The payoff for the borrower is negative i f they pay at time 1, 0 under foreclosure and positive under reinstatement. The lender's highest return is under reinstatement as well, so that is the outcome. If a was 110%, then the appreciation is not large enough to create a positive payoff for the borrower under reinstatement.  Since the borrower would not pay, then the lender chooses whether to foreclose at  time 1 or time 2. In this case, the lender prefers to foreclose at time 2. If a was 90%, then the lender would foreclose at time 1. Essentially, the lender is trading off r and a, as represented graphically by line (9) in Figure 5. The area bounded by line (9), the a axis and line (7) represents the zone where foreclosure at time 2 yields a higher return for the lender than foreclosure at time 1.  For the same values of P, M, L, F and K, reinstatement occurs in the region where r < 83.3% and a > 116.7%. When r < 41.7% (the intersection of lines (7) and (9)), then foreclosure at time 2 is an outcome for some values of a, as shown in the Figure 5.  These findings are interesting since they show that reinstatement is possible in both positive and negative equity situations. The option model of default cannot demonstrate such a finding, since it does not incorporate the borrower's reward from delinquency. In addition, the final outcome of the default process is based on the strategic actions of the two players in the process, the borrower and the  50  lender. For example, consider the case where P=\\5,M=  100, L= 10, F = 30, K = 5, r = 30% and a  = 130%. The borrower's highest payoff is under the reinstatement outcome. But the borrower does not default at time 1, because i f they do, the lender will foreclose. In option models of default, the borrower has the entire control of the default process. The model presented here introduces the role of the lender to the process.  Figure 6 displays an extension of the theoretical model to multiple periods. In the single period model, the mortgage repayment M was due in a lump sum. In the multiple period model, payment M l is due at time 1 and payment M 2 is due at time 2. A borrower can a) Default on M l at time 1 and default on M 2 at time 2. b) Default on M l at time 1, but then pay M l and M2 at time 2. c)  Pay M l at time 1, but then default on M2 at time 2.  d) Pay M l at time 1 and pay M 2 at time 2.  There are five potential outcomes to the game, as opposed to the four in the single period game. The new outcome is that there can be a foreclosure that takes place at time 2, with the first payment of M l being made as scheduled. In other words, the borrower makes the first payment but then defaults on the second payment. As in the single period model, the lender is involved in the determination of the outcome in the situations when the borrower defaults at time 1. The lender can choose to foreclose on the property, or defer the foreclosure process in order to provide an opportunity for the borrower to reinstate the loan.  The extension of the model to multiple periods has two main benefits. First, the question of whether default is affected by the relative sizes of M l and M 2 can be evaluated. Second, the issue of the contract rate deviating from the market rate can be studied. This is important because if this deviation is seen, then at time 1, the outstanding balance of the mortgage will not be equal to the market value  51  of the mortgage. If the borrower has a contract rate that is lower than the market rate, then he has a benefit that discourages him from defaulting. If, on the other hand, the borrower has a contract rate that is higher than the market rate, then he has an incentive to default, because if he were to abandon this property and go to the market to initiate a new mortgage on a similar property, he could get a lower rate mortgage.  The multiple period model includes an additional variable, V , to capture the amount of the incentive or disincentive related to movements in the market rate. Essentially, if a borrower is foreclosed upon in time 1, then they lose the value V , which would be positive if market rates have risen. In fact, V equals the mortgage outstanding balance less the market value of the mortgage, also called the premium or discount. The benefit to including this variable in the model is to determine what magnitude of V , and therefore what magnitude of changes in market interest rates, is required to induce changes in default behavior.  Based on the payoff structure in Figure 6, and using backwards induction, the outcome can be determined by evaluating the following equations. If the borrower pays at time 1, then the decision of whether to pay at time 2 is based on i f  Pa-M\-M2>-M\ a>-^r  (12)  If, on the other hand, the borrower has defaulted at time 1, and the lender has chosen to allow time for the borrower to reinstate, then the borrower will pay at time 2 i f  Pa-M\-M2-L  + K>0  MI + M2 + L-K  52  If (13) holds, then the lender will choose to foreclose at time 1 i f  (P - F){\ + r) > MX + Ml + L MI + M2 + L r>  , 1  (14)  P-F If (13) does not hold, then the lender will choose to foreclose at time 1 i f  (P-F)(\ r>\  P-F.  + r)> a-  Pa-F (15)  P-F  Given the four equations above, labeled (12) through (15), there are now multiple situations to evaluate in order to build a complete series of alternative outcomes. There are several situations in which payment at both time 1 and time 2 can arise. The first is i f (12) holds, (13) does not hold and (15) holds. In that case, the borrower would pay at time 1 i f  Pa-M\-M2>-V(\  a>  + r)  MI + M2-V r-\  (16)  P If (12) holds, (13) does not hold, (15) holds and (16) does not hold, then the outcome would be foreclosure at time 1. Similarly, i f (12) holds, (13) holds, (14) holds and (16) holds, then the borrower would pay at both time 1 and time 2. Conversely, i f (12) holds, (13) holds, (14) holds and (16) does not hold, then the outcome would be foreclosure at time 1.  An additional situation that can lead to payment at both time 1 and time 2 is i f (12) holds, (13) holds and (14) does not hold, and  Pa-Ml-M2>Pa-Ml-M2-L  +K  K <L  (17)  In this situation, i f (17) did not hold, then the outcome would be reinstatement at time 2.  53  The final situation in which the outcome will be full payment by the borrower is i f (12) holds, (13) does not hold, (15) does not hold, and  Pa-M\-M2>0 MI + M2 a>  (18)  P In this situation, i f (18) does not hold, then the outcome would be a foreclosure in time 2, and the borrower would not pay at time 1 and would not pay at time 2. To complete the list of outcome alternatives, four additional situations need to be considered. These are cases where (12) does not hold, meaning that the borrower does not have incentive to pay at time 2 if they have already paid at time 1. These are the cases where the outcome may be a foreclosure at time 2, where M l was paid by the borrower to the lender.  The first case is when (12) does not hold, (13) does not hold and (15) holds. The borrower would pay at time 1 i f  -M\>-V(\ Ml r>  + r) , 1  (19)  V Otherwise, the outcome would be that the borrower did not pay at time 1, and the lender foreclosed at time 1. Similarly, i f (12) does not hold, (13) holds, (14) holds and (19) holds, then the outcome would be foreclosure at time 2 with M l paid, and i f (19) did not hold, then the outcome would be foreclosure at time 1, M l not paid.  If (12) doesn't hold, (13) holds and (14) doesn't hold, then the borrower would pay at time 1 i f - M l > Pa - Ml - M2 - L + K  54  M2+L-K a<  (20)  P and the outcome would be foreclosure at time 2, M l paid. If (20) did not hold in this situation, then the outcome would be reinstatement at time 2. The final situation for analysis is when (12) does not hold, (13) does not hold, and (15) does not hold. Then the borrower would evaluate -M1>0 which is always false, since the mortgage payments amounts are constrained to be positive. Therefore, when (12) does not hold, (13) does not hold, and (15) does not hold, the outcome is always foreclosure at time 2, with M l unpaid.  The set of equations (12) to (20) define the outcome of the game to one of the five alternatives, which are a) Full payment b) Foreclosure at time 1, no payments made c) Foreclosure at time 2, no payments made d) Foreclosure at time 2, payment M l made as scheduled e) Delinquency and reinstatement ( M l not paid at time 1, but M l and M 2 paid at time 2)  The results are presented graphically for three cases, in Figures 7 through 9. Figure 7 is a typical negative equity case, with values of the variables set to P = 90, Ml = 13, M2 = 97, L = 10, F = 30, K = 15 and V= 12. Since F i s positive, it means that there is a loss associated with the movement in market interest rates i f the borrower were to be foreclosed at time 1. Therefore, it can be inferred that interest rates have increased since the time of loan initiation.  55  Figure 7 should be compared to Figure 5, the analogous case in the single period model. In both figures, the a =  100%  is a relevant dividing line between outcomes. Above a = 1 0 0 % , the property is  appreciating, while below it, depreciation occurs. One key difference between the two versions of the model is the existence of the new outcome where foreclosure occurs at time 2 when Ml has been paid in the multiple period version of the model. This alternative arises for relatively high values of the discount rate r and relatively lower appreciation rates. It supplants the foreclosure at time 1 region in the single period model.  It is particularly interesting that both reinstatement and full prepayment are possible outcomes in this negative equity case. Reinstatement occurs for relatively high appreciation. The reward from delinquency, K is the incentive for reinstatement. It is the money that a borrower can earn by investing the unpaid mortgage amount elsewhere. If K was larger, then the line corresponding to equation (13) on Figure 7 would move downwards, and the reinstatement region would be larger. For example, using the values listed above, then reinstatement occurs when  a>  + M2 + L—AT  _  1 ^yo^  jf  m  e  reward to delinquency K was  25  instead of  15,  then  reinstatement would occur when a > 106%.  One of the main points of the multiple period model is to study the effect of changes in market rates on loan outcomes. The variable Vis the amount of the loss that a borrower would experience i f default occurred when market rates have increased over the contract rate. The variable V is associated with equation (19) on Figure 7. at r =  8.33%.  The illustrated values have Ml ~ 13 and V= 12, so the x-intercept is  This line divides the region between the foreclosure at time  1  outcome and the  foreclosure at time 2 (with Ml paid) outcome. If V was higher, meaning a larger spread between the market rates and the contract rate, then line (19) would move to the left on Figure 7, and would eventually disappear into the y-axis when V= 13. In this case, foreclosure at time 1 would not be  56  observed - the region would be supplanted by the foreclosure at time 2 (Ml paid) outcome. Essentially, there is a disincentive associated with early default when V is relatively large. Besides the role of V, the other key aspect of the multi-period model is the ability to study how the relative sizes of Ml and M2 affect the loan outcome. In Figure 7, the values used were Ml = 13 and M2 = 97. These amounts were chosen to reflect the fact that commercial mortgage loans often have a larger balloon payment due at the end of the term. In Figure 8,1 reverse these amounts so that Ml = 97 and M2 = 13 and re-calculate the outcome regions. The key difference is that the outcome where the borrower pays Ml but then defaults at time 2 disappears. That entire region is supplanted partially by the full payment outcome and partially by the foreclosure at time 1 outcome.  When Ml  is relatively large, there would never be a situation where it would be in the borrower's interest to pay Ml but not M2. Instead, the borrower would either pay both or pay neither, depending on the relative values of the other variables, as shown along line (16) on Figure 8. The implication from this model therefore, is that loans structured with larger balloons would have larger regions where foreclosure was the outcome.  Figure 9 presents the positive equity case for the multiple period model (P = 115,1- = 10, K= 15, V = 12, Ml = 13, M2 = 97), which is analogous to Figure 4 for the positive equity single period case. We see that for both models, reinstatement is a possible outcome when there is positive equity. This is an important feature of the model and distinguishes the findings here from the standard default option model. It is also satisfying since it provides a basis for understanding why positive equity loans are observed to default. Essentially, the borrower is taking advantages of the benefits of reinstatement, and the lender does not foreclose because of the high associated costs. Foreclosure can also arise in this positive equity case when the property value is depreciating.  57  The extension of the model to multiple periods confirms the key findings from the single period model and contributes several additional points. The key findings confirmed are first, all mortgage loan outcomes are possible, depending on the relative values of the key variables of mortgage equity, the borrower's costs and rewards of delinquency, foreclosure costs, the property appreciation or depreciation rate and the discount rate. Second, the actions of the lender contribute to the outcome of the loan in this strategic model. The borrower cannot always experience the outcome that maximizes their payoff. Third, there are new insights about reinstatement behavior, especially that it can be observed for both positive and negative equity loans.  The multiple period model confirms the main findings above, and contributes two others, one related to market rate movements and one about balloon payments. The movement in market rates over the term of the loan will affect the outcome, especially in terms of the timing of default. Increases in market rates increase the loss associated with early default, and therefore provide a disincentive. The payment schedule will also affect the outcome of the loan, since a larger relative balloon size increases the set of situations where foreclosure will occur.  Data  A major Canadian commercial mortgage lender provided the dataset to test these theoretical findings. Observations are monthly, from November 1996 to May 2001, with three months of missing data, for a total of 52 months. In the first observation, there were 1,126 active loans, and each month new loans were added and some loans terminated. A total of 1,637 loans are present for at least one month during the observation window.  Every loan is secured by commercial property in Canada.  The institutional and regulatory  frameworks for commercial mortgages in Canada and the United States share many aspects. For  58  example, prepayment clauses and the rules governing delinquency are similar. The laws regarding foreclosure vary across the Canadian provinces, as they do across the American states. the incidence of a personal or corporate guarantee may be higher.  13  In Canada,  The competitive market structure  is different in that the Canadian market is dominated by a small number of large, national lenders, of which the data supplier is one. Securitization in Canada is not as common as it is in the U.S.  A l l the loans by this lender are fixed-rate mortgages with a fixed term that usually ranges between 1 year and 30 years, with the most common terms being 5 years, 10 years and 20 years. Most loans have a term shorter than the amortization period, so a balloon payment is usually due at maturity. Approximately 95% of the loans are amortizing with monthly payments of principal and interest, with the remainder making interest-only payments either monthly or annually.  The lender has a standard clause in the mortgage contract prohibiting early repayment . However, 14  the company policy is to accept early repayment when it is accompanied with a penalty large enough so that the lender can maintain the contract yield by substituting Canadian government bonds. This is identical to yield maintenance penalties observed in the U.S. except that the discount rate is the Canadian government bond yield. This penalty is sufficiently severe so that the economic incentive to refinance through prepayment is removed.  There were 190 loans that prepaid during the  observation window, of which 181 were classified as never delinquent and 9 of which were delinquent but then reinstated by prepayment.  A loan's delinquency status is defined as whether or not the loan ever had a payment 90-days past due within the observation window. The number of days, 90, was chosen because it is linked to the  88% of all loans in the Canadian dataset used here have a guarantee. I was unable to find comparable figures for the U.S. Some loans originated before the mid-1970s may have a clause in their contract specifying some other prepayment penalty, such as 6 months interest. 13  14  59  beginning of intensive servicing by the lender. Note that the lender functions as their own "special servicer".  Archer et al. (2002) also used the 90-day definition.  O f the 1637 loans, 214 were  delinquent at least once. Some loans were delinquent multiple times, with the borrower sequentially skipping payments, resuming payments and then skipping them again.  In total, there were 297  instances of delinquency on the 214 loans. Table 14 presents the loan outcome by the loan-to-value ratio, Table 15 gives descriptive statistics for the independent variables, broken down by delinquency status and Table 16 presents the correlations across the independent variables.  Time series properties of the dataset are displayed graphically in Figures 10 through 13. The dataset tracks loans from November 1996 to May 2001, which is the scale for the x-axis of these graphs. Figure 10 and 11 describe the temporal pattern of delinquency. For each month in the observation window, at least one loan experienced its first delinquency, as shown in Figure 10. During the timeframe considered, the lender reduced the number of commercial loans in their portfolio from 1435 to 1033.  The number of delinquent loans, and the percentage of the portfolio that this  represents, is shown in Figure 11.  New loans were initiated most months in the observation window. Figure 12 shows the number of new loans initiated per month, along with the average contract rate on these new loans. The number of new loans per month decreased in the latter half of the timeframe due to a deliberate policy by the lender to allocate relatively more investment dollars to corporate bonds as opposed to commercial mortgages. Figure 13 shows the average contract rate for all loans in the portfolio. This rate was above 10% at the start of the observation window, and then declined, due to the fact that the market rate used to price renewals and new loans initiations was relatively lower during this timeframe.  A critical value emerging from the game theoretic model is P - M, a measure of the borrower's equity. For the empirical estimations, the loan-to-value ratio is used, calculated as the outstanding  60  balance divided by the property value. A n advantage of this database is that there are multiple property appraisals available for each mortgage, including historical values. The lender periodically re-appraises the underlying property for loan monitoring purposes. These re-appraisals are done at irregular intervals, which vary based on the size of the mortgage and the lender's discretion. To measure the property value at the time of each observation, the appraisal closest in time, either forward or backward, is appreciated or depreciated based on returns from the Russell Canada Property Index for that property type and region.  15  In this way, the resulting property value is quite  accurate relative to other empirical studies that appreciate the property value from loan initiation.  The variable a, property appreciation, was set equal to the Russell Canada total property return for that region/property type over the previous year for empirical estimation purposes. Using an annual value eliminates the so-called smoothing bias that is present in quarterly measures of real estate returns.  If a region/type combination is unavailable, then the appreciation rate for the region is  applied. The discount rate, r, is measured as the 10-year benchmark Canadian government bond. The lender calculates late fees, L, based on the contract rate of the mortgage, which is included in the empirical estimations.  A direct measure of the foreclosure cost F was not available. Anecdotal  evidence from the lender suggests that the foreclosure costs are related to the size of the mortgage and the jurisdiction, so the outstanding balance and the region are included in the empirical estimations. The presence of a guarantee is also included in the empirical estimations as a foreclosure cost, since i f a guaranteed loan becomes delinquent, there is the potential for additional costs for the borrower through deficiency judgments.  Previous empirical work in this field has demonstrated the importance of cash flow considerations. In the model here, this is incorporated through the reward for delinquency, rM, where a borrower fails to  This index doesn't report values for all property type/region combinations. If a combination is unavailable, the appreciation rate for the region is applied. 15  61  make the mortgage payment in order to divert funds to another use. The return to this alternate use is based on r, the benchmark bond return, which is included in the empirical estimations. The debt coverage ratio is also included as a cash flow measure. Whenever a property appraisal is performed, the lender calculates and records the debt-coverage ratio. The one closest in time to each observation is selected.  16  The cash flow from the property is based on the revenues actually generated by the  property, not on the pro-forma statements.  The lender diversifies their portfolio across property type and geographic region, as illustrated in Table 13. The largest category of property types is retail, which includes shopping centers, strip malls, restaurants, auto dealerships, stand-alone fast food restaurants and other retail properties. Besides retail, the major categories are offices, apartments and industrial/warehouse. The remaining other category includes vacant land, hotels, motels, airport properties, medical buildings, government properties, nursing homes and schools.  The six geographic regions are Quebec, Ontario, Alberta, British Columbia, Atlantic (which includes the provinces of Newfoundland, Nova Scotia, Prince Edward Island and New Brunswick) and Prairie (which includes the provinces of Saskatchewan and Manitoba).  The region with the highest  proportion of loans is Ontario, followed by Quebec.  Empirical Methodology and Results  The goal of the empirical estimations is to evaluate whether the relationships predicted in the gametheoretic model hold in the determination of the loan outcomes. Unfortunately, the structure of the database limits the available methodologies. The methodology that is most closely aligned with the  1 am unaware of a Canadian rental index across property types, so I am unable to adjust the debt-coverage ratio for the passage of time. The average age of the debt coverage ratio is 337 days. 16  62  theoretical structure is a two-step Heckman model with selection. However, due to the nature of the database, only simple models with a small number of independent variables can be appropriately modeled, as will be seen in Table 23.  The proportional hazards methodology has been applied to commercial mortgage default by Vandell et al. (1993) and others. Since the dataset used in this paper includes just an observation window, and not the entire life of the loan, this method can not be used. Although the progression of a loan from delinquency to foreclosure resembles a series of nested decisions, the nested logit model is not appropriate since the decision about the loan outcome is based on characteristics of the individual loan, not the outcomes themselves.  Therefore, the methodologies used in this paper are the logit and multinomial logit. Although the sequential nature of the default decision is not empirically modeled, the key advantage of these methods is that the individual loan characteristics can be used as the independent variables and the loan outcome as the dependent variable. This means that the fundamental relationships between the loan characteristics and the outcome can be empirically examined.  The results of the empirical estimations are in Tables 16 to 23. In the first estimation (Table 16), the methodology closely resembles other empirical studies in the commercial mortgage default literature, since the characteristics of the foreclosed loans are studied in relation to the dataset as a whole. See, for example, Vandell et al. (1993), Ciochetti et al (2002), Ambrose and Sanders (2001), and Goldberg and Capone (2002). The binary dependent variable is set equal to 1 i f the loan was foreclosed during the observation window. A logit estimation technique is employed, where  e  x,p  63  The independent variables are measured at November 1996 for most loans, and at the date of the loan origination for any loans that were initiated after November 1996. Since the variable indicating the presence of a guarantee is missing for many of the observations, a modified zero-order technique is used. If the value is missing, then the variable is set equal to 0. A n additional variable is created and set equal to 1 i f the value if missing. This additional variable is essentially a control, and is not reported in the Tables.  Three specifications are reported in Table 16. In the base specification (number 1), the loan-to-value ratio is significant and positive. A higher loan-to-value ratio, meaning less equity in the property, is associated with a higher likelihood of foreclosure.  This is consistent with the prediction of the  theoretical model, and with the results from previous empirical studies. Recall that the loan-to-value is the outstanding balance divided by the property value, measured at the time that the loan is first observed in the observation window, which is November 1996 for most loans.  A n alternative  definition of the loan-to-value ratio is formulated by dividing the market value of the loan at this same point in time by the property value.  When this "market" loan-to-value ratio was used in the  estimations, there were no substantial changes in the results.  Another way to measure the loan-to-value ratio would be to use the outstanding balance divided by the property value measured at the time of loan initiation. This is similar to the approach taken by Archer et al (2002). They found that the loan-to-value at the time of loan initiation is unrelated to future default. They explain that the loan-to-value at this point in time is endogenous and therefore unrelated to future default.  When I used the "initiation" loan-to-value ratio (not reported), the  coefficient became insignificant, confirming the Archer et. al findings. The formulation reported in the tables - outstanding balance divided by property value, measured at the first observation in the window - was chosen because it mimics a watch list-type technique used by lenders to monitor their portfolio. They observe the characteristics today in order to predict future delinquencies.  64  Another key variable arising from the estimations in Table 16 is the debt coverage ratio, which has a significant and positive coefficient. As the value of the property net operating income (relative to the mortgage payment amount) increases, then the borrower has more surplus cash flow and the likelihood of foreclosure decreases. The coefficient on the variable indicating the presence of a guarantee was significant and negative, indicating that loans without a guarantee were more likely to be foreclosed. Holmes (2004) discusses guarantees in more depth.  In specification 2, dummy variables for the regions are included. The excluded regions are Ontario and the Prairies.  (The Prairie region was automatically dropped due to a small number of  observations.) British Columbia had a marginally significant negative coefficient. In specification 3, the property type dummies were included, where retail is the excluded outcome. The coefficient on apartments was marginally significant and negative.  When both property types and regions were  included, these negative but only marginally significant coefficients on apartments and British Columbia remained. The addition of the dummy variables did not affect the key results on the loanto-value ratio and the debt coverage ratio.  Table 17 reports a series of estimations that are identical to Table 16 except that the dependent variable is set equal to 1 i f the loan was ever delinquent during the observation window. This is a broader definition of default than foreclosure, and is also used by Archer et al. (2002). The key results from the foreclosure estimation also hold for the delinquency study - the coefficients on the loan-to-value ratio and the debt coverage ratio are significant, and positive and negative respectively. The absolute values of the significant coefficients are smaller in the delinquency estimation, and the pseudo R are lower. 2  65  In Table 18, the dependent variable is set equal to 1 i f the loan was ever delinquent and reinstated during the observation window. Reinstatement has not been studied in this manner, before, and the results are interesting. Although all delinquent loans (which includes those that reinstated and those that were foreclosed) can be distinguished by their loan-to-value ratio and their debt coverage ration, the subset of delinquent loans that were reinstated do not differ from the pool of all other loans in a consistent, identifiable way.  Both the loan-to-value ratio and the debt coverage ratio were  insignificant, even at the 10% level. The issue of reinstated loans is investigated further below.  One way to isolate the reinstated loans for analysis is to use a multinomial logit empirical estimation. In Table 19, the dependent variable for the empirical tests is the outcome of the loan. There are k = 4 potential outcomes for a loan: never delinquent, delinquent/unresolved, delinquent/reinstated and delinquent/foreclosed.  The empirical method is a multinomial logit specification where any  observation / = 1 to n can fall into one of the k groups.  For each observation there exists a  probability:  Pr(7ey) =  T  for all k groups.  Equation (13) is unidentified unless e  p>  (13)  = 1. The coefficients in the regression results are therefore  a measure relative to one excluded outcome, which is "never-delinquent" in this case. A loan is delinquent/unresolved when it is still delinquent at the last date of the observation window. The results for this outcome are not reported.  This estimation method has application for lenders. At any point in time, a lender may wish to look at the characteristics of their commercial loan portfolio in order to model the eventual outcome of the loan, whether it is to foreclosure or delinquency/reinstatement. This empirical study helps to identify the characteristics of the loans that are relevant in this exercise.  66  The coefficient on the loan-to-value ratio for foreclosed loans is positive and significant. Therefore, relative to the likelihood that a loan is never delinquent, the likelihood of a loan being foreclosed is increased for higher loan-to-value ratios. The same result of a positive and significant coefficient on the loan-to-value ratio also holds for the reinstated loans, although the magnitude of the coefficient is smaller. The debt coverage ratio is negative for both foreclosed loans and reinstated loans, although it is only significant across all specifications for the foreclosed loans. This result, broadly speaking, implies that the reinstated loans can be distinguished from the never-delinquent loans based on their loan-to-value ratios. In order to compare the foreclosed loans to the reinstated loans, an additional multinomial logit study is conducted and reported in Table 20.  This estimation is conditional on delinquency, meaning that the dependent variable only has a value i f the loan is delinquent. There are k = 3 possible outcomes: unresolved, foreclosed and reinstated. In Table 20, the result for the reinstated outcome is reported relative to the excluded outcome, foreclosure. The unresolved outcome is not reported. The values of the independent variables are measured at the time that the instance of delinquency occurs. Therefore, it is also possible to conduct a test of the impact of time sensitive variables. In the previous estimations, there was little variation in the values of these variables, since most of the observations were dated November 1996.  This estimation is analogous to a model that a lender would run in order to determine the most likely outcome of a delinquent loan. Table 20 reports the most important empirical finding of this paper: the characteristics of reinstated loans differ from those of foreclosed loans. The implication is that a lender can use the variables identified in this model in order to separate the loans that are more likely to become foreclosed from those that are more likely to be reinstated.  The variables that are  significant are the loan-to-value ratio, the debt coverage ratio and the guarantee variable. The signs reported in this table are the reverse of what was seen in the previous estimations, which is as  67  expected since the coefficients are reported for reinstated loans relative to foreclosed loans. For example, a negative coefficient on the loan-to-value ratio should be interpreted to mean that the likelihood of a delinquent loan becoming reinstated, relative to being foreclosed, is lower for higher loan-to-values.  Specification 2 includes the property type "other", which is marginally significant and positive. Other specifications that included dummy variables for the various property types and regions are not shown here because of a lack of significance.  The effect of time-varying variables can be explored in this estimation because the values of the independent variables are captured at the moment when a delinquency first occurs.  In previous  estimations, this was not possible since variables were measured as of the date of the first observation. The theoretical model predicts that both the discount rate and the property appreciation rate should be significantly related to the outcome of a loan. The prediction is that low discount rates and high property returns should be associated with reinstatement. The empirical estimations did not confirm these predictions, since the coefficients on both the property return and the discount rate were not significant. One limitation of the database is the relatively short length of the observation window (November 1996 to May 2001), and this may be a possible explanation for the lack of significant results on time-varying variables.  Variables to indicate the year that the delinquency occurred were included in the third specification. Loans that became delinquent in 1998 and 2001 were significantly more likely to become reinstated. When the year dummy variables, discount rate and property return were all included (in specification 4), then these significant effects disappeared.  68  Table 21 and 22 are further attempts to explore delinquency behavior using temporal variables. In Table 21, a logit estimation, the dependent variable is set to 1 i f the delinquent loan ends in foreclosure, and 0 i f it ends in reinstatement or is unresolved. The key variables of loan-to-value ratio, debt coverage ratio and guarantee were significant with the expected signs. The discount rate, property return and year dummy variables were not significant. In table 22, the dependent variable is measured at the time of delinquency, and is set to 1 i f the loan is reinstated. Again, the loan-to-value ratio, debt coverage ratio and guarantee were significant with the expected signs. Although neither the property return nor the discount rate is significant, the dummy variables indicating the year is negative and significant for 1999 and 2001. This finding holds even when the property return and discount rate are added to the set of independent variables, in specification 4. This result suggests that there is some time variation in the behavior of borrowers and lenders with respect to the resolution of delinquency to reinstatement, and provides the thinnest measure of support for the contentions to this regard from the theoretical model.  The results in Table 23 reinforce the key findings by using an empirical method that is more closely aligned with the theoretical model. This is a two-step Heckman method with selection. Due to the nature of the database, only simple models with a small number of independent variables can be appropriately estimated. In the first stage, the loan-to-value ratio is used to select the delinquent loans from the pool of all loans. In the second stage, the debt coverage ratio is used as the independent variable in a probit estimation for reinstated loans. The loan-to-value ratio is significant and positive in the selection equation, and the debt coverage ratio is positive in the reinstatement model equation. Both signs are in the expected direction, confirming results from previous estimations. A n additional specification was run where the guarantee replaces the debt coverage ratio in the probit model for reinstatement, and the coefficient was found to be significant and positive.  69  Conclusion  The goal of this paper was to examine the resolution of delinquent loans using a theoretical model and empirical tests. The model in this paper uses a game theory framework and was able to capture some realistic aspects of the default process. For example, the model incorporates a strategic role for the lender that affects the borrower's decision process.  In addition, the model allows time to elapse  between delinquency and resolution, which allows movement in property values to affect the outcome.  And finally, the incentive to be temporarily delinquent in order to divert funds to an  alternative use is present in the model. The predicted outcomes are based on the relative values of the key variables, which are the property value, mortgage amount, foreclosure costs, late fees, property return and the return on alternative investments. A unique aspect of the model presented here is that multiple outcomes are possible at positive and negative equity positions. A loan with positive equity can become delinquent and reinstate, and a loan with negative equity can be reinstated.  The key finding of the empirical tests is that the characteristics of the loan are distinguishable across delinquency outcomes. The results have applicability to lenders in the management of their loan portfolios. Models were presented that mimic a tool that could be used by lenders to predict which loans will become delinquent and how the delinquency will be eventually resolved.  70  Figure 3 - Game tree  Foreclose  Paid at time 1 (P-M)(l + r) M(l + r)  Foreclosed at time 1 0 (P-F)(l+r)  Foreclosed at time 2 0 Pa -F  Reinstated at time 2 Pa-M-L+K M +L  71  Figure 4 - Single Period Typical case for P > M  Figure 4 - Single Period Typical case for P < M  a  (8)  Reinstatement  P +  L-K (7)  Foreclosure at time 2  \9)  Foreclosure at time 1  100%  M + L  P - F  73  Figure 6 - Multiple Periods  Default at 1  Foreclose at 1  Pay at 2  Foreclosed at time 1 -V(l  +r)  (P-F)(l+r)  Default at 2  Foreclosed at time 2 (Ml was NOT paid) 0 Pa  -1^  -F  Pa-Ml-M2  -Ml  Ml  Pa -F  Reinstated at time 2 Pa-Ml-M2-L+K Ml  + M2+  L  Full payment  Foreclosed at time 2 (Ml was paid) + Ml  +M2  Figure 7 Multiple periods - Typical case P < M l + M 2 and M l < M 2  a Reinstatement (13)  M\+M2+L-K P  Full Payment M2 P  Foreclosure at 2 M l Not paid  (12)  ( 1 5 ) / ^  (HfY Foreclosure at 2 M l Paid  100% (19) Foreclosure at 1  Ml  M2-P  V  P-F  MI+M2 + L-K-P  P-F  T  75  Figure 8 Multiple periods - Typical case P < M l + M 2 and M l > M 2  76  Figure 9 Multiple periods - Typical case P > M l + M2  a Reinstatement  100%  (14) Full payment (13)  MUM2+L-K p  Full payment  MX + M2-V P  (12)  M2 P  Foreclosure at 1  Foreclosure at 2 M l Paid (19)  MX  ~V  ^  M1 + M2 + L  P-F  L  r  77  Figure 10 Number of loans that are incur their first delinquency per month 16 14 12  FigureH Number and percentage of delinquent loans 8.00%  80  T  7.00%  70  6.00%  60  o ra  50  § 5.00%  o i_  a>  a. 4.00%  40  3.00%  30  2.00%  20  Time 2001  1996 •Percentage « ~ ~ N u m b e r  o n  £  Figure 12 N u m b e r o f n e w l o a n s / A v e r a g e c o n t r a c t rate o n n e w l o a n s  (0  (/)  C CT3 O  o c o o o  £  U)  TO  3  a> > <  Time oo o  •Number of new loans  Average contract rate on new loans  Figure 13 Portfolio rate and market rate 11.00  10.00  9.00  8.00  7.00  6.00  5.00  1996  Time  Market rate — Average contract rate across all loans  2001  Table 12 - Regional and property type distributions across outcomes By Region  Atlantic 8%  \  1  9  J\[  \  Y  \ -"""^  Alberta 6%  I PrRirip  ~~f~  Quebec / 27% /  \  \  "Y  \ ^^  2%  ====  r 3%  7 %  Quebec / 27% /  \  / / // X  4  Atlantic 10%  B  Alberta  T 10%  / Quebec / 28%  =^^ Prairie J 2%  C  3 %  %  \f//  \  Prairie  / / 0 \  5  %  y  Ontario 54%  Ontario 35%  Ontario 38%  Prairie  J Alberta  Reinstated loans  Alberta  Atlantic 11%  BC —^21%  %  \  Quebec / 27% /  Atlantic 8%  BC  I  Foreclosed loans BC 1%  Never delinquent loans  All loans  —  Ontario 44%  By Type  Never delinquent loans  All loans  Apt 15%  Apt 14% Ret / 38%/  Ret / 38%/  LL Js X  Other 5%  OO  to  Foreclosed loans  Off 21%  | Ind 122%  V  Other^ 4%  N.  y Off 21%  J  Ret / 46% j  r  Reinstated loans  Apt 8%  Apt 11% Ind \15%  )  22%  Other 6%  Off 25%  Ret / 37%/  Other 12%  Ind ,22%  IS 18%  )  T a b l e 13 - L o a n O u t c o m e b y L o a n - t o - V a l u e R a t i o  TOTAL | Outcome Never delinquent  LTV < 40% 307 94.2%  TOTAL  127 94.1%  5 0 % to 6 0 %  6 0 % to 7 0 %  7 0 % to 8 0 %  188  241  272  95.4%  94.5%  91.0%  8 0 % to 9 0 % 100 83.3%  9 0 % to 1 0 0 %  LTV < 100%  67  1302  80.7%  92.0%  6  0  4  5  7  5  5  32  1.8%  0.0%  2.0%  2.0%  2.3%  4.2%  6.0%  2.3%  Delinquent and foreclosed  Delinquent and reinstated  4 0 % to 5 0 %  13  8  5  9  20  15  4.0%  5.9%  2.5%  3.5%  6.7%  12.5%  11  81 5.7%  13.3%  326  135  197  255  299  120  83  1415  100.0%  100.0%  100.0%  100.0%  100.0%  100.0%  100.0%  100.0%  1 0 0 % to 1 1 0 %  1 1 0 % to 1 2 0 %  1 2 0 % to 1 3 0 %  TOTAL Outcome Never delinquent  38 73.1%  Delinquent and foreclosed  9 17.3%  Delinquent and reinstated-  TOTAL  oo  1 3 0 % to 1 4 0 % |  1 4 0 % to 1 5 0 % |  1 5 0 % to 1 6 0 % |  LTV > 160%  LTV > 100%  11  9  7  5  3  11  84  47.8%  75.0%  50.0%  71.4%  50.0%  45.8%  60.9%  7  1  4  30.4%  8.3%  28.6%  5  5  2  3  9.6%  21.7%  16.7%  21.4%  1 14.3% 1 14.3%  3  11  50.0%  45.8%  36 26.1%  0  2  18  0.0%  8.3%  13.0%  52  23  12  14  7  6  24  138  100.0%  100.0%  100.0%  100.0%  100.0%  100.0%  100.0%  100.0%  V  T a b l e 14 - D e s c r i p t i v e statistics Panel 1 - All loans, broken down by outcome, measured at first occurence in the observation window  N Loan-to-value ratio Debt coverage ratio Proportion with a guarantee Contract rate (%) Outstanding balance (Smillions)  1588 1381 898 1637 1637  All loans Mean Std. Dev. 0.653 1.480 0.876 9.723 4.059  0.361 0.746 0.329 1.924 7.884  Never delinquent Mean Std. Dev. N 1386 1188 774 1423 1423  0.615 1.537 0.888 9.680 3.880  0.300 0.751 0.316 1.889 7.886  N 68 55 30 71 71  Foreclosed Mean Std. Dev. 1.164 0.855 0.667 10.549 5.667  0.797 0.469 0.479 2.196 8.062  t-stat 5.66 10.19 2.50 3.28 1.82  Note: T-statistic calculated versus the never-delinquent mean.  Panel 2 - All delinquency instances, broken down by outcome, measured at first incidence of delinquency  Loan-to-value ratio Debt coverage ratio Property return Treasury Bill rate Proportion with a guarantee  All delinquency instances N Mean Std. Dev.  N  0.530 0.585 0.074 0.989 0.395  67 54 70 70 29  275 274 297 297 172  0.819 1.095 0.122 4.089 0.808  Note: T-statistic calculated versus the foreclosed mean.  oo 4i>  Foreclosed Mean Std. Dev.  N  0.834 0.470 0.107 1.036 0.484  171 180 187 187 109  1.097 0.847 0.122 3.599 0.655  Reinstated Mean Std. Dev. 0.741 1.169 0.121 4.162 0.853  0.346 0.623 0.063 0.957 0.356  t-stat 3.38 4.07 0.07 3.96 2.06  N 99 98 60 103 103  Reinstated Mean Std. Dev. 0.768 1.301 0.883 9.725 4.817  0.352 0.665 0.324 2.015 8.221  t-stat 4.23 3.34 0.10 0.22 1.12  T a b l e 15 - C o r r e l a t i o n s Property Types  Regions Contract Loan-torate value ratio Debt coverage ratio Loan-to-value ratio  1.00  Debt coverage ratio  -0.41  1.00  Contract rate  -0.13  -0.12  1.00 1.00  Guarantee  British Columbia  Alberta  Quebec  Atlantic  Apartment  Industrial  Office  Outstanding balance  0.07  -0.14  -0.07  Guarantee  0.01  -0.01  -0.02  -0.08  Region: B.C.  -0.08  0.04  -0.10  -0.01  0.10  1.00  Region: Alberta  -0.05  0.05  -0.16  0.09  -0.19  -0.12  1.00  Region: Quebec  -0.05  -0.02  0.10  -0.09  0.13  -0.30  -0.16  1.00  Region: Atlantic  0.07  0.04  0.00  -0.01  0.09  -0.13  -0.07  -0.18  1.00  Property type: Apt.  -0.10  0.16  -0.08  -0.05  0.01  0.01  0.00  -0.07  -0.07  1.00  Property type: Industrial  -0.03  0.05  0.09  -0.17  -0.07  -0.12  -0.05  -0.01  -0.04  -0.16  1.00  Property type: Office  0.21  -O.08  -0.08  0.13  0.01  0.12  0.09  -0.08  0.15  -0.16  -0.27  1.00  Property type: Other  -0.04  -0.09  0.01  -0.02  0.05  -0.07  0.04  -0.01  -0.03  -0.06  -0.10  -0.10  Property Loan-tovalue ratio Debt coverage ratio return  oo  Outstanding balance  Loan-to-value ratio  1.00  Debt coverage ratio  -0.28  1.00  3-month Treasury Bill Guarantee  1.00  Property return  -0.38  0.08  1.00  Treasury Bill rate  0.28  -0.17  -0.54  1.00  Guarantee  -0.01  0.00  0.00  -0.02  Other  1.00  1.00  T a b l e 16 - R e s u l t s of L o g i t E s t i m a t i o n s ( F o r e c l o s u r e ) Specification 1  L o a n - t o - v a l u e ratio D e b t c o v e r a g e ratio  Specification 2  Specification 3  Specification 4  1 . 9 8 2 6 ***  1 . 7 9 5 6 ***  2 . 0 2 0 7 ***  1 . 8 5 3 9 ***  (0.344)  (0.342)  (0.361)  (0.362)  - 1 . 5 6 8 1 *** (0.376)  - 1 . 5 5 8 3 *** (0.377)  - 1 . 5 3 1 3 *** (0.387)  -1.5062 * " (0.390)  Guarantee  - 1 . 8 4 9 3 *** (0.489)  (0.495)  (0.491)  (0.500)  guarzordum  -0.4348  -0.4038  -0.2975  -0.2741  (0.464)  (0.479)  (0.470)  (0.484)  0 . 1 8 5 6 **  0.1645 *  0 . 1 7 9 1 **  0.1596 *  (0.088)  (0.089)  (0.087)  (0.088)  C o n t r a c t rate Outstanding balance  - 1 . 8 0 5 3 ***  - 1 . 8 2 7 4 ***  - 1 . 8 2 4 8 ***  0.0132  0.0133  0.0154  0.0177  (0.016)  (0.016)  (0.016)  (0.017)  R e g i o n : British C o l u m b i a  -2.0347 *  -1.9773 * (1.048)  (1.060) -0.5777  Region:  Alberta  -0.5012 (0.777)  (0.788)  Region:  Quebec  -0.3577  -0.3773  (0.408)  (0.412)  Region:  Atlantic  Property type:  0.4781  0.6746  (0.485)  (0.510)  Apartment  -1.8151 *  -2.0330 *  (1.045)  (1.058) -0.3236  Property type:  Industrial  -0.2009 (0.430)  (0.435)  Property type:  Office  -0.4388  -0.5917  (0.407)  (0.434)  Property type:  Other  -0.5493  -0.6325  (0.841) Constant  -4.0055 * "  N Pseudo-R  2  - 3 . 4 6 5 7 ***  -3.8148 " *  (0.847) -3.2545  (1.273)  (1.273)  (1.283)  (1.284)  1,337  1,337  1,337  1,337  28.3%  30.3%  29.6%  31.4%  Notes: The estimation method is logit and the binary dependent variable Is equal to 1 if the loan was foreclosed. 51 loans of the 1210 in the sample were foreclosed. Independent variables were measured as of November 1996, or as of the date of initiation for new loans. Standard errors are in parentheses below the coefficient. **, * represent significance at the 1%, 5% and 10% level. Ontario and Prairie are the omitted regions. Retail is the omitted property type. A dummy variable indicating whether the guarantee variable was missing was included in the estimation but is not shown here.  86  "  T a b l e 17 - R e s u l t s o f L o g i t E s t i m a t i o n s ( D e l i n q u e n c y ) Specification 1  Loan-to-value ratio Debt coverage ratio Guarantee Contract rate Outstanding balance  1.5472 *** (0.255) -0.8051 *** (0.199) -0.8026 *** (0.281) 0.0259 (0.046) 0.0015 (0.009)  Region: British Columbia Region: Alberta Region: Quebec Region: Atlantic  Specification 2  1.3743 (0.254) -0.7842 (0.193) -0.6332 (0.288) 0.0037 (0.046) 0.0011 (0.010) -1.5443 (0.367) -0.1578 (0.341) -0.4280 (0.209) -0.0725 (0.299)  Property type: Apartment Property type: Industrial Property type: Office Property type: Other Constant  N Pseudo-R  -1.5391 ** (0.701)  2  1,337 11.2%  -1.0476 (0.702) 1,337 13.6%  *** *** **  Specification 3  1.7137 *** (0.266) -0.6892 *** (0.200) -0.8557 *** (0.285) 0.0205 (0.046) 0.0025 (0.010)  ***  **  -0.6241 * (0.350) -0.0279 (0.228) -0.3197 (0.233) 1.2489 *** (0.350) -1.6693 ** (0.711) 1,337 13.0%  Specification 4  1.5168 (0.266) -0.6802 (0.195) -0.7121 (0.292) -0.0011 (0.047) 0.0020 (0.010) -1.4627 (0.372) -0.1873 (0.350) -0.4215 (0.211) 0.0203 (0.306) -0.6848 (0.353) -0.1265 (0.231) -0.2819 (0.241) 1.0839 (0.350) -1.1216 (0.716)  *** *** *'*  1,337 15.1%  Notes: The estimation method is logit and the binary dependent variable is equal to 1 if the loan was ever delinquent during between November 1996 and May 2001 foreclosed. 174 loans of the 1210 in the sample were delinquent. Independent variables were measured as of November 1996, or as of the date of initiation for new loans. Standard errors are in parentheses below the coefficient. ***, **, * represent significance at the 1 %, 5% and 10% level. Ontario and Prairie are the omitted regions. Retail is the omitted property type. A dummy variable indicating whether the guarantee variable was missing was included in the estimation but is not shown here.  87  ***  **  *  ***  T a b l e 18 - R e s u l t s o f L o g i t E s t i m a t i o n s ( R e i n s t a t e m e n t ) Specification 1 Loan-to-value ratio Debt coverage ratio Guarantee Contract rate Outstanding balance  0.4584 * (0.251) -0.3483 (0.212) 0.084 (0.424) -0.0210 (0.059) 0.0040 (0.012)  Region: British Columbia Region: Alberta Region: Quebec Region: Atlantic  Specification 2 0.3401 (0.251) -0.3524 * (0.202) 0.340 (0.431) -0.0434 (0.059) 0.0023 (0.012) -2.1502 *** (0.605) 0.2141 (0.380) -0.4053 (0.261) -0.2834 (0.403)  Property type: Apartment Property type: Industrial Property type: Office Property type: Other Constant  -2.3212 *** (0.883)  N Pseudo-R  2  1337 1.63%  -1.9024 ** (0.880) 1337 5.30%  Specification 3 0.5681 " (0.258) -0.2591 (0.208) 0.054 (0.427) -0.0233 (0.058) 0.0061 (0.012)  -0.2119 (0.411) 0.2006 (0.288) -0.1623 (0.305) 1.2776 *** (0.403) -2.5502 *** (0.889) 1337 3.21%  Specification 4 0.4310 (0.257) -0.2719 (0.200) 0.282 (0.433) -0.0437 (0.059) 0.0041 (0.012) -2.0463 (0.609) 0.2145 (0.388) -0.3697 (0.263) -0.2103 (0.410) -0.2507 (0.415) 0.1199 (0.290) -0.0949 (0.314) 1.0564 (0.408) -2.1090 (0.894) 1337 6.39%  Notes: The estimation method is logit and the binary dependent variable is equal to 1 if the loan was ever delinquent and then reinstated. 91 loans of the 1210 in the sample were delinquent and reinstated. Independent variables were measured as of November 1996, or as of the date of initiation for new loans. Standard errors are in parentheses below the coefficient. ***, **, * represent significance at the 1 %, 5% and 10% level. Ontario and Prairie are the omitted regions. Retail is the omitted property type. A dummy variable indicating whether the guarantee variable was missing was included in the estimation but is not shown here.  88  *  ***  ** **  Table 19 - Results of multinomial logit estimations (All loans) Specification 1 Foreclosure Coefficients  Loan-to-value ratio Debt coverage ratio Guarantee Contract rate Outstanding balance  2.3414 (0.362) -1.6765 (0.382) -1.9299 (0.491) 0.1749 (0.088) 0.0122 (0.016)  Reinstatement  Marg. effect  ***  0.0286  *"  -0.0208  *"  -0.0295  "  Specification 2  0.0023 0.0002  Coefficients  1.2051 * " (0.334) -0.3638 (0.230) -0.1815 (0.425) -0.0112 (0.060) 0.0029 (0.012)  Region: B.C. Region: Alberta Region: Quebec Region: Atlantic  Marg. effect  0.0738 -0.0203 -0.0083 -0.0008 0.0002  Foreclosure Coefficients  2.1267 **' (0.360) -1.6728 *** (0.384) -1.8554 " * (0.498) 0.1509 * (0.090) 0.0123 (0.017) -2.1090 " (1.051) -0.5047 (0.781) -0.4276 (0.410) 0.3957 (0.491)  Specification 3 Reinstatement  Marg. effect  Coefficients  0.0216  1.0125 (0.330) -0.3817 (0.218) 0.0923 (0.434) -0.0366 (0.060) 0.0019 (0.012) -2.2005 (0.605) 0.1292 (0.383) -0.4569 (0.262) -0.3430 (0.408)  -0.0171 -O.0234 0.0016 0.0001 -0.0132 -0.0043 -0.0039 0.0052  "* *  *  Property type: Other  N Pseudo-R  2  1337 12.50%  -3.1863 " (1.286)  1337 14.99%  -0.0184  Reinstatement  Marg. effect  *"  0.0269  *"  -0.0183  "*  -0.0266  *  0.0020 0.0002  Coefficients  1.3706 * " (0.344) -0.2762 (0.226) -0.2358 (0.427) -0.0180 (0.060) 0.0045 (0.013)  Marg. effect  0.0816 -0.0147 -0.0116 -0.0012 0.0003  -0.0739 0.0084  Property type: Office  -2.5913 '** (0.913)  2.4377 (0.381) -1.6161 (0.391) -1.9233 (0.493) 0.1673 (0.087) 0.0150 (0.016)  0.0001  Property type: Ind  -3.8083 " * (1.282)  0.0527  -0.0020  Property type: Apt  Constant  Coefficients  0.0073  *"  Foreclosure  Marg. effect  -2.0571 " (0.909)  -0.0225 -0.0167 -1.8843 * (1.048) -0.1984 (0.433) -0.5083 (0.410) -0.1293 (0.843) -3.6657 * " (1.292)  -0.0123 -0.0023 -0.0050 -0.0036  -0.3002 (0.413) 0.1593 (0.290) -0.2208 (0.306) 1.4436 *** (0.414) -2.7651 " * (0.918)  -0.0158 0.0107 -0.0124 0.1489  1337 14.30%  Notes: The estimation method is multinominal logit. The possible loan outcomes are never-delinquent, delinquent-foreclosed, delinquent-reinstated and delinquent-unresolved. Never-delinquent is the omitted The unresolved outcome is not reported. Independent variables were measured as of November 1996, or as of the date of initiation for new loans. Standard errors are in parentheses below the coeffic *",**,* represent significance at the 1%, 5% and 10% level. Ontario and Prairie are the omitted regions. Retail is the omitted property type. A dummy variable indicating whether the guarantee vari missing was included in the estimation but is not shown here. The marginal effects are computed at the mean for continuous variables, and for the change from Oto 1 for dummy variables.  oo  Table 20 - Results of multinomial logit estimations (for delinquent loans only)  Reinstated loans relative to foreclosed loans Specification 1 M a r g . effect  Coefficients Loan-to-value ratio  -1.2294 ***  Debt c o v e r a g e ratio  (0.403) 0.7766 (0.383)  Guarantee Contract rate Outstanding balance 3-month T r e a s u r y Bill rate Property return  "  1.4613 *** (0.558) -0.0753 (0.086) 0.0169 (0.022) 0.1492 (0.213) -2.5959 (6.365)  Property type: Other  Specification 2  -0.1210 0.1378 0.2325 -0.0085 0.0054 -0.0371 0.5844  Coefficients -1.0602 " (0.411) 1.0509 ** (0.420) 1.2908 " (0.567) -0.0869 (0.090) 0.0155 (0.020) 0.1615 (0.215) -2.6567 (6.276) 1.5764 * (0.823)  D u m m y for year 1999 D u m m y for year 2000 D u m m y for year 2001 0.6949 (1.657)  N Pseudo-R  \o °  2  Marg. effect -0.0990 0.1592 0.2082 -0.0096 0.0054  Coefficients -1.3223 " * (0.412) 0.7562 * (0.413) 1.6192 *** (0.592) -0.0727 (0.083) 0.0194 (0.023)  0.3231 (1.725)  Specification 4  Marg. effect -0.1708 0.1691 0.2317 -0.0112 0.0043  Coefficients -1.3606 * " (0.418) 0.7393 * (0.414) 1.6623 " * (0.594) -0.0642 (0.084) 0.0234 (0.023) 0.2614 (0.378) -5.0383 (6.505)  -0.0379 0.6741  Marg. effect -0.1781 0.1631 0.2380 -0.0093 0.0047 0.0808 -0.1751  0.0979 1.2538 *** (0.798) -0.8893 (0.470) 1.6323 (1.080) 0.0322 ***  D u m m y for y e a r 1998  Constant  Specification 3  (1.143) 1.0077 *** (1.294)  -0.1197 -0.3816 -0.3023 -0.6732  0.9317 (0.990) -1.2774 * (0.756) 1.2228 (1.280) -0.2692  -0.4541 -0.6087 -0.6327 -0.7573  (1.231) 0.1995 (1.883)  252  252  252  252  15.5%  16.7%  24.9%  25.5%  /Votes: The estimation method is multinominal logit. The possible loan outcomes are delinquent-foreclosed, delinquent-reinstated and delinquent-unresolved. Delinquentforeclosed is the omitted outcome. The unresolved outcome is not reported. Independent variables were measured at of the first delinquency. Standard errors are in parentheses below the coefficient. ****** represent significance at the 1%, 5% and 10% level. A dummy variable indicating whether the guarantee variable was missing was included in the estimation but is not shown here. The marginal effects are computed at the mean for continuous variables, and for the change from Oto 1 for dummy variables.  Table 21 - Predict foreclosed loans from all delinquent loans (logit) Specification 1 Loan-to-value ratio Debt coverage ratio Guarantee Contract rate Outstanding balance 3-month Treasury Bill rate Property return  1.2694 *** (0.397) -0.7020 * (0.378) -1.2992 " (0.531) 0.0714 (0.084) -0.0116 (0.021) -0.2664 (0.207) 4.1933 (6.270)  Property type: Other Dummy for year 1998  Specification 2 1.0829 (0.404) -0.9952 (0.415) -1.1276 (0.541) 0.0819 (0.088) -0.0105 (0.020) -0.2771 (0.209) 4.2549 (6.180) -1.6360 (0.815)  **  1.3290 (0.409) -0.6018 (0.406) -1.4960 (0.572) 0.0550 (0.082) -0.0181 (0.022) -0.2293 (0.374) 6.1146 (6.431) -1.2178 (0.979) 0.9029 (0.735) -1.6857 (1.260) -0.8717 (1.193) -0.6023 (1.846) 252 22.8%  "  -0.3652 (1.693)  252 17.0%  252 19.2%  252 22.4%  Dummy for year 2001  2  **  Specification 4  1.2926 * " (0.403) -0.6221 (0.406) -1.4672 " (0.570) 0.0626 (0.081) -0.0137 (0.022)  -0.7899 (1.621)  Dummy for year 2000  N Pseudo-R  ***  -1.4737 * (0.790) 0.5731 (0.449) -2.0251 * (1.071) -1.1252 (1.108) -1.2607 (1.264)  Dummy for year 1999  Constant  Specification 3  Notes: The estimation method is logit, and the dependent variable is whether a delinquent loan was foreclosed. Independent variables were measured at of the first delinquency. Standard errors are in parentheses below the coefficient. "*,**,* represent significance at the 1%, 5% and 10% level. A dummy variable indicating whether the guarantee variable was missing was included in the estimation but is not shown here.  T a b l e 22 - P r e d i c t reinstated l o a n s from a l l d e l i n q u e n t l o a n s (logit)  Specification 1 Loan-to-value ratio Debt coverage ratio Guarantee Contract rate Outstanding balance 3-month Treasury Bill rate Property return Property type: Other  -0.8411 ' (0.336) 0.6386 ' (0.283) 1.0588 ' (0.445) -0.0475 (0.061) 0.0259 (0.018) -0.2111 (0.166) 3.6731 (5.410)  Specification 2 -0.7796 (0.343) 0.7210 (0.308) 1.0114 (0.449) -0.0470 (0.061) 0.0254 (0.018) -0.2125 (0.166) 3.6128 (5.391) 0.3398 (0.466)  Dummy for year 1998  2  -0.4784 (0.739) -1.7999 ' (0.688) -1.1586 (0.795) -2.7912 ' (0.731) -0.4649 (1.543) 252 15.3%  0.5904 (1.250)  252 7.9%  252 8.1%  252 15.0%  Dummy for year 2001  N Pseudo-R  -1.1528 ' (0.379) 0.9599 (0.332) 1.2277 (0.468) -0.0643 (0.065) 0.0272 (0.019) 0.3112 (0.331) -1.4808 (5.540)  0.7368 (1.228)  Dummy for year 2000  Specification 4  -1.1401 ' (0.374) 0.9560 ' (0.329) 1.1977 ' (0.465) -0.0733 (0.065) 0.0252 (0.018)  0.0158 (0.499) -1.3051 (0.429) -0.5848 (0.491) -2.4077 (0.596) 0.6036 (1.031)  Dummy for year 1999  Constant  Specification 3  Notes: The estimation method is logit, and the dependent variable is whether the delinquent loan was reinstated. Independent variables were measured at of the first delinquency. Standard errors are in parentheses below the coefficient. ***, **, * represent significance at the 1%, 5% and 10% level. A dummy variable indicating whether the guarantee variable was missing was included in the estimation but is not shown here.  to  Table 23 - R e s u l t s of Probit M o d e l s with S e l e c t i o n  Specification 1 Selection equation for delinquency Loan-to-value ratio Constant  0.4964 (0.189) 0.6549 (0.204)  Probit model for reinstatement Debt coverage ratio Constant N = 252  0.3168 (0.102) 0.0416 (0.165)  Specification 2 Selection equation for delinquency Loan-to-value ratio Constant  0.5477 (0.208) 0.6595 (0.178)  Probit model for reinstatement Guarantee Constant  0.5813 (0.259) 0.0325 (0.223)  N = 275  Notes: The estimation method is probit with selection, which was implemented using the heckprob command in STATA. Standard errors are in p arentheses below the coefficient. ***, **, * represent significance at the 1%, 5% and 10% level. A dummy variable indicating whether the guarantee variable was missing was included in the second specification but is not shown here.  CHAPTER 3 Commercial Mortgage Guarantees  Introduction  A commercial mortgage is a loan that is secured by an income-producing real property, such as an apartment, office or retail building. In the U.S. and Canada, there are typically prepayment penalties that mitigate the risk of early cash flow for lenders. Therefore, the primary source of risk for lenders is default, which is when a borrower stops halts their scheduled payments. This risk of default is exacerbated by the fact that most mortgages on commercial properties cannot be insured against default by any private or government insurance, so the lender must assume the entire risk.  In addition, commercial mortgage lending in the U.S. is frequently non-recourse, meaning that the only recourse for a lender is to the secured property itself. The lender cannot access any other assets of a defaulting borrower that could have reduced the financial loss associated with the default. However, in Canada, commercial mortgage lending is often done with recourse.  The borrowing  individual or corporation pledges their guarantee, which allows the lender the possibility of realizing on the guarantor's other, general assets in the event of default.  These guarantees are an interesting feature of the Canadian commercial mortgage lending landscape, but no academic studies have examined how default risk and guarantees are empirically related. M y paper will be the first to conduct studies of the statistical relationship. I use a database from a single, large Canadian commercial mortgage lender to investigate the role of guarantees in default. The findings from this study have implications for the way that Canadian lenders underwrite and price their commercial mortgages.  In addition, this paper serves as documentation of the Canadian  experience for American lenders who contemplate recourse commercial mortgage lending.  94  The theoretical foundation for the empirical tests of the relationship between the guarantee and default is provided by Childs, Ott and Riddiough (1996). They modify the standard options-based model to consider the effect of an additional asset as security. Their finding is that recourse lending should be associated with a lower probability of default. The first empirical tests of this prediction are in my paper, and I provide support for their theoretical finding.  The empirical tests of default were conducted using the database from the Canadian lender. Information about the loan characteristics such as the loan-to-value ratio, the debt coverage ratio, property type and location were included so that loan-level estimation was possible. The payment history for a limited observation period from November 1996 to May 2001 was also available. There were 1,637 loans present during this window of time. Three alternate definitions of default were used. The first is whether the loan was ever delinquent 30-days or more. In other words, did the borrower miss one monthly payment?  There were 582 loans that defaulted in this sense.  I also  considered whether the loan was 90 days, or three months delinquent, and 214 loans met this criterion. And finally, i f default was defined as foreclosure or some alternative legal procedure that resulted in a transfer of property ownership, then 70 loans were in default.  Probit estimations were  run using these alternate definitions of default as the dependent variable. The independent variable of interest was the guarantee indicator, and appropriate controls were included based on the findings from the empirical commercial mortgage default literature. A strong empirical relationship between the guarantee and default was found, which suggests that the presence of a guarantee reduces the likelihood of default.  The main contribution of this paper is this empirical result that suggests that guarantees reduce the likelihood of default.  This is an important issue since default is the primary source of risk for  commercial mortgage lenders. M y finding provides information useful in underwriting and pricing.  95  In addition, this paper provides support to the Childs, Ott and Riddiough (1996) theoretical optionsbased model of commercial mortgage default. M y paper is the first to conduct a study of this kind, and is possible only because of the structure of the Canadian commercial mortgage market.  A secondary contribution of this paper is the documentation of guarantees in the Canadian commercial mortgage context. I use the dataset to explore how the characteristics of guaranteed loans differ from non-recourse loans. A n interesting finding is that guarantees are not associated with higher loan-to-value ratios. In other words, lenders do not appear to be trading off these two risk factors. Instead, the presence of a guarantee is linked to the regulatory conditions in the jurisdiction where the secured property is located. In addition, I examine how the presence of a guarantee affects the contract rate.  In other words, what is the pricing effect of a guarantee?  I find that the rate  reduction associated with a guarantee is negligible. The implication of the findings is that the lender is benefiting from the recourse tradition in Canada by enjoying the reduction in default risk with negligible spread reduction costs.  The remainder of this paper is structured as follows. The associated literature is reviewed, the legal aspects of default in Canada are defined, the database used in the empirical tests is presented, results are discussed and then the paper is concluded.  Literature Review  The option-based model for the value of the mortgage was developed by Foster and Van Order (1984, 1985) and applied to the commercial mortgage context by Kau et al. (1987, 1990). Childs, Ott and Riddiough (1996) use this model to explore the effect of recourse and cross-default clauses on the probability of default. They modify the Kau et al. model to include a second asset, which is the  96  additional collateral provided by the guarantee.  If B, is the subject property asset and B is the 2  recourse asset value, then the process for the asset value is modeled as dBf = (a - b )B dt + cr B dZ , i = 1,2, i  f  t  i  i  i  where a, is the instantaneous total expected return to the asset, b is the continuous rate of property t  payout, a, is the instantaneous standard deviation of property prices and Z, is a standardized Wiener process. The instantaneous correlation between changes in the asset values is p, . i2  Using standard equilibrium pricing techniques, they derive the general mortgage valuation equation as  dv dBm, 2  Variable r is the riskless rate of interest, V is the mortgage value, and m is the continuous rate of mortgage payment. The contribution of this model is to consider the value of V as a function of both assets, B and B . t  2  Boundary conditions must be defined to solve this equation, and the authors modify the standard conditions to take into account the recourse asset. For time T, at maturity, the borrower evaluates  B +yB i  2  <M(T)  and for time t < T, V(B ,B t) x  2  <B  l  +  yB  2  where V represents the mortgage value and y is a constant (0 < y < 1) that determines the proportion of asset 2 that is collateralized. In the context of a guarantee, y will be 1.  97  Since a closed-form solution is not known, the two-asset partial differential equation is solved numerically, and the probability of default is calculated for a variety of parameters. Their numerical solutions show that recourse increases the value of collateral, which reduces default risk.  The  mechanism through which this occurs is that additional security reduces the effective loan-to-value ratio, since the denominator, value, now includes both the subject property and the recourse asset. But an additional reduction in default risk occurs when the secured asset and the recourse asset are not perfectly correlated.  There are no papers in the literature that empirically test whether this  reduction in default risk occurs for commercial mortgages with recourse, so my paper will be the first.  Archer et al. (2002) present a competing view based on the idea that the loan characteristics determined at the time of loan initiation are endogenous. The lender sets the value of the variables in order to ensure that risk is at an appropriate level for loan approval. Therefore, they predict that there should be no empirical relationship between default and the loan characteristics at the time of loan initiation. They perform empirical tests using the loan-to-value ratio at initiation to predict future default, and confirm that there is no relationship. Their argument can be extended to the topic of my paper, guarantees. Since a guarantee is set at the time of loan initiation, it would also be endogenous. Therefore, based on their reasoning, there would be no relationship between the guarantee and future default. In my paper, I will be able to perform the empirical test to determine whether the prediction from Childs, Ott and Riddiough (1996) or the implication from Archer et al. (2002) holds.  There have been several studies in the residential mortgage literature related to deficiency judgments. Depending on the legal methods by which a lender forecloses on a defaulting residential borrower, and depending on the jurisdiction, it may be possible for the lender to attempt to realize on a deficiency judgment. In this case, the lender may claim other assets held by the borrowing individual, up to the amount that covers the discrepancy between the outstanding mortgage balance and the  98  property value.  Therefore, this is analogous to the guarantee offered by Canadian commercial  mortgage borrowers.  Ambrose, Buttimer and Capone (1997) explore the relationship between additional recourse and the risk of default in the residential mortgage context using a standard option-based pricing model. In their numerical results, they explore the effect of the probability that a lender will exercise their right to claim a deficiency judgment on the probability of default. Increasing the threat of a deficiency judgment lowers the probability of borrower default. Therefore, the implication for my paper would be that when a guarantee exists on a commercial mortgage loan, there is a positive probability that the lender would realize upon it, and the likelihood of default should be higher than for non-guaranteed loans. This postulated relationship is aligned with the Childs, Ott and Riddiough (1996) prediction.  Several papers empirically examine the link between default and deficiency judgments in the residential mortgage context.  Clauretie and Herzog (1990) investigate this question within the  context of state legislation on loan losses for insurers. When they perform an analysis based on the losses per state for private mortgage insurance companies, they find that the loss rate (equal to the amount of the loss divided by the original amount of the loan) is significantly related to the state legislation on deficiency judgments. When a state allows deficiency judgments, loss rates are lower. They also conduct a loan-level analysis using data on loans where the F H A paid a claim. They did not find a relationship between the legislation on deficiency judgment in the state where the property was located and the loss rate.  Therefore, they have mixed evidence supporting the idea that  deficiency judgments affect loss rates.  Jones (1993) compares the residential mortgage default  experience across two Canadian provinces, and finds that anti-deficiency judgment legislation in Alberta increases the incidence of default.  99  More recently, Lambrecht, Perraudin and Satchell (2003) investigate the default experience of a mortgage insurer in the United Kingdom.  A l l the mortgages in their sample are essentially  guaranteed, since a lender may always choose to pursue a deficiency judgment. One of their key interpretations of their results is that the amount of equity that the borrower holds in their house plays a "relatively insignificant" role in a borrower's decision to default, since the other financial assets of the borrower may also be forfeited on default.  Although no existing studies have explored the role of guarantees in commercial mortgage lending, there have been several studies that examine default, such as Ciochetti et al (2002), Ambrose and Sanders (2001), Archer et al. (2002), Chen and Deng (2002), Holmes (2004) and Goldberg and Capone (2002). These studies differ in their data sources, estimation technologies, set of independent variables and definition of default. The key findings in this literature are that the loan-to-value ratio and the debt coverage ratio play an important role in default. Other variables used as independent variables in these studies include borrower characteristics, property location and market conditions. The estimations in my paper take into account these findings by including the relevant variables as controls when investigating the empirical relationship between the guarantee and default.  The work in my paper differs from the existing empirical literature since the guarantee is studied for the first time.  Further, I use a unique Canadian commercial mortgage database that has both  guaranteed and non-guaranteed loans.  Even in existing studies of deficiency judgments in the  residential context, the data is not conducive to the type of loan-level analysis that I can conduct here. I also study the effect of a guarantee on the contract rate, and the differences between guaranteed and non-guaranteed loans.  100  Legal aspects of default in Canada  Guarantees can be offered by individuals or corporations or both. The mortgage contract, which is agreed upon at the time of loan initiation, outlines the parties involved in the guarantee.  The  guarantor usually provides financial statements so that the lender can evaluate the value of the guarantee. Specific assets are not explicitly identified when the guarantee is offered. Rather, the guarantee is linked to the assets of the entity that provided it. Therefore, a guarantee differs from a blanket mortgage, a cross-default clause and a letter of credit.  In the case of an individual, assets such as registered retirement savings plans (similar to the IRA in the U.S. context) are not actionable on the guarantee. If the primary residence of the guarantor is in the name of a family member, then it is also not actionable. A corporate guarantee may be provided by a firm that has no assets other than the subject property. For these reasons, some lenders feel that guarantees have low value.  There are four main remedies for Canadian lenders faced with a defaulting borrower. The first is that the lender may enter into possession of the subject property. The lender would apply the revenues to the loan, interest and expenses. Under possession, the borrower still retains the right of redemption, meaning that they can remedy the default and regain possession of their property. The provision for possession is usually included as part of the mortgage contract, as is power-of-sale, in jurisdictions where it is allowed. Under power-of-sale, a lender sells the property and retains the capital required to pay off the loan. If there is a deficiency between the mortgage balance and the proceeds from the sale, then the borrower can start an action to realize on the guarantee. This method is extensively used in Ontario and the Maritime provinces.  101  The remaining provinces require a judicial sale, which is more costly and time-consuming for the lender, since the court is more extensively involved in ordering and supervising the property sale. However, the lender can still realize on the guarantee in the same manner. The exception is Alberta, which has anti-deficiency legislation through the Law of Property Act (Alberta).  Therefore,  guarantees are effectively useless to the lender in Alberta.  The final common remedy for a lender is foreclosure. Under foreclosure, ownership of the secured property is transferred to the lender in exchange for full release of all the borrower's obligations. Since this action fulfills the debt in full, the lender cannot take any action on the guarantee.  Quit  claims, or friendly foreclosures, are when the borrower signs the property over to the lender without any court order.  Data  A major Canadian commercial mortgage lender provided the dataset used in the empirical estimation. Observations are monthly, from November 1996 to May 2001, with three months of missing data, for a total of 52 months. In the first observation, there were 1,126 active loans, and each month new loans were added and some loans terminated. A total of 1,637 loans are present for at least one month during the observation window. Information about the loan at the time of initiation is available, as well as the default status of the loan during the observation window.  A l l the loans by this lender are fixed-rate mortgages with a fixed term that usually ranges between 1 year and 30 years, with the most common terms being 5 years, 10 years and 20 years. Most loans have a term shorter than the amortization period, so a balloon payment is usually due at maturity. Approximately 95% of the loans are amortizing with monthly payments of principal and interest, with the remainder making interest-only payments either monthly or annually.  102  The lender diversifies their portfolio across property type. The largest category of property types is retail, which includes shopping centers, strip malls, restaurants, auto dealerships, stand-alone fast food restaurants and other retail properties.  Besides retail, the major categories are offices,  apartments and industrial/warehouse. The remaining other category includes vacant land, hotels, motels, airport properties, medical buildings, government properties, nursing homes and schools.  The lender also diversifies their portfolio by region. The ten Canadian provinces are divided to six geographic regions. The small eastern provinces of Newfoundland, Nova Scotia, Prince Edward Island and New Brunswick are labeled the Atlantic region.  The less populous provinces of  Saskatchewan and Manitoba are combined to form the Prairie region. The remaining regions are Quebec, Ontario, Alberta and British Columbia. The region with the highest proportion of loans is Ontario, followed by Quebec. In addition, a variable indicating the 1996 population (in millions) of the nearest of 20 metropolitan area is measured, as shown in Table 24.  Based on previous empirical work in commercial mortgage default, the current loan-to-value ratio is one of the primary predictors of default. In this paper, the variable is calculated as the outstanding balance divided by the property value. A n advantage of this database is that there are multiple property appraisals available for each mortgage, including the value at the time of loan initiation. The lender periodically re-appraises the underlying property for loan monitoring purposes.  These re-  appraisals are done at irregular intervals, which vary based on the size of the mortgage and the lender's discretion. To measure the property value at the time of each observation, the appraisal closest in time, either forward or backward, is appreciated or depreciated based on returns from the Russell Canada Property Index for that property type and region.  17  In this way, the resulting property  This index doesn't report values for all property type/region combinations. If a combination is unavailable, the appreciation rate for the region is applied. 17  103  value is quite accurate relative to other empirical studies that appreciate the property value from loan initiation.  The default status of a loan is measured by tracking the payment history though the observation window (November 1996 to May 2001). O f the 1637 loans, 582 were delinquent by 30 days. O f these, 214 were delinquent for 90 days or more. There were 71 loans that were either foreclosed, sold through power-of-sale or judicially, or taken into possession.  Empirical Methodology and Results  The characteristics of guaranteed loans are displayed in Table 25. Guarantees are present on 87.6% of all the loans represented in the database.  The property type with the lowest proportion of  guaranteed loans is industrial, followed by office and retail. Despite the fact that power-of-sale legislation is present in Ontario and the Atlantic provinces, there does not appear to be a similarity between their likelihood of having a loan guaranteed. Only 80.8% of Ontario loans are guaranteed, compared to virtually all of the Atlantic loans (72 of 73 loans, or 98.6%).  Alberta has a  proportionally lower number of loans with a guarantee, at only 61.5%. This is almost certainly due to the fact that legislation in that province makes it difficult for lenders to realize on a guarantee.  In order to understand how the presence of a guarantee is linked to other loan characteristics, I performed a series of probit estimations, where the independent variable is set to one of the loan has a guarantee and zero otherwise. The question being addressed is whether guaranteed loans differ from non-guaranteed loans in a systematic way. For each loan, the characteristics are measured at the time of loan initiation, when the guarantee is also determined.  The results of these estimations are  presented in Table 26 for six different specifications.  104  One of the more surprising findings is that the loan-to-value ratio, measured at the time of loan initiation was insignificant across specifications.  A reasonable expectation is that a lender would  request a guarantee on loans with higher loan-to-value ratios, to compensate for the higher risk. But this does not seem to be the case, since the lack of a statistical relationship implies that lenders are not trading off the two risk factors of loan-to-value ratio and guarantee.  The term at initiation is also not significant across specifications. The loan amount at initiation is negative and significant for three specifications.  When the regional indicator variables are added,  then the coefficient becomes insignificant, although still negative. This suggests (weakly), that larger loans are less likely to have a guarantee. In specification 2, a variable that measures the population of the nearest urban centre is included, but was found to be insignificant. Therefore, this is evidence that a guarantee is not being used to compensate for the fact that the property is located in a smaller urban centre.  Indicator variables for the property types are included in specification 3, with retail being the excluded type.  The only type with any level of significance is industrial, which was marginally  negative. This significance level disappeared in specification 5 when the regional indicator variables were added. The final specification is number 6, which includes only the regional indicator variables. The excluded value is Ontario, Canada's largest and most populous province. The only region with a negative coefficient is Alberta, which has anti-deficiency legislation.  The most important finding from this model is that the guarantee is not being used to compensate for a high loan-to-value ratio. Instead, the presence of a guarantee is linked to the region where the secured property is located.  105  In Table 27, the results of a probit estimation to determine the effect of the guarantee on the contract rate are shown. The question being addressed is whether guaranteed loans have higher or lower contract rates than non-guaranteed loans. The variables included as controls in this model are the current 10-year Canadian government bond yield, the term of the mortgage and the loan-to-value ratio at initiation. These variables are all significant at a 1% level.  The primary variable of interest in this estimation is the guarantee, and the empirical result is that the coefficient is negative but not significant. A reasonable expectation would be that a guarantee would reduce the contract rate. The lender has a credit scoring process in place that should result in a rate reduction for guaranteed loans. However, the empirical results show that the reduction in the contract rate that occurs due to the presence of a guarantee is negligible.  In the fourth specification, the property types and regions are also included. Relative to the omitted retail property type, apartment, industrial and office types have a negative coefficient, and the other property type has a positive coefficient. Relative to the omitted Ontario property type, Quebec has a positive coefficient.  Given that guarantees have a negligible effect on the contract rate, the next step is to explore whether the guarantee has any effect on the probability of default. Table 28 shows the descriptive statistics. The breakdown of defaulting loans by property type and region is presented in the top panel. The other properly type and the Ontario region appear to have more than their share of foreclosed (or equivalent) loans, while British Columbia has less. In the bottom panel of table 28, the descriptive statistics for the items that will be used as independent variables are shown, broken down by default status.  While 88% of the loans are guaranteed, only 85% of the 30-day delinquent loans are  guaranteed.  Further, only 81% of the 90-day delinquent loans are guaranteed and 67% of the  foreclosed (or equivalent) loans.  106  The remaining estimations, in Table 29, 30, and 31, represent the key contribution of this paper. I study how default is affected by the presence of a guarantee. In these estimations, the dependent variable is an indicator variable set to one i f the loan defaulted during the observation window of November 1996 to May 2001. Default is measured in three ways, as 30-days delinquent, 90-days delinquent and foreclosed or the equivalent.  A separate table has been created for each default  definition. The question being addressed is whether guarantees reduce the likelihood of default, as predicted by Childs, Ott and Riddiough (1996).  The key independent variable is the guarantee, which is an indicator variable set to one i f a guarantee exists on the loan. The model is also run using an instrumental variable approach for the guarantee. Since the guarantee is determined at the time of loan initiation, the lender has traded off the risk of default with the loan characteristics, making the presence of a guarantee endogenous. To address this endogeneity, I used the property region dummy variables as instruments for the guarantee. Specifically, the model to create the predicted value for the guarantee is specification 6 of Table 26, which includes just the regional variables (Ontario excluded) and a constant.  Other variables included in the default estimations were suggested by previous empirical studies of commercial mortgage default, such as Archer et al. (2002), Ciochetti (2002) and Holmes (2004). The initiation loan-to-value ratio is the outstanding balance divided by the property value, measured at the time that the loan was originated. The current loan-to-value ratio is measured at the first date at which the loan was observed in the time window, which is November 1996 for most loans.  Across specifications and across definitions of default, the variable with a consistently significant relationship with default is the current loan-to-value ratio, confirming the results from previous  107  empirical studies of commercial mortgage default and predictions from the theoretical options-based default model.  Table 29 presents the probit estimations for the default model, using the 30-day delinquency definition of default.  O f the alternative definitions of default, the 30-day delinquency model has the  lowest pseudo-R . The key variable, guarantee, is negative across the four specifications, including 2  number (4), which uses an instrumental variable for the guarantee. The coefficient on guarantee is marginally significant in the base model (1). When the property type dummies are included, in specification (3), then the significance level is 5%. However, the coefficient is not significant in the specification with the property region dummies or when the instrumental variable is used. Overall, there is weak evidence that a guarantee reduces the likelihood of 30-day delinquency.  As mentioned earlier, the current loan-to-value ratio is strongly positive across specifications. When properly regions are included (with Ontario as the omitted outcome), then the coefficient on the British Columbia indicator variable is significantly negative. When the property types are included (with retail as the omitted outcome), then the apartment type and the other type are significantly positive.  These same regions and property types are significant when default is measured as 90-days delinquent, as shown in Table 30. This is a more commonly used measure of default, since the length of time, 90 days is often used by lenders as the point at which default management procedures are initiated. Across the four specifications, the current loan-to-value and the current debt coverage ratio are significant at 1% with the expected signs. The guarantee variable is also significant and negative across specifications, including the one that uses the instrumental variable. This finding provides support to the prediction by Childs, Ott and Riddiough (1996) and is the central finding of this paper.  108  The results suggest that the presence of a guarantee significantly reduces the likelihood of 90-day delinquency.  These results are confirmed when default is measured as foreclosure or equivalent, shown in Table 31. In specification (1) through (3), the coefficient is also negative and significant. The coefficient in specification (4), where the instrumental variable is used is also negative, but not significant. Therefore, across definitions of default and specifications, there is a consistent negative coefficient on guarantee. In sum, evidence provided here suggests that there is a relationship between the presence of a guarantee and the likelihood of default.  Specifically, a guarantee reduces the likelihood of  default.  In Table 31, the coefficients on the current loan-to-value ratio and the debt coverage ratio are significant in the expected directions. Due to the relatively small number of foreclosures, not all property regions and property types can be included in the specifications. For example, there was only one foreclosed loan in British Columbia during the observation window.  The results from Table 31 can be used to estimate the economic significance of a guarantee. The predicted probability of foreclosure can be computed based on the cumulative normal distribution using the coefficients from specification 1 and the mean values of the independent variables. The probability of foreclosure is 5.64% i f there is no guarantee, and 0.83% with a guarantee. Given the mean loan size of $4,059,092 and assuming a loss from foreclosure equal to 30% of the outstanding balance, then the expected loss is $1,217,728. The expected loss is therefore $68,680 without a guarantee and $10,131 with a guarantee. Note that this difference of $58,548 is the reduction in the expected loss based only on the reduced likelihood of foreclosure.  A guarantee also reduces the  absolute size of the loss since the lender can seek recourse from other assets held by the provider of the guarantee.  109  The default studies in Tables 29 through 31 provide evidence that the presence of a guarantee reduces the probability of default. Across all the specifications and default definitions, the coefficient for the guarantee variable was always negative, although significance levels varied. For example, for the base specification 1, the coefficient on the guarantee was -0.24 for 30-days delinquent, -0.43 for 90days delinquent and -0.81 for foreclosed loans. In order to rigorously compare the magnitude of the effect of a guarantee across default definitions, a multinomial logit model is estimated, and results are presented in Table 32.  There are k = 4 potential outcomes for a loan:  never delinquent, 30-days delinquent, 90-days  delinquent and foreclosed. A loan is classified as 30-days delinquent i f it was 30-days delinquent at least once during the observation window, and it never became 90-days delinquent. Similarly, a loan is classified as 90-days delinquent i f it was 90-days delinquent at least once during the observation window and the loan was not foreclosed. Using these definitions, there is no overlap in which a loan is included in more than one category.  The empirical method is a multinomial logit specification where any observation i = 1 to n can fall into one of the k groups. For each observation there exists a probability  j= for all k groups. This equation is unidentified unless e  1  = 1. The coefficients in the regression  results are therefore a measure relative to one excluded outcome.  In Panel 1 of Table 32, the excluded outcome is never-delinquent. The coefficient on guarantee is negative for the foreclosed option, which implies that the likelihood of foreclosure, relative to never-  110  delinquency, significantly decreases when a guarantee is present on the loan. Since the coefficients on the guarantee for the 30-day and 90-day delinquency outcomes are not significant, the interpretation is that relative to the likelihood of a loan being never-delinquent, the impact of the guarantee is not significant.  Panels 2 and 3 show the same estimation presented with different excluded outcomes, for ease of interpretation. In Panel 4, the excluded outcome is foreclosure, and there is a significantly positive effect on guarantee for all the other outcomes. Therefore, relative to the effect on foreclosure, a guarantee increases the likelihood of the never-delinquent, 30-day and 90-day outcomes.  The  conclusion from this analysis is that the effect of a guarantee is more strongly negative for foreclosure than for other definitions of default.  Multinomial logit is the most appropriate methodology to simultaneously determine the relative effects of a guarantee across default definitions since this problem consists of characteristics specific to the individual loan used to model outcomes. If the data consisted of choice-specific attributes, then a conditional logit or nested logit would be appropriate.  The final analysis relating to guarantees and default considers whether the effect of the guarantee on delinquency depends on the location of the secured property. Table 33 shows descriptive statistics for the proportion of loans per region that ever became 90-days delinquent and of those, which proportion is guaranteed.  British Columbia has the lowest proportion of 90-day delinquent loans,  with just 4%. O f the 6 delinquent loans, every one was guaranteed.  Similarly, every one of the  delinquent loans in the Atlantic region was guaranteed. In Alberta, 5 of the 7 delinquent loans were guaranteed and in the Prairie region, 3 of the 4 delinquent loans were guaranteed.  Ill  The number of loans in Ontario and Quebec is large enough so that estimations can be performed. In order to avoid the errors associated with interaction terms on discrete probability models outlined by A i and Norton (2003), I avoid the use of a dummy variable equal to the product of the provincial and guarantee indicators. Instead, I run separate probit estimations for the two regions, Quebec and Ontario, which are reported in Table 34.  In both Ontario and Quebec, the coefficient on the guarantee variable is negative. Quebec has a higher significance level (p=1.9%) versus Ontario (p=9.2%).  The absolute magnitude of the  coefficient is larger in Quebec, which is a preliminary indication that the effect of a guarantee on default differs across jurisdictions.  Conclusion  The goal of this paper was to explore the role of commercial mortgage guarantees in default. This is an important issue because default is the primary source of risk in commercial mortgage lending. A Canadian database provided by a single large lender was used for the empirical work. The advantage of using a Canadian dataset is that recourse lending through guarantees is common but not exclusive. Therefore, there are both guaranteed and non-guaranteed loans in the database. The model that provides the foundation for the prediction of the relationship between guarantees and default is Childs, Ott and Riddiough (1996). They modify the option-theory-based model for mortgage default to include a recourse asset, and predict that guarantees should reduce the likelihood of default.  The empirical results in this paper provide evidence to confirm the Childs, Ott and Riddiough (1996) prediction. Across three alternative measures of default, the coefficient on the guarantee variable is negative, which supports the idea that a guarantee reduces the probability of default. This finding is  112  useful to Canadian lenders who commonly request and price guarantees and to American lenders who may contemplate recourse lending.  In addition to the question of default, two additional studies were conducted to document commercial mortgage guarantees in Canada. I studied whether the characteristics of guaranteed loans and nonguaranteed loans differed in a systematic way. I found no evidence that the guaranteed loans had higher loan-to-value ratios. In fact, the only variables that were significant in predicting the presence of a guarantee were the regional indicator variables. This suggests that lenders are not trading off the risk factors of guarantees and loan-to-value ratios during loan underwriting.  I also investigated the impact of a guarantee on the contract rate. Specifically, I verified whether a guarantee significantly reduced the spread. Especially given that I was able to document a reduction in default risk for guaranteed loans, it would be reasonable to assume that a borrower who provides a guarantee should enjoy a reduction in their contract rate. Although the coefficient on the guarantee was negative in the estimation, when contract rate is the dependent variable, it was not significant. In summary, a commercial mortgage guarantee reduces the likelihood of default but provides a negligible reduction in the contract rate.  113  T a b l e 24 - Population by Metropolitan A r e a , 1996  Urban Center  Province/Region  Population  Calgary Edmonton Fredericton Halifax Hamilton Kitchener London Moncton Montreal Ottawa Quebec Regina Saskatoon Saint John St. John's Toronto Vancouver Victoria Winnipeg Yellowknife  Alberta Alberta New Brunswick / Atlantic Nova Scotia / Atlantic Ontario Ontario Ontario New Brunswick / Atlantic Quebec Ontario Quebec Saskatchean / Prairie Saskatchean / Prairie New Brunswick / Atlantic Newfoundland / Atlantic Ontario British Columbia British Columbia Manitoba / Prairie Northwestern territories / British Columbia  821,628 862,597 78,950 342,966 624,360 382,940 416,546 113,495 3,326,447 998,718 671,889 193,652 219,056 125,705 174,051 4,263,759 1,831,665 304,287 667,093 17,275  Source: Statistics Canada http://www12.statcan.ca/english/census01/products/standard/popdwell/Table-CMA-N.cfm  Table 2 5 - Descriptive statistics relating to guarantee  Panel 1 - Breakdown by property type Apartment 8 No guarantee  Industrial  73 81  147 177  90.1%  83.1%  Guarantee Total % with guarantee  Panel 2 - Breakdown by property region BC 10 • No guarantee Guarantee Total % with guarantee  161 171 94.2%  30  Alberta 20 32 52 61.5%  Panel 3 - Loan characteristics by guarantee status | Initiation LTV Initiation term (months) Initiation loan amount ($millions) Total return Pop. of nearest urban centre (millions)  Office 23  Retail 46  168  353 399  898 898 898 737  Total  4 46  111 787  191 88.0%  50  898  88.5%  92.0%  87.6%  Prairie  Ontario  3 16 19  64 270 334 80.8%  Quebec 13 236  Atlantic 1  84.2%  All loans N 895  Other  Mean 0.766 150.45 5.75 8.38% 2.52  249 94.8%  | Std Dev 0.22 93.92 10.60 0.06 1.53  72 73  Total 111 787 898  98.6%  87.6%  Non-recourse loans N Mean 0.741 111 111 111  153.50 7.78  111 94  10.41% 2.51  | Std Dev 0.21 96.72 12.40 0.06 1.67  Guaranteed loans Std Dev N Mean 0.23 784 0.770 150.02 93.58 787 5.46 10.20 787 787 643  8.10% 2.52  0.06 1.51  t-test 1.32 0.36 1.88 3.71 0.03  Notes: The top two panels report the proportion of loans with a guarantee broken down by property type and by region. The prairie region includes the provinces of Manitoba and Saskatchewan, and the atlantic region includes Nova Scotia, New Brunswick, Prince Edward Island and Newfoundland. The bottom panel shows statistics for loans as of their date of initiation. The t-statistic in the far right column tests whether the mean is the same for the non-recourse and guaranteed loans.  T a b l e 26 - M o d e l to predict the p r e s e n c e of a guarantee  Initiation L T V T e r m at initiation L o a n a m o u n t at initiation  (D  (2)  (4)  (5)  0.1343  -0.2849  0.1197  0.1198  0.1201  (0.256)  (0.290)  (0.260)  (0.271)  (0.276)  -0.0035  -0.0013  -0.0022  0.0000  0.0014  (0.007)  (0.008)  (0.007)  (0.008)  (0.008)  -0.0052  -0.0062  - 0 . 0 0 9 6 ** (0.005)  T o t a l r e t u r n (prior y e a r ) for r e g i o n / t y p e  (3)  -3.2902 " * (0.908)  - 0 . 0 1 0 7 ** (0.005) - 3 . 6 0 5 4 *** (0.961)  -0.0110** (0.005) - 3 . 6 7 7 3 *** (0.962)  (0.005)  (0.005)  -1.0399  -1.3858  (1.006)  (1.080)  (6)  0.0053  Population of nearest urban centre  (0.039) Apartment  0.2644  0.2869  (0.224)  (0.234)  Office Other property type  (0.144)  (0.152)  -0.0983  -0.0206  (0.150)  (0.163)  0.1737  0.3225  (0.276)  (0.285)  British C o l u m b i a  0 . 6 8 8 8 ***  0 . 6 9 7 9 ***  0 . 6 9 5 7 ***  (0.178)  (0.183)  (0.173)  - 0 . 5 3 8 6 ***  Alberta Prairie Quebec Atlantic Constant  N Adjusted R  -0.1758  -0.2773 *  Industrial  2  - 0 . 5 2 6 5 **  - 0 . 5 7 8 5 ***  (0.202)  (0.208)  0.1100  0.0868  (0.193) 0.1311  (0.360)  (0.359)  (0.336)  0 . 6 8 9 0 ***  0 . 6 8 7 1 ***  0 . 7 5 1 9 ***  (0.163)  (0.165)  (0.154)  1 . 2 4 2 2 ***  1 . 2 2 4 7 ***  1 . 3 3 3 8 ***  (0.403)  (0.404)  (0.396)  1 . 4 5 6 8 ***  1 . 7 6 6 0 ***  1 . 5 4 7 9 ***  0 . 9 2 2 8 ***  0 . 9 4 7 0 ***  0 . 8 7 1 9 ***  (0.261)  (0.308)  (0.278)  (0.294)  (0.314)  (0.079)  895  734  895  895  895  898  2.8%  3.3%  4.0%  10.9%  11.7%  10.5%  N o t e s : T h e e s t i m a t i o n m e t h o d o l o g y is p r o b i t . S t a n d a r d e r r o r s a r e in p a r e n t h e s e s b e l o w t h e c o e f f i c i e n t . ***,**,* r e p r e s e n t s i g n i f i c a n c e at t h e 1%, 5 % a n d 1 0 % l e v e l s .  T a b l e 27 - M o d e l f o r t h e c o n t r a c t rate  Guarantee 10-year C a n a d i a n government bond yield Initiation L T V T e r m at initiation L o a n a m o u n t at initiation  (D  (2)  (3)  (4)  -0.1081  -0.1423  -0.2026  -0.2244  (0.143)  (0.140)  (0.148)  (0.146)  0 . 4 1 8 9 ***  0 . 4 2 2 3 ***  0.4122 * "  0 . 4 1 7 7 ***  (0.026)  (0.025)  (0.026)  (0.026)  1 . 1 4 1 8 ***  1 . 1 0 1 2 ***  1 . 0 9 9 5 ***  1 . 0 6 9 7 ***  (0.213)  (0.209)  (0.214)  (0.210)  0 . 1 0 8 4 *.**  0.1154 * "  0.1110 " *  0 . 1 1 7 6 ***  (0.007)  (0.007)  (0.007)  (0.007)  -0.0034  -0.0069  -0.0044 (0.005)  -0.0080 * (0.005)  (0.005)  Apartment  -0.8781 * "  Industrial  - 0 . 4 8 0 6 ***  Office  -0.2349 *  (0.169)  (0.169) -0.4520 * "  (0.128)  (0.129) -0.2178 *  (0.121) Other property type  0.4311  (0.123) 0.4866  "  (0.209) British C o l u m b i a Alberta Prairie Quebec Atlantic Constant  0.1573  0.1766  (0.138)  (0.139)  0.0230  0.0374  (0.216)  (0.214)  0.0037  -0.0760  (0.334)  (0.329)  0 . 4 0 1 8 ***  0 . 3 5 7 6 ***  (0.121)  (0.120)  0.1291  0.0678  (0.184)  (0.183)  4 . 1 8 9 2 ***  4.3546 * "  4 . 1 7 3 5 ***  4 . 3 0 2 5 ***  (0.282)  (0.297)  (0.297)  895 2  "  (0.211)  (0.282) N Adjusted R  (0.005) -0.8404 * "  52.2%  895 54.3%  895 52.6%  895 54.5%  N o t e s : T h e e s t i m a t i o n m e t h o d o l o g y is p r o b i t . S t a n d a r d e r r o r s a r e in p a r e n t h e s e s b e l o w t h e c o e f f i c i e n t , r e p r e s e n t s i g n i f i c a n c e at t h e 1%, 5 % a n d 1 0 % l e v e l s .  117  Table 28 - Descriptive statistics relating to default  P a n e l 1 - B r e a k d o w n b y p r o p e r t y type Apartment  Industrial  Office  Retail  Other  All l o a n s  14%  22%  21%  5%  37%  Ever delinquent 30 days  16%  20%  20%  7%  37%  Ever delinquent 90 days  9%  19%  21%  11%  40%  F o r e c l o s e d or e q u i v a l e n t  8%  15%  25%  6%  45%  P a n e l 2- B r e a k d o w n by property region BC  Alberta  Prairie  Ontario  Quebec  Atlantic  All l o a n s  19%  6%  2%  37%  27%  8%  E v e r delinquent 30 days  11%  6%  2%  39%  33%  9%  E v e r delinquent 90 days  4%  6%  4%  49%  27%  10%  F o r e c l o s e d or equivalent  1%  3%  4%  54%  27%  11%  P a n e l 3- I n d e p e n d e n t v a r i a b l e s by default s t a t u s |  All l o a n s  |  Ever 30 day delinquent  |  E v e r 90 day delinquent  [  Foreclosed  N  Mean  Std Dev  N  Mean  Std D e v  N  Mean  Std D e v  N  Mean  Std D e v  898  0.876  0.329  288  0.854  0.354  124  0.806  0.397  30  0.667  0.479  Initiation L T V  1630  0.724  0.257  577  0.751  0.270  213  0.829  0.261  71  0.877  0.271  Current L T V  1588  0.653  0.361  558  0.743  0.459  202  0.911  0.575  68  1.164  0.797  Current D C R  1381  1.480  0.746  511  1.370  0.748  193  1.131  0.604  55  0.855  0.469  Rate  1637  9.723  1.924  582  9.759  2.002  214  10.011  2.126  71  10.549  2.196  OSB  1637  4.059  7.884  582  3.744  7.109  214  5.252  7.783  71  5.667  8.062  Guarantee  N o t e s : A b b r e v i a t i o n s : O S B = o u t s t a n d i n g b a l a n c e , L T V = l o a n - t o - v a l u e ratio, D C R = d e b t c o v e r a g e ratio. T h e top two p a n e l s s h o w the proportion of l o a n s p e r c a t e g o r y . T h e prairie r e g i o n i n c l u d e s the p r o v i n c e s of M a n i t o b a a n d S a s k a t c h e w a n , a n d the atlantic r e g i o n i n c l u d e s N o v a S c o t i a , N e w B r u n s w i c k , P r i n c e E d w a r d Island a n d Newfoundland.  In the b o t t o m p a n e l , the c u r r e n t L T V , c u r r e n t D C R , rate a n d O S B are d e t e r m i n e d a s of N o v e m b e r 1 9 9 6 or the d a t e of initiation, if the l o a n is initiated after  N o v e m b e r 1996.  oo  Table 29 - Model to predict default (30 days delinquent) (1)  Guarantee  -0.2415 * (0.139)  (2)  -0.2047 (0.145)  (3)  -0.2829 ** (0.140)  Guarantee (IV) Initiation L T V (Based on O S B ) Current L T V (Based on O S B ) Current D C R Rate Outstanding balance (OSB)  0.0654 (0.250) 0.7131 *** (0.174) -0.1357 (0.091) -0.0175 (0.025) -0.0070 (0.005)  British Columbia Alberta Prairie Quebec Atlantic  0.1540 (0.258) 0.6660 *** (0.178) -0.1427 (0.092) -0.0295 (0.026) -0.0067 (0.005) -0.4306 *** (0.147) 0.0627 (0.207) -0.2782 (0.332) 0.1107 (0.118) -0.0460 (0.188)  Apartment Industrial Office Other property type Constant  -0.3831 (0.385)  N Number with dep. var. = 1 Pseudo-R  2  0.000 -0.2774 (0.402)  (4)  0.0063 (0.255) 0.8438 *** (0.182) -0.1159 (0.093) -0.0104 (0.025) -0.0061 (0.005)  0.3938 ** (0.170) -0.1078 (0.127) -0.1452 (0.128) 0.8763 *** (0.262) -0.5108 (0.394)  -0.5372 (0.369) -0.3485 * (0.199) 0.9878 *** (0.151) -0.0457 (0.056) 0.0018 (0.019) -0.0109 ** (0.005)  -0.17302 -0.40867  817 264  817 264  817 264  1334 509  4.6%  6.1%  6.7%  4.4%  Notes: The estimation methodology is probit. Standard errors are in parentheses below the coefficient. ***_*** represent significance at the 1%, 5% and 10% levels.  119  Table 30 - Model to predict default (90 days delinquent) (1)  Guarantee  -0.4269 *** (0.160)  (2)  -0.3264 * (0.167)  (3)  -0.4758 *** (0.162)  Guarantee (IV) Initiation L T V (Based on O S B ) Current L T V (Based on O S B ) Current D C R Rate Outstanding balance (OSB)  0.1012 (0.297) 0.5166 *** (0.181) -0.5838 *** (0.140) -0.0277 (0.030) -0.0026 (0.006)  British Columbia Alberta Prairie Quebec Atlantic  0.2377 (0.308) 0.4148 ** (0.182) -0.5535 *** (0.138) -0.0396 (0.031) -0.0037 (0.006) -0.7548 *** (0.212) -0.1597 (0.252) 0.0862 (0.358) -0.2295 (0.145) -0.2626 (0.241)  Apartment Industrial Office Other property type Constant  -0.1289 (0.471)  N Number with dep. var. = 1 Pseudo-R  2  0.0298 (0.480)  (4)  0.0280 (0.305) 0.6674 *** (0.192) -0.4904 *** (0.144) -0.0296 (0.031) 0.0006 (0.006)  -1.3509 (0.456) 0.0637 (0.245) 0.8447 (0.157) -0.3341 (0.095) 0.0171 (0.024) -0.0005 (0.005)  -0.2113 (0.259) 0.1524 (0.153) -0.1806 (0.162) 1.2421 *** (0.273) -0.3020 (0.493)  -0.30137 0.511  817 113  817 113  817 113  10.1%  12.5%  14.1%  1334 192 10.8%  Notes: The estimation methodology is probit. Standard errors are in parentheses below the coefficient. ***,**,* represent significance at the 1%, 5% and 10% levels.  120  Table 31 - Model to predict default (foreclosure) (1)  Guarantee  -0.8092 *** (0.235)  (2)  -0.8103 *** (0.239)  (3)  -0.8135 *** (0.236)  Guarantee (IV) Initiation L T V (Based on O S B ) Current L T V (Based on O S B ) Current D C R Rate Outstanding balance (OSB)  -0.6768 (0.491) 0.7633 *** (0.245) -1.0416 *** (0.258) -0.0032 (0.046) -0.0050 (0.011)  Quebec Atlantic  -0.6834 (0.502) 0.7660 *** (0.249) -1.0423 *** (0.262) -0.0033 (0.046) -0.0049 (0.011) 0.0161 (0.251) -0.0031 (0.436)  Industrial Other property type Constant  -0.0464 (0.718)  N Number with dep. var. = 1 Pseudo-R  2  817 27 27.1%  -0.0458 (0.720) 817 27 27.1%  (4)  -0.6689 (0.493) 0.7476 ** (0.248) -1.0591 *** (0.266) -0.0023 (0.047) -0.0061 (0.012)  -0.2894 (0.794) -0.1519 (0.371) -0.9709 *** (0.191) -0.7427 *** (0.179) 0.0456 (0.037) 0.0022 (0.008)  -0.1148 (0.272) -0.2119 (0.575) 0.0081 (0.738)  -1.7615 ** (0.850)  817 27 29.1%  1334 55 4.4%  Notes: The estimation methodology is probit. Standard errors are in parentheses below the coefficient. ***,**,* represent significance at the 1%, 5% and 10% levels. Only selected property types and regions are used when the dependent variable is foreclosure-or-equivalent  T a b l e 32 - M u l t i n o m i a l logit m o d e l - role o f g u a r a n t e e a c r o s s default d e f i n i t i o n s  Panel 1 - Excluded  outcome  is  never-delinquent  Guarantee Current L T V ( B a s e d o n O S B ) Current D C R  3 0 - d a y s delinquent (0.292)  (0.337)  1.1060 ***  1.1595 ***  1.7835 " *  (0.309)  (0.341)  (0.423)  0.1815  is 30-days  delinquent  Current L T V ( B a s e d o n O S B )  N e v e r delinquent 0.0199 (0.292) -1.1060 * " (0.309)  Current D C R  -0.1815  Constant  outcome  is 90-days  delinquent  -1.1408 (0.584)  -0.4170 (0.401)  (0.524) 0.6775  (0.358)  (0.424)  (0.311)  2 . 2 5 9 7 ***  1.1189 (0.665)  (0.542)  3 0 - d a y s delinquent 0.4170  Current D C R  (0.358) 1.0435 *** (0.311) -1.1189 *  outcome  is  foreclosed  N e v e r delinquent 1.8213 *** (0.479)  Current L T V ( B a s e d o n O S B )  - 1 . 7 8 3 5 *** (0.423)  Current D C R Constant  **  Foreclosed -1.3844 ** (0.534)  (0.341) 0.8621 *** (0.286)  Panel 4 - Excluded Guarantee  1.8136 (0.878)  (0.401) -0.0535  *  - 2 . 4 5 9 7 ***  *  - 1 . 1 5 9 5 ***  1.1408 (0.584)  Foreclosed -1.8014 ***  0.0535 - 1 . 0 4 3 5 ***  N e v e r delinquent 0.4369 (0.337)  -0.4461 (0.823)  Current L T V ( B a s e d o n O S B )  Constant  -2.2783 *** (0.528)  *  9 0 - d a y s delinquent  (0.166) (0.463)  Panel 3 - Excluded Guarantee  (0.479)  (0.286)  - 2 . 2 5 9 7 ***  outcome  -1.8213 * "  -0.8621 ***  (0.463)  Panel 2 - Excluded Guarantee  Foreclosed  -0.4369  (0.166) Constant  9 0 - d a y s delinquent  -0.0199  0.6240 (0.411) -1.4162 (0.564) 0.6947  (0.665)  **  (0.901)  3 0 - d a y s delinquent 1.8014 ***  9 0 - d a y s delinquent  (0.524)  1.3844 (0.534)  -0.6775 (0.424)  -0.6240 (0.411)  2 . 2 7 8 3 ***  2 . 4 5 9 7 ***  1.4162  (0.528)  (0.542)  (0.564)  0.4461  -1.8136  (0.823)  (0.878)  **  -0.6947 (0.901)  N=820 a n d p s e u d o R - s q u a r e d is 6 . 7 7 % for all p a n e l s . T h e estimation m e t h o d o l o g y is multinominal logit. S t a n d a r d errors are in p a r e n t h e s e s b e l o w the co-efficient. " , " , * represent s i g n i f i c a n c e at the 1%, 5 % a n d 1 0 % l e v e l s . T h e four potential o u t c o m e s for the d e p e n d e n t v a r i a b l e are: the l o a n w a s n e v e r delinquent; the loan w a s 3 0 - d a y s delinquent but n e v e r b e c a m e 9 0 - d a y s delinquent; the loan w a s 9 0 - d a y s delinquent but w a s not f o r e c l o s e d ; a n d f o r e c l o s e d .  122  "  "  T a b l e 33 - Effect of g u a r a n t e e s by re g io n  Province British Columbia Alberta Prairie Ontario Quebec Atlantic  to  Total loans  Number of loans 90-days delinquent  Percent of loans 90-days delinquent  Number 90-days delinquent and guaranteed  Percent 90-days delinquent and guaranteed  171 52 19 334 249 73  6 7 4 65 33 9  4% 13% 21% 19% 13% 12%  6 5 3 48 29 9  100% 71% 75% 74% 88% 100%  Table 34 - Probit m o d e l b y region  Estimation variable  Ontario  Quebec  Guarantee  -0.3623 * (0.215) 0.3148 (0.442) 0.2304 (0.213) -0.8599 *** (0.187) -0.0274 (0.045) -0.0080 (0.009) 0.3951 (0.652)  -0.9445 (0.402) -0.3946 (0.710) 0.4938 (0.559) -0.2162 (0.264) -0.1009 (0.062) 0.0157 (0.014) 0.9199 (1.051)  Initiation LTV (Based on OSB) Current LTV (Based on OSB) Current DCR Rate Outstanding balance (OSB) Constant N Pseudo R*  311 14.8%  230 8.1%  The estimation methodology is probit, and the dependent variable is a measure of whether the loan ever became 90-days delinquent. 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