DETERMINANTS OF MULTIFAMILY 

MORTGAGE DEFAULT 

By 

Wayne R. Archer 

Peter J. Elmer 

David M. Harrison 

and 

David C. Ling 

June, 1999 

Working Paper 99-2 

(Electronic copies of FDIC Working Papers are available at www.fdic.gov) 

Federal Deposit Insurance Corporation 
DETERMINANTS OF MULTIFAMILY MORTGAGE DEFAULT 

Wayne R. Archer 

Center for Real Estate Studies 

Department of Finance, Insurance & Real Estate 

University of Florida 

Peter J. Elmer 

Division of Research and Statistics 

Federal Deposit Insurance Corporation 

David M. Harrison 

School of Business Administration 

University of Vermont 

David C. Ling* 

Center for Real Estate Studies 

Department of Finance, Insurance & Real Estate 

University of Florida 

Abstract 

Option-based models of mortgage default posit that the central measure of default risk is the loanto-value (LTV) ratio. We argue, however, that an unrecognized problem with extending the basic 

option model to existing multifamily and commercial mortgages is that key variables in the option 

model are endogenous to the loan origination and property sale process. This endogeneity implies, 

among other things, that no empirical relation may be observed between default and LTV. This 

is because lenders may require lower LTVs in order to mitigate risk, so mortgages with low and 

moderate LTVs may be as likely to default as those with high LTVs. Mindful of this risk 

endogeneity and its empirical implications, we examine the default experience of 9,639 

multifamily mortgage loans securitized by the Resolution Trust Corporation (RTC) and the 

Federal Deposit Insurance Corporation (FDIC) during the period 1991!1996. The extensive 

nature of the data supports multivariate analysis of default incidence in a number of respects not 

possible in previous studies. 

* The views expressed in this paper are those of the authors and not necessarily those of the 

Federal Deposit Insurance Corporation. Correspondence may be directed either to Center for 

Real Estate Studies, Department of Finance, Insurance & Real Estate, University of Florida, 

Gainesville, FL 32611-7168. Phone: (352) 392-9307, Fax: (352) 392-0301, E-mail: 

ling@dale.cba.ufl.edu or to Peter Elmer, FDIC Division of Research and Statistics, 550 17th St. 

N.W., Washington, D.C. 20429. Phone: (202) 898-7366, Fax: (202) 898-7189, E-mail: 

pelmer@fdic.gov. 
DETERMINANTS OF MULTIFAMILY MORTGAGE DEFAULT 

1. INTRODUCTION 

Default of commercial mortgage loans during the last decade has been a significant 

investment risk. The collective evidence suggests that default may occur with over 15 percent of 

commercial (income-producing property) loans (Snyderman [1994]) and that the resultant yield 

degradation, given foreclosure, may approach 1,000 basis points (Ciochetti [1998]). Although many 

partial bodies of data attest to this default risk, available sources have revealed only very limited 

views of the problem. Early studies rely primarily on the foreclosure experience of major life 

insurance companies. However, although this experience is important, insurance companies 

represent less than one-fifth of the multifamily investor market and the analysis focuses on only one 

form of commercial mortgage default (foreclosure).1 Recent work examines the experience of other 

investors in the same activity class as life insurance companies, such as Freddie Mac and Fannie Mae 

(Goldberg and Capone [1998]) and FHA (Follain et al. [1999]), and also focuses on restricted 

definitions of default. 

This paper examines the determinants of multifamily mortgage default for the largest class of 

multifamily originators and investors, banks and savings institutions, using a broad definition of 

default that recognizes all types of default-related events, such as loan modifications and workouts as 

1

Bradley, Nothaft, and Freund (1998) show that the share of multifamily mortgages held 

by life insurance companies and pension funds declined steadily from 17.8 percent in 1980 to 9.0 

percent in 1997. The largest recent growth occurred in the private-label commercial mortgage 

security sector, which jumped from 0 to over 12 percent between 1990 and 1997. The Freddie 

Mac and Fannie Mae share rose from 10.5 to 12.3 percent between 1990 and 1997. Banks and 

savings institutions maintained the largest share, although their share fell from 50.5 percent in 

1980 to 33.8 percent in 1997. 
well as foreclosures.2 We examine the default experience of multifamily mortgages found in 22 pools 

of loans securitized by the RTC and the FDIC during the 1991!1996 period. These pools contain 

mortgages of all sizes located in almost every state and originated by many institutions. As a result, 

these RTC/FDIC loans may be closer than life insurance loans to the quality of typical conduit loans.3

 The loan-level data contain extensive property, loan, and underwriting data, plus a record of loan 

performance over time. The loans are also unique by virtue of the fact that most are believed to have 

been held as portfolio investments by the originating institution. Interestingly, the overall default rate 

of our sample is 17.5 percent, which is not significantly different from the default frequencies 

reported for the loan portfolios of major life insurance companies over similar time periods.4 The 

extensive nature of the data supports multivariate analysis of default in a number of respects not 

possible in previous studies. 

In formulating our empirical model, we look for guidance to option-based models of 

commercial mortgage default. Although these models clearly suggest LTV and related factors as 

central to the default “story,” their meaning fails to transfer to the case of multifamily mortgages. 

2

Snyderman (1994) reports a variety of default-related data from all types of commercial 

mortgages held by life insurance companies, 10!20 percent of which are multifamily. Vandell et 

al. (1993) and Episcopos et al. (1998) distinguish multifamily loans from other types of 

commercial mortgages, but only in the context of a general model of commercial mortgage 

default. Interestingly, these two studies consistently find multifamily to be one of the strongest 

property-type variables in their default analysis. 

3

 Although conduit loans are generally “thrift” quality, Quigg (1998) argues that they 

differ from our RTC/FDIC loans in that they are originated with more recent underwriting 

standards and are subject to the scrutiny of rating agencies and investors. 

4

 Fitch (1996) provides a practitioner analysis of multifamily and commercial loans that 

includes portions of the data covered by our analysis. Unfortunately, all of the analyses in the 

Fitch report were done by looking at the effects of a single variable on default and losses (that is, 

univariate regressions). For a thorough discussion of the drawbacks of the Fitch report, see 

Quigg (1997). 
We hypothesize that option-based models encounter problems in the commercial mortgage arena 

because they fail to recognize key variables as endogenously affected by the loan origination process. 

In particular, rational lenders will react to higher risk by setting LTV to offset or mitigate the risk. 

Moreover, the observed “value” may vary with the availability and/or terms of the financing. These 

endogenous elements imply that no empirical relationship may be found between default and LTV. 

Overall, our results strongly suggest that the borrower’s ability to service the debt, or debt coverage 

ratio (DCR), is more important in explaining default than LTV---a result inconsistent with the 

predictions of option-based models. 

In addition to examining the role of LTV and DCR, we also estimate the effects of property 

characteristics, originating institution, and location on the incidence of default. The general finding is 

that a limited explanatory role is played by each of these characteristics. For example, one of our 

four property characteristics (number of units) is significant along with several location and lender 

control variables. However, since many similar control variables have little explanatory power, 

default rates appear more closely related to the characteristics of the loans than to those of the 

property, originator, or location. Although the extent to which our results can be generalized 

remains an open question, our findings contribute to the sparse collection of evidence on the 

determinants of multifamily mortgage default. 

In Section 2, we summarize the results of several previous default studies and clarify the 

various phases of default experience that they represent. Section 3 discusses mortgage default in the 

context of option theoretic models while exploring complications introduced when key elements of 

those models are endogenously determined. The pervasive problem of censuring is also addressed. 

In Section 4, we describe the RTC/FDIC data and compare them with other data that have been 

studied. A logistic regression model is specified and estimated in Section 5, while a number of 
 

robustness checks are detailed in Section 6. Section 7 summarizes the results, and concludes. 

2. EXISTING EMPIRICAL STUDIES 

Empirical analysis of commercial mortgage default is limited to a handful of studies. Two 

important characteristics of existing studies are the sample source and the point in the process of 

default that is the focus of the study. The significance of the latter issue is highlighted in figure 1. 

Clearly, the “default rate” indicated by data can depend on how early in the process the point of 

“default” is chosen. This is particularly important, as the diagram suggests, because various studies 

have focused on different points in the default process. 

Of the two components of the default problem, incidence and loss severity, studies have 

tended to focus on one or the other. Two benchmark analyses rely on data from life insurance 

company annual statements to regulators. Snyderman (1994) examines both the incidence of default 

and loss severity using all individually reported commercial mortgage loans of eight large life 

insurance companies originated from 1972 through 1986, as reported in 1991 annual statements. 

The commercial mortgages in this study represented roughly 25 percent of the commercial 

mortgages held by life insurance companies, and approximately 5 percent of all commercial 

mortgages. The default rates from these data are potentially affected by size bias (all loans are $1 

million or greater) and by censuring, and have no control for property type. 

Ciochetti (1997) looks at loss severity using the same data source as the Snyderman study.5 

He examines only foreclosed loans, estimating the loss recovery through the point when a loan is 

transferred to REO (real estate owned). Ciochetti’s data set is slightly more comprehensive (loans 

down to $500,000 and taken from 14 companies). This gives coverage of roughly 30 percent of life 

5 However, he expands to 14 companies and updates the data to 1995. 
insurance company commercial loans and approximately 6 percent of all commercial mortgage loans. 

The Ciochetti study is limited by the same sparse set of information as in the Snyderman study. 

Ciochetti (1998) extends his analysis of loss recovery rates. From a single lender, he obtains 

308 foreclosed loans with complete histories through the final property sale. These records have 

extensive detail on loan and property characteristics, property sale prices, and expenses between 

foreclosure and property sale. Thus, for this small set of data, Ciochetti constructs decidedly the 

most complete estimates to date of the loss recovery from foreclosure and the factors affecting it. 

The study does not attempt to deal with broader definitions of default that include, for example, loan 

modifications, discounted payoffs, note sales, or other loss-related resolutions commonly observed in 

multifamily and commercial mortgage default. 

Vandell (1992) examines default incidence using a time series of aggregate loan commitment 

data reported by 20 of the largest life insurance companies.6 From the same source he uses 

aggregate foreclosure rates representing approximately two-thirds of all commercial mortgage loans 

made by life insurance companies. He examines the ability of the estimated average loan market 

value/property value ratio to explain the aggregate foreclosure rate. Dealing strictly in aggregate 

ratios, he is not able to examine any other factors affecting the aggregate foreclosure rate. 

The study using the most complete data is Vandell et al. (1993). This study includes every 

commercial mortgage loan from 1962 through 1989 made by one large life insurance company. Each 

loan record is very extensive, supporting analysis of foreclosure rates by loan characteristics, 

underwriting ratios, property type, and borrower type. The method of analysis is estimation of a 

proportional hazards model. In summary, this is the most extensive and complete analysis of default 

6

 Data are from various quarterly Investment Bulletins of the American Council of Life 

Insurance. 
incidence (as defined by foreclosure). However, the study is nevertheless restricted to the loans of a 

single life insurance company and, by ending with loans originated through the third quarter of 1989, 

stops at the beginning of a very important period in commercial mortgage foreclosure history. 

Moreover, this study fails to consider loan modifications and other loss-related resolutions commonly 

observed in multifamily and commercial default. 

A more recent study, conducted by Fitch (1996), uses data from the same source as this 

study, namely the securitized pools of commercial loans arising from the operations of the RTC and 

the FDIC. The Fitch study examines incidence of default through bivariate analysis of default over 

numerous characteristics of individual loans. Although the study benefits from extensive data, it is 

naturally limited by the bivariate nature of its analysis. 

The most recent studies of commercial mortgage default include papers by Goldberg and 

Capone (1998) and by Follain, Huang, and Ondrich (1999). These two papers have in common that 

they estimate proportional hazard models that focus on post-origination changes in metropolitan 

rental market conditions to explain default. The two papers also have numerous significant 

differences. Goldberg and Capone use multifamily loans purchased by Fannie Mae and Freddie Mac 

during the years 1983!1995, while Follain et al. use data from FHA 221(d)(4) market-rate loans 

made between 1965 and 1995. Goldberg and Capone use a “structured” approach to modeling 

where they synthesize current LTV, current DCR, and tax depreciation value from empirical data to 

use as explanatory variables. On the other hand, Follain et al. use market data directly as explanatory 

variables, and they use a more elaborate competing risks version of the proportional hazards model. 

Both of these studies confirm the importance of post-origination events as factors in default. Both of 

them observe important loan populations, but populations that are largely complementary to the loan 

pools studied here. Neither study appears to consider property characteristics or original loan 
underwriting information at the level of detail considered here. 

Finally, a study by Ciochetti and Vandell (1999) focuses on the performance of commercial 

mortgages using a contingent claims model of default behavior. Their approach is a unique 

departure in examining commercial mortgage returns. However, it derives default probability only 

implicitly, in the context of the model (a theoretically attractive approach). As a result, their default 

analysis is not easily compared with explicit estimates of default risk. Since they derive costs of 

default from other studies, their most important contribution to default analysis is to estimate implied 

volatilities of property prices using a data set from a single large insurance company. 

Several points are clear from the analysis to date of default experience with commercial 

mortgage loans. First, extremely valuable information has been derived by past investigations. 

However, on at least two fronts vast challenges remain. All of the published investigations of default 

except the Fitch study have relied on a subset of loans from a small number of life insurance 

companies and have considered only very narrow definitions of default. This leaves approximately 

95 percent of commercial mortgage lending experience in dollar volume, and a much greater share by 

number of loans, largely unexamined, while omitting many loss-related events from consideration. 

Second, much of the research to date, with the important exceptions of Ciochetti (1998), Ciochetti 

and Riddiough (1998), and to some extent Fitch, does not account for the “stress test” of the 

economy of the early 1990s. 

With respect to specification, prior studies have not considered the importance of the location 

of the collateral property---despite the significant cross-sectional variation in price appreciation 

across metro markets and across time. In addition, no evidence has been presented on whether the 

observed variation in default rates by originating lender is attributable to the characteristics of the 

loans or to the characteristics of the lenders. Finally, little is known about the reliability of other loan 
and property attributes (property age, size, quality, etc.) as predictors of default. 

3. MODELING ISSUES 

Option Theoretic Factors 

Option-based models of mortgage default view default as a put option according borrowers 

the right to demand that lenders purchase their properties in exchange for mortgage elimination.7 

The central theme of these models is that the value of the put (the likelihood of default) increases as 

the market value of equity declines, which occurs if either property value declines or mortgage value 

increases.8 Because the two variables most directly responsible for these movements are local 

property prices and interest rates, they serve, along with related volatilities, as the primary variables 

explaining default.9 Cash flow variables, such as DCR, play a secondary role distinct from LTV. For 

example, Vandell et al. (1993) include DCR as a proxy for a cash shortfall effect that is “irrelevant” 

in a transaction-costless option environment.10 

7

 Elmer and Seelig (1999) emphasize that significant implications of option-based models 

of default encounter difficulties in recourse lending environments, which are common in the 

single-family mortgage arena. However, since multifamily mortgages often have nonrecourse 

clauses and prepayment penalties, option-based models provide a reasonable starting point for 

modeling the determinants of default. Moreover, in contrast to single-family borrowers, 

multifamily borrowers may be partnerships, subsidiaries, or other vehicles that have limited 

resources to cover liability even in the event the lender pursues a claim. 

8

 See, for example, Kau et al. (1987, 1990) or Cox and Rubinstein (1985), chap. 5. 

9

 Capozza, Kazarian, and Thomson (1998) point out that a higher dividend rate, that is, a 

lower reinvestment in the property, should lower the expected growth rate in value and increase 

the default rate. 

10 The application of option-based models to default decisions and commercial mortgage 

valuation has received substantial criticisms. For example, Riddiough and Wyatt (1994) argue 

that the strategic effect of foreclosure costs on the default and foreclosure decisions are neglected, 

while Vandell (1995) and others have repeatedly stressed the importance of transaction costs. 
 

A second theme of option-based models is that prepayment and default are “competing” 

risks.11 Exercising one option terminates the other, and increasing the probability of exercising one 

option tends to diminish the probability of exercising the other. Competing risk issues seem 

especially relevant to multifamily and commercial mortgage default because prepayment penalties are 

common. In the absence of the right to prepay, a decline in interest rates increases the value of the 

default option, as default becomes a means for gaining more favorable mortgage terms. From 

another perspective, competing risk issues also enhance the likelihood of default because of collateral 

constraint problems.12 That is, eroding equity increases the difficulty of finding lenders willing to 

refinance a project or otherwise provide replacement debt. This problem is also relevant to 

multifamily and commercial mortgages because credit availability is more volatile and less subsidized 

at the national level than for single-family mortgages. Combining this effect with the widespread use 

of prepayment penalties appears to underscore the importance of declining interest rates as an 

option-based variable that carries over to the multifamily and commercial arena. 

The Endogeneity Problem 

An important and as yet unrecognized problem with extending option-based models to 

multifamily and commercial mortgages is that key variables in the option model are endogenous to 

the loan origination and property sale process. That is, rational lenders can manage default risk by 

adjusting the terms of the mortgage in a manner that offsets or mitigates risk of loss. For example, 

lenders confronted with high-risk loan applications may simply request higher down payments (lower 

11 Two examples from single-family analysis are Deng (1997) and Hilliard, Kau, and 

Slawson (1998). 

12 See Archer, Ling, and McGill (1996). 
LTVs). If the lender perceives a low level of default risk, the response might be to accept a larger 

loan (higher LTV), all other things being equal. Similarly, the lender may reduce the loan term, 

impose recourse requirements, or enact other modifications in an effort to mitigate risk. This type of 

negotiation can be expected to be common for multifamily mortgages because their balances are 

relatively large, borrowers are sophisticated, and loan documentation is not standardized. It is also 

likely in the case of portfolio lenders that expect to live with the risk of the mortgages they 

originate.13 

Endogenous influences may extend to the sale process and the price paid, or value assumed, 

for the property. Multifamily and commercial property markets are far more heterogeneous than 

single-family markets, and sales often require long negotiation periods and complex financing 

arrangements. Buyers may be willing to pay a number of prices depending on the availability and/or 

terms of the financing, especially if the loan is nonrecourse. Comparable sales may be sufficiently 

difficult to obtain that appraisers cannot check the sale “price” against other market transactions or 

otherwise account for interdependency between financing and sale price or property value. The 

reported LTV may be contaminated by these influences, thereby limiting its usefulness as a measure 

of risk. 

Endogeneity issues may also affect the interaction between prepayment and default in a 

competing risk framework. Given that prepayment fees or penalties can be contracted to offset the 

value of the prepayment option, the same penalties can be easily extended to offset the incentive to 

13 Endogeneity may be less of an issue for mortgages earmarked for sale to investors, such 

as life insurance companies or conduits. Purchasers in the secondary markets may be more willing 

to set standard underwriting limits that effectively reduce the need to negotiate restrictions or 

credit enhancements beyond those required by the secondary market purchaser. 
use default as a means of prepayment.14 That is, prepayment penalties can be contracted to apply in 

the event of default in the same manner that they apply in the event of prepayment. The value of 

default as a strategic alternative to prepayment is thereby eliminated, at least with respect to the gain 

accruing to lower interest rates. 

Endogenizing option-related measures of risk into the loan origination and contract process 

has several implications for evaluating the default risk of existing mortgage pools. First, no empirical 

relation may be observed between default and the most basic risk variable found in option models, 

LTV. If lenders require lower LTVs to offset higher risk, then low and moderate LTVs may be as 

likely to default as high LTV mortgages. Moreover, if the value of the property is at least partially 

influenced by the availability or terms of financing, then the importance of LTV as a measure of risk 

is further diminished. These factors counter the simple option theoretic notion that default risk 

necessarily increases with LTV. 

A second implication is that other variables in option-based models may be contaminated or 

reoriented as a result of negotiated risk arrangements. In particular, if lenders recognize higher-risk 

applications, they may react by incorporating a premium into the mortgage contract rate to 

compensate for the added risk. In this case the mortgage rate would vary positively with residual 

risk, but only after adjustment for LTV, loan term, and other variables.15 This effect necessarily 

clouds interpretation of the value that accrues to declining interest rates. For example, the 

prepayment option for a high-risk, high-rate mortgage may not come into the money until observed 

14 In fact this endogenous element may be common, as it appears in standard multifamily 

mortgage contracts found in Nelson and Whitman (1993), sections 14.16 and 14.17. 

15 It is important to note, however, that the risk-adjusted interest rate does not necessarily 

map monotonically to variation in the contractual interest rate. The risk adjustment may occur 

through points charged at origination, or through requirement of mortgage insurance. 
mortgage rates fall several hundred basis points below the contract rate, as any refinancing would 

require the same risk premium as the initial mortgage. If high rates are associated with high default 

risk, then the value of the prepayment option is also reduced by the fact that substitute refinancing 

may be difficult to find. Similarly, the inclusion of a recourse provision does not imply a lower risk 

of default if the reason for the inclusion is to protect against a higher level of perceived risk not 

controlled for by the other underwriting variables.16 

The Problem of Censuring 

All empirical databases on mortgage loans can be subject to both “left” and “right”censuring, 

as suggested in figure 2. Data can be censured at origination with underwriting rules or restrictions 

imposed by individual lenders. In practice, restrictions along these lines are common at the 

individual-lender level, which attests to the importance of sampling from multiple lenders. As loans 

season, “left censuring” also occurs when loans with specific properties disappear from the database. 

This can happen if the loan is paid off before the reporting date or if it is foreclosed and the property 

is sold before the observation date. Data are subject to “right censuring” to the extent that loans are 

still current as of the observation date but subsequently default. The existence of censuring can 

significantly limit the conclusions drawn from univariate analysis of the sample. 

A Proposed Solution to Risk Rating with Typically Available Data 

The RTC/FDIC data we use allow us to address numerous issues not considered in prior 

studies. First, the loans in our sample were originated by a large number of lenders. Thus, we avoid 

16 For more on the role of recourse clauses in commercial mortgage contracting, see 

Childs, Ott, and Riddiough (1996). 
the sample selectivity problem associated with data from one lender (for example, life insurer) while 

changing the focus from life insurance loans---the subject of most published default studies. Second, 

our sample period includes the commercial real estate recession of the early 1990s. The data also 

allow us to control at least partly for the effect of local appreciation rates because the location of the 

property is available at the metropolitan (or, in the largest cities, submetropolitan) level. In addition, 

the loans vary greatly by date of origination, with some originated in years of high price inflation and 

others in periods of low price inflation. 

Other factors captured in our analysis that may affect default incidence include property 

characteristics such as age, size, and quality, as well as the riskiness or volatility of the property 

value. These risks, as perceived by the lender, may be inculcated in the size of the spread between 

the original loan interest rate and the contemporaneous risk-free market interest rate.17 Increased 

loan size should reduce the resistance of any fixed default transactions costs, thus increasing default 

risk. Finally, decreases in the interest-rate level since origination should increase default risk, unless 

either the prepayment option is freely available or related penalties extend to default as they do to 

prepayment. The greater the decline in interest rates since loan origination, the greater the strike 

price of the default option and the likelihood of its being exercised. 

As noted above, the relationship between standard underwriting criteria and default risk is not 

clear. If lenders under-adjust LTV or DCR, a relation to default may arise despite endogenous 

influences. If lenders over-adjust either ratio, there could be the opposite relationship. 

A number of variables in the study also relate to the prepayment option. Most important, the 

change in interest-rate level since loan origination should strongly indicate the incentive to prepay. 

However, since this change affects the likelihood of both default and prepayment, it should be 

17 After adjustment for points charged and any mortgage insurance. 
strongly associated with default only if access to the prepayment option is limited. 

4. DATA 

Description 

The data for our analysis arise from multifamily mortgages securitized by the RTC and FDIC 

during the 1991!1996 period. These mortgages came from the portfolios of a large number of 

savings and loans taken over by the RTC. During this period the RTC created 11 securitization 

pools composed entirely of multifamily mortgages (“M” deals), followed by other pools that mixed 

multifamily with other commercial mortgages (“C” deals). The mortgages placed in these pools 

included fixed as well as adjustable rates, with a wide variety of seasoning, term, geographic, and 

other characteristics. The mortgages were generally performing when placed in the securitization 

pools. 

The data set was constructed by assembling information on all multifamily and commercial 

loans incorporated in the RTC/FDIC securitizations. This yielded 42,165 loan records, of which 

13,747 represented multifamily loans. As shown in table 1, the loans in most deals came from many 

institutions. The percentage of original loans contained in our sample varies across the 22 

multifamily and commercial deals. For example, our data set contains 50.2 percent of the original 

1991-M5 loans, but 84.9 percent of the original 1991-M1 loans. Subsequent to the issuance of the 

1992-C1 deal, multifamily loans were included in commercial deals. We obtained data from 11 

commercial deals with 5,362 multifamily loans. Our data set contains 4,017 (or 75 percent) of these 

5,362 multifamily loans. In 1994, the FDIC began tracking status and performance data for each 

loan on a monthly basis. These post-origination records were available for 9,639 (or 70 percent) of 
the 13,747 multifamily loans.18 Of the 9,639 loans contained in our performance data set, we have 

sufficient data for multivariate analysis on 6,985 (or 72 percent). 

Loans were classified as having defaulted if they were ever 90 days or more late.19 The righthand column in table 1 contains default rates, by deal and in total, for our sample of 9,639 

multifamily mortgages. As can be seen, the rate of default varies significantly across the 22 deals, 

ranging from a low of 6.9 percent (1996-C1F) to a high of 68.5 percent (1992-C6). The mean 

default rate is 17.5 percent. 

Summary Statistics 

Censuring effects naturally limit conclusions arising from single dimensions of the sample. 

Nevertheless, comparing simple (one-way) distributions of default rates with our subsequent 

multivariate findings provides insight on the validity of the more-common univariate analysis. 

Therefore, we report origination, and by selected originating lenders. Default rates by loan size, 

LTV, and DCR are of special interest and are also shown. 

Variation across States 

Table 2 contains default rates by state. Panel A sorts these rates by sample size, while panel 

18 Because many of the data fields in this performance data set either are sparsely 

populated or contain unreliable information, the analyses that follow must often use a subset of 

the 9,639 observations. 

19 A broad definition of default is useful because, in addition to foreclosure, a variety of 

loss-related workout arrangements are common to multifamily default resolution, such as 

modifications, discounted payoffs, and note sales. As discussed by Elmer and Haidorfer (1997), 

RTC deals began requiring a special servicer to deal with these arrangements in 1992. Since 

loans are typically referred to special servicers when they become 60 days delinquent, and special 

servicer fees are substantially higher than those of other types of servicers, delinquency-related 

costs begin to accrue very early in the default process. 
B sorts by default rates. Loans originated in California dominate the multifamily loans securitized by 

the RTC, accounting for 42.9 percent of our sample. Florida is a distant second, providing 6.2 

percent of our sample. Texas, Arizona, Pennsylvania, and Oregon follow Florida in sample weight, 

providing 5.9, 5.1, 3.7, and 3.6 percent, respectively, of our sample loans. 

Panel B in table 2 displays a tremendous amount of variation in default rates across states. In 

states with a sample size of at least 100, Maine has experienced the highest rate of default, at 44.1 

percent.20 New York, New Jersey, Virginia, and California follow, with default rates of 29.0, 25.6, 

24.1, and 22.3 percent, respectively. Conversely, seven states with 100 or more loans in our sample 

have experienced default rates of less than 10 percent: Florida, Arizona, Iowa, Kansas, Washington, 

Colorado, and most noatably Oregon, whose default rate has been just 2.9 percent on 349 loans. 

Variation across Local Markets 

The tremendous variation in default rates across states suggests, not surprisingly, that the 

location of the collateral property is a fundamental determinant of default. To investigate this issue 

further, we identified submetropolitan areas (using three-digit zip codes) that contain at least 75 of 

our multifamily observations. Information on these 26 market areas is reported in table 3. The 

largest percentage of our loan sample (8.9 percent) comes from the CBD of Los Angeles. 

Southwestern LA accounts for an additional 3.4 percent of our total 9,639 loan sample, while 

Tucson and San Francisco account for 2.1 and 2.0 percent, respectively. The remaining three-digit 

zip codes each contain less than 2 percent of our total sample, although the combined weight of the 

LA market areas is significant. Again, the variation in default rates across these market areas is 

20 According to the FDIC, the 52 percent default rate in Lewiston, Maine, was the result 

of fraud, which accounts for the anomalous summary statistics at the related state or local levels. 
stunning. Lewiston, Maine, experienced the highest rate of default, at 51.6 percent. LA!San 

Fernando Valley, LA!Northridge, Philadelphia, and LA!San Fernando Valley follow with default 

rates of 45.7, 44.9, 39.1, and 34.0 percent, respectively. Conversely, several markets with 75 or 

more loans experienced default rates of less than 10 percent, including El Paso, San Diego, Miami, 

Phoenix, and San Francisco. Two areas of Portland, Oregon, had default rates of just 2.4 and 1.2 

percent. These statistics strongly suggest that local market conditions are a prime determinant of 

multifamily defaults. 

Variation by Year of Origination

 To control for the effects of loan seasoning and real estate cycles on multifamily default 

rates, we also desegregate our sample by year of loan origination. As can be seen in table 4, 

multifamily default rates vary substantially by year of origination, in addition to varying significantly 

across local markets. Table 4 also breaks the sample into ARM and fixed-rate loans. For the 8,051 

loans with information on the date of origination, 41 percent are ARMs, while 59 percent are fixedrate loans. The default rate on ARMs has averaged 19.3 percent, exceeding the 14.8 percent rate on 

fixed-rate loans. 

Variation by Originating Lender 

All analyses of residential and commercial mortgage default of which we are aware ignore the 

characteristics of the originating lenders and focus solely on the characteristics of the loan and 

borrower. However, some recent evidence suggests that cross-sectional variation in lender 

characteristics explains a significant proportion of the variation in various mortgage lending 
outcomes.21 To consider the effects of variation in lender characteristics and to be able to control for 

this variation in our regression analysis below, we identified the 26 originating lenders that were 

responsible for at least 50 of our multifamily observations. As indicated in table 5, these 26 lenders 

originated 54.0 percent of our sample. Consistent with our other subsamples, the average default 

rate for this subsample is 18.7 percent. However, the variation in default rates across originating 

lenders is truly stunning, ranging from a high of 51.6 percent to a low of 1.9 percent. It is not clear 

from these summary statistics whether observable property and loan characteristics simply differ by 

lender or whether there is additional, unobserved information associated with the lender. However, 

this variation strongly suggests that lender characteristics are a useful indicator of multifamily 

defaults, and should be controlled for in our multivariate regressions. 

Variation by Original Size, LTV, and DCR 

Table 6 contains information on default rates by original loan size, by original LTV ratio, and 

by original DCR. In our sample of 9,639 loans, 9,190 observations contain information on the 

original loan size. Of these, 4,786 (or 52.1 percent) had an original balance of less than $250,000; 

1,856 (20.2 percent) had an original balance between $250,000 and $500,000; 847 (9.2 percent) had 

an original balance between $500,000 and $750,000; 483 (5.3 percent) had an original balance 

between $750,000 and $1 million; and 1,218 observations (13.3 percent) had an original balance in 

excess of $1 million. The mean loan size is $630,000, which is significantly less than the mean size 

of the life insurance company loans analyzed by Vandell (1992), Vandell et al. (1993), Snyderman 

(1994), and Ciochetti (1997, 1998). The average default rate across this subsample is 17.1 percent, 

with an ample amount of variation by size around the mean. Interestingly, the default rate of 11.1 

21 See, for example, Harrison (1998) and its references. 
percent on smaller (<$250,000) loans is significantly lower than the rate for larger loans, and the 

default rate is highest for loans above $750,000. This variation strongly suggests a need to control 

for loan size. 

Panel B of table 6 contains information on default rates by original LTV---a critical variable 

in the origination and initial pricing of commercial loans. Of the 4,850 observations in our sample 

that contain information on original LTV, 56.5 percent had LTVs between 50 and 75 percent, 34.6 

percent between 75 and 85 percent, 5.1 percent between 85 and 95 percent, 1.5 percent between 95 

and 100 percent, and 2.4 percent between 100 and 125 percent. The mean LTV for this subsample is 

74 percent, and the average default rate is 16.5 percent. Interestingly, however, there is little 

variation around this mean. This is consistent with our hypothesis that LTV is endogenous with 

respect to perceived default risk and therefore should have no effect on default rates. This issue is 

investigated more fully in our multivariate regressions. 

Another key variable in the origination and pricing of commercial mortgages is DCR. As can 

be seen in panel C of table 6, just 1,668 loans in our sample contain information on original DCR. 

However, the average default rate on this subsample is 17.4 percent, once again strongly suggesting 

that the subsample is highly representative of our broader 9,639-loan sample. The mean DCR is 

1.27, and approximately 64 percent of loans in this subsample have original DCRs less than 1.3. 

Moreover, this 64 percent has experienced significantly higher default rates than the remainder of the 

subsample. In fact, default rates appear to decline significantly and consistently with increases in the 

DCR. 
A Comparison with Other Samples 

It is also of interest to ask how the RTC/FDIC loans compare with loans of large life 

insurance companies represented in previous studies. Information from Snyderman (1994) and 

Vandell et al. (1993) enables a partial comparison, shown in table 7. Also informative is a 

comparison of RTC/FDIC loans with a broader representation of commercial mortgage loans of 

similar vintage. For this purpose, table 7 includes average characteristics of commercial loans 

committed by major life insurance companies during the third quarter of 1983.22 This year was 

selected because it is the mean year of origination for the RTC/FDIC loans. The mean loan size in 

our sample, $630,000, is significantly smaller than the average ACLI loan of $8.8 million and than 

the average loan size examined by Snyderman and by Vandell et al. By comparison, our sample also 

has longer maturities and is much less likely to require balloon payments. 

5. MULTIVARIATE ANALYSIS 

Model Specification 

Our analysis focuses on explaining the binary default variable: whether the loan has ever been 

90 days or more late. This focus suggests a logistic regression model of the form: 

DEFAULTi = b xi + ìi, (1) 

where DEFAULTi is a binary variable indicating whether the ith loan has defaulted, b is a row vector 

of coefficients, xi is a vector of variables that explains defaults, and ìi is the random error term. 

Summary statistics in table 4 show that ARMs exhibit different default patterns over our 

sample period from fixed-rate loans. This suggests either that ARM loans are underwritten 

22 Data are for 20 large life insurance companies as reported by the American Council of 

Life Insurance (ACLI) Investment Bulletin series. The data are reported to represent two-thirds 

of all life insurance company loan commitments. 
differently from fixed-rate loans or that the underlying properties may differ between the two types 

of loans, causing the “right-hand-side” variables to have relationships that differ between the two 

cases. We therefore estimate separate logistic regressions for ARMs and fixed-rate mortgages. 

Cleaning procedures are used to ensure that only reliable data enter our regression specifications.23 

To mitigate the effect of missing values among explanatory variables, we use a technique 

known as modified zero-order regression. Right-hand-side missing values for the five variables of 

primary interest are set to zero. Then a companion dummy variable is created for each of the five 

dummy variables, which are assigned the value of one for cases with missing data, and zero 

otherwise. The regression coefficient of the dummy takes on the average incremental value 

associated with the “missing value” cases, while the main coefficient of the variable represents the 

marginal effect of the main variable within the set of nonmissing cases. The benefit of the technique 

for this application is that it permits a very large number of cases to be used that otherwise would 

have to be discarded.24 Our final fixed-rate logistic regression uses 2,966 observations; our ARM 

regression sample uses 4,019. Variable definitions are provided below. 

Loan and Underwriting Variables 

Notwithstanding the discussion in Section 3 about the complexity of the spread variable, in 

the regressions that follow a naive measure of the interest-rate risk premium is used as a predictor of 

23 Only mortgage loan observations exhibiting an original contract interest rate in excess of 

the corresponding ten-year constant maturity risk-free rate, an original LTV less than or equal to 

100 percent, an original DCR greater than or equal to 0.9 and less than 5.0, and an original 

contract interest rate greater than 5 percent and less than 20 percent were included in our 

regression sample. 

24 See Green (1977), 431. 
default (SPREAD). The premium is measured as the simple difference between the reported interest 

rate at origination and the contemporaneous value of the ten-year constant maturity Treasury rate 

(without consideration of points or mortgage insurance as substitutes for the risk premium). 

SPREAD is expected to vary positively with default probability. 

In addition to SPREAD, the ten-year Treasury yield (TREASYLD) also is used as a proxy 

for default risk. As noted in Section 2, a higher level of interest rates at origination implies greater 

subsequent decline and a greater increase in the value of the outstanding obligation, with greater 

resultant reduction of borrower equity. Another argument for the variable is that mortgage rates on 

loans made in a high Treasury-rate environment will be higher, and higher contract rates should be 

associated with an increased probability of default, all other things being equal. Consistent with the 

effect of interest-rate change on loan obligation value, the value of the borrower’s refinancing option 

at any time is also higher, all other things being equal, the higher the original contract rate of interest. 

Models of strategic default predict that default incidence is positively related to the incentive to 

refinance. Thus, option-based models of mortgage termination predict that default rates will vary 

positively with the level of interest rates at origination. 

If original LTVs and DCRs are not perfect controls for loan risk, they may still correlate with 

default, even after the best loan underwriting. Therefore, these ratios are also included in our 

empirical analysis. Default is expected to vary positively with LTV, though if the lender over-adjusts 

the ratio in underwriting, it is possible that the reverse could be true. Default is expected to vary 

negatively with DCR, though again an over-adjustment of the ratio in underwriting could result in 

the opposite. 

All of the loans in the performance data set were/are in securitized pools. To control for 

unobserved differences in pool (deal) structures, such as the presence and effectiveness of special 
servicers, we include deal dummies in the logistic estimations. 

Finally, all of the loans in our study were originated by financial institutions that were 

eventually closed. It is likely that much variation existed in the lending and underwriting strategies of 

these firms. However, by not including lender characteristics, we would effectively be assuming that 

lenders are homogeneous with respect to their risk tolerances and preferences as well as their 

information-gathering and processing capabilities. Therefore, controls are also constructed whereby 

each financial institution represented by 50 or more loans is distinguished by a unique control 

variable (INSTj). Twenty-six financial institutions are explicitly represented, with all other lenders 

representing the default case. These binary variables have no expected sign. Rather, they are 

intended to control for variation by lender in underwriting practices, and to test for the importance of 

this variation. 

Size and Property Variables 

Characteristics of the collateral property may affect the likelihood of default even after 

underwriting adjustments are made in the loan terms. Prominent characteristics that may be factors 

are size, quality, age, and whether the property is new. It is argued in some lending circles that 

larger properties are more prone to default. To account for this possibility, the number of apartment 

units is included in the estimating equations to represent size (NUMUNITS), which would be 

expected to have a positive sign. It has also been argued that default varies with quality. Some 

have suggested that middle-quality apartments are the safest because during slumps they gain tenants 

moving down and in a strong economy they gain tenants moving up. Others have argued that luxury 

apartments are more risky than any others. As a measure of apartment quality, we use market value 
per square foot at the time of loan origination (VALUE/SF). With mixed arguments as to the quality 

effect, the expected sign is ambiguous. 

The final property characteristic examined is age. It has been suggested by some that very 

new properties present greater risk because of uncertain market acceptance, and that older properties 

are risky because of cost uncertainty. Two variables are used to account for property age. A shift 

variable is used to represent properties that are less than one year old at origination (NEWPROP). 

In addition, the year the property was built is used to account for property age and vintage 

(YRBUILT). 

Seasoning and Location Variables 

Both real estate markets and the interest-rate environment have shown extreme variation over 

the years the loans in the study were originated, and this variation has affected default behavior in 

complex ways. Rather than attempting to specify the relationship of market conditions to default, 

the strategy here is to use annual shift or seasoning variables that identify either the time period 

(YR71!75, YR76!79, YR83!86) or the year (YR87, . . . ,YR95) of loan origination.25 Distant 

origination years are generally expected to have lower default rates than recent years because of a 

higher likelihood of price appreciation. 

Similarly, property location may also relate to default by capturing effects of local economic 

conditions. Although this possibility is recognized by other studies, their models tend to include 

location only at the state or, more commonly, regional levels. The richness of our data enable us to 

distinguish location by MSA, and even sub-MSA, using three-digit zip codes. To capture the effects 

of location, we identified every three-digit zip-code area represented by at least 75 loans with a shift 

25 As the base case, the years 1980!1982 are omitted. 
variable (ZIPCODEj). Twenty-six explicit three-digit zip-code areas are thus represented, as shown 

in table 3, with all other areas represented in our sample constituting the default location. 

Default rates may vary by state as well as by locality because of laws governing the 

foreclosure process. Evidence from home mortgage loans, as shown by Clauretie (1987), indicates 

that the more costly and time-consuming judicial foreclosure required by 15 states reduces the 

likelihood of foreclosure relative to the likelihood in “power of sale” states.26 Ciochetti (1997) finds 

that the incidence of foreclosure on commercial loans also correlates with the type of foreclosure 

process. Using data reported by Ciochetti (1997), we control for the effect of foreclosure laws using 

a binary variable (JUDFORE) that equals one for “judicial” states and zero for “power of sale” 

states. If the requirement of judicial foreclosure inhibits foreclosure, we expect JUDFORE to have a 

positive coefficient, reflecting a tendency for mortgagors to risk default more readily if foreclosure is 

more difficult to effect. 

Table 8 contains a comparison of our fixed-rate and ARM regression samples with all FDIC 

loans that have a performance history, as well as with all 13,551 multifamily loans. The figures in 

table 8 strongly suggest that our regression samples are representative of the larger multifamily data 

sets. Mean loan size, percent ARMs, and the percentage of the regression sample from various 

regions are generally very comparable to the larger data sets. Table 9 contains a complete list of 

variable definitions for our regression sample. 

Logistic Regression Results 

Table 10 contains logistic regressions with parameter estimates, p-values of the associated 

26 States with judicial foreclosure include Connecticut, Delaware, Florida, Illinois, Indiana, 

Kansas, Kentucky, Louisiana, New Jersey, New York, North Dakota, Ohio, Pennsylvania, South 

Carolina, and Wisconsin. 
Wald Chi-Square statistics (in parentheses), and a measure of goodness-of-fit. The table also 

contains simulation results that are discussed in the next section. The -2 Log Likelihood statistics are 

highly significant for both models, indicating that the independent variables provide explanatory 

power. 

Loan and Underwriting Variables 

None of the LTV shift variables contributes significantly to the explanatory power of the 

fixed-rate default model. As discussed earlier, this would be expected if underwriters effectively use 

LTV to control the level of risk. The significance of LTV for ARMs is higher, but more difficult to 

interpret. The ARM LTV coefficient with the highest significance is for LTVs between 75 and 80 

percent, which is the lowest risk class of the three LTV classes shown. The coefficient for the nexthigher LTV risk class (80!90 percent) is much smaller and insignificant, while the coefficient for the 

highest risk class (90!100 percent) is barely significant at the 10 percent level. The LTV zero-order 

coefficient is not distinguishable from zero in either the fixed-rate or ARM estimation, indicating that 

the average default rate for loans missing LTV information is no different from the average default 

rate on loans with LTV data. These results serve to reiterate the implications of the univariate 

results shown in table 6B, which fail to show any consistent relation between LTV and default. 

The coefficients on the DCR variables display some statistical significance. The probability of 

default on fixed-rate and ARM loans with original DCRs between 1.1 and 1.3 are not statistically 

different from loans with original DCRs between 0.90 and 1.1 (the base or omitted range). 

However, the probability of default decreases as DCR increases in a reasonably consistent fashion. 

For ARMs, the default rate on loans with DCRs greater than 1.3 is significantly lower (at the 7.3 

percent confidence level) than the base case. The propensity to default is even lower when the DCR 
exceeds 1.4. The effect of increasing DCRs on fixed-rate default is slightly less pronounced but still 

statistically significant (at the 8.3 percent level) for DCRs greater than 1.4. The average default rate 

for loans missing DCR information is no different from the average default rate on loans with DCR 

data. In short, these DCR effects suggest that cash flow at the time of loan origination is an 

important factor in default risk that is not fully controlled for by endogenous influences.

 The interest-rate-risk premium coefficient (SPREAD) for both fixed-rate and ARM loans is 

positive and highly significant. This suggests that lenders are cognizant of differential loan risk and 

that lenders are able to rate-sort borrowers. A different effect is suggested by the positive and highly 

significant coefficient on the variable for the level of interest rates at the time of origination 

(TREASYLD). This coefficient suggests that higher initial interest-rate levels, hence greater decline 

in rates subsequent to origination, are associated with a higher likelihood of default. From option 

theory, this suggests a pattern of “strategic” default by borrowers seeking better debt terms, as 

discussed in Section 2. 

Size and Property Variables 

There is no evidence that the probability of default varies inversely with either of the property 

age variables (YRBUILT and NEWPROP) or with property quality (VALUE/SF). However, default 

risk does vary positively with project size (NUMUNITS), possibly indicating that transactions costs 

of default tend to be fixed and that they are less of a factor as the amount of debt is larger. The fact 

that three of our four property characteristics are not significantly related to default is consistent with 

the idea that lenders recognize and adjust for property risk issues, although it may also be explained 

by underwriting restriction. In any event, their value as default indicators, subsequent to loan 

origination, appears to be limited. 
 

Seasoning Variables 

An important set of coefficients concerns the year of loan origination (YR71!75, . . ., YR95), 

which controls for seasoning effects. Although difficult to interpret, these coefficients provide a test 

of whether changing market conditions over time are a factor in default risk. In the case of fixed-rate 

mortgages, the results show the most recent (1995) and most distant origination-year (1971!1975; 

1976!1979) coefficients as negative and significant, which is consistent with a “humped” shaped 

default pattern commonly found in single-family mortgages. Unfortunately, since the coefficients on 

the remaining fixed-rate origination-year variables cannot be distinguished from zero (not reported), 

a consistent humped-shaped pattern does not emerge. 

For ARMs, the story is much different. In this case the probability of default in the distant 

1976!1979 period is lower than the base case, and in the more recent 1988!1991 period it is higher 

than the base case. A tell-tale “hump” around the second most recent origination year is also 

apparent in the ARM coefficients, and almost all are significant. Clearly, year of origination affects 

ARM default rates. 

Location and Lender Control Variables 

An additional set of variables is included to control for the effects of local market conditions. 

Six of the 26 zip-code locality variables (ZIPCODEj) dropped out of the fixed-rate model because of 

a scarcity of default events. These dropout areas are effectively included in the base case. For the 

remaining 20 zip-code areas, three shift coefficients are positive and significant in the fixed-rate 

estimation, showing greater default likelihood.27 

27 These include MSA191 (Central Philadelphia), MSA606 (Central Chicago), and 

MSA921 (San Diego). Note that all location dummy variables are included in the estimation. 

However, to conserve space in table 10, we report estimated coefficients and p-values only for 
 

Considerably more variation in default rates across zip codes is observed in ARMs. In fact, 

12 of the three-digit zip-code areas experienced default rates significantly different from the base 

case. Four of the ARM zip-code coefficients are negative and have relatively small standard errors, 

indicating that the default experience in these areas was significantly below the base case, even after 

controlling for other loan and property characteristics.28 Conversely, eight of the ARM zip-code 

coefficients are significantly positive. Particularly interesting is that five of the eight are in the 

greater Los Angeles area, which experienced economic weakness in the early 1990s. These results 

suggest that more-refined submetropolitan data could be productive in explaining default probability, 

especially for ARMs.29 

The judicial foreclosure variable is difficult to interpret. Although the variable is highly 

significant for fixed-rate loans, it has the opposite sign from what was expected, that is, it is negative 

rather than positive. The variable also has an anomalous sign in the ARM model, although it is not 

significant. 

A final set of variables is included to control for the effect of lending institutions. Of the 26 

originating institutions that account for at least 75 percent of the loans in our regression data sets, all 

but 10 drop out because of scarcity of defaults. Of the surviving 10, 2 institutions have significant 

shift coefficients in the fixed-rate regression. Only 4 institutions are associated with significantly 

those location variables that are significant at the 10 percent level or greater (that is, variables 

with p-values less than 0.100). 

28 These include MSA852 (NE Phoenix), MSA857 (Tuscon), MSA920 (San Diego), and 

MSA941 (San Francisco). 

29 This conclusion is supported by the fact that omission of the location variables decreases 

the overall explanatory power of the equation, as indicated by pseudo R2

, from 0.2025 to 0.1904 

in the fixed-rate regression and from 0.1544 to 0.1308 in the ARM estimation. 
different default rates in the ARM regression (2 positive, 2 negative).30 This indicates that the 

extreme variation in default rates among lenders (see table 5) is attributable largely to the 

characteristics of the loans rather than the lenders. 

Simulated Effects of Regression Variables on Default 

The previous analysis highlights the statistical significance of each loan-level attribute in 

predicting default but gives no clear indication of the economic magnitude, or sensitivity, of the 

characteristic. Therefore, a sensitivity analysis is performed to gauge the importance of statistically 

significant characteristics. This analysis begins by constructing a base case in which each 

independent variable is set at its mean value, so that it can be multiplied by its estimated regression 

coefficient to determine the simulated probability of default for a standard loan. The simulated base 

case probability of default is 4.1 percent for fixed-rate loans and 17.9 percent for ARMs. The base 

case probabilities are similar to the actual default rates in our regression samples (8.0 percent for 

fixed rate; 22.6 percent for ARMs). To simulate the magnitude of the effects of continuous variables 

on default, we independently “shock” each statistically significant continuous variable by one 

standard deviation, and calculate the revised probability of default. Finally, factor sensitivities are 

constructed by comparing the revised probability of default with the base case. Columns two and 

four of table 10 present simulated factor sensitivities for both the fixed-rate and ARM subsamples. 

For example, a one standard deviation increase in the ten-year Treasury yield increases the 

probability of fixed-rate and ARM default by 1.0 and 2.5 percentage points, respectively. 

To simulate the effects of original DCR and LTV on default, the base case probability of 

default is set to reflect the default propensity of loans with missing DCR and/or LTV data. For 

30 Omission of the lender identifiers decreases the pseudo R2

 from 0.2025 to 0.1913 in the 

fixed-rate regression and from 0.1544 to 0.1448 in the ARM estimation. 
example, a loan with a debt coverage ratio of 1.4 or greater has a simulated default rate that is 2.1 

percentage points lower than the average default rate of loans with no DCR data. With ARM loans, 

by contrast, the same probability differential is 10.8 percentage points. Overall, the effects of 

increasing LTVs and decreasing DCRs are much more significant for ARMs. 

To simulate the effects of three-digit zip-code location, the base case probability of default is 

set to reflect the default propensity of loans from zip codes not separately identified in our sample 

(that is, those with less than 100 loans in our sample). As can be seen in column two, just four zip 

codes experienced higher fixed-rate default rates than the average of our noncoded zip codes. 

However, location played a much more significant role in the ARM loans. In four specific zip-code 

areas the probability of default was more than 25 percentage points above the base case. In two zipcode areas it was more than 10 percentage points below. 

Increases in initial DCRs are associated with decreasing default probabilities, but the effect on 

ARM default rates is much more pronounced. For example, ARMs with initial DCRs in excess of 

1.4 have a simulated probability of default that is 10.8 percentage points lower than ARMs with 

DCRs below 1.1 (the base case). The corresponding reduction in simulated default for fixed-rate 

loans is just 2.1 percentage points. Fixed-rate loans originated in states with judicial foreclosure 

have a default rate that is 2.5 percentage points lower than fixed-rate loans originated in nonjudicial 

foreclosure states. The existence of this characteristic has no significant effect on ARM loan default. 

The simulations confirm the importance of origination year. Fixed-rate loans originated in the 

1971!1975 period have an 8.8 percentage point lower probability of default than loans originated 

1980!1982 (the base case range). Fixed-rate loans originated in 1976!1979 have an 8.2 percentage 

point lower default probability than 1980!1982 loans. Similarly, the default probability of ARMs 

originated between 1976 and 1979 is 10.5 percentage points lower than the base case ARMs. More 
drastic is the effect on ARMs of origination during 1989, 1990, and 1991. Origination in these years 

is associated with a 13.4, 19.6, and 18.3 percentage point increase, respectively, in default 

probability. 

The simulations also demonstrate significant effects, both positive and negative, for five 

particular lending institutions. In summary, our logistic simulations provide strong evidence that our 

estimated determinants of default are economically as well as statistically significant. 

6. ROBUSTNESS CHECKS 

Tests for Specification Sensitivity 

To examine the sensitivity of our core results to variation in the specification of the logit 

models, we selectively removed various combinations of variable groups. The results of this 

sensitivity analysis are extremely comforting. Although overall explanatory power is reduced when a 

set of control variables is eliminated, the magnitude and significance of our core loan variables 

remain virtually unchanged.31 

Tests for Left-Censuring Effects 

As discussed in Section 3, left censuring is difficult to avoid in default studies and can clearly 

bias univariate estimates of default frequency. Thus, all of the simple marginal distributions of 

default frequency reported here are likely to understate or overstate the overall frequency of default 

in the original loan population, depending on whether early defaults or early payoffs were 

disproportionately high. However, the effect of left censuring is less obvious for the results of 

multivariate analysis. The issue in the multivariate context is whether early exits from the loan 

31 These sensitivity regressions are available from the authors upon request. 
population, because of payoff or default, alter the interrelationships among the variables of the 

analysis for the surviving population. While early exits may have a persuasively clear effect on 

frequency distributions, they do not have a clear effect on multivariate relationships.32 

To test for the effect of left censuring on multivariate findings, we identified all loans in the 

sample that were originated within two and three years of the time of securitization (the beginning of 

our records). Note that the substance of this distinction is “new” versus “seasoned” loans. The 

conventional wisdom appears to be that loans with high original LTVs and loans with low original 

DCRs will tend to default at high rates, and early. Thus the “seasoned” pool will evidence less 

relationship of these underwriting variables to default as the high-risk loans are censured out through 

default. The “new” versus “seasoned” distinction enables us to test for this possibility. If there is a 

difference in the multivariate relationships, “new” loans should evidence positive coefficients for our 

LTV categories and negative coefficients for our DCR categories. 

The “new” loans constitute a relatively small portion of the entire sample of 9,637 (640 were 

originated within two years before securitization and 1,262 were originated within three years). 

Rather than analyzing them separately, we created interactive “dummy” variables in our main 

equations (both fixed rate and ARM) for each underwriting variable category, including all LTV 

categories, all debt coverage categories, and the interest-rate-spread variable. 

The results of our tests can be summarized succinctly. Not one underwriting variable had an 

additional significant coefficient result from the “new” loans for either fixed-rate loans or ARMs. 

Only one “new” loan coefficient was significant, but this was for ARMs with DCRs above 1.4, which 

32 To illustrate the point, consider a set of 1,000 loans, of which 100 have defaulted. 

Further, suppose that some characteristic of the loans exhibits a 70 percent correlation with 

default, and that half of the defaulted loans have left the sample. While the estimated default rate 

clearly will be biased downward (50/950), there is no implied change in the observed correlation. 
were already significant when “new” loans were not distinguished. The related base coefficient 

ceases to be significant when “new” loans are distinguished. Meanwhile, when “new” is defined as 

two years before securitization, the interest-rate-spread variable for fixed-rate loans is positive and 

significant at the 4 percent level of probability. (The latter result is consistent with the hypothesis 

discussed in Section 2, that lenders adjust the spread to control for residual default risk.) In 

summary, these results do not support the argument that populations of seasoned loans and new 

loans show different relationships between underwriting variables and default risk. 

Multicolinearity among Underwriting Variables 

We have argued that the three variables LTV, DCR , and interest-rate spread are likely to be 

endogenously and simultaneously determined. If so, they may also be strongly correlated, and this 

multicolinearity may explain the insignificant coefficients for the underwriting variables. We test this 

possibility using three modified sets of regressions. In each set only one of the three variables is used 

in the regression. (However, the distinction between “new” and “seasoned” loans is maintained, 

using both the two-year and three-year definition.) If multicolinearity is the explanation for 

insignificant coefficients, removing two of the three variables should eliminate the problem, allowing 

the remaining variable to proxy for the effect of all three. 

The results of our tests for multicolinearity, again, may be summarized succinctly. In every 

test, removing two of the three variables reduced the explanatory power of the equation as measured 

by pseudo R2

. However, only two underwriting coefficients became significant that previously were 

not, and one of these has the wrong sign.33 Of 64 regression coefficients that could have signaled 

33 This is the ARM coefficient for DCRs between 1.3 and 1.4 on “new” loans, where new 

loans are defined as three years before securitization. By conventional wisdom, this coefficient 

should be negative, but it is positive, and significant at the 5 percent level. The second coefficient 
some evidence of multicolinearity (16 in each of four test equations), only one was significantly 

changed and carried the correct sign. In short, we see little support for the hypothesis that the 

general lack of significance of our underwriting coefficients is due to multicolinearity. 

7. SUMMARY AND CONCLUSIONS 

The large growth in commercial mortgage securities during the past decade has led to 

substantial research on the valuation and pricing of these securities. However, in contrast to research 

involving the residential mortgage market, the available data have severely constrained research on 

the patterns and causes of commercial mortgage defaults and prepayments. Despite the strong 

implications of option-based default models regarding default risk indicators, little testing of their 

usefulness has occurred. Further, little is known about the influences of property values, cash flows, 

and other loan, property, and lender characteristics on default. 

This paper examines the default experience of multifamily mortgages that were incorporated 

in RTC/FDIC CMBS brought to market between 1991 and 1996. This unique data set contains 

extensive property, loan, and underwriting data, plus a recent record of loan performance. The 

performance record also contains the month of default and the default resolution (modification, 

foreclosure, etc.). These data support multivariate analysis of default not possible in previous 

studies. 

Our loan performance data set contains 9,639 multifamily mortgages. The descriptive 

statistics we report display substantial variation in default rates across states, zip codes, year of 

origination, originating lender, original loan size, LTV, DCR, and loan type (fixed rate versus ARM). 

that becomes positive is the ARM coefficient for LTVs between 90 and 100 percent on new 

loans. This coefficient is positive and significant at the 9 percent level. 
The dependent variable is a binary classification: whether the loan has ever been 90 days late. 

Recognizing that fixed-rate and ARM default patterns are very distinct, we performed separate 

regressions on each loan type. 

The original LTV does not contribute significantly to the explanatory power of the fixed-rate 

model, and its significance in the ARM model is difficult to interpret. In contrast, the expected 

inverse relation between incidence of default and DCR seems more consistent, although this effect is 

again stronger in the ARM specification. The spread between the contract interest rate and the tenyear Treasury yield at origination is positive and highly significant, which is consistent with the 

notion that lenders recognize differential loan risk and are able to rate-sort borrowers. Moreover, 

the coefficient on the interest-rate level at the time of origination is positive and highly significant, 

suggesting that higher initial interest rates increase the likelihood of default, all other things being 

equal. Somewhat surprisingly, the level of interest rates affects both ARM and fixed-rate defaults, 

thereby limiting the ability to interpret the effect in a traditional option framework. More generally, 

the results suggest that endogenous elements appear to interact with option-related factors to 

produce considerable complexity in the determinants of multifamily default. 

Three of our four property characteristics---year built, a proxy for quality, and an indicator of 

a newly constructed property---are not significant. A number of our shift variables that capture (and 

control for) the effects of origination year are statistically significant, especially in the ARM 

regression. In addition, the inclusion of location control variables (three-digit zip codes) contributed 

significantly to the explanatory power of the models, suggesting that even more refined 

submetropolitan data could be productive in explaining default probability. Finally, the extreme 

variation in default rates among lenders appears to be largely, but not entirely, attributable to the 

characteristics of the loans rather than the lenders. 
The degree to which the findings can be generalized is, of course, not fully clear, and further 

investigation is needed. For example, although the mortgages studied in this paper came from many 

institutions and geographic areas, they also came from institutions that were, or became, insolvent. 

Although the loans were performing before being placed into the RTC/FDIC CMBS, we do not 

know whether or how their derivation from insolvent institutions affects the results. However, this 

concern is considerably assuaged by the fact that the cumulative default rate of the sample is 17.5 

percent, which does not differ significantly from the apparent default frequency experience of loans 

held by major life insurance companies. This fact is especially notable, given that our definition of 

default is considerably broader than that employed by previous studies. 

To the extent that our findings are valid, they generally confirm (for fixed-rate loans, though 

less for ARMs) that underwriting variables, especially LTV, are endogenously affected by the loan 

origination process and that this renders them poor indicators of subsequent default. On the other 

hand, the spread between loan and market interest rates, which logically should reflect default risk in 

an endogenous risk framework, shows empirical evidence of doing so. 
References 

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Constraints on Residential Mortgage Terminations. Regional Science and Urban Economics 

26:235!261. 

Bradley, Donald S., Frank E. Nothaft, and James L. Freund. 1998. Financing Multifamily 

Properties: A Play with New Actors and New Lines. Cityscape: A Journal of Housing and 

Urban Development 4:5!17. 

Capozza, Dennis R., Dick Kazarian, and Thomas Thomson. 1998. The Conditional Probability of 

Mortgage Default. Real Estate Economics 26:359!390. 

Childs, Paul D., Steven H. Ott, and Timothy Riddiough. 1996. The Value of Recourse and CrossDefault Clauses in Commercial Mortgage Contracting. Journal of Banking and Finance 

20:511!536. 

Ciochetti, Brian A. 1997. Loss Characteristics of Commercial Mortgage Foreclosures. Real Estate 

Finance 14:53!69. 

) . 1998. Investment Loss Characteristics Associated with Commercial Mortgage Foreclosures. 

Working Paper, University of North Carolina. 

Ciochetti, Brian A., and Timothy J. Riddiough. 1998. Timing, Loss Recovery and Economic 

Performance of Foreclosed Commercial Mortgages. Working Paper, University of North 

Carolina and M.I.T. 

Ciochetti, Brian A., and Kerry D. Vandell. 1999. The Performance of Commercial Mortgages. 

Real Estate Economics 27:27!61. 

Clauretie, Terrence M. 1987. The Impact of Interstate Foreclosure Cost Differences and the Value 

of Mortgages on Default Rates. AREUEA Journal 15:152!167. 

Cox, John C., and Mark Rubinstein. 1985. Options Markets. Prentice Hall. 

Cunningham, Donald, and Patric H. Hendershott. 1995. Pricing FHA Mortgage Default Insurance. 

Housing Finance Review 13:373!392. 

Deng, Yongheng. 1997. Mortgage Termination: An Empirical Hazard Model with a Stochastic 

Term Structure. The Journal of Real Estate Finance and Economics 14:309!332. 

Elmer, Peter J., and Anton E. Haidorfer. 1997. Prepayments of Multifamily Mortgage-Backed 

Securities. Journal of Fixed Income 6:50!63. 
Elmer, Peter J., and Steven A. Seelig. 1999. Insolvency, Trigger Events, and Consumer Risk 

Posture in the Theory of Single-Family Mortgage Default. Journal of Housing Research 

(forthcoming). 

Episcopos, Athanasios, Andreas Pericli, and Jianxun Hu. 1998. Commercial Mortgage Default: A 

Comparison of Logit with Radial Basis Function Networks. The Journal of Real Estate 

Finance and Economics, 17:163!178. 

Fitch. 1996. Trends in Commercial Mortgage Default Rates and Loss Severity. Fitch Investors 

Service, LP, Special Report, November 11. 

Follain, James R., Wenyi-Vivien Huang, and Jan Ondrich. 1999. Stay, Pay or Walk Away: A 

Hazard Analysis of FHA-Insured Multifamily Mortgage Terminations. Draft paper. 

Foster, Charles, and Robert Van Order. 1985. FHA Terminations: A Prelude to Rational Mortgage 

Pricing. Journal of the American Real Estate and Urban Economics Association 

13:292!316. 

Gau, George W., and Ko Wang. 1994. The Tax-Induced Holding Periods of Real Estate Investors: 

Theory and Empirical Evidence. The Journal of Real Estate Finance and Economics 

8:71!85. 

Goldberg, Lawrence, and Charles A. Capone, Jr. 1998. Multifamily Mortgage Credit Risk: Lessons 

from Recent History. Cityscape: A Journal of Housing and Urban Development 4:93!113. 

Green, William H. 1997. Econometric Analysis, 5th ed. Prentice Hall. 

Harrison, David M. 1998. The Importance of Lender Heterogeneity in Mortgage Lending. 

Working Paper, University of Vermont. 

Hilliard, Jimmy E., James B. Kau, and Carlos Slawson, Jr. 1998. Valuing Prepayment and Default 

in a Fixed-Rate Mortgage: A Bivariate Binomial Options Pricing Technique. Real Estate 

Economics 26:431!468. 

Kau, James B., Donald C. Keenan, Walter J. Muller, and James F. Epperson. 1987. The Valuation 

of Commercial and Multifamily Mortgages. Journal of Banking and Finance 11: 525!546. 

) . 1990. Pricing Commercial Mortgages and Their Mortgage-Backed Securities. The Journal 

of Real Estate Finance and Economics 3:333!336. 

Nelson, Grant S., and Dale A. Whitman. 1993. Real Estate Finance Law. 3d ed. West Publishing 

Co. 

Quigg, Laura. 1997. Analyzing CMBS Performance–A Discussion of the Fitch Study. J.P. Morgan 

Securities Inc. Credit Research, January 6. 
) . 1998. Default Risk in CMBS Bond Classes. In Trends in Commercial Mortgage-Backed 

Securities, edited by Frank J. Fabozzi Associates. 

Riddiough, Timothy J., and Steve B. Wyatt. 1994. Strategic Default, Workout, and Commercial 

Mortgage Valuation. Journal of Real Estate Finance and Economics 9:5!22. 

Snyderman, Mark P. 1994. Update on Commercial Mortgage Defaults. The Real Estate Finance 

Journal (summer) 22!32. 

Vandell, Kerry D. 1995. How Ruthless Is Mortgage Default? A Review and Synthesis of the 

Evidence. Journal of Housing Research 6:245!264. 

) . 1992. Predicting Commercial Mortgage Foreclosure. Real Estate Economics 20:55!88. 

Vandell, Kerry D., Walter Barnes, David Hartzell, Dennis Kraft, and William Wendt. 1993. 

Commercial Mortgage Defaults: Proportional Hazards Estimation Using Individual Loan 

Histories. Journal of the American Real Estate and Urban Economics Association 

21:451!480. 
Figure 1 

Left and Right Censuring of Loan 

Default Data 

Observation 

Date 

Pay Off 

Loan 

Origination 

Default 

Sale 

Defaulted 

Current 

Recovery Default 

Right

Censure Censure 

Left 
Figure 2 

The Stages of Default and the Focus of 

Various Default Studies 

Recovery 

Ciochetti, 

Modification 1998 

Default 

Foreclosure Final 

Sale 

To REO 

Snyderman, 

1994: 

Default 

Incidence 

Vandell, 

1992 & 

Vandell et al., 

1993 

Ciochetti, 

1997 

Snyderman 

1994: 

Loss Severity 
Table 1 

Tabulation of Default Rates by Deal 

# of Multi Total # of % of Original Sample 

# of Loans Multi Multi Loans Loans in Sample 

Lenders Originally in Loans in in Sample Deal as % of Default 

Deal in Deal Deal Sample Total Sample Rate (%) 

Multifamily Deals 

1991-M1 2 218 185 84.9 1.9 41.6 

1991-M2 1 517 406 78.5 4.2 48.5 

1991-M3 5 137 100 73.0 1.0 28.0 

1991-M4 5 1,388 917 66.1 9.5 15.7 

1991-M5 3 548 275 50.2 2.9 10.2 

1991-M6 3 391 281 71.9 2.9 21.7 

1991-M7 21 591 334 56.5 3.5 14.4 

1991-M1 2 787 582 74.0 6.0 13.4 

1991-M2 52 1,410 962 68.2 10.0 13.3 

1991-M3 89 1,410 895 63.5 9.3 12.0 

1991-M4 75 988 685 69.3 7.1 19.9 

8,385 5,622 67.0% 58.3% 18.4% 

Commercial Deals* 

1992-C4 68 303 174 57.4 1.8 15.5 

1992-C5 169 538 280 52.0 2.9 12.5 

1992-C6 136 633 54 8.5 0.6 68.5 

1992-C7 78 368 237 64.4 2.5 21.1 

1993-C2 272 662 556 84.0 5.8 21.4 

1993-C3 237 287 225 78.4 2.3 15.1 

1994-C1 238 941 875 93.0 9.1 16.8 

1994-C2 234 453 437 96.5 4.5 22.7

1995-C1 222 629 606 96.3 6.3 8.3 

1995-C2 111 263 283 107.6 2.9 11.7

1996-C1F 183 285 290 101.8 3.0 6.9 

5,362 4,017 74.9% 41.7% 16.2% 

Total Multi Loans in Multi and Com Deals 

13,747 9,639 70.1% 100.0% 17.5% 

*The number of multifamily loans in commercial deals is estimated from the prospectus. Thus, this number may 

vary slightly from the actual number of loans in the transaction at closing. 
Table 2 

Tabulation of Default Rates by State 

A. Sorted by Sample Size B. Sorted by Default Rate 

Total # Loans as % of Default Total # Loans as % of Default 

State of Loans Total Sample Rate (%) State of Loans Total Sample Rate (%) 

California 4,136 42.9 22.3 Delaware 2 0.0 50.0 

Florida 601 6.2 9.3 Maine 111 1.2 44.1 

Texas 566 5.9 12.2 New Hampshire 19 0.2 42.1 

Arizona 487 5.1 8.8 South Carolina 26 0.3 30.8 

Pennsylvania 355 3.7 18.9 New York 207 2.1 29.0 

Oregon 349 3.6 2.9 West Virginia 7 0.1 28.6 

Illinois 249 2.6 10.8 Maryland 67 0.7 26.9 

New Jersey 238 2.5 25.6 New Jersey 238 2.5 25.6 

Ohio 232 2.4 13.4 Connecticut 77 0.8 24.7 

New York 207 2.1 29.0 Virginia 108 1.1 24.1 

Minnesota 160 1.7 12.5 California 4,136 42.9 22.3 

Louisiana 151 1.6 17.9 Tennessee 37 0.4 21.6 

Kansas 150 1.6 7.3 Pennsylvania 355 3.7 18.9 

Washington 139 1.4 7.2 Louisiana 151 1.6 17.9 

Massachusetts 133 1.4 13.5 North Carolina 63 0.7 17.5 

Georgia 123 1.3 15.4 Michigan 18 0.2 16.7 

Maine 111 1.2 44.1 Mississippi 30 0.3 16.7 

Virginia 108 1.1 24.1 Kentucky 31 0.3 16.1 

Colorado 103 1.1 6.8 Georgia 123 1.3 15.4 

Iowa 102 1.1 8.8 Arkansas 26 0.3 15.4 

Oklahoma 101 1.0 11.9 DC 26 0.3 15.4 

Connecticut 77 0.8 24.7 North Dakota 7 0.1 14.3 

Missouri 69 0.7 13.0 Rhode Island 7 0.1 14.3 

Maryland 67 0.7 26.9 Massachusetts 133 1.4 13.5 

New Mexico 67 0.7 13.4 New Mexico 67 0.7 13.4 

North Carolina 63 0.7 17.5 Ohio 232 2.4 13.4 

Alaska 61 0.6 4.9 Missouri 69 0.7 13.0 

Utah 61 0.6 0.0 Minnesota 160 1.7 12.5 

Nevada 52 0.5 9.6 Texas 566 5.9 12.2 

Tennessee 37 0.4 21.6 Oklahoma 101 1.0 11.9 

Kentucky 31 0.3 16.1 Illinois 249 2.6 10.8 

Mississippi 30 0.3 16.7 Nebraska 28 0.3 10.7

Nebraska 28 0.3 10.7 Nevada 52 0.5 9.6

Indiana 27 0.3 3.7 Florida 601 6.2 9.3

Arkansas 26 0.3 15.4 Arizona 487 5.1 8.8

DC 26 0.3 15.4 Iowa 102 1.1 8.8

South Carolina 26 0.3 30.8 Kansas 150 1.6 7.3

New Hampshire 19 0.2 42.1 Washington 139 1.4 7.2

Michigan 18 0.2 16.7 Colorado 103 1.1 6.8

South Dakota 11 0.1 0.0 Alaska 61 0.6 4.9

Wisconsin 9 0.1 0.0 Indiana 27 0.3 3.7

North Dakota 7 0.1 14.3 Oregon 349 3.6 2.9

Rhode Island 7 0.1 14.3 Arkansas 3 0.0 0.0

West Virginia 7 0.1 28.6 Hawaii 2 0.0 0.0

Arkansas 3 0.0 0.0 Idaho 2 0.0 0.0

Delaware 2 0.0 50.0 Montana 1 0.0 0.0

Hawaii 2 0.0 0.0 South Dakota 11 0.1 0.0

Idaho 2 0.0 0.0 Utah 61 0.6 0.0

Montana 1 0.0 0.0 Wisconsin 9 0.1 0.0 

Total 9,637 100.0% 17.5% 9,637 100.0% 17.5% 
Table 3 

Tabulation of Default Rates by MSA 

A. Sorted by Sample Size B. Sorted by Default Rate 

Loans as Default Loans as Default 

Total # % of Total Rate Total # % of Total Rate

MSA of Loans Sample (%) MSA of Loans Sample (%) 

Los Angeles (CBD), CA 861 8.9 24.3 Lewiston, ME 93 1.0 51.6 

Los Angeles (SW), CA 332 3.4 19.6 L.A. (San Fernando Valley), CA 127 1.3 45.7 

Tucson, AZ 206 2.1 6.3 L.A. (Northridge), CA 107 1.1 44.9 

San Francisco, CA 192 2.0 5.2 Philadelphia, PA 115 1.2 39.1 

San Diego, CA 178 1.8 28.7 L.A. (San Fernando Valley), CA 106 1.1 34.0 

Los Angeles (Long Beach), CA 169 1.8 29.0 L.A. (Long Beach), CA 169 1.8 29.0 

Portland, OR 162 1.7 1.2 San Diego, CA 178 1.8 28.7 

Los Angeles (East), CA 160 1.7 24.4 New York (Manhattan), NY 92 1.0 25.0 

San Diego, CA 138 1.4 8.7 L.A. (East), CA 160 1.7 24.4 

Garden Grove, CA 132 1.4 12.9 L.A. (CBD), CA 851 8.9 24.3 

Phoenix, AZ 128 1.3 12.5 Chicago (CBD), IL 106 1.1 20.8 

L.A. (San Fernando Valley), CA 127 1.3 45.7 L.A., CA 85 0.9 20.0 

Philadelphia, PA 115 1.2 39.1 L.A. (SW), CA 332 3.4 19.6 

L.A. (Northridge), CA 107 1.1 44.9 Columbus, OH 94 1.0 19.1 

Chicago (CBD), IL 106 1.1 20.8 L.A., CA 85 0.9 14.1 

L.A. (San Fernando Valley), CA 106 1.1 34.0 Garden Grove, CA 132 1.4 12.9 

Columbus, OH 94 1.0 19.1 Phoenix, AZ 128 1.3 12.5

Lewiston, ME 93 1.0 51.6 El Paso, TX 85 0.9 9.4

New York (Manhattan), NY 92 1.0 25.0 San Diego, CA 138 1.4 8.7

Miami (Homestead), FL 92 1.0 5.4 Miami, FL 85 0.9 8.2

Miami, FL 85 0.9 8.2 Phoenix (NE), AZ 78 0.8 6.4

El Paso, TX 85 0.9 9.4 Tucson, AZ 206 2.1 6.3

Los Angeles, CA 85 0.9 14.1 Miami (Homestead), FL 92 1.0 5.4

Los Angeles, CA 85 0.9 20.0 San Francisco, CA 192 2.0 5.2

Portland, OR 82 2.4 2.4 Portland, OR 82 0.9 2.4

Phoenix (NE), AZ 78 6.4 6.4 Portland, OR 162 1.7 1.2

 4,090 42.4% 20.0% 4,090 42.4% 20.0% 
70

75

80

85

90

95

Table 4 

Tabulation of Default Rates by Origination Year 

All Loans ARM Loans Fixed-Rate Loans 

Year of Total # of Loans as % Default Total # of Loans as % of Default Total # of Loans as % of Default 

Origination Loans of Sample Rate ARM Loans Total Sample Rate (%) Loans Total Sample Rate (%) 

34 0.4 14.7 2 0.0 0.0 32 0.4 15.6 

71 149 1.9 4.7 5 0.1 0.0 144 1.8 4.9 

72 340 4.2 2.9 4 0.0 25.0 336 4.2 2.7 

73 264 3.3 1.9 2 0.0 0.0 262 3.3 1.9 

74 128 1.6 6.3 4 0.0 50.0 124 1.5 4.8 

242 3.0 3.7 20 0.2 0.0 222 2.8 4.1 

76 384 4.8 3.9 81 1.0 2.5 303 3.8 4.3 

77 463 5.8 3.7 97 1.2 5.2 366 4.5 3.3 

78 322 4.0 5.9 61 0.8 3.3 261 3.2 6.5 

79 138 1.7 7.2 10 0.1 20.0 128 1.6 6.3 

68 0.8 17.6 23 0.3 17.4 45 0.6 17.8 

81 41 0.5 12.2 20 0.2 5.0 21 0.3 19.0 

82 49 0.6 24.5 29 0.4 20.7 20 0.2 30.0 

83 233 2.9 10.7 178 2.2 9.6 55 0.7 14.5 

84 272 3.4 16.5 211 2.6 11.4 61 0.8 34.4 

373 4.6 18.5 258 3.2 14.7 115 1.4 27.0 

86 618 7.7 17.3 365 4.5 14.0 253 3.1 22.1 

87 764 9.5 21.5 473 5.9 18.4 291 3.6 26.5 

88 1,077 13.4 28.2 723 9.0 27.2 354 4.4 30.2 

89 817 10.1 33.9 346 4.3 27.2 471 5.9 38.9 

327 4.1 31.5 151 1.9 35.1 176 2.2 28.4 

91 174 2.2 23.6 89 1.1 30.3 85 1.1 16.5 

92 138 1.7 13.0 54 0.7 20.4 84 1.0 8.3 

93 158 2.0 12.7 40 0.5 20.0 118 1.5 10.2 

94 353 4.4 7.4 56 0.7 14.3 297 3.7 6.1 

121 1.5 5.8 9 0.1 0.0 112 1.4 6.3 

96 3 0.0 0.0 1 0.0 0.0 2 0.0 0.0 

97 1 0.0 0.0 1 0.0 0.0 0 0.0 

8,051 100.0% 16.6% 3,313 41.2% 19.3% 4,738 58.8% 14.8% 
Table 5 

Tabulation of Default Rates by Financial Institution 

Institution Number Total # of 

Loans 

Loans as % of 

Total Sample 

Default 

Rate (%) 

INST956 93 1.0 51.6 

INST439 430 4.5 47.9 

INST180 130 1.3 40.0 

INST828 119 1.2 38.7 

INST218 104 1.1 36.5 

INST2172 74 0.8 28.4 

INST2197 95 1.0 26.3 

INST711 108 1.1 23.1 

INST7119 785 8.1 20.4 

INST8602 128 1.3 20.3 

INST1300 576 6.0 18.1 

INST7705 442 4.6 13.6 

INST7258 141 1.5 13.5 

INST1310 142 1.5 12.0 

INST7275 109 1.1 11.0 

INST7203 146 1.5 11.0

INST7187 161 1.7 9.3

INST7285 543 5.6 8.3

INST7386 85 0.9 8.2

INST7367 78 0.8 7.7

INST6939 56 0.6 5.4

INST7201 85 0.9 4.7

INST8243 158 1.6 4.4

INST7734 119 1.2 4.2

INST7267 89 0.9 2.2

INST7054 209 2.2 1.9 

5,205 54.0% 18.7% 
Table 6 

Default Rates by Original Loan Size, Original 

Loan-to-Value (LTV) Ratio, and Original DCR 

A. By Original Loan Size 

Original Loans 

Loan Size Total # as % of Default 

($000) of Loans Sample Rate (%) 

Below $250 4,786 52.1 11.1 

$250<$500 1,856 20.2 20.5 

$500<$750 847 9.2 22.4 

$750<$1,000 483 5.3 29.4 

Over $1,000 1,218 13.3 27.1 

9,190

B. By Origi

 100.0%

nal LTV 

17.1% 

Original Loans 

Loan Size Total # as % of Default 

($000) of Loans Sample Rate (%) 

50%<75% 2,738 56.5 15.2 

75%<85% 1,677 34.6 18.8 

85%<95% 246 5.1 16.3 

95%<100% 75 1.5 14.7 

100%<125% 114 2.4 14.9 

4,850 100.0% 16.5% 

C. By Original Debt Coverage Rate 

Loans 

DCR Total # as % of Default 

of Loans Sample Rate (%) 

Below 1.0 390 23.4 23.1 

1.0<1.1 224 13.4 22.8 

1.1<1.2 244 14.6 26.6 

1.2<1.3 206 12.4 18.4 

1.3<1.4 140 8.4 10.0 

1.4<1.5 100 6.0 10.0

1.5<1.6 64 3.8 7.8

1.6<1.7 62 3.7 4.8

1.7<1.8 42 2.5 2.4

1.8<1.9 50 3.0 8.0

1.9<2.0 23 1.4 8.7

2.0<3.0 123 7.4 5.7 

1,668 100.0% 17.4% 
Table 7 

Comparison of Life Insurance Company Loans 

with FDIC Multifamily Loans 

Snyderman Vandell et al. ACLI New Loan RTC/FDIC 

Study Study Averages Data 

Ending Date of Loan Dec. 1991 Sept. 1989 Sept. 1983 Jan. 1998 

Information 

Mean Loan Size $3 million $5.8 million $8.8 million $0.63 million 

Mean Term NA 13.4 years 9.8 years 21 years 

Mean L/V Ratio NA 73% 69% 74% 

Mean Debt Coverage Ratio NA 1.29 1.28 1.27* 

Mean Year of Origination 1979 1979 1983 1983 

Median Year of Origination 1979 1979 1983 1986 

Range of Year Originated 1972 ! 1986 1962 ! 1989 1983 1954 ! 1995 

Percent Balloon Loans NA NA 92% 45% 

Percent Foreclosed or in 13% 6% -- 10% 

Foreclosure 

*Based on all loans reporting DCR in the range of 0 to 3. 
Table 8 

Comparison of Regression Sample to Loans with Performance 

History and to All Multifamily Loans 

Total M.F. M.F. Loans in M.F. Loans 

Loans with Fixed-Rate in ARM 

Total M.F. 

Loan Records 

Performance 

History 

Regression 

Sample 

Regression 

Sample 

Number of Loans 13,551 9,639 2,966 4,019 

Default Rate ----- 17.50% 7.97% 22.63% 

Mean Loan Size $562,615 $625,288 $341,360 $670,176 

Percent Pacific 45.96 45.42 37.71 55.33 

Percent Mountain 8.5 8.94 6.91 6.34 

Percent Southwest 9.17 9.34 10.71 5.05 

Percent Southeast 8.33 8.66 10.81 5.47 

Percent Mideast 3.72 3.88 3.33 2.79 

Percent Northeast 12.02 12.5 13.65 11.65 

Percent East North 6.39 5.32 8.96 6.83 

Percent West North 5.88 5.97 7.92 6.54 
Table 9 

Definitions of Regression Variables 

Dependent Variable 

DEFAULT Equals 1 if mortgage payments were ever more than 90 days late. 

Loan and Underwriting Variables 

LTV75-80 Equal to 1 if original LTV was greater than 75 percent and less than or equal to 80 percent (LTV 

less than or equal to 75 percent is the omitted case). 

LTV80-90 Equal to 1 if LTV at origination was greater than 80 percent and less than or equal to 90 

percent. 

LTV90-100 Equal to 1 if LTV at origination was greater than 90 percent and less than or equal to 100 

percent 

LTV_MIS LTV zero order coefficient. Equal to 1 if LTV data are missing for the observation. 

DCR1.1 Equal to 1 if original DCR was greater than 1.1 and less than or equal to 1.2 (DCR less than or 

equal to 1.1 and greater than 0.90 is the omitted case). 

DCR1.2 Equal to 1 if original DCR was greater than 1.2 and less than or equal to 1.3. 

DCR1.3 Equal to 1 if original DCR was greater than 1.3 and less than or equal to 1.4. 

DCR1.4 Equal to 1 if original DCR was greater than 1.4. 

DCR_MIS Original DCR zero order coefficient. Equal to 1 if DCR data are missing for the observation 

JUDFORE Equal to 1 if mortgage originated in judicial foreclosure state. 

TREASYLD Yield on constant maturity ten-year Treasury bond when mortgage was originated. 

SPREAD Contract interest rate at origination, minus yield on constant maturity ten-year Treasury bond. 

INSTi Equals 1 if loan was originated by institution number I. Each of the 26 dichotomous variables 

represents a lending institution that originated 50 or more of the loans in our sample. 

Size/Property Variables 

YRBLT Year in which collateral property was built. 

YRBLT_MIS Year-built zero order coefficient. Equal to 1 if year-built data are missing for the observation. 

UNITS Number of apartment units in complex. 

UNITS_MIS Number of units zero order coefficient. Equal to 1 if number of units data are missing. 

VALSF Value per square foot of the collateral property at loan origination. 

VALSF_MIS Value per square foot zero order coefficient. Equal to 1 if value per square foot data are

 missing. 

NEW Equals 1 if collateral property less than one year old at origination. 

Location/Seasoning Variables 

ZIPCODEj Equals 1 if loan was originated in the j

th three-digit zip code. Each of the 26 (i is 1 

to 26) dichotomous variables represents a three-digit zip code in which 75 or more of our sample loans 

were originated. 

Yri Equals 1 if loan was originated in year i, where i = 1987, 1988, . . . 1995. 

YR71!75 Equals 1 if loan was originated in years 1971!1975. 

YR76!79 Equals 1 if loan was originated in years 1976!1979. 

YR83!86 Equals 1 if loan was originated in years 1983!1986. 
Table 10 

Logistic Regressions Explaining Loan Default 

and Associated Simulation of Percentage Change in Probability of Default 

Simulation of Simulation 

% Change in of % 

Logistic Prob. of Logistic Change in 

VARIABLE Regressiona Default-b Regressiona Prob. of 

Defaultb 

Intercept 

Loan and Underwriting 

Loan-to-Value Ratio 75!80%c 

(LTV75!80) 

Loan-to-Value Ratio 80!90% 

(LTV80!90) 

Loan-to-Value Ratio 90!100% 

(LTV90!100) 

LTV Zero Order Coefficient 

(LTV_MIS) 

Debt Coverage Ratio 1.1!1.2d 

(DCR1.1) 

Debt Coverage Ratio 1.2!1.3 

(DCR1.2) 

Debt Coverage Ratio 1.3!1.4 

(DCR1.3) 

Debt Coverage Ratio 1.4 + 

(DCR1.4) 

DCR Zero Order Coefficient 

(DCR_MIS) 

Judicial Foreclosure State (yes=1) 

(JUDFORE) 

Yield on ten-year Treasury 

(TREASYLD) 

Contract Rate - ten-year Treasury 

(SPREAD) 

Size/Property Variables 

Year Collateral Prop. Built 

(YRBUILT) 

Year-Built Zero Order Coef.

 (YRBLT_MIS) 

Number of Units 

(UNITS) 

Fixed-Rate Mortgages Adjustable-Rate Mortgages 

-10.292 4.129 

(0.446) 

-0.100 0.431 1.2% 

(0.673) (0.002)*** 

0.049 0.138 

(0.848) (0.389) 

-0.343 0.487 2.1% 

(0.494) (0.097)* 

-0.276 0.351 

(0.370) (0.230) 

0.808 0.247 

(0.135) (0.287) 

-0.452 -0.342 

(0.508) (0.190) 

-1.469 -0.610 8.0% 

(0.132) (0.073)* 

-0.964 2.1% -0.929 10.8% 

(0.083)* (0.002)*** 

-0.272 -0.031 

(0.482) (0.889) 

-0.568 2.5% -0.151 

(0.006)*** (0.362) 

0.199 1.0% 0.104 2.5% 

(0.026)** (0.072)* 

0.246 1.0% 0.099 3.2% 

(0.005)*** (0.026)** 

-0.006 -0.004 

(0.124) (0.119) 

-11.645 -8.371 

(0.128) (0.112) 

0.003 0.5% 0.003 2.2% 

(0.074)* (0.007)*** 
Simulation of Simulation 

% Change in of % 

Logistic Prob. of Logistic Change in 

VARIABLE Regressiona Default-b Regressiona Prob. of 

Default-b 

No. of Units Zero Order Coef.

 (UNITS_MIS) 

Value per Square Foot 

(VALUE/SF) 

Value/SF Zero Order Coef.

 (VALSF_MIS) 

Property < Year Old (yes=1) 

(NEWPROP) 

Seasoning Variablese 

Originated 71!75 (yes=1) 

(YR71!75) 

Originated 76!79 (yes=1) 

(YR76!79) 

Originated 88 (yes=1) 

(YR88) 

Originated 89 (yes=1) 

(YR89) 

Originated 90 (yes=1) 

(YR90) 

Originated 91 (yes=1) 

(YR91) 

Originated 95 (yes=1) 

(YR95) 

Location Variablese 

ZIPCODE #042 (yes=1) 

(Lewiston, ME) 

ZIPCODE #191 (yes=1) 

(Central Philadelphia, PA) 

ZIPCODE #432 (yes=1) 

(Columbus, OH) 

ZIPCODE #606 (yes=1) 

(Central Chicago) 

ZIPCODE #850 (yes=1) 

(Phoenix, AZ ) 

ZIPCODE #852 (yes=1) 

(NE Phoenix, AZ) 

ZIPCODE #857 (yes=1) 

(Tuscon, AZ) 

Fixed-Rate Mortgages 

-0.263 

(0.461) 

0.000 

(0.581) 

0.201 

(0.498) 

-0.297 

(0.343) 

-1.512 8.3% 

(0.027)** 

-1.469 8.2% 

(0.018)** 

-1.726 8.8% 

(0.090)* 

0.921 5.9% 

(0.014)** 

1.063 7.3% 

(0.046)** 

-1.412 3.3% 

(0.099)* 

Adjustable-Rate Mortgages 

-0.624 9.1% 

(0.063)* 

0.000 

(0.181) 

0.460 7.8% 

(0.033) 

-0.144 

(0.448) 

-1.638 10.5% 

(0.001)*** 

0.708 10.5% 

(0.076)* 

0.862 13.4% 

(0.033)** 

1.157 19.6% 

(0.007)*** 

1.097 18.3% 

(0.025)** 

1.606 33.2% 

(0.000)*** 

0.935 17.0% 

(0.016)** 

1.546 31.7% 

(0.022)** 

-1.831 13.5% 

(0.007)*** 

-1.392 11.9% 

(0.012)** 
Simulation of Simulation 

% Change in of % 

Logistic Prob. of Logistic Change in 

VARIABLE Regressiona Default-b Regressiona Prob. of 

Default-b 

ZIPCODE #900 (yes=1) 

(Central L.A., CA) 

ZIPCODE #908 (yes=1) 

(Long Beach, CA) 

ZIPCODE #913 (yes=1) 

(Northridge, CA) 

ZIPCODE #914 (yes=1) 

(San Fernando, CA) 

ZIPCODE #916 (yes=1) 

(San Fernando, CA) 

ZIPCODE #920 (yes=1) 

(San Diego, CA) 

ZIPCODE #921 (yes=1) 

(San Diego, CA) 

ZIPCODE #941 (yes=1) 

(San Francisco, CA) 

Financial Institution Identifierse 

Institution #7054 (yes=1) 

Institution #7275 (yes=1) 

Institution #7285 (yes=1) 

Institution #7439 (yes=1) 

Institution #7828 (yes=1) 

Number of observations 

-2 Log-likelihood statistic 

Pseudo R2 

Fixed-Rate Mortgages Adjustable-Rate Mortgages 

0.392 

(0.009)*** 

6.2% 

0.893 

(0.001)*** 

16.1% 

1.333 

(0.000)*** 

26.4% 

1.440 

(0.000)*** 

29.0% 

0.509 

(0.082)* 

8.3% 

-0.858 

(0.025)** 

8.8% 

1.190 

(0.020)** 

8.7% 

-0.823 

(0.0089)* 

8.6% 

-2.385 

(0.033)** 

12.1% 

2.381 

(0.000)*** 

50.5% 

-17.915 

(0.000)*** 

34.6% 

2.473

 (0.000)*** 

51.5% 

0.643 

(0.044)** 

9.4% 

2,966 4,019 

-699*** -1,841*** 

0.2025 0.1541 a P-values of Wald chi-squared statistics are shown in parentheses. 

b Reported values simulate the marginal effect of each independent variable on the probability of default. In the 

base case, each continuous and binary independent variable is set at its mean value, then multiplied by the related 

regression coefficient to determine the probability of default for a standard loan. In the case of continuous 

variables, each variable is independently “shocked” one standard deviation to simulate the marginal change in the 

probability of default, which is compared with the base case probability of default to calculate the factor 

sensitivities reported in this table. In the case of binary variables, the sensitivity “shock” involves setting the 

independent variable to its binary value before simulating the new probability of default and factor sensitivity. 

c Loans with LTVs less than or equal to 75 percent are the omitted case. 

d

 Loans with DCRs less than or equal to 1.1 (and greater than 0.9) are the omitted case. 

e

 All seasoning, location, and financial institution variables are included in the estimation. However, to conserve 

space we report estimated coefficients and p-values only for those variables that are significant in either the fixedrate or ARM regressions at the 10 percent level or greater (that is, variables with p-values less than 0.100).