Commercial mortgage underwriting: How well do lenders manage the risks?

JOURNAL OF

Journal of Housing Economics 14 (2005) 355–383

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HOUSINGECONOMICS

Commercial mortgage underwriting:How well do lenders manage the risks? q

Robert A. Grovenstein a, John P. Harding b,*, C.F. Sirmans c,Sansanee Thebpanya d, Geoffrey K. Turnbull e

a University of Texas at Arlington, USAb School of Business Administration, University of Connecticut, 2100 Hillside Road,

Unit 1041F, Storrs, CT 06269, USAc University of Connecticut, USA

d Bangko‘k University, USAe Georgia State University, USA

Received 16 February 2005

Abstract

Loan-to-value ratio and debt service coverage ratios have long been viewed as the two mostimportant quantitative measures of the default risk of commercial mortgages. Option-based modelsof default provide strong theoretic support for the importance of original loan-to-value ratio. Thesame theoretical predictions have found strong empirical support in residential single-family mort-gage analyses. However, recent empirical studies of commercial mortgage default have raised ques-tions about the role of loan-to-value ratio in assessing the riskiness of commercial mortgages. Thesestudies generally either find no relationship or a puzzling negative relationship between loan-to-valueratio and default. This paper uses a very large database of commercial loan histories to thoroughlyinvestigate this issue. It finds strong evidence that loan-to-value and debt service coverage ratios areendogenous to the underwriting process. Lenders react to other—unmeasured—risk factors withcredit rationing and pricing. As a result, unusually low loan-to-value ratio loans appear to haveabove average risk in other dimensions and their default probabilities are equal to or higher thanaverage. The results show that the pricing spread that lenders establish as part of the underwritingprocess serves as an excellent summary measure of the riskiness of the loan. A test of lenders� abilityto appropriately price loan-to-value risk finds that, while there is some unpriced effect of

1051-1377/$ - see front matter � 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.jhe.2005.09.003

q The authors are grateful to the participants of the 2004 AREUEA International Conference and especially ourdiscussant, Charles A. Capone, for helpful comments and suggestions.* Corresponding author. Fax: +1 860 486 0349.E-mail address: [email protected] (J.P. Harding).

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356 R.A. Grovenstein et al. / Journal of Housing Economics 14 (2005) 355–383

loan-to-value ratio after controlling for the lender�s pricing, introducing lender pricing into themodel removes the otherwise puzzling negative loan-to-value and default relationship previouslyobserved in the literature.� 2005 Elsevier Inc. All rights reserved.

1. Introduction

This paper examines whether lenders systematically adjust key underwriting ratios andpricing to reflect the default risk of commercial mortgage loans. In residential mortgagelending, loan-to-value ratio at origination has consistently been shown to be correlatedwith default risk. The empirical results for commercial mortgage loans have been less con-sistent. Several recent papers suggest that loan-to-value ratio and debt service coverage ra-tios are set endogenously in the underwriting process and consequently the observedvalues of these ratios at origination do not adequately measure the riskiness of commercialmortgage loans (Archer et al., 2002 and Ambrose and Sanders, 2003).

Option theory implies that the loan-to-value ratio and the debt service coverage ratioshould be related to commercial mortgage default.1 The borrower�s option to default isgenerally viewed as a put option giving the borrower the right to ‘‘sell’’ the pledgedcollateral (the property) for a price equal to the market value of the remaining loan pay-ments. The borrower will exercise this put option when the property value declines below acertain threshold level.2 At origination, the value is above the threshold and, since the loanamount approximates the market value of the remaining loan payments, the loan-to-valueratio provides a measure of the ‘‘cushion’’ a lender has before default becomes optimal forthe borrower. Similarly, following Merton (1974), non-recourse, collateralized debt can beviewed as giving the borrower a call option on the pledged property. The borrower can‘‘purchase’’ the property by making the remaining scheduled payments on the loan (orequivalently, making a single payment sufficient to service the debt over its remainingterm). In the case of commercial real estate, the property generally provides enough cashflow to cover the required monthly mortgage payments. Therefore, as long as the propertygenerates enough net operating income (NOI) to cover the required debt service, theborrower can keep the call option alive at no out-of-pocket cost. Thus, the ratio ofNOI to required debt service at origination provides a measure of how much NOI candecline before the borrower faces a liquidity problem. Goldberg and Capone (1998,2002) describe and estimate a ‘‘double-trigger’’ model of commercial mortgage default thatformally incorporates both loan-to-value ratio and debt service coverage ratio in an optionmodel of default.

Academic scholars are not the only ones focusing on LTV and debt service coverage(DSC) ratios as measures of risk. Industry newsletters describing current underwritingtrends emphasize these two variables. For an example, see the quarterly surveys publishedby RealtyRates.com at http://www.realtyrates.com. For further discussion of the industryviews on the importance of these two measures of risk, see Gichon (1997).

1 The application of option theory to commercial mortgages and commercial mortgage-backed securities beginswith Kau et al. (1987), Titman and Torous (1989), and Kau et al. (1990).2 The threshold level is a function of the coupon rate on the loan, the remaining term of the mortgage, market

conditions, and volatility of the property value. Consequently, the threshold level of value will vary over time.

http://www.realtyrates.com

R.A. Grovenstein et al. / Journal of Housing Economics 14 (2005) 355–383 357

Empirical studies of residential single-family mortgages verify the link between originalLTV and default risk.3 On the other hand, it has proven difficult to empirically document asimilar relationship between LTV and default for commercial mortgages. Until recently,very few researchers had access to the requisite loan level data to properly test the predict-ed relationships.4 One exception is Vandell et al. (1993) who estimated a Cox proportionalhazard model of default using 2899 loans from a single life insurance company. Vandellet al. included an estimate of the contemporaneous ratio of the market value of theremaining loan payments to the current estimated market value of the property (i.e.,‘‘time-varying LTV ratio’’) along with the original DSC ratio. They found a significant po-sitive effect of the time-varying LTV ratio but the coefficient on DSC was not significantlydifferent than zero. Archer et al. (2002) provide a good survey of the early literature. Theyconclude that the ability of most early studies to provide a clear understanding of the rela-tionship between the two key underwriting variables and default was severely limited—pri-marily by the lack of loan level data but also by the generally restrictive focus on loans thathad been foreclosed. Foreclosure is generally the last resort for a lender and limiting thestudy of default risk to foreclosed loans excludes a large fraction of all problem loans thatwere modified or ‘‘worked out.’’5

In recent years, new data from commercial mortgage-backed securities (CMBS) have be-come available enabling researchers to investigate and test these theoretical relationships.Several recent studies use this new data source tomodel the incidence of default, and in somecases, prepayment.6 The empirical support for using LTV and DSC ratios as indicators ofrisk in commercial mortgage lending has been mixed. For example, Ambrose and Sanders(2003) use data from 33 different CMBS issues and estimate a multinomial logit competingrisks model for prepayment and default. They find no significant relationship between origi-nal LTV and either default or prepayment. Their models include a time-varying indicatorvariable flagging loans that had a high probability of negative equity (i.e., having a loan bal-ance greater than current property value). This indicator variable is significant in the prepay-ment model but not in the default model. Ciochetti et al. (2003) estimate a maximumlikelihood competing risks model of prepayment and default using 2043 loans drawn froma single life insurance companyportfolio. Ciochetti et al. (2003) use a time-varyingLTV ratioand the original DSC ratio as explanatory variables. They find that the time-varying LTVratio is not significant in either the default or prepayment model. The original DSC ratiois significant in the default model but with an anomalous positive coefficient implying thatloans with high DSC ratios default more frequently.

3 For example, see Avery et al. (1996). Note that owner-occupied houses do not generate cash flow that can beused to make debt payments, so the debt service coverage argument and double trigger theory does not apply. Forthese loans, the second key underwriting variable is a measure of the borrower�s credit history. For example,FICO scores have been shown to be reliably related to default.4 Vandell (1992) documents a positive relationship between an estimated contemporaneous LTV ratio and an

aggregate measure of default rates in life insurance company commercial mortgage portfolios.5 In addition to loan modifications, lenders may permit a sale of the property and accept a smaller payoff or

even accept a discounted payoff from the current borrower.6 See, for example, Archer et al. (2002) and Ambrose and Sanders (2003). Goldberg and Capone (2002) use data

from Fannie Mae and Freddie Mac purchases of multifamily loans during the period from 1983 to 1995. Otherauthors have studied the same issues using single lender data. Examples here include Ciochetti et al. (2002) andCiochetti et al. (2003).


Archer et al. (2002) offer an explanation for these puzzling results. They argue that LTVis endogenous to the loan underwriting process. In that process, lenders observe a full vec-tor, h, of measures of risk including location attributes, developer track record, and cur-rent and prospective competition for the property. There are limits on the lender�s abilityto price risk when underwriting loans. Stiglitz and Weiss (1981) point out that lenders can-not always just raise the interest rate as the risk of default increases because the higherinterest rate itself increases default risk.7 Consequently, lenders frequently respond tohigher perceived overall risk (based on a multidimensional analysis including factors otherthan LTV and DSC ratios) by limiting the amount they will lend, thereby lowering theloan-to-value ratio and increasing the debt service coverage ratio.8 While it is possible thatlenders could attempt to adjust the risk level of every loan to a common target level, it ismore likely that they use a combination of underwriting adjustments and pricing. We be-lieve this approach is more likely because most borrowers have limited additional funds toclose a transaction and therefore have limited ability to accept a lower loan amount andstill complete the transaction. On the other hand, the cash flow from the property can beused to pay a higher interest rate.

Once we recognize that the LTV and DSC ratios are determined endogenously withinthe loan underwriting and pricing process, we see that some loans with very low LTV andhigh DSC ratios will have above average risk if the required LTV and DSC are set by thelender to partially compensate for other high risk characteristics. In evaluating loan appli-cations, lenders consider many different factors (other than simply initial LTV and DSC)potentially related to the riskiness of the loan. For example, they consider current and pro-jected levels of economic growth, interest rates, property values and the volatilities of all ofthese state variables. Thus, it is possible that a loan with high LTV could have many off-setting favorable risk factors that make it a low risk loan when all factors are considered.9

Archer et al. (2002) study a sample of multifamily loans and conclude that LTV at orig-ination is not a significant predictor of default. Surprisingly, they find that DSC ratio wassignificantly related to default with the expected sign despite the fact that DSC and LTVare generally closely related. They interpret the failure to find a relationship between LTVand default as evidence supporting the above notion that LTV is endogenous in the under-writing and pricing process. They suggest DSC at origination as a better measure of theriskiness of a commercial loan. That study, however, is based on a small number of some-what atypical loans and consequently their results cannot be viewed as definitive.10

7 The increased risk can arise because a higher interest rate imposes a greater debt payment burden, but can alsoarise from adverse selection if the higher interest rate causes lower risk borrowers to withdraw leaving a higherrisk pool of potential borrowers.8 DSC is defined as the ratio of NOI to debt service and debt service is equal to the loan constant times the loan

amount, so lowering the loan amount will raise DSC, other things held constant. Therefore, even though lenderscan theoretically adjust LTV and DSC separately, these two measures are linked and will tend to move together.9 Goldberg and Capone (2002) estimate the joint probability that a loan has crossed the default LTV boundary

and experiences negative cash flow at the same time. Their approach requires estimating the joint probabilitydistribution of these events and depends upon both the means and variances of the random variables describingfuture property value and future cash flow.10 The Archer et al. (2002) sample comprises loans taken over by the Resolution Trust Corporation from failedsavings and loan associations. Many of these failed savings and loan associations were new entrants to thecommercial mortgage business and inexperienced in commercial mortgage underwriting. Furthermore compe-tition with established lenders forced many of these new entrants to push the established underwriting boundaries.


This paper exploits a new large data set of commercial mortgages in order to evaluatehow effectively lenders adjust underwriting ratios and pricing to manage their risk. It con-tributes new results that help resolve outstanding empirical issues in the literature con-cerned with LTV and DSC ratios and default and prepayment risks. The larger andmore comprehensive data provide more complete information than available to previousresearchers. This allows us to more carefully incorporate the endogeneity of LTV andDSC implied by the mortgage underwriting and pricing process into a competing risksmodel of prepayment and default.

The basic premise of the model is that lenders adjust LTV (and DSC indirectly) so thatthe overall risk of default falls into an acceptable range and then price the residual risk. Iflenders are fully effective in this process, there should be no unpriced contribution of LTVto default risk. We find some unpriced contribution of LTV to default risk, but this un-priced risk appears to be isolated in the hotel and residential property sectors. The hotelresult is consistent with the unforeseen implications of the terrorist attacks of September11, 2001. The result for the multifamily property category is consistent with the preferenceof many investors for multifamily loans and the restrictions on Government SponsoredEnterprises that affect the mix of mortgages they can purchase. In any event, endogenousloan pricing accounts for the anomalous negative relationship between LTV and defaultrisk found in earlier studies and in our simpler model without the pricing effects.

The paper is organized as follows. Section 2 provides an outline of the relevant aspectsof the underwriting process. Section 3 explains the data and key variables in the study.Section 4 develops the models for underwriting, default and prepayment. Section 5 reportsthe empirical results for several different specifications of competing risk models of defaultand prepayment. The final section concludes.

2. The underwriting process

The underwriting process involves five major steps. We describe those steps in the num-bered points below.11 Table 1 summarizes the definitions of key terms for easy reference.

Step 1. After investigating rates and underwriting criteria, a potential borrower submitsa request for a loan to a lender. The loan application specifies the amount of the loanrequested and describes the borrower and the collateral that will be pledged to securethe mortgage loan. The borrower will normally provide projections of operations andthe income generating capacity of the property. The lender will request or perform anappraisal of the property and analyze the risks of making the loan. The appraisal reportprovides an operating history of the property, an analysis of existing leases and expectedlease rollover, an assessment of local market conditions, pro forma operating results(which generally differ in terms of assumptions and cash flows from those provided bythe borrower), and a conclusion about the value of the property.

Step 2. Based on the information gathered in step 1, the lender develops informationabout a vector, h, of risk characteristics associated with the loan. h includes the requested

11 The underwriting process described here is a very simplified, generic, description based on conversations withseveral different commercial mortgage lenders. It is not intended to describe the actual process for any specificlender. The actual process is more complex and involves more interaction between the lender and borrower. Forconduit commercial mortgages, the process also involves other parties including rating agencies and subordinatedtranche investors.

Table 1Definitions of symbols

Symbol Definition

Lt Loan amount at t (t = 0 at loan origination)c Interest rate on mortgageT Maturity of mortgageA Amortization period for mortgagea Mortgage constant = f(c,L,A)Vt Property value at tNOIt Net operating income of property at tLTVt Lt/Vt

DSCt NOIt/aS Spread between interest rate on the mortgage and riskless rate for maturity T

rf0 Riskless rate at time 0 for maturity T

Mt Market value of remaining loan paymentsYt Vector of variables describing the prepayment rules that apply from t to T

h Vector of risk factors observed by the lender in underwriting the loan�h vector of risk factors, excluding LTV0 and DSC0

k Cap rate = NOI/value at originationc Vector of prepayment rules incorporated into the mortgage


LTV and proposed DSC ratio as well as other risk factors including location, operatinghistory, current tenants, and lease structure, competitive factors, borrower track record,and general economic conditions, including volatilities.

Step 3. The lender makes a preliminary judgment regarding the overall risk of default.If the risk level is deemed unacceptably high, the lender can either reject the loan or reducethe loan amount to lower the overall risk to an acceptable level. Note that the lender candirectly control the loan amount, L, and therefore also affects the initial loan-to-value ra-tio, LTV0. The lender cannot control or alter the property characteristics such as NOI orproperty value, V. Once the lender finds the risk level acceptable, he moves on to pricingthe loan.12

Step 4. The lender determines the interest rate on the modified loan (c) as a function ofthe current risk free or benchmark rate, r0, the cost of administering the loan, c, and thecompensation required for bearing the associated risk of default, l(h), which dependsupon the vector of risk characteristics:

c ¼ f ðlðhÞ; r0; cÞ. ð1ÞEven though conduit lenders originate loans with the intent to resell them through a sub-sequent CMBS issue, the economics of the securitization process are such that these orig-inators have the same incentives to set an appropriate interest rate as do portfolio lenders.

The separation of the determination of loan terms other than the interest rate and thesetting of the coupon rate implied by the Steps 3 and 4 is only a descriptive device. Lendersand borrowers negotiate over all the loan terms and there is a great deal of looping backover Steps 3 and 4. An important reason for separating these steps, however, is that there

12 Lenders can make adjustments to other loan terms as well. For example, lenders can require crosscollateralization using other properties owned by the borrower, additional reserves for maintenance andoperations, or a shorter amortization period. Such adjustments to the loan terms are part of the more complexnegotiations between lender and borrower mentioned in Footnote 11.


is a limit on the lender�s ability to price risk (see Stiglitz and Weiss, 1981) and as a result,lenders simply reject loan applications if they believe the risk of default is unacceptablyhigh and that the modification of terms that would be required to lower the risk wouldbe unacceptable to the borrower.13

Step 5. Once the loan terms are established,Vt, NOIt, and rt evolve stochastically. In eachtime period after origination, the borrowermust decide whether tomake the regularly sched-uled payment, default on the loan or prepay the loan.14 Our basic assumption is that the bor-rower acts to maximize its wealth in making that choice. As discussed above, a standardapproach to modeling the borrower�s decision views the borrower as deciding whether ornot to exercise a joint option to default or prepay (Kau et al., 1987, 1990;Ambrose and Sand-ers, 2003).Following the standardapproach, the jointdistributionof thesevariablesover timewill determine the value to the borrower of either defaulting or prepaying. Thus, we canwritethe following reduced form equations for the probability of default and prepayment:

Pr½Default�t ¼ f 1ðLt;Mt; V t; rt;NOIt; ct; a; �hÞ;Pr½Prepay�t ¼ f 2ðLt;Mt; V t; rt;NOIt; ct; a; �hÞ;

ð2Þ

whereMt is the market value of remaining loan payments, c is a vector of rules that restrictthe borrower�s right to prepay, a is the mortgage constant, and �h is the vector of risk char-acteristics excluding LTV and DSC.

The basic empirical problem is that, because they have been traditionally viewed as themain proxies for risk, analysts can observe the original LTV and DSC ratios but few, ifany, of the other elements of h. In general, the literature on commercial mortgage under-writing focuses on the original LTV and DSC as the key proxies for risk. However, themixed empirical results and endogeneity arguments raise significant questions about theseconvenient, short-cut measures.

3. The data

We collected data on 20,117 loans that comprise the collateral for 133 conduit and fu-sion CMBS transactions issued between 1997 and 2001.15 We chose conduit and fusiontransactions because they are backed by large diversified pools of recently originated com-mercial mortgage loans. Each pool is diversified in several dimensions: geographically, by

13 Although much of the Stiglitz and Weiss (1981) article deals with borrowers that appear to the lender to beidentical (leading to credit rationing) the commercial lending process described here is more closely linked to thesection of the Stiglitz and Weiss (1981) paper that addresses a world where lenders face n observationallydistinguishable borrower types. In that case, different borrower types receive different interest rates and certaintypes of borrowers receive no loan. One could view Step 3 as sorting borrowers by type and Step 4 as assigningthe rate.14 Most commercial mortgage loans contain provisions that limit or preclude the borrower�s right to prepay.15 A conduit deal is a CMBS where the collateral pool is originated by financial intermediaries that originateloans with the intent of reselling all loans to investors in the CMBS market as soon as sufficient volume has beenaccumulated. A fusion deal is a CMBS issue where the collateral pool includes some unusually large loans as wellas the standard conduit type loans. We use the Commercial Mortgage Alert designation of conduit and fusiontransactions. The characteristics and subsequent performance of conduit loans may differ from those of loansoriginated for portfolio investment. According to Harding et al. (2004), conduit transactions represent roughly60% of all CMBS volume during the period from 1997 through 2001. The excluded types of CMBS transactionsare single large loan deals, single-borrower deals, lease-backed transactions, and seasoned collateral transactions.


property type and by lender. The original underwriting of these loans is reviewed at severallevels: first by the conduit CMBS issuer, second by the rating agency that rates the CMBSand third by the subordinated tranche investor who buys the unrated portion of theCMBS. By combining loans from many originators, our data are not unduly influencedby the special needs and/or underwriting of any one lender.

In order to assure that we have a reasonably long observation period for every loan inthe final sample, we restricted the sample to loans originated during 1996, 1997, and 1998.On average, there is a five month ‘‘warehousing’’ period for newly originated conduitloans between loan origination and the closing of a CMBS transaction. In our data,95% of the loans had warehouse periods of 13 months or less. In addition to screeningby origination date, we excluded loans collateralized by property other than the five majorcommercial real estate property types: multifamily, office, retail, hotel, and industrial/warehouse. The excluded property types tend to have unique income characteristics or val-uation problems (for example, medical facilities, nursing homes, mobile home parks, etc.)Finally, we deleted loans if the records were missing information for critical variables or ifthere were apparent data entry errors. Specifically, we restricted our sample to loans withLTV ratios between .4 and .95 and loans with DSC ratios between 1.0 and 3.0. Our finalsample comprises 10,547 commercial mortgage loans originated between 1996 and 1998.See Table 2 for summary statistics.

Conduit loans differ somewhat from the overall CMBS loan population. Office buildingsare themost commonproperty type used as collateral for large loan transactions and lodgingcollateral is frequently sold in single-borrower transactions. As a result, a sample based onconduit transactions alone should be expected to underweight these property types and over-weight the remaining types. Based on the data reported by Harding et al. (2004), the overallCMBS market in 1997–1999 included 29% multifamily, 7% industrial, and 28% retail. Oursample weights for these property types are 39, 13, and 30%, respectively. Our sample in-cludes 8% hotel loans and 10% office loans, whereas the overall CMBS population includes10% hotel and 19% office. Nevertheless, our sample loan-to-value ratio, debt coverage ratioand pricing margin are very similar to the overall CMBS averages.

Using reports provided by Trepp, we monitor the performance of these loans from thethird quarter of 1997 through the second quarter of 2002.16 In each quarter, we observewhether the loan continued to make its contractual payments, voluntarily prepaid ordefaulted. This creates a panel data set comprising up to 16 quarters of observations oneach of the 10,547 loans. Our total sample includes 133,950 quarterly loan observationsbecause once a loan terminates, it is removed from the sample. The basic data on loan per-formance is available monthly, but we use a quarterly observation period to assure that wehave a sufficient number of prepayment and default events.17

During the observation period, we have 398 defaulted loans representing 3.8% of the loansample. Hotels and retail properties experienced the highest default rates (14 and 4%, respec-tively). Despite the common use of restrictions on prepayment, the overall prepayment ratefor these loans was 2.9% with multifamily and office loans experiencing above average

16 Most of the loans in the sample have payments calculated based on 25–30 year amortization periods butballoon maturities of approximately 10 years. Our observation period is not long enough to observe defaults thatmay result from the inability to refinance the unpaid loan balance at maturity.17 Collapsing the data further into annual periods would, in our opinion, result in too much averaging of ourtime-varying control variables for interest rate and property value fluctuations.

Table 2Summary statistics for non time-varying variables

Variable All loans Defaulted loans Prepaid loans10547 loans 398 loans 308 loans

Mean SD Min Max Mean SD Mean SD

Loan size ($,mil) 4.94 7.92 0.18 273.13 4.70 6.10 4.26 4.98ln(Loan size) 1.15 0.87 �1.73 5.61 1.13 0.88 1.05 0.91

Underwriting variables

Original LTV (%) 71.01 8.45 40.00 95.00 69.99 7.94 69.24 8.17Original DSC 1.43 0.22 1.00 2.97 1.42 0.20 1.43 0.21Residual LTV 0.0000 0.0778 �0.4301 0.3225 0.0045 0.0700 �0.0113 0.0742

Residual LTV interactions

With hotel 0.0000 0.0248 �0.2407 0.3225 0.0026 0.0341 0.0009 0.0078With office 0.0000 0.0263 �0.3035 0.2251 0.0011 0.0205 �0.0013 0.0242With retail 0.0000 0.0445 �0.3083 0.2634 �0.0032 0.0495 �0.0033 0.0324With industrial 0.0000 0.0278 �0.4301 0.2416 0.0005 0.0137 �0.0018 0.0246With multifamily 0.0000 0.0446 �0.3456 0.1686 0.0036 0.0258 �0.0058 0.0572Pricing margin (%) 1.93 0.45 0.70 3.00 2.22 0.38 2.02 0.47Property cap rate (%) 8.99 1.52 0.59 24.91 9.30 1.41 9.18 1.54AAA subordination req. (%) 28.72 1.85 16.50 33.00 28.79 1.77 29.03 1.45

Other loan descriptors

Cross collaterization indicator (%) 6.27 — — — 7.54 — 7.79 —Balloon indicator (%) 77.94 — — — 74.12 — 89.61 —Lockout time (mo.) 57.10 43.08 0 300 59.47 46.44 26.82 28.80Defeasance time (mo.) 18.37 40.25 0 329 22.69 49.46 1.66 10.91Lockout + Defeasance (mo.)a 115.02 55.71 4.5 360 136.3942 58.46 110.84 45.46

Property descriptorsProperty type indicators

Hotel (%) 7.52 — — — 28.14 — 2.92 —Industrial (%) 13.32 — — — 9.80 — 12.01 —Retail (%) 29.90 — — — 34.17 — 18.18 —Office (%) 10.50 — — — 5.28 — 7.14 —Multifamily (%) 38.76 22.61 59.74

Region indicators

East (%) 28.14 30.65 27.60West (%) 29.07 — — — 24.12 — 26.95 —South (%) 28.73 — — — 32.16 — 33.77 —Midwest (%) 14.06 — — — 13.07 — 11.69 —

Market conditions at origination

10 year treas at issue (%) 5.47 0.44 4.65 6.52 5.64 5.64 5.76 5.76Yield curve slope (%) at issue 0.3291 0.2028 �0.3233 0.7667 0.3864 0.3864 0.4484 0.4484BBB–AAA spread (%) 0.7188 0.1598 0.5500 1.0100 0.6686 0.6686 0.6157 0.6157

a Lockout + Defeasance is the sum of the lockout period plus the defeasance period (in months) for thesubsample of loans that that have a defeasance provision. A total of 2390 loans (22.7% of the sample) have adefeasance provision. The average defeasance time for loans with a defeasance provision is 81 months. Theaverage defeasance period of 18.37 months is for the full sample.


prepayment rates (4.5 and 2.6%, respectively). Almost all of the prepaid loans were prepaidafter the lockout provisions expired. The average lockout period for these loans was just un-der five years, but 25% of the sample had lockout periods of less than 3 years.


Our data sources include the Commercial Mortgage Alert data base which providesinformation about each CMBS deal including the number of loans, the deal structure,the rating of each tranche and the level of subordination required by the rating agenciesafter reviewing the full pool of loans. We obtained additional descriptive variables fromthe prospectus supplements for each deal. These supplements provide information onthe loan size, the original18 loan-to-value ratio, net operating income, and debt service cov-erage ratio. The prospectus supplements also provide information about the prepaymentprotection incorporated into each loan�s note. We supplement this loan level data withvariables describing current market conditions at the time of origination and over the fullobservation period. 19 These market variables include the level of interest rates on Trea-sury securities, the volatility of interest rates and property values, the yield curve shapeand bond credit spreads. We obtained the interest rate variables from the Federal Reserveand other public data sources discussed in Section 5.

Finally, we combine this descriptive information with data provided by Trepp, describ-ing the performance of each loan. Trepp monitors the servicing reports for each CMBSdeal and provides monthly reports on the performance of the loans backing the deal.These reports identify prepaid loans, delinquent loans and loans that receive special servic-ing to resolve delinquencies.20 We define an event of default as the transfer of loan servic-ing to a special servicer charged with resolving problem loans because such a transfer onlyoccurs after a serious delinquency problem and signals a significant risk of loss from de-fault. The rationale for this definition is discussed in greater detail in Section 5.

The large size of our database enables us to explore the relationship between the LTVand DSC ratios and default in some detail before turning to more formal multivariateanalysis. We first grouped the loans into cohorts based on LTV and DSC. We calculateda default rate for each cohort. Panels A and B of Fig. 1 show the calculated default ratesfor different values of LTV and DSC. We also categorized the data by the original pricingmargin, defined as the difference between the coupon rate on the loan and the 10-yearTreasury rate at origination.21 The relationship between default and this pricing marginis shown in Panel C of Fig. 1. In all three panels, the horizontal line at 3.8% marks theoverall default rate for the sample.22

18 We use the term ‘‘original’’ in this paper to refer to the loan characteristics at the cutoff date for the CMBSissue. Typically, the CMBS issue occurs 3–6 months after the individual loans were originated. This time periodallows for enough loans to be accumulated to support a large issue and for the rating agency review beforeissuance.19 Our choice of variables to control for changing market conditions is motivated by previous research (e.g.,Ambrose and Sanders (2003), Childs et al. (1996), Maxam (1996), and Maris and Segal (2002)).20 In general, when a loan has been delinquent for between 60 and 90 days, the servicing of the loan is transferredfrom the master servicer to the special servicer. The special servicer�s responsibilities include working with theborrower to bring the loan current, if possible. If that is not possible, the special servicer will either foreclose onthe loan to obtain title to the pledged property and sell that property or develop a workout plan that couldinclude loan modifications. The special servicer is charged with maximizing the recovery from the problem loan.21 For the purpose of calculating the pricing margin, we used the actual loan origination month, not the CMBSissue date and compared the coupon rate with the Treasury rate in the month of origination. We use the 10-yearTreasury because that is the traditional benchmark for loans of this type and because most loans had balloonmaturities of approximately 10 years. We use the coupon rate on the loan, not the effective borrowing cost,because we do not have data on the points and fees charged at origination.22 Because none of the loans in our sample reach their balloon maturity during the observation period, none ofthe defaults analyzed here is due to the inability to refinance the balloon amount.

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Rat

e

<50% 50-55% 55-60% 60-65% 65-70% 70-75% 75-80% 80-85% 85-90% 90-95%

Default Rate by LTV Categor y

0.0

2.0

4.0

6.0

8

Def

ault

Rat

e

<1.1 1.1-1.2 1.2-1.25 1.25-1.3 1.3-1.35 1.35-1.4 1.4-1.1.45 1.45-1.5 1.55-1.6 1.6-1.7 >1.7

Default Rate by DSC Category

0.0

2.0

4.0

6.0

8.1

Def

ault

Rat

e

<1.2 1.2-1.4 1.4-1.6 1.6-1.8 1.8-2.0 2.0-2.2 2.2-2.4 2.4-2.6 2.6-2.8 2.8-3.0

Default Rate by Margin Category

A

B

C

Fig. 1. Univariate analysis of default rate.


Panel A shows that the highest default rate occurs for loans with LTV ratio between 65and 70%. This is the category just below the average LTV of 71%. This peaking of defaultcould be the result of lenders requiring slightly larger than average down payments forloans they deem to be marginally riskier than average in other dimensions. The categories

Table 3Univariate logit models of default

Independent variable Coefficient z statistic Log-likelihood p value Psuedo R2

Original LTV ratio �1.46 �2.54 6.23 0.0126 0.0018Original DSC ratio �0.38 �1.53 2.43 0.1187 0.0007Pricing margin 141.74 12.56 161.01 0.0000 0.0477

Dependent variable is indicator of default (value = 1) or continuation (value = 0) in a given quarter. Table 3reports the results of three separate logit models of default incidence.


with above average LTV ratios all have below average default rates. This is consistent witha view that lenders only accept significantly higher than average LTV ratios when there areother favorable factors that mitigate the risk. The loans that fall into the four lowest LTVcategories have higher default rates than the four highest categories—although the defaultrates for the low LTV loans are near the overall average. This too is consistent with theview that an unusually low LTV does not signal an unusually safe loan, but rather signalsa loan for which the lender has required a large down payment in order to offset other sig-nificant risk factors. The overall visual impression from Panel A is of a weak negative rela-tionship between LTV and default. This visual impression is confirmed by a simple logitmodel of default based solely on original LTV ratio in Table 3. This negative relationshipis the exact opposite of what a narrow interpretation of option theory predicts and is alsocontrary to what we observe for large cohorts of residential loans. However, the observedrelationship is consistent with the endogeneity argument of Archer et al. (2002).

Panel B shows the relationship between DSC and default rate. With the exception of thevery first bar, there is no apparent pattern between DSC and default rate. A simple uni-variate logit model based on DSC (Table 3) confirms this visual impression—the coeffi-cient on DSC, although negative, is not statistically different from zero. A finding of norelationship is consistent with the view that lenders adjust LTV, and consequently DSC,to compensate for other risk factors.

Finally, the third panel displays the relationship between pricing margin and default.Here we see an intuitive relationship where loans with below average margins (which musthave been deemed to be less risky than average by the originator) tend to have lower de-fault rates while loans with above average margins (i.e., loans deemed to have higher risk)have higher default rates. The logit results in Table 3 confirm this observation and the rela-tionship between default and pricing margin is the strongest of the three univariate rela-tionships as measured by the z statistic, the likelihood ratio test or the pseudo R2.

The evidence is consistent with the notion that LTV and DSC are both endogenous inthe underwriting process. It further suggests that the pricing margin—which the lender setsafter observing the full set of risk factors and adjusting the LTV (and associated DSC)—may well serve as a summary measure of the overall risk. It is to this aspect that we nowturn.

4. Default and prepayment with endogenous LTV and DSC

Strict application of option theory suggests that models of default and prepayment ofcommercial mortgages should include measures of the current market value of theproperty (Vt), the current market value of the remaining payments (Mt), the current net


operating income (NOIt), and the current periodic debt service payment. As a practicalmatter, accurate measures of all four variables are not available over time for each prop-erty and mortgage loan. Researchers have generally utilized proxies for these variables.The simplest and most broadly available proxies are original loan-to-value ratio and ori-ginal debt service coverage ratio. Since many defaults occur in the first few years after orig-ination and the loan amortization period is generally quite long, these variables are highlycorrelated with their time-varying contemporaneous measures during the first few criticalyears.

Other researchers have attempted to improve on these measures by updating the prop-erty value using indices of changes in price for similar properties and/or updates of netoperating income based on indicators of change in cash flow from similar properties. Giv-en an updated estimate of the time-varying property value, one can calculate the scheduledloan balance and calculate a time-varying loan-to-value ratio (LTVt) and a time-varyingdebt service coverage ratio (DSCt). The existing literature on commercial mortgage defaultuses various combinations of these estimated time-varying variables and the originalunderwriting variables. Table 4 summarizes the key variables used in several recent studiesand also reports the sign and significance of the estimated coefficient in a default model.The definition of ‘‘default’’ varies for the studies in Table 4. Archer et al. (2002) definea default as a 90-day delinquency. Vandell (1992) and Vandell et al. (1993) define adefaulted loan as one that has completed the foreclosure process. Ciochetti et al. (2003)define a default as any loan that completed the foreclosure process, was currently in fore-closure or a loan that had been modified as part of a workout arrangement. The remainingtwo papers do not define default precisely. Since many delinquent loans are ‘‘worked out’’and resolved before completing the foreclosure process, these differences in definition canbe quite significant. We define a default as the transfer of loan servicing to a special ser-vicer charged with working out problem loans. This definition is closest to that used inArcher et al. (2002).

Table 4 reveals mixed results for the relationship between the two key underwritingvariables and default. Although some authors have found that LTV enters their modelswith the expected positive sign (and is statistically significant), in general, these resultshave been obtained when the authors use time-varying LTV. One explanation for thesomewhat better performance of time-varying LTV is that default is triggered when thecontemporaneous property value falls well below the current loan balance creating a highvalue for the contemporaneous LTV ratio.23 There are, however, two different routes to ahigh LTV ratio. The first is to start out with a high LTV0 and then observe a stable ormodestly declining property value. But the same end point can be reached starting witha much lower LTV0 ratio followed by a much sharper decline in property value. Clearly,there are two distinct risk factors at work: the initial starting LTV ratio and the change inLTV after origination (DLTVt). Previous studies using the time-varying LTV ratio gener-ally find a positive relationship while the relationship between initial LTV and default isfrequently estimated to be negative. This suggests that DLTVt may be more important

23 The Goldberg and Capone (1998, 2002) double-trigger theory provides a second, possibly complementary,explanation. Under the double-trigger theory, default does not occur until both a high LTV is achieved and debtservice coverage drops below 1. Since the loans in our sample are all fixed-rate, the debt service is fixed over timeand NOI must fall to reduce the DSC ratio below one. Because the contemporaneous property value is closelyrelated to the NOI, this line of reasoning leads to the same conclusion expressed in the text.

Table 4Summary of underwriting measures used in models of default

Study Loan-to-value ratio Debt service coverage ratio

Archer et al. (2002) Categorical indicator for the levelof original

Categorical indicators for thelevel of original

LTV (<70%, 70–80, 80–90,90–100%)

DSC (<1.2,1.2–1.4,1.4–1.6, >1.6)

Loan level data from RTC None significant All significantMultifamily only 495 loans Highest category of LTV has

negative signNegative sign, similar magnitude

Vandell (1992) Estimated proportion of loanswith Mt/Vt falling into differentcategories

Not included

Aggregate data from ACLIAll property types Generally significant with

expected positive sign

Vandell et al. (1993) Time-varying estimated Mt/Vt Original DSCSignificant Not significant

Loan level data from single insurancecompany

Positive Negative

2899 loans1962–1989

Ambrose & Sanders (2003) Original LTV and indicator ofLt/Vt > 1

Not included

Original LTV Not Significantand negative

Loan level data from CMBS Indicator variable not significantand negative

All property types1994–19984257 loans

Goldberg and Capone (2002) Time-varying LTV (Model 4) Time-varying DSC (Model 4)Significant Significant

Loan level data from GSEs Multifamilyonly

Positive Negative

1983–199514,990 loans

Ciochetti et al. (2003) Time-varying LTV ratio Time-varying DSC ratioNot significant Significant

Loan level data from single insurancecompany

Negative in unweighted model Negative in both modelsPositive in weighted model

1974–19902043 loans


than the initial ratio. Notice also that using LTVt rather than LTV0 gradually reduces thecorrelation between LTV and DSC that exists at origination.24

Absent concerns about the endogeneity of LTV0 in the underwriting and pricing pro-cess, one could estimate the separate effects of original LTV and the change in LTV after

24 It is difficult to estimate the separate effects of LTV0 and LTVt in the same model of default because of theextremely high correlation between LTV0 and the early values of LTVt.


origination by including both LTV0 and DLTVt in the empirical default risk model. How-ever, the discussion and evidence from the preceding section strongly support the LTV0

endogeneity argument making such a model specification subject to simultaneous equationbias.

The standard solution to such an endogeneity problem is to use instrumental variablesor 2SLS estimation. In the current setting, this solution is difficult to implement because ofthe paucity of instruments for LTV. One needs to find variables that influence the originalLTV but do not influence the default risk. While it is possible that some borrower or prop-erty characteristics might serve as instruments,25 we could not find any credible instru-ments in our data that met the requirements of being significantly related to originalLTV but not related to loan risk.

The evidence in the preceding section strongly suggests that the pricing margin may be asufficient statistic for default risk. The lender sets this margin after careful analysis of allrisk factors. Therefore, to the extent that lenders fully price all observable risk factors, thismargin should reflect the contribution to risk embodied in the final selected loan-to-valueratio. If this is the case then one could simply use the pricing margin in the empirical modeland exclude the original loan-to-value ratio and original debt service coverage ratio. Ifavailable, one could also include the change in loan-to-value and change in debt servicecoverage over time to capture the contribution of the post-origination events. In theempirical section that follows, we report the results from this approach.

In addition, we further test the underwriting theory using a different modeling ap-proach. Our model is based on a combination of option-theoretical models of defaultand prepayment and the underwriting process described above. We use the definitionsfrom Table 1 in what follows.

We assume that the lender sets the contract rate on the loan by adding two spreads tothe benchmark risk-free rate. The first adjustment is for risk (l) and the second is compen-sation for the costs of making and administering the loan (c). Thus we have for (1):

c ¼ r0 þ lþ c. ð3ÞWe assume that c is constant for all loans (including loans from different lenders andbacked by different property types) but that l varies across loans based on the lender�sassessment of the unique risk characteristics of that loan, or

l ¼ lðLTV0;DSC0; �hÞ; ð4Þwhere the risk factor vector �h refers to all the elements of the vector h excluding LTV0 andDSC0. Eq. (4) for the pricing margin can be viewed as describing the lender�s pricing sur-face. Under appropriate regularity conditions, we can solve Eq. (4) for LTV0, to get

LTV0 ¼ gðDSC0; l; �hÞ. ð5ÞWe further simplify Eq. (5) using the definition of DSC. To do so, note that the debt ser-vice for loans with long amortization periods is approximately equal to the periodic cou-pon rate times the loan amount, so that

25 For example, borrower and property characteristics could explain the borrower�s initial requested loanamount, which is likely to be related to the initial LTV ratio.


DSC0 �NOI0cL0

¼ kV 0

cL0

¼ klþ r0 þ c

� �1

LTV0

� �; ð6Þ

where k represents the property capitalization rate (cap rate). But the property cap rate, k,is itself a function of r0 and the risk factor vector �h. As a result, we can write

DSC0 ¼ hðr0;l; �h;LTV0Þ. ð7ÞSubstituting (7) into (5) and solving for LTV0 yields

LTV0 ¼ /ðr0;l; �hÞ. ð8ÞIn general, �h can be thought of as comprising two subvectors: a vector of ‘‘group’’ riskfactors affecting all loans backing a particular CMBS, and a vector of ‘‘individual’’ factorsuniquely affecting a particular loan. The former risk factors include lender and servicertrack records and general market conditions at the time of origination. We proxy forthe group risk factors using the level of subordination required by the rating agency forthe CMBs and selected market variables such as the BBB–AAA bond spreads, the yieldcurve shape and the volatility of rates. We proxy for the individual factors using the lend-er�s pricing margin for the loan, the cap rate for pledged property and other contractualprovisions of the loan.

We estimate a model for LTV based on Eq. (8) above and then calculate the residual foreach loan ðLTV0 � LbTV0Þ. This residual provides information about the unmeasuredproperty and loan characteristics.26 A positive residual indicates favorable unmeasuredcharacteristics while a negative residual implies unfavorable unmeasured characteristics.We model default and prepayment using a multinomial logit model that uses pricing mar-gin, l, as the key underwriting measure of risk, but also includes changes in LTV and DSCover time to capture evolution in market conditions after origination and the residual er-ror from the LTV model. If the lender is properly incorporating the full effect of all ele-ments of h (including LTV0 and DSC0) into the pricing margin, then the residual termLTV0 � LbTV0 should contribute nothing significant to the explanation of default. A sig-nificant positive relationship between the residual and default indicates that the lender isnot correctly adjusting LTV0 and setting the pricing margin in the underwriting processand is in fact underpricing LTV risk. A negative relationship suggests that the lender isoverpricing or over adjusting LTV0 in the underwriting process.

The same rationale applies to prepayment risk. However, the lender who lowers LTVand raises l to adjust for default risk simultaneously creates more incentive and greatercapability to refinance. Because of the conflicting effects, lenders tend not to try to controlprepayment risk using LTV0 and l, but rather use loan covenants to prevent voluntaryprepayment. Therefore, because the two risks (prepayment and default) respond different-ly to the same underwriting adjustments the problem is basically one of having a singlecontrol variable for two different risks. As a result, it is likely that we will find unpricedeffects of the LTV residual on prepayment, even when lenders are correctly pricing the ef-fects of LTV0 on default risk.

26 We use the term unmeasured characteristics to refer to risk factors that are observed by the lender but are notincluded in our data. These characteristics could include measures of the volatility of the property value and cashflows.


5. Data and empirical results

5.1. Methodology and data

In this section, we estimate a series of competing risk models for default and prepay-ment. We use essentially the same multinomial logit framework used by Clapp et al.(2001) and Bennett et al. (2001).27 In that framework, the borrower is viewed as makinga sequence of decisions to prepay, default or continue with regular payments on a quar-terly basis. We organize the data set to include repeated observations on the same loanat different points in time (quarterly). For each loan/quarter observation we observe theborrower�s decision and that decision serves as the dependent variable in the multinomiallogit analysis.

We use several different model specifications in the analysis. We first use specificationsthat are similar to those already in the literature that ignore the endogeneity of the under-writing variables. Our results for these specifications are consistent with previously pub-lished literature—including the failure to identify a significant positive relationshipbetween original LTV and default. We then estimate models that explicitly deal withthe endogeneity issue by using the initial pricing margin and the residual LTV.

The loan data are the same as that discussed in Section 3 above and summarized inTable 2. For commercial mortgages, the key factors influencing the borrower�s decisionto default or prepay are economic factors related to the borrower�s goal to maximize itsfuture benefits from ownership. The standard option theory discussed earlier capturesmost of these factors. However, because we cannot measure the option values directly,we use a combination of loan characteristics, property characteristics, and market condi-tions to proxy for the economic drivers. Therefore, we extend the basic loan data toinclude several time-varying variables that capture changing market and property condi-tions over the life of the loan.

Consistent with the previous discussion, we include some form of the underwriting vari-ables in all specifications. In several of the specifications, we include either a time-varyingLTV and DSC ratio or the change in LTV and DSC. The main driver of the change inLTV is the change in property value. We estimate the change in property value usingthe National Council of Real Estate Investment Fiduciaries (NCREIF) data.28 For eachproperty, we use the NCREIF property value index that matches both the property typeand property location by state. We use the quarterly change in the index for each quarterafter origination to estimate the change in property value.29 We combine the estimated

27 We refer to these as ‘‘competing risk’’ models because prepayment and default are mutually exclusive and theoccurrence of one event precludes the other. Multinomial logit is an appropriate methodology to estimate thesemodels simultaneously because an increase in the probability of one event occurring results in lower estimates forthe probability of the alternative choices. Examples of early application of multinomial logit to mortgagetermination decisions include Campbell and Dietrich (1983), Zorn and Lea (1986), and Cunningham and Capone(1990). For more recent applications, see Clapp et al. (2001), Goldberg and Harding (2003), Calhoun and Deng(2002), and Bennett et al. (2001).28 NCREIF is an association of institutional real estate professionals. It accumulates data on commercial realestate performance reported by investment managers who own or manage commercial real estate and generates aset of indices measuring both income and capital appreciation over time by property type and location.29 If there were too few properties included in a given state/property type/time period index value, we used theapplicable regional index.


property value with the scheduled loan balance to calculate a time-varying LTV ratio.Finally, for each period, we define the cumulative change in LTV (DLTVt) as the differencebetween the current estimated LTVt and LTV0. We estimated a time-varying DSC ratioand the change in DSC in a similar manner, using the NCREIF income indices and theoriginal DSC ratio.30

The time-varying market condition variables are separated into two categories: interestrate variables and real estate return variables. The interest rate variables included are thecurrent level and the change in the 10-year Treasury rates since loan origination, the slopeof the Treasury yield curve, the spread between BBB and AAA corporate bond yields, andthe volatility of the Treasury rate and the bond credit spread. The current level of theinterest rate and the change in rates since origination are clearly related to the value ofthe option to refinance. For example, when rates fall after loan origination, the borrowerhas a strong incentive to refinance the original loan and take advantage of the lower levelof interest rates. Because the option to prepay and the option to default are substitutes, thelevel of interest rates influences both the prepay and default models. (See Ambrose andSanders, 2003 for more discussion.) Childs et al. (1996) discuss the theory of pricingCMBS and argue that the slope of the yield curve is a potentially significant factor. Wemeasure the yield curve slope by the difference between the ten-year and one-year Treasuryrates. We include this variable as an indicator of market expectations concerning futureinterest rates. We include a measure of interest rate volatility because theory predicts thata high level of volatility increases the value of the prepay option and thus deters borrowersfrom prepaying. We measure volatility by the standard deviation of the daily 10-year Trea-sury rate over the last 12 months.

Although real estate values are primarily driven by local market conditions (and as not-ed above, we use state level, property-type specific indices to capture local market condi-tions), we also include two variables related to national real estate returns. We include thequarterly returns on REIT stocks (as reported by the National Association of Real EstateInvestment Trusts or NAREIT) as a proxy for the overall national market for real estate.We expect fewer defaults when markets are strong because market values will be increas-ing. We include the volatility of REIT returns because it is related to the value of the op-tion to default. It is well established that an increase in option value resulting from anincrease in volatility will deter default since the borrower loses the remaining option valueby exercising. The volatility of real estate returns has been used in previous research byMaxam (1996). We include a dummy variable for observations before September 11,2001 because of the event�s significant impact on real estate markets.

There has been a great deal of variation in the literature regarding the definition of de-fault. Using a strict definition, default occurs when a borrower first becomes delinquent.However, most loans that become delinquent do not result in losses for the lender, muchless end in foreclosure. At the other extreme, one could limit the definition of default toloans that end in foreclosure and therefore result in the transfer of title from the borrowerto the lender. In commercial lending, foreclosure is frequently not the best way to resolvefinancial distress (Riddiough and Wyatt, 1994; Harding and Sirmans, 2002). There are

30 We used a four-quarter moving average of the NCREIF income indices because several of the indices at thestate/property type/quarter level of detail showed occasional large increases in NOI followed by sharp declines(and vice versa). In our opinion, these large swings were related to occasional errors in one quarter being offset inthe following quarter.


substantial transaction costs associated with foreclosure and lenders almost always at-tempt to resolve problem loans with some form of workout arrangement. Previous re-search uses a wide variety of default definitions ranging from 90 days delinquent toforeclosure completion. In general, data availability determines these definitions.

In this paper, we define an event of default to be the transfer of loan servicing from theCMBS master servicer to the designated special servicer.31 Our rationale for this definitionis the following. The master servicer of the underlying loans collects monthly payments,submits payments to the CMBS trustee, and administers the loans. When a loan becomesdelinquent, the master servicer investigates the problem and prepares a preliminary eval-uation of the likelihood that the borrower will be able to catch up on the payments. If theservicer determines the problem to be temporary and expects the borrower to catch up, themaster servicer continues to service the loan while closely monitoring the property andborrower. If the master servicer determines that there is a significant problem with the loanrequiring significant forbearance, loan modification or foreclosure, then the loan is trans-ferred to the special servicer whose job is to workout problem loans and/or institute fore-closure proceedings. Although the master servicer�s compensation is based on the volumeof loans serviced, the master servicer must also make advances to the trustee for all delin-quent loans that have not been transferred to the special servicer. Consequently, the mas-ter servicer�s economic interest is served by only transferring loans that have significantproblems. Delinquency of 60 days generally triggers such a transfer, but if the master ser-vicer believes there are special circumstances, the transfer can be delayed. Such delays arelimited to special cases because the servicer wants to minimize its obligation to make cashadvances for delinquent loans. Transfer to the special servicer can arise for other reasonsas well. For example, a mortgagor with a problem property may admit the inability tomaintain the current payment or make a final balloon payment and initiate negotiationsfor loan modification without technically defaulting on the loan. In conclusion, the trans-fer of servicing is a significant event and reflects a reasoned judgment by a motivated ex-pert that the loan is impaired and at significant risk of generating a loss for the owner.

5.2. Model specification

The first model we estimate, reported in the first two columns of Table 5, uses originalLTV and original DSC ratio as the primary measures of fundamental loan risk. In addi-tion, we include loan size, an indicator of cross collateralization, an indicator flagging bal-loon loans, and a measure of the lockout/defeasance protection provided in the loancovenants. We expect that large loans are subject to greater scrutiny in the underwritingand CMBS issuance process and are likely to be somewhat less likely to default. Theorysuggests that cross collateralization32 should increase diversification benefits and increasethe cost of default for the borrower (Childs et al., 1996). In practice, though, it appearsthat lenders require cross collateralization on riskier loans. Thus, the net effect is an empir-ical issue. Approximately, 78% of the loans in our sample are balloon loans. Balloon loans

31 Kay et al. (2002) provide a description of servicing agreements used in the commercial mortgage backedsecurity market.32 Cross collateralization is a provision in a mortgage by which the collateral for one mortgage also serves ascollateral for other mortgages. A default on any one of a group of cross-collateralized loans could result in theforeclosure on all the cross-collateralized loans—even if the other loans are still current.

Table 5MLN model of termination using original LTV & DSC and time-varying LTV & DSC

Independent variable Original LTV & DSC Time-varying LTV & DSC

Default Prepayment Default Prepayment


LTV (original or time-varying) �1.5134 �2.1358 0.6606 �3.7037�(1.78) �(2.48) (.99) �(5.77)

DSC (original or time-varying) �1.6202 �0.2043 �0.5276 �0.4537�(4.03) �(.59) �(2.36) �(1.8)


ln(size of loan) �0.1699 0.0375 �0.1826 0.0483�(2.29) (.52) �(2.45) (.67)

Cross collaterization indicator 0.1708 0.2914 0.1593 0.3007(.76) (1.25) (.7) (1.29)

Balloon indicator �0.0373 0.2852 �0.0823 0.3397�(.26) (1.41) �(.57) (1.68)

Lockout/defeasance �0.0141 �2.6306 �0.0163 �2.6552�(.09) �(13.91) �(.1) �(14.1)


Hotel 2.3150 �0.2349 2.1264 �0.2560(10.53) �(.5) (9.96) �(.55)

Industrial �0.0809 �0.9220 �0.0228 �0.9163�(.32) �(3.69) �(.09) �(3.68)

Retail 0.6032 �0.8600 0.6784 �0.6778(4.08) �(5.03) (4.57) �(3.93)

Office 0.2668 �0.4863 0.3690 �0.5206(1.24) �(2.32) (1.72) �(2.5)

Region indicators

West 0.1012 �0.1172 0.1105 �0.1236�(.59) �(.69) �(.65) �(.72)

South 0.1656 �0.1346 0.0778 0.0560(1.07) �(.85) (.5) (.34)

Midwest 0.0283 �0.1514 �0.0593 �0.1017(.14) �(.7) �(.29) �(.46)

Market conditions

10 year treas at issue 28.1523 �36.4509 33.3937 �43.5802(1.31) �(1.56) (1.54) �(1.87)

Change in 10 year to t �3.8389 �0.1303 �4.2401 0.2015�(4.19) �(.12) �(4.57) (.18)

Yield curve slope �0.8523 �0.4039 �0.8515 �0.4073�(5.18) �(2.9) �(5.18) �(2.92)

Volatility �0.5972 �0.0604 �0.6371 �0.1124�(.4) �(.05) �(.43) �(.09)

REIT returns �0.0232 0.0406 �0.0231 0.0417�(.72) (.95) �(.71) (.97)

Reit volatility 0.2064 0.1718 0.1888 0.1544(1.08) (.88) (.99) (.79)

BBB–AAA spread 0.8961 0.1252 0.8398 0.1369(2.33) (.27) (2.17) (.29)

Other

Time since issue 0.2368 0.2489 0.2339 0.2255(3.75) (3.24) (3.69) (2.92)


Table 5 (continued)

Independent variable Original LTV & DSC Time-varying LTV & DSC

Default Prepayment Default Prepayment

Time squared �0.0102 �0.0039 �0.0100 �0.0040�(3.41) �(1.36) �(3.32) �(1.4)

Indicator of period prior to 9/11 �2.4723 �0.1045 �2.4395 �0.1665�(5.4) �(.34) �(5.35) �(.54)

Constant �4.1760 �3.7414 �7.3427 �1.8432�(1.38) �(1.27) �(2.51) �(.65)

Number of observations 133,950 133,950LR v2 975.47 990.67p value 0.0000 0.0000Pseudo R2 0.1224 0.1244

Dependent variable: Indicator of either default or prepayment. Coefficient above, z statistic below in parentheses.


are generally viewed as being riskier than fully amortizing loans because the borrower maynot be able to refinance the unpaid loan balance in the balloon year—especially if interestrates increase. Ciochetti et al. (2002) offer evidence supporting this view. However, the bal-loon risk is concentrated near maturity and very few of our loans mature during the obser-vation period. Consequently, we do not expect to see much effect of this variable in ourdata. Strong lockout and defeasance protection should play a major role in deterring pre-payment, but arguably have only a small impact on default.33

We include property type indicators (using multifamily as the base case) in the models.Historically, office buildings and hotels have been viewed as riskier than average becauseof greater sensitivity to the business cycle. In the time period covered by our study, hotelswere especially hard hit by a combination of reduced travel after the September 11, 2001terrorist attacks and the general slowdown in the economy.

The first model using original LTV and DSC is closest to Archer et al. (2002), and likethat model, the coefficient on original LTV is negative and marginally significant at the10% level. Also like Archer et al., original DSC enters the default model with a significantnegative coefficient. In the prepayment model, original LTV enters with a significant neg-ative coefficient. This effect is reasonable because a high loan amount relative to valuemakes it harder to refinance. Basically, the borrower must convince another lender, severalyears later, that there are enough offsetting positive risk factors to support a larger thanaverage loan. Since the favorable offsetting risk factors may have changed with time, highLTV loans are likely to be harder to refinance.

Other factors that enter the default model are the dummy variables for hotels and retailproperties, loan age, and the pre-September 11 indicator. Among the time-varying marketconditions, decreases in the long-term Treasury rate and increases in credit spreads areassociated with higher default risk (decreases in Treasury rates and increases in spreadsover the observation period are associated with weaker economic growth and vice versa).

33 There is some anecdotal evidence that stronger lockout/defeasance provisions contribute to increased so-called ‘‘strategic’’ defaults resulting from borrowers with above market rate loans trying to negotiate a reductionin their debt burden.


Our primary focus in this paper is on the underwriting variables. Our results are con-sistent with those reported by Archer et al. (2002). The anomalous sign on original LTVsupports the endogeneity argument and suggests that the coefficient on this variable suffersfrom simultaneous equation bias. We take little comfort in the fact that the coefficient onDSC has the expected sign because LTV and DSC are highly correlated.34 It seems that ifone argues that the coefficient on LTV0 is affected by omitted variable bias, the same logicapplies to DSC0. We suspect that the coefficient on DSC0 may be somewhat less affectedbecause lenders have less direct control over DSC0.

The second model is reported in columns three and four of Table 5. This model substi-tutes time-varying LTV and time-varying DSC for the original LTV and DSC. In theory,these time-varying measures should be more closely related to default and less subject tobias (because, over time, market changes in property value, and NOI will reduce the cor-relation with original LTV and DSC) and the goodness of fit measures for this model areconsistent with that prediction. The v2 test and pseudo R2 are both somewhat higher whenwe use time-varying LTV and DSC. Although there are differences, this model resemblesAmbrose and Sanders (2003) and Ciochetti et al. (2003) in its use of time-varying LTV in-stead of LTV at origination. Like the coefficient in the latter�s weighted model, our estimat-ed coefficient on LTVt is positive, but not significant, in the default model. The other effectsare similar to those discussed in Model 1: a significant negative effect of high DSC ratios inthe default model and a significant negative effect of time-varying LTV on prepayment.

Taken as a whole, these first two models show weak, inconsistent, and sometimescounter intuitive relationships between the LTV ratio and default—results consistent withArcher et al. (2002), Ambrose and Sanders (2003), and Ciochetti et al. (2003).

Table 6 reports our estimates of the third model incorporating the underwriting andpricing process explained earlier. This model excludes the original LTV ratio and DSC ra-tio and instead introduces the pricing margin as the sole underwriting measure of loan riskat origination. It also includes the time-varying estimated change in LTV ratio and DSCratio over the loan�s life. The remaining explanatory variables are unaltered from the pre-vious models.

Table 6 shows a very strong positive relationship between pricing margin and defaultrisk. The coefficient is economically and statistically significant with the expected positivesign. The coefficient on the change in LTV after origination is also statistically significantwith the expected positive sign in the default model and negative sign in the prepaymentmodel. The change in DSC is not significant in either model, a result possibly attributableto the higher level of noise in the NCREIF income indices, which makes it harder to esti-mate the time-varying DSC.

The coefficients on the other explanatory variables resemble those estimated in the pre-vious two specifications. Loans backed by hotels and retail properties are estimated to de-fault more frequently than multifamily loans during this time period. The interest rate onthe 10-year Treasury bond, the yield curve slope and the size of the BBB–AAA spread allhave effects with similar signs and magnitudes to the earlier specifications. One difference isthat loan size no longer has a significant effect on default risk in the current specification.In the prepayment model, the extent of the prepayment protection in the note is stillstrongly related to prepayment.

34 The correlation coefficient in our sample is �.53.

Table 6MLN model of termination using pricing margin, DLTV & DDSC

Independent variable Default Prepayment

Coefficient z statistic Coefficient z statistic


D in LTV 2.6337 2.28 �4.3634 �5.25D in DSC �0.1242 �0.49 �0.3831 �1.05Pricing margin 133.8318 9.17 10.5573 0.63


ln(size of loan) 0.0402 0.55 0.0046 0.95Cross collaterization indicator 0.1677 0.74 0.2932 0.21Balloon indicator �0.0944 �0.65 0.1977 0.33Lockout/defeasance 0.1556 0.95 �2.6791 �14.19


Hotel 1.3511 5.62 �0.0178 �0.04Industrial �0.3742 �1.48 �0.7984 �3.14Retail 0.3181 2.03 �0.5672 �3.13Office 0.0304 0.14 �0.3602 �1.71

Region indicators

West �0.0483 �0.28 �0.0807 �0.47South 0.1152 0.73 0.0805 0.48Midwest 0.0186 0.09 �0.0883 �0.40

Market conditions

10 year treas at issue 34.2169 1.67 �37.1175 �1.59Change in 10 year to t �4.3225 �5.36 �0.1499 �0.14Yield curve slope �0.8837 �5.27 �0.4114 �2.95Volatility �1.4420 �0.95 �0.1002 �0.08REIT returns �0.0078 �0.25 0.0382 0.89Reit volatility 0.1216 0.64 0.1645 0.84AAA–BBB spread 0.9375 2.44 0.1217 0.26

Other

Time since issue 0.2432 3.92 0.2067 2.66Time squared �0.0108 �3.78 �0.0033 �1.15Indicator of period prior to 9/11 �2.5699 �5.49 �0.1624 �0.52Constant �9.1883 �3.27 �5.5520 �2.04

Number of observations 133,950LR v2 1062.62p value 0.0000Pseudo R2 0.1334

Dependent variable: Indicator of either default or prepayment.


We test whether lenders have fully incorporated LTV ratio in their underwriting andpricing by adding a residual LTV variable to the model just described. As a first step,we model the observed LTV ratio at origination as a function of four groups of variables:loan risk measures, property type indicators, region indicators, and market conditions.The loan risk measures are: pricing margin, property cap rate, the level of subordinationrequired by the rating agency below the AAA CMBS tranche, the length of the lockoutperiod, and the length of the defeasance period. The market conditions included are the


10-year Treasury bond rate at origination, the yield curve slope, the BBB–AAA corporatebond spread, and the volatility of the Treasury rate and the credit spread. We estimate thismodel using OLS and then use the predicted LTV ratio for each loan in our sample to cal-culate the residual ðLTV0 � LbTV0Þ. (See Table A1 in the Appendix for the estimated mod-el.) Recalling our earlier discussion, a positive residual implies that there are favorableunmeasured risk factors associated with the loan application; a negative residual impliesthat there are unfavorable unmeasured risk factors associated with the loan application.35

Table 7 reports the results from adding the residual ðLTV0 � LbTV0Þ to the previousmodel reported in Table 6. The coefficient on the residual is positive and significant atthe 8.5% level in the default model, suggesting that lenders may not fully incorporateLTV0 effects into their underwriting process. When averaged over all property types, thereis some residual effect of LTV0. The coefficient on the residual is significantly negative in theprepayment model. Following our earlier argument, this relationship could arise becausewhen a loan applicant is given favorable treatment in terms of LTV0, DSC0 and pricing be-cause of a favorable assessment of other risk factors, the borrower subsequently is less likelyto prepay. This result arises because the more favorable loan terms the borrower receivesare harder to improve upon after origination, or because, on average, such favorable char-acteristics gradually revert toward the mean —also making the loan harder to refinance.The other coefficients in Table 7 are little changed from those reported in Table 6.

Table 8 reports the final model. This model interacts the residual LTV ratio with theproperty type to test whether lenders were equally effective in underwriting the varioustypes of loans. The set of coefficients on the residual interaction variables show that theunpriced residual effect of the initial LTV identified in Table 7 is largely attributable tomultifamily and hotel loans. Multifamily loans have always been viewed as one of the safercommercial mortgage categories and certain investors have a clear preference for thisproperty type.36 This preference carries over to the CMBS market where some investorsprefer deals backed by a significant fraction of multifamily loans. This preference is reflect-ed in the fact that, on average, 38% of all collateral backing conduit CMBS are multifam-ily loans. Some market participants have reported that issuers strive to meet certainminimum percentages of multifamily loans in a CMBS deal to broaden the universe ofinvestors willing to buy tranches from the deal. For example, investment grade tranchesfrom deals with more than 30% multifamily loans may be deemed to be eligible forpurchase by the two major Government Sponsored Enterprises (GSEs).37 In effect,

35 This interpretation of the sign of the residual rests upon our maintained hypothesis that the lender observesmany aspects of the borrower and property that are not included in our data and further that the lender makes itsunderwriting decision based on those observed characteristics. The residual in the LTV model reflects randomfluctuations in these unmeasured risk factors as well as pure white noise. We interpret a positive residual as anindication that, on average, the particular loan had lower than average risk associated with the variables omittedfrom our model but observed by the lender.36 The two mortgage Government Sponsored Enterprises (Freddie Mac and Fannie Mae) are restricted topurchasing residential mortgages only and so the only commercial mortgage they can buy are multifamily loans.In addition, the two companies are required to meet annual goals for purchases of mortgages related to low andmoderate income families and underserved areas. Multifamily loans are especially helpful in meeting those goals.37 Further evidence that many commercial mortgage investors view multifamily loans as safer investments can befound in newsletters such as Emerging Trends in Real Estate published by PriceWaterHouseCoopers and LendLease Real Estate Investments. During the observation period studied here, multifamily was frequently reportedas having the lowest risk level.

Table 7MLN model of termination using pricing margin, DLTV, DDSC & resdiual LTV




D in LTV 2.7171 2.36 �4.7481 �5.64D in DSC �0.1396 �0.55 �0.3348 �0.93Pricing margin 134.6956 9.21 14.0317 0.85Residual LTV 1.4345 1.72 �2.2610 �2.79


ln(size of loan) 0.0208 0.28 0.0535 0.51Cross collaterization indicator 0.1698 0.75 0.3012 0.20Balloon indicator �0.0953 �0.65 0.2769 0.17Lockout/defeasance 0.1651 1.01 �2.6789 �14.20


Hotel 1.3503 5.62 �0.0355 �0.07Industrial �0.3821 �1.51 �0.7944 �3.13Retail 0.3245 2.08 �0.5925 �3.26Office 0.0440 0.20 �0.3992 �1.88

Region indicators

West 0.0538 0.32 �0.0598 �0.35South 0.1136 0.72 0.0954 0.57Midwest 0.0086 0.04 �0.0761 �0.34

Market conditions


Other

Time since issue 0.2426 3.92 0.2111 2.71Time squared �0.0108 �3.77 �0.0036 �1.26Indicator of period prior to 9/11 �2.5611 �5.48 �0.1806 �0.58Constant �9.2360 �3.28 �5.7947 �2.13




multifamily loans have positive externalities for the overall deal and it appears that thoseexternalities influenced the pricing of multifamily loans during this period.

The coefficient on hotels is significant at the 7.5% level and signals unpriced LTV0 riskfor this loan category as well. Ex-post, this is not surprising. Hotels were the hardest hitproperty type after September 11, 2001, but there was no way that lenders in 1996–1998could have foreseen the problems. If lenders had perfect foresight, they would have scaled

Table 8MNL model of termination using pricing margin, DLTV, DDSC & resdiual LTV and Pre 9/11 interactions for residualLTV & property type




D in LTV 1.0210 0.89 �4.7617 �5.66D in DSC �0.2938 �1.05 �0.2909 �0.81

Residual LTV interactions

With hotel 3.4531 1.78 1.2632 0.30With office 2.6178 0.96 �1.7628 �0.75With retail �1.0731 �0.89 �2.4515 �1.34With industrial 1.6682 0.59 �3.9906 �1.65With multifamily 3.9910 2.11 �2.1870 �2.11Pricing margin 136.3298 14.79 14.3986 0.87


ln(size of loan) 0.0263 0.36 0.0570 0.49Cross collaterization indicator 0.1653 0.72 0.3162 0.18Balloon indicator �0.1065 �0.71 0.2650 0.20Lockout/defeasance 0.1731 1.06 �2.6789 0.00


Hotel 3.0103 7.79 0.0708 0.93Industrial 0.3532 0.70 �1.5688 0.01Retail 1.1521 3.31 �1.0265 0.00Office 0.8076 1.89 �0.3356 0.33

Region indicators

West 0.0853 0.50 �0.0486 �0.28South 0.1486 0.93 0.1010 0.60Midwest 0.0572 0.27 �0.0645 �0.29

Market conditions


Other

Time since issue 0.2020 3.22 �0.0037 2.72Time squared �0.0095 �3.32 0.0708 �1.27Pre 9/11 interactionsWith hotel �4.7453 �7.33 �0.4819 0.9655With office �2.4929 �4.24 �0.4187 0.4738With retail �2.4849 �4.97 0.2822 0.4458With industrial �2.4296 �3.63 0.6736 0.6910With multifamily �1.5563 �2.81 �0.3174 0.3251Constant �9.8874 �3.45 �5.7445 �2.11





back their loans on hotels, underwritten them more conservatively and charged a higherrisk premium.

In the same model, we also replaced the single dummy variable for pre September 11,2001 with a set of property type interactions with that dummy variable. This enables us toseparately measure the effect of September 11 on the different property types. The estimat-ed coefficients confirm that although all property types were adversely affected, hotels werethe most severely impacted by the aftermath of 9/11.

Interestingly, in this model specification, the estimated effect of the change in LTV ondefault is smaller than it is before we introduce the interactive terms. This no doubt reflectsthe fact that estimated LTVs rose most rapidly for hotels and the two interaction variableswith the hotel dummy have captured some of that effect. The other coefficients are essen-tially unchanged. The overall goodness of fit measures for the last specification show thatthis model explains more of the variability in termination rates than any of the otherspecifications.

6. Conclusion

According to option theory, the loan-to-value ratio and the debt service coverage ratiojointly determine commercial mortgage default. According to the economic model of theloan underwriting and pricing process, both of these ratios should be endogenous with thelender�s pricing margin for borrower risk. In this paper, we argue that the integration ofthese two frameworks provides a rationale for the apparently contradictory results foundin earlier empirical studies. The validity of this rationale hinges upon whether lenders ad-just underwriting ratios and pricing to efficiently manage risk.

This paper exploits a new large data set of commercial mortgages in order to testwhether lenders adjust loan-to-value (LTV) and debt service coverage (DSC) ratios andpricing margin price to manage default and prepayment risks. The data set is larger andprovides a more extensive range of variables than available to earlier studies.38 The richerdata allow us to integrate the implications of both option theory and the model of debtunderwriting into the empirical models of competing default and prepayment risks. Iflenders are fully effective in this process, there should be no unpriced contribution ofLTV to default risk. In fact, we find some unpriced contribution of LTV to default riskfor the model pooling property types. Further investigation reveals, however, that the mis-pricing arises from the hotel and residential sectors. The hotel result is consistent with theunforeseen implications of the terrorist attacks of 9/11. The residential result is consistentwith the preferences of many investors for multifamily loans and the restrictions on Gov-ernment Sponsored Enterprises that affect the mix of mortgages they can purchase.

Appendix A

See Table A1.

38 The data set is, however, restricted to commercial mortgages originated by conduit lenders and the results maydiffer from those that would be obtained by analyzing portfolio lenders.

Table A1OLS Model for loan-to-value ratio

Coefficient t statistic

Group risk factors

10-year treasury rate �1.4115 �5.43Yield curve slope 0.0036 0.74Volatility of 1-year treasury 0.0079 0.44AAA–BBB spread 0.0053 0.73Spread volatility �0.1220 �3.81Required subordination 0.2563 5.19

Individual loan risk factors

Pricing margin �2.1725 �11.2Length of lockout 0.0001 4.67Length of defeasance 0.0002 10.72Property cap rate 1.1542 22.11Originated in 1997 indicator 0.0201 5.16Originated in 1998 indicator 0.0206 4.34

Region indicators

West �0.0168 �8.33South 0.0060 2.97Midwest 0.0089 3.57

Property type indicators

Hotel �0.0720 �22.63Industrial �0.0420 �15.5Retail �0.0152 �8.02Office �0.0365 �14.78Constant 0.6426 21.88

Number of Observations 10,547Adjusted R2 0.1505F(19,10527) 99.31p value 0.0000

Dependent variable: Cutoff loan-to-value ratio. Table A1 presents the OLS estimated coefficients of a model forloan-to-value ratio at origination. It is based on Eq. (8) in the text. The residuals from this model are used in themodels reported in Tables 7 and 8.


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Commercial mortgage underwriting: How well do lenders manage the risks?