University of Southern California Dissertations and Theses

Essays on commercial real estate and commercial mortgages

(USC Thesis Other)

Essays on commercial real estate and commercial mortgages

PDF

Download

Open document

Flip pages

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content ESSAYS ON COMMERCIAL REAL ESTATE AND
COMMERCIAL MORTGAGES
Copyright 2003
by
Jun Chen
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PLANNING)
August 2003
Jun Chen
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
U M I Number: 3116677
Copyright 2003 by
Chen, Jun
All rights reserved.
INFORMATION TO USERS
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, colored or poor quality illustrations and
photographs, print bleed-through, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if unauthorized
copyright material had to be removed, a note will indicate the deletion.
®
UMI
UMI Microform 3116677
Copyright 2004 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, Ml 48106-1346
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNIVERSITY OF SOUTHERN C A L IFO R N IA
THE GRADUATE SCHOOL
UNIVERSITY PARK
LOS ANGELES, CALIFORNIA 90089-1695
This dissertation, written by
JUN CHEN
under the direction o fh \§ . dissertation committee,
and approved by all its members, has been
presented to and accepted by the Director o f
Graduate and Professional Programs, in partial
fulfillment o f requirements for the degree o f
DOCTOR OF PHILOSOPHY
•ector
XLSfe Date A u gu st 1 2 . 2003
Dissertation Committee
Chair
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Dedication
To my family that supported me all the way
and
To Prof. Rena Sivitanidou who left the world too early to see this dissertation
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
iii
Acknowledgements
I wish to thank my family and my friends for helping me pursue doctoral
study in the U.S.. Without them, my journey to the U.S. would not be possible, let
alone the completion of my dissertation. During my study at USC, I received the
most generous helps from almost everyone I met in the school. I am particularly
grateful to Rena Sivitanidou, whose dedication to work and devotion to students will
always be remembered, to Rick Peiser, who helped me tremendously both inside and
outside academia, to Martin Krieger, who is an incredible mentor, especially in the
early stages of my Ph.D. study, and to Peter Gordon, who kindly introduced me into
the academic field of urban economics. I wish to thank Susan Hudson-Wilson and
Ruijue Peng for their constructive input on the dissertation and gratefully
acknowledge Property & Portfolio Research, Inc. (PPR), which provided most of the
data sets and a home for a substantial part of the dissertation. I also thank Jarl
Kallberg for his comments and suggestions at the AREUEA Conference 2003.
Special thanks go to Stuart Gabriel and David Dale-Johnson for their advice
and encouragement. My greatest debt and gratitude is to Yongheng Deng, who is not
only the best advisor with distinguished scholarship but also a true friend to his
students.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table of Contents
Dedication ........... ii
Acknowledgements ............ iii
List of Tables ................................................................................... v
List of Figures ........... vii
Abstract.......................................................................................... viii
Chapter 1. Momentum and Forecastability in Office Rental Growth Rates ........... 1
Introduction ......... 1
Literature Review ......................................................................... 3
D ata.......................................................................................... 6
The M odel ................... 11
Testing for the Determinants of Equilibrium Rent and Structural Vacancy Rate 15
Testing for Momentum Effect and Market Efficiency ........ 20
Cross-validation and Forecast Application of the Models ...... 24
Conclusions ........................................ 30
Chapter 2. Default Risk and Loss Severity of Commercial Construction Loans 33
Introduction ...................... 33
Literature Review ............. 35
Model Setup .............. 38
Data and Empirical Estimation of the Parameters ............ 49
Numerical Results ................... 53
Conclusions ........... 6 8
Chapter 3. Workout Strategy and Conditional Default Probability of
Special-serviced CMBS Loans.................. 71
Introduction ........ 71
Default Process ........... 77
Data ...... 79
Empirical Analysis ........... 82
Conclusions ........... 106
Bibliography ........... .........109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V
List of Tables
Table 1.1: Regression Results (Full Model with All Variables)........................ 17
Table 1.2 Panel A: Model Results (Model 1 - A R 1)..................................... 22
Table 1.2 Panel B: Model Results (Model 2 - O LS)..................................... 23
Table 1.2 Panel C: Model Results (Model 3 - Best F it) .............. 24
Table 2.1: Regression Results on Vacancy Process Estimation ......................... 51
Table 2.2: Regression Results on Rent Growth Process ............ 51
Table 2.3: Regression Results on Cap Rate Process ........ 53
Table 2.4: Default Probabilities and Expected Losses by Simulation Scenarios 60
Panel A. Assumes construction loan LTV is 70% and loan term is 4 quarters ... 60
Panel B. Assumes construction loan LTV is 70% and loan term is 8 quarters ... 60
Panel C. Assumes construction loan LTV is 70% and loan term is 12 quarters .. 61
Table 2.5: Default Probabilities and Expected Losses by Simulation Scenarios 64
Panel A. Assumes construction loan LTV is 75% and loan term is 4 quarters ... 64
Panel B. Assumes construction loan LTV is 75% and loan term is 8 quarters ... 64
Panel C. Assumes construction loan LTV is 75% and loan term is 12 quarters .. 65
Table 2.6: Default Probabilities and Expected Losses by Simulation Scenarios 65
Panel A. Assumes construction loan LTV is 70% and loan term is 4 quarters ...6 5
Panel B. Assumes construction loan LTV is 70% and loan term is 8 quarters ... 6 6
Panel C. Assumes construction loan LTV is 70% and loan term is 12 quarters .. 6 6
Table 3.1: Sample Loan Statistics by Property Type ...................... 80
Table 3.2: Sample Loan Statistics by Workout Strategy ........ 81
Table 3.3: Correlation Matrix of the Variables Used in Multinomial Logit Analysis 87
Table 3.4: Multinomial Logit Analysis of Workout Strategy ............ 89
Table 3.5: Descriptive Statistics ......... 96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.6: Descriptive Statistics at the Date Loans either Went “Bad” or Were
Censored ...... 97
Table 3.7: Proportional Hazard Model Analysis Results ....... ....102
Panel A. Hazard Model 1 ...... ........102
Panel B. Hazard Model 2 .................................1 0 2
Table 3.8: Proportional Hazard Model Analysis Results ........ 104
Panel A. Hazard Model 3 ......... ............104
Panel B. Hazard Model 4 ............... 104
Table 3.9: Logit Model Analysis Results Using Event History Data .................105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vii
List of Figures
Figure 1.1: Rent-Vacancy Relationship (Prototype 1 )................................. 8
Figure 1.2: Rent-Vacancy Relationship (Prototype 2 ) ............... 9
Figure 1.3: Diagram of Theoretical Rent-Vacancy Relationship ........ 10
Figure 1.4: Model Fitting - Actual and Dynamically Predicted Rents ................. 26
Figure 1.5: Forecasting Rents - An Example of Boston Office ......................... 29
Figure 2.1: Flowchart of the Structured Dynamic M odel ........... 46
Figure 2.2: Office Market Vacancy Rates for Selected U.S. MS As .................... 50
Figure 2.3: Office Market Rent Indices for Selected MS As .............. 52
Figure 2.4: Implied Office Cap Rates from NCREIF NPI Data Set for Selected
MSAs ........ 52
Figure 2.5: Simulated Diffusion Process of Vacancy R ates.................. 57
Figure 2.6: Distribution of Capital Value at the End of the Fourth Quarter ........... 57
Figure 2.7: Standard Deviations of NOI and Value Over Time ......... 58
Figure 2.8: Default Probabilities by Loan Term ................................. 63
Figure 3.1: The Default Process ....... 78
Figure 3.2: Survival Functions by Property T ype ............ 95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abstract
viii
This dissertation consists of three related essays on the dynamics of
commercial real estate markets and the risk assessment of commercial mortgages.
Chapter 1 examines the momentum effect in rental growth rates in the office-
commercial markets. Using data from fourteen U.S. metropolitan office markets, the
study finds that momentum effect exists but the degree of rental growth persistence
varies significantly across markets. The study also finds that space market variables
are more important than capital market variables in determining the implicit
equilibrium rents. Furthermore, forecast simulations show that a parsimonious model
structure behaves better and produces more consistent and plausible rent forecasts
than would a more exhaustive structure.
Chapter 2 examines the default probabilities and loss severities of
commercial construction loans. The study proposes a more realistic structured
dynamic model of the commercial real estate market. The model consists of three
key stochastic processes that are serially correlated: vacancy process, rent process,
and cap rate process. NOI process and capital value process are then derived. The
simulation results show significant variation in default probabilities of construction
loans for different initial states of the commercial real estate market, suggesting that
the simplified assumption without taking into account the persistence in commercial
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ix
real estate markets may lead to inaccurate estimates of default probability, especially
when the initial market is not flat.
Chapter 3 examines a previously unexplored aspect in the whole default
process of commercial mortgages, that is the stage between the initial delinquency
and eventual default. The study distinguishes the servicers’ behavior from the
borrowers’ behavior. A multinomial logit model is applied to analyze the servicers’
behavior and a proportional hazard model is applied to analyze the borrower’s
behavior. The empirical results show that cash flow condition is the most significant
factor in the servicers’ decision making process and that borrowers make default
decisions based upon both the equity position in the mortgages and the cash flow
condition in the space market. The study also finds that key real estate space market
variables, such as market-level vacancy rates, provide useful information in
explaining commercial mortgage defaults.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
Chapter 1
Momentum and Forecastability In Office Rental Growth Rates
L Introduction
Commercial real estate rents are the price space users pay for a certain type
of space for a certain period as specified in a lease agreement. In any given time,
market-clearing rent is determined in the space market according to the relationship
between the demand and the supply of space. Understanding and modeling the rental
adjustment process is not only of interest to academics, it is of particular use to
practitioners in the commercial real estate market since rental growth forecasts are
usually the key input in the business decision-making process of the market
participants, either explicitly or implicitly. In this chapter, I use a time-series cross-
sectional data set of fourteen U.S. metropolitan office markets to examine a key
aspect of the office rental adjustment process, that is the momentum effect, i.e. the
persistence of rental growth rates that may exist in the office space market. 1
While the existing literature generally acknowledges the persistence of the
level of office rents, current rent models fail to address whether the persistence (or
the momentum effect) also exists in the growth rates of market-clearing office rents.
This is rather surprising since the persistence of growth rates in price is well
1 To clarify, momentum effect in this paper is referred to the statistically significant positive
correlation between the rental growth rates of two adjoining periods.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
documented in the single-family housing market (e.g., Case and Shiller 1989,1990,
and Abraham and Hendershott 1996), and in the markets for other asset classes (e.g.,
Jegadeesh and Titman 1993,2002, and Grundy and Martin 2001). Because the
existence of the persistence of rental growth rates would indicate an inefficient
market, the study also serves as a direct test of the efficiency of the office space
market with implications for its forecastability. The empirical investigation of
fourteen U.S. metropolitan office markets reveals varying degrees of persistence in
rental movement. In a number of markets, the excess rental growth rates are quite
forecastable, at least in the short term.
This study also makes two additional contributions to the literature. One is
related to the continued debate on the determinants of equilibrium rents and
equilibrium vacancy rates. It is found that space market variables dominate capital
market variables in determining equilibrium office rents. Another contribution in on
the robustness of the alternative rental adjustment models in their application to
forecasting. It is well known in econometrics that the model that best fits the
historical data is not necessarily the most stable in forecasting. The forecasting
simulations in the study show that a parsimonious model structure behaves better and
produces more consistent and plausible rent forecasts than would a more exhaustive
structure.
The remainder of the chapter is organized as follows. Section II starts with a
literature review. Section III describes the data, and Section IV discusses the
modeling approach and empirical regression specifications. Section V presents the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tests for the determinants of equilibrium rents and structural vacancy rates, and
Section VI provides the test on the momentum effect and the persistence of office
rental growth rates. Section VII presents the dynamic cross-validation results and
also shows an example of the application in forecasting. Section VIII concludes.
IL Literature Review
There is now a substantial body of literature on the commercial real estate
rental adjustment process. Recent studies appear to have agreed upon the implicit
equilibrium-based mean-reverting process for commercial real estate rents despite
the differences in defining equilibrium. Early models relate the change in
commercial real estate rents to the gap between the actual vacancy rate and the
implicit equilibrium vacancy rate. The basic vacancy-rental adjustment model can be
summarized as:
= l(v * - v w )+A T (1.1)
where v* is the natural vacancy rate2 , vt.i is the lagged actual vacancy rate, X is the
adjustment factor, X is a vector of other explanatory variables, and j5 represents the
coefficients associated with the vector X 3 Blank and Winnick (1953) provide an
early and exquisite explanation of this basic relationship. Rosen and Smith (1983)
2 Natural vacancy rate is also called equilibrium vacancy rate or structural vacancy rate, and is used
interchangeably in this paper.
3 In empirical regression models, the explicit definition of natural vacancy rate is not necessary, since
the effect of natural vacancy rate would be absorbed in the estimate of regression constant in the
absence of explicit natural vacancy rate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4
initiate formal research on natural vacancy rates, and Wheaton (1987) suggests a
persistent theoretical relationship between the real rent series and the vacancy series,
if appropriately lagged.4
Because the basic model failed to include the role of equilibrium rent, which
is the level actual rents should end up with at a M l equilibrium, later models do
incorporate the concept of equilibrium rent. There are two approaches to incorporate
equilibrium rent in the rental adjustment model. One approach emphasizes how
equilibrium rent is determined in the context of the space market. This approach is
best represented by Wheaton and Torto (1994). Within the space market context,
they suggest that office rents should slowly move toward the equilibrium rent level:
(1-2)
where R* is the implicit equilibrium rent andR* + t 2Fm (At.j is a space
absorption measure such as tenant turnover rate and Vt.j is the lagged actual vacancy
rate). The major contribution of their model is to introduce the implicit equilibrium
rent that is both time-varying and conditional upon major space market drivers. The
application of this approach is exemplified in Wheaton, Torto and Evans (1997) and
Wheaton and Rossoff (1998).5
4 For early empirical evidence to the basic model, see Smith (1969, 1974) and de Leeuw and Ekanem
(1971). For the application of the basic model to the office sector, see Rosen (1984), Hekman (1985)
and Shilling, Sirmans and Corgel (1987).
5 Hendershott, MacGregor and Tse (2002) and Hendershott, MacGregor and White (2002) are two
recent studies that employ modem econometric techniques. Both develop a reduced-form equation
based on the supply and demand for occupied space within the framework ofError Correction Model
(ECM). In their model, long-run model also is a function of purely space market variables.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
Another approach suggests that equilibrium rents are determined mainly in
the context of capital markets through the user-cost-of-capital relationship as the link
between the space market and the capital market. This approach is represented by
Hendershott (1996a, 2000) and Hendershott, Lizieri and Matysiak (1999). They
specify the growth rate of rent as a function of deviations from both the structural
vacancy rate and the equilibrium rent. The fundamental assumption underlying these
models is that, in full equilibrium, the level of the net rental rate must equal the user
cost of capital such that the real effective gross rental rate, adjusted for vacancies,
will continuously equal the real financing rate plus the economic depreciation (and
maintenance) rate and the operating expense ratio. The rental adjustment process is
then generalized as:
=My - v,)+ m : - ) (i s)
where the percentage change in real effective rents is related to gaps between both
the natural and actual vacancy rates and equilibrium and actual real rental rates. The
inclusion of the rent gap guarantees that actual rents will eventually return to their
equilibrium level.
In summary, the typical existing rental adjustment models have a mean-
reverting property, the “mean” could be equilibrium rent, or equilibrium vacancy, or
both. The mean-reverting process is sluggish, with the process likely to vary across
markets6. Both equilibrium vacancy rate and equilibrium real rent could vary cross-
6 See, for example, Pollakowski, Watchter and Lynford (1992) for the varying vacancy rate effect by
market size on office rental adjustment.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
sectionally and intertemporally7. In a general equilibrium framework, equilibrium
rents should be determined by factors from both the space and capital markets, but
the dominance of each in the real world is less clear.
However, despite the general consensus that the adjustment of rent levels is
slow, the existing literature on the commercial real estate rent adjustment process
does not explicitly consider the momentum effect, i.e. the persistence of rental
growth rates. In other words, holding everything else equal, it is still unclear whether
increases in rents over one period would be followed by increases in the subsequent
period. Suppose that the rental growth rate is nonzero in period 1, and vacancy rate
and rent both reach implicit equilibrium levels at the end of period 1, existing models
would predict a zero rental growth rate in period 2 - whether this is empirically true
is untested, and this is the focus of this study.
IIL Data
The MSA-level data of the fourteen U.S. metropolitan office markets are
collected from various sources. The data of office rents on new leases are provided
by National Real Estate Index (NREI). NREI collects commercial real estate data on
historical rents, cap rates, and prices at the property level and publish the data series
at the MSA level. The quarterly office rent data series go back as far as 1985. The
time-series data of office market vacancy rates at the MSA level are provided by
7 For studies on cross-sectional and intertemporal variations of natural vacancy rates, see Wheaton
and Torto (1988), Gabriel andNothaft (1988, 2001), Voith and Crone (1988) and Sivitanides (1997).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7
Property & Portfolio Research, Inc. (PPR)8. The time-series of office employment
for each MSA is estimated by PPR from the aggregation of industry-by-industry
office space using patterns over time, and the interest rate on the ten-year Treasury
Note is collected from government sources by Economy.com (formerly Regional
Financial Associates) and supplied by PPR. The rental data series are deflated using
MSA-level consumer price indices (also from Economy.com) to derive real rent
series. The study does not estimate the real interest rate due to the difficulty to
accurately extract the expected inflation component from the nominal interest rate.
Because office leases are usually long term (normally run from five to ten years),
using the nominal interest rate (ten-year rate) is probably appropriate.
Initial examination of the rent and vacancy data shows a pattern similar to
that first suggested by Blank and Winnick (1953). Figure 1.1 and Figure 1.2 provide
two typical examples of the rent-vacancy relationship, other MSAs exhibit similar
patterns. The graphs show that, from the mid-1980s (the cyclical peak of real estate
market) to the late 1980s, despite the very high vacancy rates, the rent level did not
experience significant decline. This inertia lasted for a few years until the office
market finally collapsed after around 1990. Rents then hovered around the lowest
level despite the continued gap between the actual vacancy rate and equilibrium
vacancy rate. After the mid-1990s when the real estate market started to recover,
rents did not exhibit a significant increase until the vacancy rates were well below
8 Property & Portfolio Research, Inc. (PPR) is a Boston-based commercial real estate research and
consulting firm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
the equilibrium level (one can guess the equilibrium vacancy rate as a point around
the average historical vacancy rate).
Figure 1.1: Rent-Vacancy Relationship (Prototype 1)
Prototype 1 shows a stronger relationship between vacancy rates and real rents than nominal rents.
Real Rent
Rent vs V acancy: Boston
$28
$26
$24
$22
$20
$18
$16
$14
$12
02
8 10 12 14 16 18 20
Vacancy Rate
Nomina, Rent Rent vs Vacancy: Boston
$50
$45 -
$40 -
$35 -
$30 -
$25 -
$20
6 4 8 10 12 14 16 18 20
Vacancy Rate
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9
Figure 1.2: Rent-Vacancy Relationship (Prototype 2)
Prototype 2 shows a stronger relationship between vacancy rates and nominal rents than real rents.
Rent vs Vacancy: Atlanta
Real Rent
$20
$19 -
$17 -
$16 -
$15 -
$14 -
$12 -
$11
Vacancy Rate
Nominal Rent R ®n t vs Vacancy: Atlanta
$25
$24 -
$21
$20 -
$ 16
9 11 13 15 17 19 21
Vacancy Rate
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
In essence, this rent-vacancy relationship can be described by Figure 1.3.
There are two periods of inertia in rents, one at the period when the market just starts
to recover and the other at the period when the market just starts to deteriorate. There
also appears to be tremendous run-up in office rents as the space market approaches
a cyclical peak (when vacancy reaches cyclical low) and an equally disastrous drop
in office rents as the space market approaches a cyclical low once the inertia periods
have passed. This relationship not only seems to support the rental adjustment
models that incorporate equilibrium rents, but the persistence of the rent level also
seems to indicate the possible momentum effect in rental growth rates.
Figure 1.3: Diagram of Theoretical Rent-Vacancy Relationship
A
Rent
Equilibrium
rent
Market Peak
A~ ~ > _ —
“Inertia” period
\M arket deteriorating
Improving market" ' ‘Inertia” period >
~------- - < --------------- - V
Cyclical low
Equilibrium vacancy Vacancy
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11
In the following analysis, I farther break down the total sample into two
parts, using semi-annual data. Sample Set 1 contains all the data points in the first
and third quarters of each year, and Sample Set 2 contains the data points in the
second and fourth quarters of each year. The model is developed based on Sample
Set 1, and dynamic cross-validation is performed using Sample Set 2.
IV. The Model
The model used in this study extends the general form of (1.3) and takes the
following specification:
(R, =Vv,’ _ , - V , ) + -R,_,) + p(AR,JR_2) + 1 X (1.4)
where R is the real rent with subscripts to denote time periods, v* is the structural
vacancy rate, R* is the implicit equilibrium rent, X and /? are the adjustment speeds, p
is the autocorrelation coefficient, X is a vector of other exogenous factors affecting
rental growth rates, and t represents the coefficients associated with X. In empirical
investigation, both v* and R* are not observable, and we have to rely on other
observable proxies to capture the potential intertemporal variation of both9. Based on
the available data, the structural vacancy equation can be specified as:
A v* = f{Av„AEmpt / Empt_ x) (1.5)
where Ernp is the total office employment in a metropolitan area, and Avt = v, - v,.;. If
9 If the structural vacancy rate and equilibrium rent are not time-varying, then both would be absorbed
in the constant term of an empirical regression, and we don’t need to specify them.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
Avt is positive, then landlords and real estate developers would anticipate that supply
growth will outweigh demand growth and so would be less likely to hold vacant
stock, hence positive Avt would have the effect of reducing the structural vacancy
rate, and vice versa. If AEmpt /Empt.i is positive, then landlords and developers
would anticipate a faster space absorption rate and would be more likely to hold
vacant stock as they would be expecting higher rents in the future, hence positive
AEmp/Empt-i would have the effect of increasing structural vacancy rates, and vice
versa1 0 .
The next step is to specify the implicit equilibrium rent equation. While the
user-cost-of-capital relationship seems more appealing in a general equilibrium
framework that consists of both the space and capital markets1 1 , the major difficulty
is to specify a real replacement cost at each point in time in order to calculate
equilibrium rents. Since the time-series data on real replacement cost is not available,
a constant replacement cost is implicitly assumed in all the previous studies using the
user-cost-of-capital approach. However, because the real replacement cost also
includes the cost of land, which is unlikely to be constant through time, the
assumption appears to be a very strong one, as acknowledged by Hendershott,
MacGregor and Tse (2002). However, they also argue that changes in real interest
1 0 Note these expectations are consistent with option theory.
1 1 For more extensive discussions of how equilibrium rents are determined in the general equilibrium
between space market and capital market, refer to Fisher (1992) and Fisher, Hudson-Wilson and
Wurtzebach (1993). It should be noted that Hendershott and Ling (1984) provides the first brief
discussion of this ftmdamental relationship although the later studies by Fisher (1992) and Fisher,
Hudson-Wilson and Wurtzebach (1993) are independently developed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
rates are not capitalized into land prices therefore the assumption of a constant real
replacement cost may still be valid. They present a weak test supporting their
argument using Sydney and London office market data. The empirical evidence from
other studies suggests that this simple treatment may not hold in reality. For
example, Sivitanidou (2002) includes variables from both the space and capital
markets in the analysis of office rental processes. In addition to confirming a
sluggish rental adjustment process and persistent disequilibria across markets, the
empirical results of her study also identify the role of office employment factors
(such as size, diversity, spatial organization, growth rates, and volatility),
construction costs, interest rates, amenities, and zoning in shaping interarea
differentials in the equilibrium component of office rents. In a related study,
Sivitanidou and Sivitanides (1999) also finds a pivotal role for specific local office-
market traits and a lesser role for national capital-market effects in determining
office capitalization-rate variations, implying equilibrium rents may be influenced
more by space market variables than capital market variables.
Thus, based on these studies, the implicit equilibrium rent equation is
specified as:
R* = f(E m p,rt,Avt,AEmpt IEmpt_ x) (1.6)
where rt is the ten-year Treasury Note rate, a proxy for the capital market effect. If
the user-cost-of-capital relationship suggested by Hendershott (1995,1996a, 2000)
holds, then R* should have a perfect correlation with rt if the real replacement cost is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
approximately constant. Following classic theory from urban economics, I also
include the term Emp to test for the effect of metropolitan size on the equilibrium
rent. As the cities grow large with more employment, the benefits from
agglomeration economies would increase space productivity. Meanwhile the
distance to work/amenities would also increase on average. Because these two
effects tend to increase land value, we expect to find a positive relationship between
R* and Emp. Av should have negative effect on R* because a negative Av indicates
reduced available supply therefore pushing up the equilibrium rents in the space
market, and vice versa. AEmp/Empt-! should have positive effect oni?* since more
office employment would shift the demand curve outward, which would push up the
equilibrium rents as long as the supply curve is not perfectly elastic. To keep the
model as parsimonious as possible, I do not include other variables as suggested by
Sivitanidou (2002).
Substituting (1.5) and (1.6) into (1.4), we obtain the following empirical
equation:
ARt + x / Rt = a lvt + a 2Rt + a 3 rt + a 4 Emp + a 5 AEmptl Empt_ x + a 6 Av, + p(ARt / )
(1.7)
where «; and 02 are expected to be negative, Oj, a4 and 0 5 are expected to be
positive, and O fe is expected to be negative, p should be positive and significant if the
momentum effect exists in the office space market. All the explanatory variables
enter the right side of equation in lagged form. Note this test is consistent with the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15
methodology used by Case and Shiller (1989,1990) and Abraham and Hendershott
(1996) in testing the efficiency of the single-family housing market. The empirical
analysis can therefore be considered as a strong-form test on the efficiency of the
office space market.
V. Testing for the Determinants of Equilibrium Rent
and Structural Vacancy Rate
The first test is on the determinants of equilibrium rents and structural
vacancy rates as hypothesized in (1.5) and (1.6). The test not only provides
additional evidence to compare with previous studies but also helps to refine the
model specifications to best test for the momentum effect and market efficiency in
the next stage of analysis. To do this, we estimate (1.7) with all the variables
included. Table 1.1 shows the results of this test.
The cross-section time-series nature of the sample data enable us to compare
the impact and significance of the variables tested and to draw conclusions based on
the evidences across metropolitan office markets. This has significantly raised the
confidence level on the tests performed and appears to be a big improvement over
some of the previous studies that rely on the data from only a few cities. For
instance, the long-term interest rate shows up as statistically significant only in the
equation for the Philadelphia office market (one out of fourteen equations). This
makes one suspect that the significant effect of the long term interest rate for
Philadelphia office market is more likely to be an artifact of imperfect data. It is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
16
therefore concluded that the long-term interest rate probably does not have a
significant impact on rental growth rates (or, at least not consistently). From (1.6),
this finding suggests that the implicit equilibrium rents in the U.S. office markets are
either not significantly correlated with long-term risk-free interest rates, or that the
real replacement costs are not constant, contrary to the tentative conclusions from
Hendershott, MacGregor and Tse (2002) that use data from the London and Sydney
office markets. Because the actual cap rates on commercial real estate also do not
seem to move quite perfectly with the long-term risk-free interest rate1 2 , this finding
is not surprising. It appears that equilibrium rents are largely determined by space
market variables rather than capital market variables. In other words, rent on new
leases is indeed determined by the intersection of the demand and supply in the space
market. The impact of the capital market might be too indirect (or too long term) to
be felt in the office rent adjustment process. Because the data on real replacement
cost is not available, we can not rule out the possibility that capital markets do have a
significant impact on office rents, but the impact is offset by the time-varying real
replacement cost1 3 .
1 2 See the second chapter of this dissertation for actual “implied” cap rate series estimated from
NCREIF Property Index.
1 3 For this possibility to be true, real replacement cost must have a negative correlation with real
interest rate. The examination from Means Construction Cost Index does not support this negative
correlation. Of course, since Means Construction Cost Index does not accounts for the cost of land,
we are not able to draw definitive conclusions. More data is needed to settle this issue.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17
Table 1.1: Regression Results3 (Full Model with All Variables)
Vacancy Vacancy
Change Rate
Lag 1
Real
Rent
Lag 1
Office
Employ-
Mentb
Office
Employ
ment
Growth
Long
Term
Rate
RhO R2 Adj.
R
Durbin
Watson
Atlanta -0.171 -0.778 -0.0096 -0.178 0.468 0.834 -0.08 58.2% 45.9% 2.17
(0.35) (3.23) (2-64) (1.18) 1.38 1.27 (0.40)
Boston -1.818 0.040 -0.0365 2.798 -0.349 -0.137 0.92 75.7% 68.6% 2.04
(2.21) 0.07 (4.68) 3.72 (0.45) (0.16) 19.18
Chicago -1.860 -2.633 -0.0183 -0.485 -0.013 1.469 0.19 58.6% 46.5% 1.99
(2.05) (1.85) (2.08) (1.07) (0.02) 1.43 0.73
Dallas -0.901 -0.779 -0.0029 -0.138 0.442 0.832 0.07 70.8% 62.3% 2.02
(1.22) (2.72) (0.96) (1.10) 1.03 1.33 0.29
Denver -1.226 -0.743 0.0016 -0.635 0.188 0.619 -0.29 71.4% 63.1% 2.05
(2.04) (3.23) 0.41 (1.93) 0.33 1.38 (1.28)
Houston -0.110 -1.393 -0.0640 1.490 0.002 0.260 0.90 74.7% 67.3% 2.21
(0.18) (2.41) (3.94) 1.87 0.01 0.46 24.67
Los Angeles -1.195 -1.513 -0.0057 -0.682 0.002 0.746 0.28 78.0% 71.5% 1.96
(1.88) (4.83) (2.64) (3.03) 0.01 1.35 1.31
Minneapolis -0.315 -1.132 -0.0103 -0.554 0.207 0.475 0.53 75.2% 68.0% 1.96
(0.52) (3.29) (2.25) (1.34) 0.38 0.61 2.25
New York -2.441 -1.177 -0.0229 1.049 -0.713 0.615 0.27 73.6% 65.8% 1.62
(1.92) (1.51) (3.98) 2.36 (0.96) 1.03 0.78
Philadelphia 1.210 -0.138 -0.0142 0.262 1.490 0.935 0.02 60.7% 49.2% 1.98
1.68 (0.31) (3.51) 0.99 3.51 2.05 0.07
San Diego ■ -0.768 -0.768 -0.0031 -0.628 1.197 0.08 0.11 68.0% 58.7% 2.01
(1.23) (2.18) (1.01) (1-07) 2.14 0.10 0.54
San -3.721 -0.351 -0.0117 3.696 1.689 2.27 0.30 82.1% 76.9% 2.11
Francisco (2.90) (0.67) (3.23) 3.23 2.00 1.61 1.23
Seattle -0.670 -0.544 -0.0490 5.885 -0.791 0.44 0.96 83.0% 78.1% 1.83
(1.93) (1.48) (5-53) 4.82 (1.80) 0.99 73.75
Washington, -0.743 -1.761 -0.0013 -0.520 -0.321 -0.76 0.19 67.7% 58.3% 1.71
DC (1.03) (4.55) (0.43) (3.26) (0.42) (1.14) 0.70
a Regression constants are not reported here, and t-statistics are reported underneath parameter
estimates.
b Office employment is measured in millions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
The tests also fail to find an effect from total office employment size on
equilibrium rents for most MSAs in the sample. The coefficient signs of the office
employment variables are actually negative in eight MSAs, possibly reflecting the
fact that the overall office rents have not fully recovered during the sample period
1985 to 2002. Another possible reason is that the ongoing suburbanization trend has
offset the effect of growing workforce and larger city - the city is larger, but the
employment is distributed across an ever broadened area. The negative coefficients
of office employment might actually suggest that more office jobs are possibly
decentralized into suburban areas in most U.S. metropolitan areas, with the
consequence of driving down the average office rents during the sample period1 4 .
However, there are four MSAs that report a positive and significant effect of the size
of office employment on equilibrium rents. These four MSAs are Boston, New York,
San Francisco, and Seattle. Interestingly, all these MSAs have traditional, and
vibrant 24/7 type urban cores, with office jobs still highly concentrated in the
downtown area. Therefore, the size of office employment may only matter in these
metropolitan areas with dominant downtown office employment and have little
impact on those more suburbanized metropolitan areas.
The results also do not support a significant effect for office employment
growth rates, which is used as a proxy for the space absorption effect and expected
1 4 As the percentages of suburban office workers grow, the average office rents would go down even
if rents in both CBD and suburban areas are held constant. This is because suburban rents in most
MSAs are lower than CBD rents. The market-average rent will be lower if the weight of suburban
office increases.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
19
growth effect. Only three MSAs exhibit significant positive effects from this proxy,
with mixed signs for the other MSAs. It is likely that the effects of space absorption
and expected future growth rates are better captured by the change in vacancy rates,
which have the correct sign in all of the equations.
The tests for the remaining three variables - R, v, and Av - appear much better
and behave mostly as we expected. It is obvious from the equations that these three
variables have negative relationships with rental growth rates, despite the occasional
insignificant and positive signs that show up in a few of the equations. The
significance of both v and R appear to support the general form of (1.3), while the
significance of Av appears to support the hypotheses that either structural vacancy
rates or equilibrium rents, or both, do vary through time, and that they move with the
condition of the space market. It also seems that these three space market variables
alone may be sufficient to explain the office rental adjustment process. The preferred
rental adjustment model is therefore defined as:
ARl+ l / Rt = a x vt + a 2 Rt + a 3 Av, + p(Ai?r / Rt_ x ) (1.8)
Note that all the explanatory variables enter the equation in lagged form. This
is required because current vacancy and current market-clearing rent are determined
simultaneously in the space market so that they can not enter both sides of the
equation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
VI. Testing for Momentum Effect and Market Efficiency
The rental adjustment process is essentially the price adjustment process for
space use in the space market. If the space market is efficient, then the rental growth
rate in one period cannot be used to forecast the rental growth rate in the subsequent
period. On the other hand, if the space market is not efficient, then lagged
independent variables can be used to forecast rental growth in subsequent periods
due to informational inefficiency. The existence of a momentum effect in rental
growth rates would clearly indicate market inefficiency because increases in rents in
one period would likely to be followed by increases in rents in the subsequent period,
all else equal. Market players could then take advantage of the momentum effect by
picking the winners and achieving above-average returns over the next period. For
example, if a momentum effect exists and is large enough in commercial real estate
markets, then market participants could simply pursue a strategy of investing in
“winning” MSAs that have demonstrated strong rental growth rates in the previous
period. If the market were to start to deteriorate, investors could cut their potential
losses by exiting the declining market1 5 .
Since the variables of the long-term interest rate, the size of office
employment, and the growth rate of office employment do not show up as
consistently significant in the previous test, the specification (1.8) is used in the
1 3 Because commercial real estate market is characterized as illiquid thin market with substantial
transaction cost, the informational inefficiency may not lead to abnormal profitability. Future research
is needed to examine whether market participants can profit from the persistence in the real estate
market in a realistic setting.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21
following analysis. However, for the four MSAs that do show a significant positive
effect for the size of office employment on equilibrium rents, the size of office
employment is retained in the further test.
Table 1.2 Panel A-C show the results from the best fitting models and
suggests that momentum effect exists although the effect varies by market, and that
real office rental growth rates are forecastable in quite a few metropolitan areas. An
examination of the coefficients on lagged rental growth rates (or the RhO term for
the AR1 specifications) suggest that the average magnitude of rental growth
persistence is probably in the range of 0.2 to 0.6 for the semi-annual data series1 6 .
This magnitude of persistence is less than that reported by Case and Shiller (1989)
and Abraham and Hendershott (1996) for the single family housing market. And this
is certainly possible because the office space market is a direct market between space
owners and space users and should be more responsive to changes in market
conditions. The results also show that some office markets actually have surprisingly
strong persistence in rental growth. For example, the Boston office market has a
RhO=0.91 and San Francisco office market has a RhO=0.90, this means that
approximately 80% of the excess (above the equilibrium level) rental growth rate
from the previous year is carried over to the next year. This is a very large
magnitude. There is apparently market inefficiency in these markets, and this
inefficiency appears to have contributed to the wide swings of office rents in San
1 6 Readers can verify this by plotting the coefficients on lagged rental growth rates or the RhO terms
in a bar chart.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Francisco and Boston, as observed by market participants1 7 . It seems that rental
growth momentum carries over in these markets over a long period until there is a
meaningful change in space market conditions.
Table 1.2 Panel A: Model Results (Model 1 - AR1)
Vacancy Rate
Lag 1
Real Rent
Lag 1
Vacancy
Change
RhO R2 Adjusted
R2
Durbin-
Watson
Atlanta -1.626 -0.0601 -0.168 0.91 44.2% 36.0% 2.19
-(3.44) -(4.92) -(0.32) (23.76)
Boston -0.722 -0.0034 -1.818 0.41 60.2% 54.3% 1.80
-(2.34) -(0.89) -(2.82) (1.83)
Chicago -0.699 -0.0038 -2.703 0.18 49.2% 41.7% 2.10
-(2.41) -(1.58) -(3.34) (0.92)
Dallas -0.501 0.0002 -2.068 0.17 65.8% 60.7% 2.12
-(3.90) (0.09) -(4.38) (0.82)
Denver -0.278 -0.0019 -1.898 -0.10 61.9% 56.3% 1.99
-(4.62) -(0.50) -(5.60) -(0.47)
Houston -0.455 -0.0039 -1.559 0.25 69.6% 65.1% 2.09
-(4.96) -(1.05) -(3.25) (1.21)
Los Angeles -0.672 -0.0041 -1.409 0.58 70.4% 66.0% 2.15
-(2.37) -(1.91) -(2.43) (3.17)
Minneapolis -1.001 -0.0201 -0.215 0.84 73.8% 69.9% 2.11
-(2.65) -(2.66) -(0.42) (7.25)
New York -2.073 -0.0130 -1.886 0.32 66.1% 61.1% 1.62
-(3.90) -(3.29) -(1.99) (1.29)
Philadelphia -0.557 -0.0084 -0.190 0.25 34.9% 25.2% 1.97
-(2.38) -(1.85) -(0.26) (0.94)
San Diego -0.486 0.0003 -1.591 0.19 56.5% 50.0% 2.03
-(3.94) (0.13) -(2.80) (0-91)
San Francisco -1.240 0.0018 -4.452 -0.04 61.9% 56.2% 1.97
-(3.73) (0.64) -(4.63) -(0.15)
Seattle -0.756 -0.0067 -1.201 0.58 68.2% 63.4% 1.75
-(3.02) -(1.48) -(2.70) (2.61)
Washington, DC -0.900 -0.0047 -0.757 0.63 65.3% 60.2% 2.03
-(2.31) -(1.22) -(1.17) (3.24)
1 7 The rental growth persistence could also be caused by the inability of the market participants to
accurately estimate the supply change in these markets.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23
Table 1.2 Panel B: Model Results (Model 2 - OLS)
Vacancy
Rate Lag 1
Real Rent
Lag 1
Vacancy
Change
Real Rent
Growth Lag 1
R2 Adjusted Durbin-
R2 Watson
Atlanta -0.441 -0.0022 -1.091 0.031 41.6% 32.7% 2.20
-(2.50) -(0.72) -(2.52) (0.16)
Boston -0.519 -0.0025 -1.361 0.306 57.8% 51.3% 1.75
-(2.13) -(0.90) -(2.12) (1.67)
Chicago -0.494 -0.0030 -2.429 0.206 50.1% 42.4% 2.15
-(1.69) -(1.46) -(2.81) (1.14)
Dallas -0.396 0.0004 -1.881 0.189 66.1% 60.9% 2.19
-(2.37) (0.18) -(3.59) (1.03)
Denver -0.253 -0.0031 -1.660 0.086 61.8% 56.0% 2.26
-(2.65) -(0.73) -(3.24) (0.40)
Houston -0.310 -0.0025 -1.437 0.270 70.6% 66.1% 2.16
-(2.70) -(0.87) -(2.86) (1.46)
Los Angeles -0.215 -0.0015 -1.441 0.510 72.3% 68.1% 2.24
-(1.20) -(1.60) -(2.69) (3.37)
Minneapolis -0.135 -0.0046 -0.357 0.694 72.6% 68.4% 2.17
-(1.17) -(1.78) -(0.67) (4.92)
New York -1.519 -0.0100 -1.474 0.255 66.3% 61.1% 1.64
-(3.22) -(2.99) -(1.53) (1.59)
Philadelphia -0.415 -0.0067 -0.139 0.244 35.1% 25.1% 2.00
-(1.84) -(1.79) -(0.17) (1.10)
San Diego -0.344 0.0001 -1.458 0.259 57.8% 51.4% 2.20
-(2.16) (0.04) -(2.41) (1.26)
San Francisco -1.458 0.0036 -5.274 -0.191 62.8% 57.0% 1.94
-(3.37) (0.93) -(3.59) -(0.81)
Seattle -0.330 -0.0023 -1.136 0.475 67.6% 62.6% 1.71
-(2.09) -(0.88) -(2.29) (2.73)
Washington, DC -0.366 -0.0028 -0.492 0.623 66.8% 61.7% 2.17
-(1.68) -(1.54) -(0.97) (4.66)
The mean-reverting process causes the model to eventually stabilize at the
equilibrium level, but the persistence factor (momentum effect) creates prolonged
cyclic movements of rental growth patterns. Due to the interaction of these two
offsetting forces, office rents are unlikely to smoothly settle into an equilibrium
level, as posited by Hendershott (1996a, 1996b) in valuing properties when the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24
Table 1.2 Panel C: Model Results (Model 3 - Best Fit)
Vacancy
Rate
Lag 1
Real
Rent
Lag 1
Vacancy
Change
Office
Employ
ment
Real Rent
Growth
Lag 1
RhO R2 Adjusted Durbin-
R2 Watson
Boston -0.035 -1.616 2.525 0.91 75.5% 71.8% 2.11
-(5.29) -(2.70) (4.50) (19.27)
New York -0.016 -1.267 0.987 0.26 70.6% 66.1% 1.59
-(3.83) -(1.40) (3.98) (1.80)
San Francisco -2.716 -0.031 -3.704 8.676 0.89 79.3% 75.3% 2.10
-(3.07) -(6.49) -(3.74) (5.48) (15.11)
Seattle -0.040 -0.387 5.110 0.97 78.6% 75.4% 1.92
-(5.37) -(1.19) (5.22) (70.69)
market is in disequilibrium. The existence of rental growth momentum implies
oscillation of rental growth even in an equilibrium real estate market. That is, as long
as there is nonzero rental growth in the last period, rents will continue to change
even if vacancy and rents both reach equilibrium at the end of last period1 8 . This is a
very important aspect of the rental adjustment process and serves as an important
extension to the models developed by Hendershott et al. and Wheaton et al.
Cross-validation and Forecast Application of the Models
This section discusses the methodology for cross-validation in testing the
models developed in the preceding section. Following Hendershott (1996a, 2000), I
perform a dynamic model fitting test, that is to first set the initial forecast rent equal
1 8 Because vacancy rates also enter the equation as explanatory variables, the serial-correlation of
vacancy changes (i.e. the forecastability of vacancy trend) can also reinforce the forecastability of
rental growth rates. See the second chapter of this dissertation for empirical evidence.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25
to the actual rent at a starting date, and then apply the model to forecast rental growth
rates from period to period letting the errors accumulate. Because the forecast errors
are allowed to build up through time, this type of exercise provides a better test of
the model’s fit than the simple and standard examination of fitted values versus
actual values. The major difference between Hendershott’s test and the test in this
paper is that, his test is on the same set of data used in the model development, and
test performed here is on a different set of data. As discussed in the data section, half
of the sample data are purposely held back from the model development which
makes possible this cross-validation. Because the data set used to test the model is
different from the one used to develop the model, the test performed here is
relatively more rigorous. While one could certainly argue that the held-back sample
should be very similar to the sample used in model development, the point here is
that the estimated coefficients from one sample are very robust and little affected by
the random measurement errors in the actual data.
Figure 1.4 shows an example of the dynamic model fitting test. I use San
Francisco office as the sample since San Francisco office market experienced
dramatic swings in office rents through the sample period. The model appears to fit
the actual rents very well, it nicely captures the continued fall-off in office rents from
the mid-1980s through early 1990s and the breathtaking rise and fall of office rents
during the turn o f the last century as the technology sector in San Francisco
experienced a boom and a bust. As expected from the regression results Model 3 (the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26
Figure 1.4: Model Fitting - Actual and Dynamically Predicted Rents
Rea! Rent S a n F ra n c isc o O ffice R e n ts
$50 -r
$45 -
$40 -
$35 -
$30 -
$25 -
$20 -
$15 -
$10 -
$5 -
$0 J --------------,--------------,--------------,--------------, --------------,--------------,------------- ,--------------,------------- ,--------------,-------------- ,--------------,--------------,--------------,--------------,--------------I --------------r
l O C O ^ Q O C D Q ’r - C M C O ^ s n t p N - C O O O - . r - C V
G 0 C 0 0 0 C 0 C 9 0 > 0 ) O 0 > G * G ) 0 > 0 ) O » O O O O
Actual — • — Model 1 ■■■+-■ Model 2 — & — Model 3
best fit model), that includes office employment as one of the explanatory variables,
registers the tightest fit between the dynamically predicted rents and actual rents.
Note Model 3 also reports a very high rental growth momentum factor, suggesting a
surprisingly persistent rental growth pattern in the history of San Francisco office
market. In fact, the coefficients on lagged real rents have insignificant, and wrong
signs in both Model 1 and Model 2, implying that San Francisco office rents did not
exhibit the general equilibrium-rent-mean-reverting pattern. In other words, while
Model 1 and Model 2 reject the significance of the persistence term in rental growth
rates, they also suggest that higher rents in one period would lead to higher rental
growth in the following period. Therefore Model 1 and Model 2 essentially tell the
same story as Model 3, but in a less theoretically straightforward way. Model 3 is the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
27
recommended specification for San Francisco office market because the coefficients
of this specification all have the correct sign and are theoretically more coherent.
Next, I use another office market to illustrate the application of rent models
in the context of forecasting. It is the author’s strong belief that the best way to test a
model is to apply it to forecasting under reasonable assumptions. As well understood
by econometricians, one model could explain the data very well (e.g. high R2 ) but
have little out-of-sample predictive power, and another model could explain the data
i j
a little less well (e.g. a little less R ) but have much stronger out-of-sample predictive
power. The second model is considered to be more robust and preferred. The
alternative models are applied to forecasting in order to directly examine the
robustness of the three models developed in the study. As mentioned earlier, the full
three models were developed for only four MSAs. Model 1 and Model 2 were
rejected for San Francisco office market for theoretical reasons as explained above.
The following comparison therefore uses the Boston office market where we have all
three models and have correct signs for all of the coefficients.
Figure 1.5 shows both the dynamic fit test of the Boston office rent model
with the held-back sample and the forecasts beyond the sample ending period. It
appears that Model 3 best fits the actual data in the held-back sample, but the relative
robustness of these three models is in the eye of the beholders’. All three models use
the same vacancy forecast as supplied by PPR. The vacancy rates in Boston are
forecast to monotonically decline throughout 2012, which seems to be a very
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
reasonable assumption for the purpose of forecasting1 9 . Model 3 also assumes a
modest annual office employment growth rate of 2.4% over the forecasting period,
as suggested by Economy.com. Extrapolating the historical relationship between
total office employment and office rents, from Model 3 we would expect the real
office rents in Boston to go up to $35 in 10 years, a 40% increase from today’s rent
level. In the meantime, Model 1 and Model 2 both project a modest real rent increase
of 10% from today’s rent level by 2012.1 tried different employment growth
assumptions, and found that the expected real rent would be $30 in year 2012
assuming that the annual office employment growth rate is 1.0% and that the
expected real rent would be $24 assuming no office employment growth in the next
10 years. The drastic differences in forecast rents due to varying office employment
growth assumptions make it more difficult to apply Model 3 to forecasting because
of the added difficulty of forecasting office employment growth and the difficulty of
simultaneously accounting for the correlation between office employment, new
supply and vacancy rates. Model 1 and Model 2 appear a lot more stable due to the
strong mean-reverting structure of both models. Both models are stabilized by the
implicit equilibrium vacancy rates and equilibrium real rents, contrasting to the
structure of Model 3 in which office employment has no set boundary. In order to
apply Model 3 to forecasting, one should introduce a simultaneous model forecasting
1 9 If we believe that vacancy rates follow a slowly-adjusting mean-reverting process where the mean
is approximately the long-term average vacancy rate, this assumption seems not only fits the mean-
reverting theory but also has some empirical similarity with the vacancy rate history from the peak of
early 1990s to the low of late 1990s, as can be seen in Figure 5.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29
Figure 1.5: Forecasting Rents - An Example of Boston Office
Vacancy Rate 2q%
20% Rea! Rant Growth Rate (Semiannual)
15%
10%
5%
0%
■ ■ Forecast
— M odels -
- -5% -5%
■ 10% - 10%
-15%
-I Model 2 Vacancy Actual Model
Forecast of Real Rent: Boston
$40
$35
$30
$25
$20
$15
$10
Forecast
$5
$0
i f l ( D N C O f f l O r W ( O t l f i C O N 0 3 0 5 0 r ( M n ' f l i ) ( £ I N S ) C ! ) O T - M
c o o o e o c o c o o > o © o > d » © < » o > O J © o © © o o © o © © © * - T - T -
Actuai © Model 1 Model 2 — &— Model 3
Forecast of Nominal Rent: Boston
$90
$80
$70
$60
$50
$40
$30
$20
Forecast
$10
$ 0
a o c Q c o c o c Q © © a > © C 5 © o > © a > © 5 © o © o © Q © © o o ,«-*-
Actuai — © — Model 1 -- + * -- M odei2 — A— M odels
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
new office supply corresponding to the employment growth scenario, a task that is
beyond the scope of this study2 0 .
In summary, the dynamic cross-validation proves that the three models
developed here have all done a reasonable job in explaining the historical rental
growth patterns in the U.S. metropolitan office markets. While the rental growth
appears to be historically strongly correlated with office employment in several
office markets, the application of such model to forecasting is not an easy task
because more variables would have to be forecast. If one is interested in rough, yet
more consistent estimates of future rents, models without office employment variable
appear to be more robust and plausible. In fact, because of the errors inherent in
office employment forecasts, the structures of Model 1 or Model 2 are preferred to
more sophisticated models like Model 3.
VIII. Conclusions
This chapter examines a very important aspect of the office rental adjustment
process, that is the momentum effect. Using a set of previously unexplored cross-
sectional time-series data in fourteen U.S. metropolitan office markets, the study
empirically investigates whether the rental growth in one period (semi-annual
interval) would be followed by rental growth in the same direction over the next
period. The momentum effect of office rental growth is found to exist and to vary
2 0 DiPasquale and Wheaton (1996) is an excellent textbook on how to set up such a complex system
model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
31
significantly across markets. In several MSAs, office rental growth rates exhibit very
strong persistence, which has probably contributed to the wide swings of office rents
in these markets. The strong momentum effect of rental growth in these markets
suggests that, as long as there is nonzero rental growth in the last period, rents would
not smoothly fall into equilibrium even if vacancy and rents both reach equilibrium
at the end of last period. In other words, oscillation of rental growth can exist even in
an equilibrium real estate market. This is a finding in contrast to the popular existing
rental adjustment models, which would predict a zero rental growth rate when both
vacancy and rent reach equilibrium levels.
This study also contributes to the continued debate on the determinants of
equilibrium rents. The empirical results show that the implicit equilibrium office
rents are mainly determined by space market variables rather than capital market
variables. In order to test for the robustness of the rent adjustment models, the study
not only performs cross-validation using a held-back test sample but also applies
different types of models to real world forecasting. The simulation results confirm
that the parsimonious model structure produces more stable and consistent forecasts.
It is also important to incorporate the momentum effect in rent forecasting models,
especially in the short run.
Because lagged independent variables can be used to forecast the future
growth rates of real rents, the office-commercial space market is shown to be
inefficient. Knowledgeable market participants could take advantage of this
informational inefficiency to time their entry to and exit from markets. Robust rental
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
adjustment models, such as the ones developed here, are of genuine use to market
participants.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
Chapter 2
Default Risk and Loss Severity of Commercial Construction Loans
1. Introduction
While there is a very large body of academic literature on residential
mortgages, much less research has been conducted on commercial mortgages. For
the limited number of studies on commercial mortgages, the focus is exclusively on
the performance of permanent loans collateralized by the existing property. None of
them examines the default probability of construction loans although this asset class
has a considerable presence on the balance sheet of many commercial banks and
savings and loans institutions. There are about 193 billion dollars of these mortgages
outstanding on the balance sheet of FDIC-insured commercial banks as of 20012 1
(compared to $572 billion of permanent loans on multifamily and nonfarm
nonresidential real estate). Understanding the default risk of these construction loans
is of particular interest to the financial institutions holding these assets.2 2
This chapter focuses on the estimation of default risks of construction loans
for commercial real estate in an option-based modeling framework. Option pricing
theory provides a natural link between the property market risk and construction loan
2 1 Source: The Federal Deposit Insurance Corporation (FDIC), “Statistics on Banking - Historical
1934-2001 Commercial Banks”, 2002.
2 2 According Bureau of Census, the total private nan-residential construction put in place in the U.S.
amounts to $201 billion in 2001. If 60-70% of these were financed, then the commercial construction
loan volume would be about $120-140 billion in 2001, significantly more than the aggregate CMBS
volume in the same year.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
risk. Within this framework, commercial mortgages are viewed as derivative assets
in a stochastic economy. A unique feature of the default model in this paper is that,
the underlying commercial real estate market dynamics is modeled with greater
realism than previous option-theoretic studies. Instead of following the traditional
simplified assumption that the property value follows a geometric Brownian motion
process with a constant mean and serially uncorrelated disturbances23, this model
proposes that the commercial real estate market consists of three key interdependent
stochastic processes that are also serially-correlated: vacancy rate process, rent
process, and cap rate process. NOI process and capital value process are modeled as
derived from these three processes. The goal of this model setup is to take advantage
of the intrinsic persistence and forecastability of the space market movement2 4 to
more precisely estimate default probabilities in different real estate market
conditions. In other words, while the traditional option model treats the property
value process as an independent process in the real estate asset (capital) market, this
study considers the property value process as dependent on both markets for space
and capital. Because this setup involves several state variables that prohibit the use
of backward-solving numerical methods, the forward Monte Carlo simulation
technique is applied to handle both issues of multi-dimensionality and path-
dependence. The goal here is to investigate the implications of this structured
2 3 See Hendershott and Van Order (1987) and Kau and Keenan (1995) for overviews on this option-
theoretic approach to mortgage valuation and related assumptions.
2 4 For an overview of the literature and recent empirical evidences, see the first chapter of this
dissertation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
dynamic model on default probabilities of commercial construction loans in different
real estate market scenarios.
As such, the contribution of this study is twofold. It not only provides the
first investigation on the default probabilities of commercial construction loans, a
subject that has not been explored in the literature, it also examines the implications
on default probabilities of the more realistic model that captures the commercial real
estate market dynamics. The simulation results show that the structured dynamic
model with serial correlation and interdependence result in significantly different
estimates of default probabilities during different phases of the market cycle.
The chapter is organized as follows: Section II provides a brief literature
review on commercial mortgage default studies, Section III explains the model setup
and describes the structured dynamic model of the commercial real estate market,
Section IV describes the data and empirical results, Section V presents the numerical
results from the Monte Carlo simulation runs, and Section VI summarizes the
findings and discusses areas for future research.
II. Literature Review
Although the vast majority of mortgage default research focuses on
residential housing markets, research agenda on commercial mortgages has caught
considerable amount of attention recently. Vandell (1984) is the first to theoretically
explore the issues in modeling commercial mortgage default. Following the pioneer
works by Dunn and McConnell (1981a, 1981b) on the application of the option
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
pricing theory to residential mortgage valuation, Kau, Keenan, Muller, and Epperson
(1987,1990) and Titman and Torous (1989) start to model commercial mortgage
defaults as contingent claims. They all use numerical methods to solve the mortgage
values. Foster and Van Order (1984,1985) develop option-based empirical models in
residential mortgage research. Vandell (1992) and Vandell, Barnes, Hartzell, Kraft,
and Wendt (1993) are the first to conduct empirical studies on commercial mortgage
defaults at both aggregate and disaggregate levels. The empirical modeling technique
on commercial mortgage defaults is later enriched by Ciochetti and Vandell (1999),
Archer, Elmer, Harrison and Ling (2002), Goldberg and Capone (2002), Ciochetti,
Deng, Gao and Yao (2002), Ciochetti, Yao, Deng, Lee and Shilling (2003), Ambrose
and Sanders (2003), and Chen and Deng (2003), among others. Due to the scarcity of
actual commercial mortgage performance data, another line of research is conducted
using simulation methods. Noticeable examples include Riddiough and Thompson
(1993), Childs, Ott and Riddiough (1996)2 5 and Tu and Eppli (2002). For
comprehensive overviews, Vandell (1993, 1995) provides insightful surveys of the
default studies in both residential and commercial mortgages. Hendershott and Van
Order (1987) and Kau and Keenan (1995) also synthesize the option-theoretic
approach to mortgage valuation.
It should be noted that all these studies in commercial mortgage defaults
focus on long-term commercial mortgages, i.e. permanent loans on operationally-
2 5 To be exact, a combined backward/forward approach similar to that in McConnell and Singh (1994)
is used in Childs, Ott and Riddiough (1996).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
stabilized income-producing properties. None of the existing literature has explored
the default risks of construction loans for commercial real estate, which is the subject
of this chapter.
To overcome the over-simplification of the underlying collateral process, this
paper builds a more realistic structured model that captures the commercial real
estate market dynamics. Recent empirical evidences suggest that the real estate
market is not a pure random walk, which calls into question the basic assumption
underlying the traditional option-theoretic model that assumes the property value
follows a standard stochastic process with a constant mean and serially un-correlated
disturbances. For example, Case and Shiller (1989,1990) and Abraham and
Hendershott (1996) documented the persistence of growth in price in single-family
housing market, and Chen, Peng and Hudson-Wilson (2002) provide new evidence
on the persistence in office rental growth rates in the commercial real estate space
market. Meese and Wallace (1994) also find that house prices do not follow a
random walk.
The structure of the proposed dynamic model recognizes that property value
process is not an isolated process in the real estate asset market but rather a process
influenced by both the space market, that is largely forecastable in the short run, and
the capital market, that is more stochastic with some degree of mean-reverting26. The
2 6 The established theory is that, real estate space market is slow in supply adjustment due to lengthy
construction period therefore the vacancy trend (and consequently rent change) is largely forecastable
in the short run, and that real estate capital market is more fluid therefore less forecastable.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
model benefits from a large body of earlier literature on the dynamics of the
commercial real estate market. Fisher, Hudson-Wilson and Wurtzebach (1993),
Fisher (1992) and Archer and Ling (1997) present general equilibrium theory
encompassing both the real estate space market and the real estate capital market.
Wheaton and Torto (1994), DiPasquale and Wheaton (1996) and Hendershott,
Lizieri and Matysiak (1999) provide elegant and well-specified models to capture the
complex dynamics of the commercial real estate market with sufficient realism.
HL Model Setup
In this section, I describe the traditional option-theoretic model. I also discuss
recent empirical evidences pointing to the violation of the assumptions underlying
the traditional model. A new structured dynamic model will then be proposed to
reflect the more realistic assumptions along with discussions on the default rule and
the treatment of unique contract terms of commercial construction loans.
A. Traditional Option-theoretic Model
Following standard assumptions in the finance literature, the traditional
option-theoretic model in mortgage research assumes two uncertainties driving the
risk and valuation of mortgages: the instantaneous risk-free interest rate, r, and the
value of the mortgaged building, B. The instantaneous risk-free interest rate, r, is
typically assumed to follow a mean-reverting square root process as in Cox, Ingersoll
and Ross (CIR, 1985):
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
dr = y(9 - r)dt + ex,-Jrdz (2.1)
where y is the speed of adjustment, 0 is the steady-state mean of the process, and
G r 2 r is the variance.
The value of the mortgaged building, B, follows a geometric diffusion
process2 7 that can be specified as28:
dB = ( a - b)Bdt + GB BdZB (2.2)
where a is the instantaneous expected return on building, b is the continuous rate of
building payout, G b is the instantaneous standard deviation, and Zg is a standardized
Wiener process.
If the trading takes place continuously and there is no transaction cost29, then
the standard hedging argument leads to the solution to the mortgage valuation as
satisfying the following partial differential equation (PDE):
1 2 d2M r B d2M 1 2 d2 d2 M
— VGr — -T -+ p y r B G rG B — — + - G bB ——r-
2 r dr2 F r drdB 2 B dB2
+ r(9-r>— ^ - r M = 0 ^
where p is the correlation coefficient between the disturbances to the building value
process and those to the interest rate process.
2 7 This assumption has become standard since the pioneer works by Black and Scholes (1973) and
Merton (1973, 1974).
2 8 See Titman and Torous (1989), and Kau, Keenan, Muller and Epperson (1987, 1990) for more
details.
2 9 These assumptions are not satisfactory in the commercial real estate market because commercial
real estate is illiquid asset traded in a thin market with significant transaction costs, see Kuo (1996)
for a detailed discussion.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
Kan, Keenan and Kim (1994) extend the theoretical valuation model of
Equation 2.3 to estimate the default probabilities and show that such a probability, p,
satisfies the Kolmogorov backward equation, that is:
- ro) + p 4 r B d r(tb + —c \B 2 + y(& -r)* ~ Mfic- b ) B - k ~ - = 0
2 ? dr2 F r drdB 2 B dB2 J dr dB dt
(2.4)
Despite its wide use in the literature, the assumption that real estate prices
evolve according to standard geometric diffusion process does not fit the actual data
very well. In fact, Kau and Keenan (1995), the major proponents of the option-
theoretic approach, acknowledge that the lognormal form for the house price process
is not above reproach. Recent empirical studies have also documented the
persistence and forecastibility of real estate price appreciation30. Based on some of
these new findings, Kuo (1996) sets up a more realistic house price model with three
return components: an AR(1) market return, and AR(1) persistent idiosyncratic error,
and a property-specific random error due to the transaction of the property. He uses
actual transaction data to estimate the house price process with the results indicating
that variation in the forecastable returns produce significant variation in the mortgage
default option price. The serial correlation of the market return is shown to have
strong impacts on the price of the default option. He concludes that the random walk
model is unable to use the information of current market return and persistent
3 0 See Case and SMIler (1989, 1990), Mankiw and Weil (1989), Clapp and Giaccotto (1994), Meese
and Wallace (1994), Abraham and Hendershott (1996), and Chen, Peng and Hudson-Wilson (2002),
among others.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
idiosyncratic error and may lead to mispricing of the mortgage default options.
B. The Proposed Model
The key to modeling the possibilities of loan defaults is to adequately model
the underlying collateral process because the decision whether to default largely
depend on the value of the physical asset collateralize the loan . The model
proposed in this study attempts to capture the collateral value process with more
realistic specifications. In this model, there are three basic stochastic processes and
three derived processes. The three basic stochastic processes: vacancy process, rent
process, and cap rate process, are inter-dependent and serially-correlated. The three
derived processes: operating expense process, NOI process, and capital value
process, are functions of the basic processes. The model benefits from the works by
Wheaton and Torto (1994), DiPasquale and Wheaton (1996), Hendershott, Lizieri
and Matysiak (1999) and Chen, Peng and Hudson-Wilson (2002) on the workings of
commercial real estate markets. The model extends these works and provides a
functional form that is usable in mortgage default modeling. Not only the stock-flow
nature of the commercial real estate market is captured in the model, the linkage
between the real estate space market and the real estate capital market is also
established. Essentially, the three basic processes in the structured dynamic model
3 1 In fact, assuming zero transaction cost (both tangible and intangible) and a constant interest rate
environment, the ruthless option-exercising rule states that the collateral value is the only variable
determining default decisions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
capture three levels of the commercial real estate market: the first level pertains to
the demand and supply of real estate space - since supply is fixed in the short run
and demand is largely exogenous, vacancy rate process can be modeled independent
of other processes in the short run ; the second level is on the pricing of real estate
rental space - market-clearing rent on a new lease is determined by the short-term
fundamentals (i.e. demand and supply) in the space market and can therefore be
modeled as a function of vacancy rates; and the third level is on the pricing of real
estate assets in the capital market - because real estate value is not only determined
by the performance in the space market but also by the returns of alternative
investments whose movements are largely unrelated to the real estate space market3 3,
the capitalization rate of real estate assets at this level can be modeled as a stochastic
process that is only partially dependent upon the space market movement, which is
proxied by the NOI growth rates in this study.
The details of these processes are described as follows.
(1) Vacancy process
The vacancy rate is assumed to follow a serially-correlated lognormal
diffusion process3 4. The log of vacancy rate for an individual property at time t is
given by:
3 2 There is certainly a feedback process between the market vacancy, rent, real estate price and new
development. The point here is that the feedback process happens over a relatively long period of time
because it takes quite some time to add new supply into the commercial real estate market.
3 3 This is because commercial real estate capital market is just a subset of the much larger general
capital market where alternative investments dominate real estate assets in terms of size.
3 4 The lognormal form is assumed because actual vacancy rates can range from 0% to 100% while the
average is probably around 10% therefore vacancy rates are likely to be log-normally distributed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
dvt - pdvt_ x +flt +W' (2.5)
where dvt is the change of the log of vacancy rate, p is the persistence parameter,
p t is the expected vacancy change at the market level after the auto-correlation
effect, wt represents the idiosyncratic error for a particular property and is an i.i.d.
noise term. Note this process assumes a persistent trend of the market-level
vacancy change that is captured by the market-level auto-correlation term, it does
not assume a persistent idiosyncratic error. This is a reasonable assumption for
the vacancy process of a new building because a new building does not have a
unique history of vacancy rates and is leased to the general market in a short
period of time. The idiosyncratic term wt therefore has fully captured the leasing
risk of a new building.
(2) Rent Process
The rent process is given by a function similar to that used in the first chapter
of the dissertation, that is to specify the growth rate of the market-clearing rent,
dRt, as a function of the change o f market vacancy rate, the gap between the
market vacancy rate and the structural vacancy rate, and a persistence term:
dRt = p t + + A (Vi ~ v) + PdRt-1 (2-6)
where vis the structural vacancy rate.
(3) Cap Rate Process
Real estate cap rates follow a mean-reverting stochastic process. Unlike risk
free interest rate that could frequently go close to zero, the cap rates for
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
commercial real estate never gets anywhere close to zero, as evidenced by a
variety of data sources. Therefore, to simplify the implementation of the model,
instead of the CIR process as in Equation 2.1, a stationary AR(1) process is
assumed for the cap rates:
drt = 0, + prt_x + pdNOI + o,,dz (2.7)
where dNOI is the NOI growth rates, because positive NOI growth should raise
investors’ expectation of NOI growth rates therefore reduce the required cap
rates and negative NOI growth would increase the cap rates in equilibrium .
This specification differs from the CIR process (Equation 2.1) in the disturbance
term and its relationship to the space market. Otherwise, they are similar because
Equation 2.7 is an empirical model while Equation 2.1 is a theoretical model
where it is not possible to identify separately the parameters yand 9 in empirics.
Kim (1991) also points out that the service flow from commercial properties
should be correlated with interest rates. While this is presumably correct in
theory, the empirical evidence points to a rather weak correlation between the
interest rates and the income returns of commercial properties. I opt not to have
another independent stochastic process of the risk-free interest rate in order to
reduce the number of variables and to make the model cleaner and more
tractable.
The three derived processes are:
3 5 In theory, a cap rate should equal to the discount rate for a property less its expected growth in NOI.
For details, see DiPasquale and Wheaton (1996), pp. 58-59.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
(4) Operating expense
Presumably the operating expense could also take the form of a stochastic
process. This m aybe unnecessary since the operating expenses are not expected
to change as dramatically as the vacancy rates and market-clearing rents . To
simplify the model while still incorporating its interaction with the vacancy rate,
I assume the operating expense for the vacant space is half of that for the leased
space. The operating expense is estimated as a function of the fixed cost and the
vacancy rate:
E, =Es(l — vt /2) (2.8)
where Es is the total operating cost assuming zero vacancy, vt is the vacancy rate,
and Et is the total operating expense net of vacancy.
(5) NOI process
NOI is defined as the identify:
NOIt = Rt - E t (2.9)
where Rt m d E t are total collectable rents and total operating cost, respectively.
(6) Capital value process
Capital value is simply calculated as the capitalized NOI:
Vt = N O I/rc (2.10)
where rc is the capitalization rate.
3 6 Operating expense includes management fees, real estate taxes, professional fees, and other costs
related to utilities, janitorial, general & administrative, and maintenance and repair, most of these are
not likely to change very much.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
Figure 2.1 illustrates the structure of the whole model. Since the absence of
either cash flow issues or interim defaults/prepayments significantly reduces the
complexity of the default model, construction loans provide an excellent opportunity
to investigate the differential default probabilities using this more realistic structured
dynamic model of the commercial real estate market. Once the structure of the
underlying collateral process is set up, we will only need to specify the default rule at
loan maturity in order to complete the default probability model.
Figure 2.1: Flowchart of the Structured Dynamic Model
NOI Process
Rent Process Operating Expense
Cap Rate Process
Vacancy Process
Capital Value Process
C. Default Rule
In this model, construction loans are assumed to be either paid off or default
only at the time of project completion when the loans are matured3 7 . In other words,
no interim defaults are allowed in the model because the interest payments on
construction loans are usually carried over (no re-payments are necessary before loan
3 7 Here I assume the leasing time is zero and the default to loss time is zero although in reality both
takes quite long time - these assumptions can easily be relaxed. In this study I keep the model simpler
for the ease of exposition.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
maturity) therefore few developers would want to stop before the projects are
completed. The model also assumes that no cost overruns would occur. Since no
empirical default data are available, I assume a ruthless default rule, that is, default
will happen whenever the market value of the new property falls below the balance
of construction loans38. The intrinsic opportunistic nature of the commercial real
estate developers also suggest that the ruthless default rule is not a bad assumption. It
is argued in the literature that the owners of commercial properties have less
psychological attachment to the collateral therefore the exercise of default options is
more “ruthless” than their residential counterpart. Following the same logic, the
default option exercise should be even more ruthless for the borrowers of
construction loans because commercial real estate developers are mostly short-term
opportunistic players, as opposed to the investors in stabilized income properties that
-IQ
are relatively long-term players .
3 8 There are significant differences between permanent financing and construction loans. For
permanent loans, the default risks come from two major sources: equity effect and cash flow effect.
Along the line of Jackson and Kaserman (1980), Vandell (1984) surmised that it was the
contemporaneous LTV ratio and possibly the contemporaneous debt-coverage ratio, along with
variables representing transaction costs that would be expected to be significant in influencing
commercial mortgage defaults. Borrowers of permanent loans use the cash flows generated from the
existing property to pay for the regular debt service, while in construction loans, interests on loans are
usually carried over and calculated as a part of the total loan commitment amount. As such, the
realizable sales value of the new property at completion has the dominant role, therefore making it
more appropriate to apply the ruthless default rule based on the ending value of the new property.
391 acknowledge that large developers may be able to hold the new properties in their long-term
portfolio and therefore do not have to face the “live or die” situation at the maturity of construction
loans. That would mean the defaults of these construction loans should be treated as compound
European options for these developers. This possibility can be added to the model but would
significantly increase the complexity of the model. Since it would not affect the primary conclusions
of this study, I leave this possibility for future research.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
D. Other Modeling Issues
Construction loans are complex financial instruments, I describe some of the
normal terms of construction loan contracts and discuss how these terms are treated
in the model.
Interest rate - Construction loans are generally floating-rate instruments
where the interest rate is often quoted as a spread over a published interest rate
index, e.g., LIBOR or U.S. treasury rate. While allowing for stochastic interest rates
would add more realism to the model, it is unlikely to change the conclusions of the
study since construction loans have relatively short maturity, I opt to leave
exogenous interest rate as fixed to reduce the unnecessary complexity.
Construction cost and periodic draws - The cost of construction is relevant
to the extent that lenders generally advance loan funds not to exceed a certain loan-
to-cost ratio that is roughly in line with the LTV ratio. If the cost of construction
fluctuates dramatically, then the total advanced loan amount would also fluctuate. In
the simulations, I hold the construction cost as constant. The relaxation of this
assumption is beyond the scope of this study and is a subject for future research.
Monthly draw method is often used in construction loans, that is, the construction
lender disburses funds to the developer each month based on the work completed
during the preceding month. Because the interest payments are often carried over and
included in the total loan commitment amount, if the interest rate follows a stochastic
process, the period draw method would affect the total funds available for the actual
construction and therefore the equity requirement for the developers. Since the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
interest rate is assumed to be constant during the loan term, ignoring the periodic
draws should not have significant impact on the model.
Construction Length - The time to completion is important. While the total
commitment amount has a pre-determined ceiling, in cases that a project takes longer
to complete, the construction lender may be forced to extend the loan term. Is cases
that it takes less than expected time to complete the project in a hot market, the
developer may be able to realize a higher price for the new property therefore reduce
the risk of construction loans. In the model, I first fix the construction length, and
then allow the length of the construction period to vary according to a lognormal
distribution, which appears be sufficient for simulation purposes.
Pre-leasing - Pre-leasing is required by more and more lenders in originating
commercial construction loans. To the extent pre-leasing agreement is fully
enforceable, leasing risk is significantly reduced, so is the default probability of
construction loans. The simulations in this study assumes no pre-leasing, but the
possibility can be added to the model if desired, that is, one can simply treat the
future rents and occupancy on pre-leases as a fixed component and the model will
then become a hybrid with a fixed component and a stochastic component.
IV. Data and Empirical Estimation of the Parameters
There are two levels of risks for construction loans: one is at the market level,
the other is at the individual project level. The performance data at the individual
commercial property level are generally not available to the public. The market-level
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
data are used to estimate the parameters of the diffusion processes in the commercial
real estate market, where the market is defined as property-type/MSA (i.e. Boston
office, Los Angeles apartment, etc.). In this study, I only use office sector as the
example while the qualitative results should be applicable to all the commercial
property types.
Figure 2.2: Office Market Vacancy Rates for Selected U.S. MS As
U.S. Office Market Vacancy Rates
Vacancy { % )
30 -.......
2 5 .....
20 -
!lll!l!l!l!!!lilliilllllll!li!illi!
I obtained the quarterly market level vacancy data of the fifty four major U.S.
metropolitan office markets from Property & Portfolio Research, Inc. (PPR) to
perform the empirical estimation. Figure 2.2 shows the time-series office vacancy
rates by MSA. While there is certainly a national trend in office vacancy rates, the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
differences among MSAs are very pronounced. Using the empirical specifications of
Equation 2.540, the estimated coefficients using MSA level data are reported in Table
2.1 (intercept and time dummies are not reported). The persistence parameter is
estimated as 0.69 with a t-statistics of 71.1, suggesting the vacancy change at the
market level is largely forecastable. It should be noted that the parameters of the
diffusion process of the individual properties could differ significantly from these
estimated here.
The historical time-series office rent data at the MSA level are originally
published by National Real Estate Index (NREI) and supplied by PPR. Figure 2.3
shows the indexed office rent series for selected MSAs.
Table 2.1: Regression Results on Vacancy Process Estimation
ALogVacancy
(lagged 1 quarter)
Root MSE R2 Adjusted R2
Parameter Estimate 0.6892 0.03145 71.3% 70.8%
t-stat 71.12
Note: Intercept and time dummies are not reported in the table.
Table 2.2: Regression Results on Rent Growth Process
ALogVacancy LogVacancy Rent Growth Root R2 Adjusted
(lagged 1 Gap (lagged 1 (lagged 1 MSE R2
quarter) quarter quarter)
Parameter Estimate 0.1496
f-stat 8.84
-1.0899
-7.17
0.4616
29.52
1.7270 50.1% 49.1%
Note: Intercept and time dummies are not reported in the table.
4 0 The actual regression includes time dummies as in a standard repeated-measures regression to
capture the trend in the mean vacancy rates. The time dummies are used in all the other empirical
regressions on the estimation of diffusion parameters.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2.3: Office Market Rent Indices for Selected MSAs
52
Rent Index
U.S. Office Market Rents
180
160
140
120
100
8 £
8 e g
Figure 2.4: Implied Office Cap Rates from NCREIF NPI Data Set for Selected MSAs
ImpHsd Cap Rate
14%
8 % -
4%
2%
U.S. Office Market Implied Cap Rates
l i l i i
CO X- C O
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
The regression results using Equation 2.6 are reported in Table 2.2.
Figure 2.4 shows the implied cap rates4 1 for selected MSAs estimated from
the NCREIF NPI data set, and Table 2.3 reports the regression results using Equation
2.7, which shows that there is great variation of cap rate series across MSAs. The
coefficient of NOI growth is positive in the regression, contradictory to the
theoretical prediction. This is probably because we use implied cap rates rather than
the actual cap rates. Because implied cap rates are calculated as annualized income
returns, it is not surprise that the implied cap rates have positive relationship with
NOI growth rates. This suggests that more efforts are needed to collect more
accurate cap rate time series.
Table 2.3: Regression Results on Cap Rate Process
Cap Rate
(lagged 1 quarter)
NOI Growth
Rate
Root MSE R2 Adjusted
R2
Parameter Estimate 0.9343 0.0088 0.00506 91.2% 90.8%
t-stat 108.27 16.77
Note: Intercept and time dummies are not reported in the table.
V. Numerical Results
In this section, I use the Monte Carlo technique to model the default
probabilities of commercial construction loans in an option-theoretic framework.
4 1 The NCREIF implied cap rate series are essentially the annualized income returns. See Fisher
(2000) and Sivitanides, Southard, Torto and Wheaton (2001) for more discussions on the implied
NCREIF cap rates and the calculation methodology.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
When mortgages are viewed as derivatives whose value is contingent upon the
underlying assets, there are basically two solution methods to value the contingent
claims: forward versus backward methods42. The backward approach is more
appropriate when rational termination is permitted in the case where borrowers need
to make repeated decisions regarding default or prepayment. This is because the
answer to whether termination is to occur at any given moment depends on the
borrower’s calculations of future values. The backward approach leads to the
solution to the PDE Equation 2.3. Kau, Keenan and Kim (1994) extend this
methodology to estimate the default probabilities of residential mortgages. However,
it is much more difficult to implement the backward approach if there are more than
two state variables and there is auto-correlation in the underlying asset processes
because the later values would then depend on the earlier values. It turns out that the
backward approach is unnecessary for valuing construction loans. Because
construction loans can be viewed as more like European options with a single
exercise date, that is, at the time of project completion (i.e., the maturity of
construction loans), the borrower must pay off the construction loans therefore
rendering the future value of the property irrelevant43. In other words, for
construction loans, the default decision criteria only require knowing the current net
4 2 See Kau and Keenan (1995) for an overview.
4 3 As mentioned earlier, I acknowledge that well-capitalized developers would be able to keep the new
buildings in their portfolio as long-term investment, but this possibility is beyond the exercise of this
study.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
equity level of the new property at completion (or when leased-up which we simply
assume to take no time in the model).
Because there is no analytical solution to the structured dynamic model
developed in this paper, the Monte Carlo simulation approach is used. The Monte
Carlo method is especially suitable for modeling the default risk of construction
loans because:
a) There are several stochastic processes in the model, which essentially
prohibits the feasibility of the backward approach. On the other hand, the
Monte Carlo technique can easily handle several inter-related state
variables and complex dynamic models as developed in this paper.
b) The three basic stochastic processes are all serially-correlated. The Monte
Carlo technique is perfect in handling path-dependent processes, while
the backward approach would be very difficult to implement in this type
of situations.
c) Only the ending market value of the new construction matters in setting
the default boundary under our assumptions. There is no need to work
backwards.
To examine the impact of the structured dynamic model on default
probabilities, I vary both the initial states Av and AR'ma, number of scenarios. When
the property value follows a random walk process, the variance of value growth rates
is proportional to the holding period. This is not true in this model when there are
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
three interdependent serially-correlated processes. Since the average variance in the
AR model is growing over time due to positive serial correlation, the random walk
model will have relatively higher variance in the near term and relatively lower
variance in the longer term compared to the AR model. In other words, the variance
of the AR model as used in this study should be closer to a straight line than that of
the random walk model.
There are a total of 3000 drawings for the simulation of each scenario. In
these simulations, the default cost is assumed to be zero but the cost of selling the
new property is allowed to vary44. The ruthless default assumption can be relaxed by
assuming the default cost to be a function of the value of the new property as in
Riddiough and Thompson (1993)45.
Figure 2.5 shows the diffusion process of vacancy rates under one simulation
scenario, and Figure 2.6 shows the distribution of simulated capital values at the end
of the 4th quarter. These distributions are taken from 3000 draws based on the
structured dynamic model. In these simulations, the initial vacancy rate is 10%, the
initial rent is $20/sqft, the initial NOI is $ 10.4/sqft assuming 40% expense ratio, and
the initial value is $130/sqft assuming the initial cap rate is 8.0%.
4 4 For opportunistic players like commercial real estate developers, if they do not have the capacity to
hold new projects in their portfolios, then the cost of marketing and selling a new property would
raise the default threshold because the developers will also need to pay for the cost which would not
occur if they choose to default. In other words, more defaults are expected if the developers are to pay
for the costs of selling new properties.
4 5 Specific borrower default transaction costs can include legal fees, additional loss of non-property
assets if the loan has recourse and indirect costs resulting from a reduced ability to secure credit in the
future. Costs associated with lost credit opportunities may be particularly large and are unobservable
to the lender.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
Figure 2.5: Simulated Diffusion Process of Vacancy Rates
Diffusion Process of Vacancy Rale Over Time
Figure 2*6: Distribution of Capital Value at the End of the Fourth Quarter
Distribution of Properly Capita! Value at the End of 4th Quarter
From 3000 Draws
Frequency
350 - ]
300
250-
200
150
100
160 100 120 140 180 200 220
Capita! Value ($)
240
— Scenario: Vacancy Up, Rent Down
— Scenario:VacancyDown, R ent Up
- - Construction Loan Amount (75% L T V )
- — Scenario: Vacancy Flat, Rent Flat
Min Value To Qualify Permanent Loan
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58
Figure 2.7: Standard Deviations of NOI and Value Over Time
Standard Deviations of NOI and Value by Quarters
- Assuming zero expected changes in vacancy and rent
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
10 16 18 0 4 12 14 20 2 6 8
S t.D e v o f Log(NOI) S t.D ev o f Log(Value) Quarter
Figure 2.7 shows the standard deviations of both NOI and property value
from 3000 draws over the course of simulation periods. We find that the standard
deviation of capital value is much higher than that of NOI in the early quarters and
the two eventually converge in approximately 20 quarters. This is not a surprise
because the volatility of property value is influenced by risk factors in both markets
for space and capital meanwhile the NOI is influenced only by factors in the space
market. Over a long period, the incremental influence of capital market (represented
by the stochastic process of cap rate in the structured model) diminishes - overall,
the sum of the two risks in two markets appear to be only minimally higher than the
individual risks over a long period. This in itself is a very important finding,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
suggesting that the empirical results on the volatility of NOI could be extended to the
volatility of capital value. I compare the results from these simulations to that from
Deng, Fisher, Sanders and Smith (2003) on the volatility of NOI growth and find
comparable risks reported in about 20 quarters.
The quarterly standard deviation of the property value growth rate is in the
range of 7.0%-8.0% (about 14.0-16.0% annually), this range is plausible and is
consistent with the parameters used by earlier studies on the value processes of
individual buildings. For example, Titman and Torous (1989) use annualized
standard deviation of 15% to 22.5% for building returns. They also estimate that the
implied building value process parameters are < 7= 15.5% for the building value
volatility, b = 9.03% for the rate of building payout, and p - 0.1435 for the
correlation between building value changes and changes in the instantaneous risk
free interest rate. Riddiough and Thompson (1993) apply Gp = 12% in their
simulation study. Ciochetti and Yandell (1999) estimate the average implied price
volatility of about 17% to 18% from a large commercial mortgage data set. While
there is certainly more research needs to be done in order to obtain more precise
estimates of the parameters of the building NOI/value growth process, these
comparisons nevertheless suggest that the structured dynamic model proposed in this
study has produced realistic results consistent with those observed in the marketplace
and previously estimated in the literature. Judging from the results, it appears that the
diffusion parameters inferred from the market-level time series data of the fifty-four
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
metropolitan markets may also be applicable to the building-level processes of a new
construction.
Table 2.4: Default Probabilities and Expected Losses by Simulation Scenarios
Panel A. Assumes construction loan LTV is 70% and loan term is 4 quarters
1-1 1-2 1-3
Scenario
1-4 1-5 1-6 1-7 1-8 1-9
Initial Vacancy Change
State Rent Growth
0.7%
-2.1%
0.7%
0.0%
0.7%
2.1%
0.0%
-2.1%
0.0%
0.0%
0.0%
2.1%
-0.7%
-2.1%
-0.7%
0.0%
-0.7%
2.1%
Zero Default Probability
saies cost Ross severity
Expected Loss
3.1%
5.4%
0.2%
1.6%
5.2%
0.1%
1.6%
5.5%
0.1%
1.2%
6.4%
0.1%
0.6%
3.6%
0.0%
0.6%
2.9%
0.0%
0.4%
5.1%
0.0%
0.1%
2.2%
0.0%
0.1%
2.0%
0.0%
3% Default Probability 5.0% 3.2% 2.5% 2.0% 1.1% 0.9% 0.9% 0.3% 0.3%
sates cost Losg Severity
5.6% 4.8% 6.1% 6.2% 4.5% 4.5% 4.8% 3.4% 2.7%
Expected Loss 0.3% 0.2% 0.2% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0%
5% Default Probability 6.2% 4.3% 3.1% 2.7% 1.6% 1.2% 1.2% 0.5% 0.4%
sates cost Loss Severity
6.3% 5.4% 6.8% 6.5% 4.8% 5.1% 5.4% 3.4% 3.7%
Expected Loss 0.4% 0.2% 0.2% 0.2% 0.1% 0.1% 0.1% 0.0% 0.0%
Panel B. Assumes construction loan LTV is 70% and loan term is 8 quarters
1-1 1-2 1-3
Scenario
1-4 1-5 1-6 1-7 1-8 1-9
Initial
State
Vacancy Change
Rent Growth
0.7%
-2.1%
0.7%
0.0%
0.7%
2.1%
0.0%
-2.1%
0.0%
0.0%
0.0%
2.1%
-0.7%
-2.1%
-0.7%
0.0%
-0.7%
2.1%
Zero
sates cost
Default Probability
Loss Severity
Expected Loss
14.9%
11.2%
1.7%
12.2%
10.9%
1.3%
9.9%
10.9%
1.1%
7.3%
9.9%
0.7%
5.3%
8.7%
0.5%
3.8%
9.4%
0.4%
3.2%
8.6%
0.3%
2.6%
8.6%
0.2%
1.8%
9.9%
0.2%
3% Default Probability 18.1% 14.7% 12.1% 8.9% 6.6% 5.0% 4.4% 3.3% 2.5%
sales cost
Loss Severity 12.0% 11.8% 11.6% 10.8% 9.7% 9.8% 8.8% 9.4% 9.9%
Expected Loss 2.2% 1.7% 1.4% 1.0% 0.6% 0.5% 0.4% 0.3% 0.2%
5% Default Probability 20.4% 16.9% 13.6% 10.4% 7.8% 6.0% 5.4% 4.1% 3.3%
sates cost
Loss Severity 12.5% 12.1% 12.2% 11.1% 10.0% 10.0% 9.1% 9.4% 9.1%
Expected Loss 2.5% 2.1% 1.7% 1.2% 0.8% 0.6% 0.5% 0.4% 0.3%
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
Table 2.4: Continued
Panel C. Assumes construction loan LTV is 70% and loan term is 12 quarters
1-1 1-2 1-3
Scenario
1-4 1-5 1-6 1-7 1-8 1-9
Initial
State
Vacancy Change
Rent Growth
0.7%
-2.1%
0.7%
0.0%
0.7%
2.1%
0.0%
-2.1%
0.0%
0.0%
0.0%
2.1%
-0.7%
-2.1%
-0.7%
0.0%
-0.7%
2.1%
Zero
sales cost
Default Probability
Loss Severity
Expected Loss
24.3%
18.6%
4.5%
21.2%
16.7%
3.5%
18.2%
16.3%
3.0%
13.9%
14.5%
2.0%
12.0%
13.0%
1.6%
8.9%
14.1%
1.3%
6.9%
11.9%
0.8%
5.2%
13.0%
0.7%
5.1%
13.0%
0.7%
3% Default Probability 27.5% 24.2% 20.7% 16.3% 13.6% 10.6% 8.1% 6.6% 6.0%
sales cost
Loss Severity 19.3% 17.5% 17.2% 15.1% 14.3% 14.6% 12.9% 12.8% 13.9%
Expected Loss 5.3% 4.2% 3.6% 2.5% 1.9% 1.6% 1.0% 0.8% 0.8%
5% Default Probability 29.8% 25.6% 22.3% 17.9% 14.9% 11.9% 9.2% 7.8% 6.6%
sales cost
Loss Severity 19.7% 18.5% 17.8% 15.7% 15.0% 14.9% 13.2% 12.7% 14.7%
Expected Loss 5.9% 4.7% 4.0% 2.8% 2.2% 1.8% 1.2% 1.0% 1.0%
Table 2.4 Panel A-C report the expected default probabilities and expected
losses from simulations by scenarios and maturity terms for 70% LTV loans. Note
that the initial state refers to the initial market movement in the quarter immediately
preceding the simulation period. For example, scenario 1-1 is based on the
assumptions that the market vacancy goes up by 0.7% (e.g. from 9.3% to 10.0% in
one quarter) and the market rent declined by 2.1% in the quarter prior to the
simulations. The loss severity and expected loss include principal loss and the cost of
property sale only — neither the interest loss nor the property carrying cost during the
default/foreclosure/REO period is accounted for46.
4 6 One can easily account for these items in the loss severity calculation. But then we would need to
estimate the time frame from the initial default to the final property disposal, which is a subject
beyond the scope of this study. The qualitative conclusions from the current study should not change
once the more realistic assumptions are incorporated.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
Observing from the table, we find that the default probabilities change
dramatically from scenario to scenario meanwhile the mean loss severity does not
change as dramatically. For instance, if the loan term is 2 years (8 quarters), the loss
severity in the worst case (Scenario 1-1) is 11.2% and that in the best case (Scenario
1-9) is 9.9%. In comparison, the default probability in the worse case (Scenario 1-1)
is 14.9% while that in the best case is a merely 1.8%, which implies a difference of
more than eight times. This is expected in our option-based theoretical framework.
Because the default boundary should not change in any real estate market conditions,
either good or bad, but the default incidence would increase almost exponentially in
a worsening market when the default boundary is easily hit. A closer look reveals
that the differences of loss severity in different scenarios are caused by the fact that
the borrowers can wait to default at loan maturity with larger loss severity than
would be the case if the default option needs to be evaluated repeatedly during the
loan term. Since there is no feasible way to estimate the new property value
accurately, the longer the construction loan term, the higher the default probabilities,
and potentially the larger losses to the lenders.
Figure 2.8 shows the default probabilities of construction loans by maturity
terms with origination LTV at 70%. It appears that the default probabilities are
relatively very low for short-term construction loans, but the probabilities increase
almost linearly for longer term loans, suggesting the variance using the serially-
correlated processes are larger over the long run than a random walk model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
Figure 2.8: Default Probabilities by Loan Term
Default Probability by Construction Loan Term
- Assuming zero expected vacancy, rent and cap rate change
20%
15%
10%
5%
0%
Loan Term (Quarter)
Table 2.5 Panel A-C report the expected default probabilities and expected
losses from simulations by scenarios and loan terms for 75% LTV loans. We find
that the default probabilities increase drastically from 70% LTV loans to 75% LTV
loans, which seems to validate the rules-of-thumb in the commercial construction
lending industry where 75% is often the upper limit of commercial construction
A n
loans . In fact, when the commercial real estate market condition is not favorable,
many lenders would limit the LTV to 70%.
4 7 The supervisory LTV limit is 80% for commercial construction loans. See Office of Comptroller of
the Currency: “Commercial Real Estate and Construction Lending - Comptroller’s Handbook,
November 1995”.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
Table 2.5: Default Probabilities and Expected Losses by Simulation Scenarios
Panel A. Assumes construction loan LTV is 75% and loan term is 4 quarters
Scenario
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9
Initial Vacancy Change 0.7% 0.7% 0.7% 0.0% 0.0% 0.0% -0.7% -0.7% -0.7%
State
Rent Growth -2.1% 0.0% 2.1% -2.1% 0.0% 2.1% -2.1% 0.0% 2.1%
Zero Default Probability 8.1% 5.7% 4.0% 3.7% 2.3% 1.4% 1.6% 0.9% 0.5%
sales cost
Loss Severity 6.3% 5.4% 6.7% 6.1% 4.7% 6.0% 5.3% 3.3% 4.0%
Expected Loss 0.5% 0.3% 0.3% 0.2% 0.1% 0.1% 0.1% 0.0% 0.0%
3% Default Probability 11.4% 8.4% 5.8% 5.5% 3.8% 2.3% 2.7% 1.6% 1.1%
sales cost
Loss Severity 7.0% 6.2% 7.1% 6.7% 5.2% 6.1% 5.6% 4.2% 4.0%
Expected Loss 0.8% 0.5% 0.4% 0.4% 0.2% 0.1% 0.2% 0.1% 0.0%
5% Default Probability 13.2% 10.6% 7.2% 7.0% 4.8% 3.2% 3.9% 2.1% 1.6%
sales cost
Loss Severity 7.9% 6.7% 7.6% 7.0% 5.9% 6.0% 5.5% 4.8% 4.5%
Expected Loss 1.0% 0.7% 0.5% 0.5% 0.3% 0.2% 0.2% 0.1% 0.1%
Panel B. Assumes construction loan LTV is 75% and loan term is 8 quarters
1-1 1-2 1-3
Scenario
1-4 1-5 1-6 1-7 1-8 1-9
Initial
State
Vacancy Change
Rent Growth
0.7%
-2.1%
0.7%
0.0%
0.7%
2.1%
0.0%
-2.1%
0.0%
0.0%
0.0%
2.1%
-0.7%
-2.1%
-0.7%
0.0%
-0.7%
2.1%
Zero Default Probability 22.8% 19.3% 16.0% 12.6% 9.0% 6.8% 6.4% 4.9% 4.1%
sales cost
Loss Severity 12.3% 11.8% 11.5% 10.4% 10.0% 10.1% 9.0% 9.1% 8.8%
Expected Loss 2.8% 2.3% 1.8% 1.3% 0.9% 0.7% 0.6% 0.4% 0.4%
3% Default Probability 26.5% 23.3% 18.9% 15.2% 11.6% 8.7% 8.1% 5.9% 5.2%
sales cost
Loss Severity 13.3% 12.5% 12.6% 11.3% 10.4% 10.5% 9.7% 10.3% 9.7%
Expected Loss 3.5% 2.9% 2.4% 1.7% 1.2% 0.9% 0.8% 0.6% 0.5%
5% Default Probability 29.6% 25.6% 21.5% 17.3% 13.6% 9.9% 9.3% 6.7% 6.4%
sales cost
Loss Severity 13.9% 13.3% 12.9% 11.8% 10.8% 11.1% 10.3% 10.9% 9.6%
Expected Loss 4.1% 3.4% 2.8% 2.1% 1.5% 1.1% 1.0% 0.7% 0.6%
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
Table 2.5: Continued
Panel C. Assumes construction loan LTV is 75% and loan term is 12 quarters
Scenario
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9
Initial Vacancy Change 0.7% 0.7% 0.7% 0.0% 0.0% 0.0% -0.7% -0.7% -0.7%
State Rent Growth -2.1% 0.0% 2.1% -2.1% 0.0% 2.1% -2.1% 0.0% 2.1%
Zero Default Probability 32.0% 27.5% 24.2% 19.4% 16.3% 13.4% 10.6% 8.7% 7.4%
sales cost Lqss Severfty
19.1% 18.0% 17.3% 15.5% 14.6% 14.3% 12.6% 12.5% 14.0%
Expected Loss 6.1% 4.9% 4.2% 3.0% 2.4% 1.9% 1.3% 1.1% 1.0%
3% Default Probability 35.3% 30.5% 26.8% 21.9% 19.1% 15.4% 12.3% 10.5% 8.9%
sales cost Loss Severity
20.1% 19.1% 18.5% 16.5% 15.3% 15.2% 13.6% 13.2% 14.4%
Expected Loss 7.1% 5.8% 5.0% 3.6% 2.9% 2.3% 1.7% 1.4% 1.3%
5% Default Probability 37.9% 32.5% 29.3% 23.8% 21.1% 16.6% 13.9% 11.8% 10.2%
sales cost Loss Severity
20.7% 19.8% 18.8% 17.1% 15.8% 16.0% 13.9% 13.6% 14.4%
Expected Loss 7.8% 6.4% 5.5% 4.1% 3.3% 2.7% 1.9% 1.6% 1.5%
Table 2.6: Default Probabilities and Expected Losses by Simulation Scenarios
Panel A. Assumes construction loan LTV is 70% and loan term is 4 quarters
2-1 2-2 2-3
Scenario
2-4 2-5 2-6 2-7 2-8 2-9
Initial
State
Vacancy Change
Rent Growth
1.4%
-4.2%
1.4%
0.0%
1.4%
4.2%
0.0%
-4.2%
0.0%
0.0%
0.0%
4.2%
-1.4%
-4.2%
-1.4%
0.0%
-1.4%
4.2%
Zero Default Probability 11.2% 5.7% 2.7% 2.1% 0.6% 0.3% 0.3% 0.0% 0.0%
sales cost
Loss Severity 7.2% 5.5% 6.3% 6.0% 3.6% 1.7% 5.3% 0.0% 0.0%
Expected Loss 0.8% 0.3% 0.2% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0%
3% Default Probability 14.7% 8.1% 3.8% 3.3% 1.1% 0.6% 0.7% 0.1% 0.0%
sales cost
Loss Severity 8.2% 6.4% 7.1% 6.3% 4.5% 3.0% 4.2% 1.9% 0.0%
Expected Loss 1.2% 0.5% 0.3% 0.2% 0.0% 0.0% 0.0% 0.0% 0.0%
5% Default Probability 18.3% 10.3% 5.0% 4.2% 1.6% 0.9% 0.9% 0.2% 0.0%
sales cost
Loss Severity 8.3% 6.8% 7.1% 6.6% 4.8% 3.7% 4.7% 2.0% 0.6%
Expected Loss 1.5% 0.7% 0.4% 0.3% 0.1% 0.0% 0.0% 0.0% 0.0%
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
Table 2.6; Continued
Panel B. Assumes construction loan LTV is 70% and loan term is 8 quarters
2-1 2-2 2-3
Scenario
2-4 2-5 2-6 2-7 2-8 2-9
Initial Vacancy Change 1.4% 1.4% 1.4% 0.0% 0.0% 0.0% -1.4% -1.4% -1.4%
State
Rent Growth -4.2% 0.0% 4.2% -4.2% 0.0% 4.2% -4.2% 0.0% 4.2%
Zero Default Probability 33.6% 24.4% 17.2% 9.1% 5.3% 3.0% 2.0% 1.2% 0.8%
sales cost
Loss Severity 14.9% 13.4% 12.2% 10.7% 8.7% 8.7% 7.7% 6.8% 7.9%
Expected Loss 5.0% 3.3% 2.1% 1.0% 0.5% 0.3% 0.2% 0.1% 0.1%
3% Default Probability 38.7% 28.5% 20.1% 12.0% 6.6% 3.8% 2.7% 1.5% 0.8%
sales cost
Loss Severity 15.7% 14.3% 13.3% 10.7% 9.7% 9.5% 8.3% 8.1% 10.1%
Expected Loss 6.1% 4.1% 2.7% 1.3% 0.6% 0.4% 0.2% 0.1% 0.1%
5% Default Probability 41.9% 31.2% 22.2% 13.7% 7.8% 4.3% 3.3% 1.9% 1.0%
sales cost
Loss Severity 16.4% 15.0% 13.9% 11.3% 10.0% 10.3% 8.7% 8.3% 10.2%
Expected Loss 6.9% 4.7% 3.1% 1.5% 0.8% 0.4% 0.3% 0.2% 0.1%
Panel C. Assumes construction loan LTV is 70% and loan term is 12 quarters
2-1 2-2 2-3
Scenario
2-4 2-5 2-6 2-7 2-8 2-9
Initial
State
Vacancy Change
Rent Growth
1.4%
-4.2%
1.4%
0.0%
1.4%
4.2%
0.0%
-4.2%
0.0%
0.0%
0.0%
4.2%
-1.4%
-4.2%
-1.4%
0.0%
-1.4%
4.2%
Zero Default Probability 44.5% 35.9% 28.2% 16.6% 12.0% 7.5% 3.9% 2.3% 1.8%
sales cost
Loss Severity 23.1% 20.6% 19.3% 15.0% 13.0% 13.5% 11.1% 12.0% 13.4%
Expected Loss 10.3% 7.4% 5.5% 2.5% 1.6% 1.0% 0.4% 0.3% 0.2%
3% Default Probability 47.8% 39.1% 31.9% 19.1% 13.6% 8.8% 5.1% 3.0% 2.3%
sales cost
Loss Severity 24.4% 21.8% 19.9% 15.9% 14.3% 14.2% 11.3% 12.0% 12.8%
Expected Loss 11.7% 8.5% 6.4% 3.0% 1.9% 1.3% 0.6% 0.4% 0.3%
5% Default Probability 49.4% 41.1% 34.4% 20.5% 14.9% 9.9% 5.8% 3.7% 2.7%
sales cost
Loss Severity 25.6% 22.7% 20.4% 16.7% 15.0% 14.6% 11.6% 11.6% 13.1%
Expected Loss 12.6% 9.3% 7.0% 3.4% 2.2% 1.4% 0.7% 0.4% 0.3%
Table 2.6 Panel A-C report the expected default probabilities and expected
losses from simulations by scenarios and loan terms for 70% LTV loans. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
difference between Table 2.6 and Tables 2.4-2.S is that in Table 2.6 1 assume the
initial real estate market movement is about two times the total standard deviations
of the historical quarterly vacancy changes and rental growth rates.
Table 2.4 through Table 2.6 show that there exist a significant difference in
the default probabilities for alternative current market scenarios. I also perform
simulations that allow the construction periods (i.e. loan maturity) to vary and obtain
similar results. The results indicate that serial correlation and initial trends in the
commercial real estate market are important factors in determining the default
probabilities of commercial construction loans. The big differences between an
improving market and a worsening market suggest that the forecastable components
in the real estate market movement is of dominant importance to market participants
in different cycles of the market. Rational construction lenders should take advantage
of the forecastability of the commercial real estate market and adjust their
underwriting guidelines according to the prevailing market conditions. It appears that
the industry has been doing so as evidenced by the more strict credit rationing during
real estate downturns. This paper is the first to provide such quantitative statistics on
the default probabilities of commercial construction loans and should be of particular
use to the lenders and investors who wish to quantify more precisely the risks of
commercial construction lending during different phases of commercial real estate
cycles.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68
VI. Conclusions
The existing mortgage theoretic literature typically assumes a pure random
walk for the property value process that enables the application of the standard
option-pricing valuation technique. Recent empirical studies have generally
invalidated the random walk assumption. Both commercial and residential real estate
markets are found to have considerable persistence and are largely forecastable in the
short run.
In order to capture more realistically the behavior of commercial real estate
markets, I set up a structured dynamic model that consists of three basic inter
dependent serially-correlated stochastic processes and three derived processes. The
three basic processes are vacancy rate process, rent process as well as cap rate
process. The three derived processes are operating expense process, NOI process and
capital value process. This model set up not only incorporates the unique stock-flow
characteristics of the commercial real estate space market, it also takes into
consideration the linkage between the space market and the capital market. The
parameters of these processes are empirically estimated from the market-level time-
series data. Compared to a random walk model, this model setup produces lower
variance in the short run and higher variance in the long run as results of both serial
correlation within each variable and inter-dependence between them.
With negligible interim defaults, commercial construction loans provide an
excellent opportunity to study the implications of this structured dynamic model. The
Monte Carlo approach is employed to overcome multi-dimensionality and path-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
dependence issues associated with several numbers of serially-correlated variables.
A ruthless default option exercise rale is assumed. The simulation results from a
number of scenarios show that the default probabilities of commercial construction
loans are determined not only by the random disturbances of the property value
growth rates, but also by the forecastable components of vacancy change and rental
growth rate that drive the values of new properties. The serial correlations of the
market variables are found to have strong impacts on the probabilities of
construction loan default, and the variation in the initial trends of the commercial
real estate market produces significant variation in the default probabilities of
construction loans. Under the same underwriting criteria, the default probabilities of
commercial construction loans in a deteriorating market can be ten times or more
than these in an improving market. This suggests that it is very important for the
market participants to correctly assess the current market condition and to take
advantage of the intrinsic persistence and cyclicality of the commercial real estate
market when underwriting and servicing construction loans. Because the traditional
random walk model does not use the information of the current market condition, it
may lead to miss-estimation of the default probabilities and expected losses of
construction loans.
This study is the first to provide estimates of the default probabilities and loss
severities of commercial construction loans using a relatively more realistic model.
Simple assumptions are made in regard to the usually complex construction loan
contract terms. Future research is needed to examine the implications from relaxing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
these simplified assumptions. With additional computational sophistication, the
structured dynamic model proposed in this study can easily accommodate stochastic
interest rate process, stochastic construction cost process, as well as the possibility
that the expected time to completion will vary. Instead of the ruthless default rule,
the model can also be extended to incorporate the influence of default transaction
costs as in Riddiough and Thompson (1993). That is to introduce the developer’s
default behavior as a probability function that is based upon the property value and
other explanatory variables. While the NOI and capital value volatilities produced
from the current model seem to be consistent with the building-level volatilities as
used or estimated from other studies, more empirical data and research are needed to
obtain more precisely the parameter values of the processes at the property-level.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
Chapter 3
Workout Strategy and Conditional Default Probability of
Special-serviced CMBS Loans
I. Introduction
Commercial mortgage-backed security (CMBS) is an important asset class
AO
with aggregate outstanding balance of $372 billion as of December 2001. CMBS
now constitutes about 20% of the total commercial mortgage market. The major risks
of CMBS investment include default risk, prepayment risk, extension risk, and
liquidity risk. Contrary to residential MBS where prepayment risk dominates,4 9
CMBS is much better protected from this risk due to prevailing commercial
mortgage contractual clauses, such as enforced prepayment penalty, prepayment
lockout, yield maintenance and defeasance. This study focuses on a previously
unexplored aspect of the default risk, that is the conditional default risk after
problematic loans become special serviced.
Commercial mortgage default rates skyrocketed during the last commercial
real estate market downturn in the late 1980s to early 1990s. The outstanding
foreclosure rate of the loans held by the life insurance companies reached a high of
4 8 Source: Institutional Real Estate Newsline, “Roulac Capital Flows Database.”
4 9 See, for example, Richard and Roll (1989), Schwartz and Torous (1989), and Quigley and Van
Order (1990) for a discussion of prepayment risks in residential mortgage lending, and Downing,
Stanton and Wallace (2001) for a more recent development in this field.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
72
7.53% in the second quarter of 1992 (ACLI), and the delinquent rate of commercial
mortgages held by commercial banks reached 12.57% in the first quarter of 1991
(the Federal Reserve Board). These high default rates were certainly a result of the
devastating commercial real estate market crash in the last business cycle, and this
incidence has profoundly affected many financial institutions’ confidence on the
performance of commercial mortgages. Anecdotal evidences indicate that lenders
and investors have become much more cautious in recent years. They have tightened
underwriting standards, and have stepped up servicing effort to prevent the
reoccurrence of the skyrocketing commercial mortgage default rates as experienced
in the late 1980s to the early 1990s. As commercial mortgages have been
increasingly securitized, investors in the CMBS market also pay particular attention
to the default risk of collaterals and require various measures to be taken to mitigate
the default probabilities and potential loan losses. One of these measures is to have a
problem loan special serviced, which is to transfer the problem loan to a special
servicer that has more expertise in handling problem loans than regular servicers.
Of the three types of servicers in a CMBS deal, the master servicer oversees
the deal and monitors the timely collection and distribution of principal and interest
payments at the deal level, the subservicer deals with borrowers directly and
performs regular servicing routines such as collecting payments and bookkeeping,
etc., and the special servicer starts to take over the servicing responsibility when a
loan goes into serious trouble, usually when a loan becomes 30 to 60 days
delinquent. Special servicers are often granted the power to decide the most effective
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
workout strategy (e.g., decide whether to modify the loan term, to cure the
delinquency, or to foreclose the property, among other options) with the ultimate
goal as to maximize the expected net present value of the loans in problem. Because
special servicers usually possess more expertise in managing delinquent loans, they
charge a higher fee that is in the magnitude of 50 to 100 basis points for servicing
delinquent loans and 150 to 200 basis points for foreclosure and liquidation (Han
1996). As a comparison, the regular annual servicing fee is in the range of 3 to 17
basis points (Han 1996 and Shilling 1995). In addition to the higher cost, a potential
moral hazard problem may also arise as the special servicer may act in their self-
interest rather than in the interest of CMBS investors (Fathe-Aazam 1995, Sanders
1999 and Riddiough 2000). As such, special servicers play a critical role in the
CMBS market. Their business practice and their effectiveness in managing
delinquent loans have significant impact on the collateral performance and
consequently on the pricing of CMBS tranches, especially the lower-rated first-loss
pieces.
This study examines the performance of the loans that are special serviced.
Because both borrowers and servicers collectively affect the outcome of loan
servicing, this study distinguishes the servicers’ behavior from the borrowers’
behavior and performs two-stage analysis. That is to first study the decision making
process from the servicers’ perspective, and then to study the variables affecting loan
default while they are special serviced. The later is mainly the borrowers’ decision
making process although servicers still play a role during the second stage. Because
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
transferring loans to the special service category already reflects the servicers’ initial
view in regard to the borrowers’ potential behavior and the outcome of loan
servicing, a Heckman style two-stage modeling approach is employed to correct this
sample selection bias that also establishes the link between the two behaviors of the
servicer and the borrower.
This study benefits from many insights of earlier literature. As the first study
on default risk assessment of commercial mortgages, Vandell (1984) hypothesizes
that default could be due to the occurrence of either adverse cash flow or negative
equity in the property. He recognizes the interactions between cash flow and equity
conditions in affecting default risk. He also recognizes the importance to consider the
timing of default and to incorporate the time-varying information about the property,
market, and economic conditions. Kau, Keenan, Muller and Epperson (1987,1990)
and Titman and Torous (1989) start to apply contingent-claims approach to valuing
commercial mortgages. Vandell (1992) carries out empirical study using aggregate
commercial mortgage foreclosure experience and confirms the equity theory of
default. He also attributes the possible high transaction costs as the cause of the
under-exercise of the default option.
Vandell, Barnes, Hartzell, Kraft and Wendt (1993) were the first to use loan-
level commercial mortgage data from a large life-insurance company. Empirical
results confirm the dominance of loan terms and property value trends in affecting
default. Ciochetti, Deng, Gao and Yao (2002) use a similar data set (also from a
major life insurer), and apply the competing risk framework developed by Deng,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
Quigley and Van Order (1996,2000) in the residential mortgage market to
commercial mortgages. Their findings confirm that the put and call options are
highly significant in explaining commercial mortgage default and prepayment.
Transaction costs are also found to be important in explaining mortgage termination.
In particular, solvency conditions reduce default risk, and small borrowers default
much more frequently. Goldberg and Capone (2002) incorporate both equity and
cash-flow considerations (so called double-trigger) in default models. Their
empirical analysis using the data of multi-family loans purchased by Fannie Mae and
Freddie Mac confirms the importance of double-trigger theory. They find that
models relying solely upon property equity may have a tendency to overstate
potential default rates, and those relying only on cash flows understate default risk.
Archer, Elmer, Harrison and Ling (2002) argue for the endogeneity in commercial
mortgage underwriting in terms of LTV ratio, which would imply no empirical
relationship between default and LTV because lenders would require lower LTVs for
high risk mortgages. They examine 495 multifamily mortgages securitized by the
Resolution Trust Corporation (RTC) and the Federal Deposit Insurance Corporation
(FDIC) and find no evidence of LTV effect on default, while the strongest predictors
of default are property characteristics, including property location and initial cash
flow. Ambrose and Sanders (2003) are the first to conduct empirical study on CMBS
loans.
While the aforementioned studies provide excellent theoretical guide and
empirical evidence on the determinants of commercial mortgage defaults, they all
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
focus on the default probabilities for loans from performing status to default status.
Several studies, Riddiough and Wyatt (1994a, 1994b) and Harding and Simians
(2002), start to consider theory of workout strategy of troubled debt and its
implication on loan defaults and valuation, although none of these studies provides
empirical evidence. This study not only empirically analyzes servicers’ workout
strategic decisions but also analyzes the performance of troubled loans after they
caught servicers’ attention (i.e. being special serviced). It shares some similarity with
Ambrose and Capone (1998) on single-family mortgage default resolutions. While
both recognize that default is not a one-step process, their study focuses on the step
from initial default (90-day delinquency) to final foreclosure, this study focuses on
the step from initial delinquent (first enter special service) to default. Another related
study is Springer and Waller (1993) who examine lender forbearance and find that
the primary factors influencing the timing of the lender’s foreclosure decision are the
borrower’s equity position and the erosion of that position with continuing
delinquency. Capone (1996) also provides excellent review of the workout
alternatives to foreclosure in the residential mortgage industry.
The rest of the chapter is organized as follows: Section II discusses the
default process in commercial mortgage lending; Section III describes the data used
in this study; Section IV discusses the estimations and the empirical results; Section
V is a conclusion.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
II. Default Process
There are several stages for loans in non-performing status. First, the
borrower decides to miss a scheduled monthly payment and the loan becomes
delinquent. Since default is generally considered as the exercise of the implicit put
option embedded in the mortgage contracts5 0 , the initial delinquency can be
considered as the borrower’s tentative step to exercise the put option. Note the
borrower still has lots of room to relinquish the put option exercise at this stage since
it is relatively less financially stressful to make up the missed one-month payment.
The special servicer usually steps in when the loan becomes 60 days past due, i.e.
when the loan has missed two scheduled payments. The transfer of servicing
function from the regular servicer to the special servicer is usually an indication that
the loan is intentionally non-performing, i.e. the servicers determine that the missed
payments are not due to inadvertent mistakes but rather due to the borrower’s
deliberate action. The special servicer then decides the best workout strategy
meanwhile the borrower continue to re-evaluate the financial situation in order to
finalize the implicit put option. Following industry convention, 90 days past due is
defined in this study as default because this status shows the borrower’s
determination to exercise his put option. While there could be jumps between these
stages, the general process can be summarized as in Figure 3.1.
5 0 See Hendershott and Van Order (1987), and Ambrose, Capone and Deng (2001) for a discussion of
put option theory and mortgage default.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
Figure 3=1: The Default Process
Current
Current + • Delinquent
£ Default + ■ Foreclosure
Special S e rv ic e * ■ Modification
Current
As mentioned earlier, the route from delinquent to special service is a
common practice in the CMBS market although it is less so for life insurance
companies and commercial banks. Archer, Elmer, Harrison and Ling (2002) provide
more discussion on the post-default process of commercial mortgages, while
Ambrose and Capone (1998) and Ambrose and Buttimer (2001) provide theoretical
and empirical analysis on post-default options for single-family mortgages.
This study focuses on the process from delinquent to special service to
workout outcomes. Note there are two perspectives to look at the process. The first
perspective is from the servicers’ point of view. After examining the financial
condition of the collateral, the market condition, the borrower’s own financial
situation, and other relevant factors, the servicers decide the best workout strategy,
which in theory should lead to the “expected” outcome. The major categories of
“expected” outcome include foreclosure, modification, and return to current, among
others. If the servicer expect the borrower to default for a prolonged period,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
foreclosure is usually the best strategy. The “expected” outcome does not necessarily
equal the actual outcome because the later is also determined by the borrower’s
behavior. This leads to another perspective that is from the borrower’s point of view.
We expect borrowers would still follow the rules of default put option when they are
being special serviced. In fact, the borrowers could be more ruthless in this stage
because they have already showed their intention to exercise the put option. Of
course, cash flow condition may still play a critical role as found by some other
studies. A rational borrower would be hesitant to complete the put option if there is
still positive cash flow from the collateral, while negative equity must be the
necessary condition for the borrower’s final completion of the default put option.
in. Data
The special serviced loan data are gathered from Standard & Poor’s Conquest
CMBS deal library.5 1 The data collection date is September of 2002, and loan status
was recorded as of August 2002. The data set includes 144 CMBS deals, most of
them are conduit deals. After excluding the records with missing data and cross
collateralized loans, a total of 13,132 loans, both performing and non-performing, are
obtained for the first stage estimation in the framework of the Heckman approach.
There are originally 577 loans in the special service status. Out of these 577 loans,
there are 74 loans that are either cross-collateralized or apparently backed up by the
5 1 Courtesy access of Standard & Poor’s Conquest CMBS deals library is through the University of
Southern California.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
same borrower. Noticeable borrowers that have multiple loans include several hotel
chains, retail chains, and restaurant chains, among others. These loans are excluded
from the analysis due to the difficulty to analyze the business failures. A final data
set of 493 loans is retained for the second-stage analysis. Because the reporting
procedure and style are quite different across servicers, it is possible that cross-
connection between some of the loans may still exist in the final data set. But the
possible error should be insignificant so that the loans in the final data set are mostly
independent therefore satisfying the data requirement for the following statistical
analysis.
Table 3.1: Sample Loan Statistics by Property Type
Property No. of Sum of Average % by No. of % by Cutoff
Type Loans Cutoff Balance Cutoff Balance Loans Balance
Apartment 118 $377,842,605 $3,202,056 23.9% 13.3%
Hotel 132 $690,546,855 $5,231,416 26.8% 24.3%
Office 62 $660,493,930 $10,653,128 12.6% 23.2%
Retail 131 $898,368,902 $6,857,778 26.6% 31.6%
Warehouse 50 $216,746,746 $4,334,935 10.1% 7.6%
Total 493 $2,843,999,036 $5,768,761 100.0% 100.0%
Table 3.1 shows the breakdown of the final data set of the special serviced
loans by property type of the collateral. While mortgages of retail properties register
the most percentage in terms of loan balance (31.6%), hotel, retail and apartment
have similar percentages in terms of loan counts. A closer look at the average loan
balance reveals that retail loans have slightly larger balance than the average, while
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
office loans have the largest average balance among all property types. Apartment
loans have the smallest average balance as one would expect, and warehouse loans
rank the second smallest by balance. Table 3.2 shows the breakdown of the final data
set by servicers’ workout strategy. It is interesting to see that close to half of the
sample loans do not contain information on servicers’ workout strategy. This
suggests the difficulty in collecting complete CMBS data because CMBS deals have
a diverse universe of originators, servicers, trustees, and investors, all of them have
different reporting standards and requirements. Of the loans that have the
information of servicers’ workout strategy, about half are modified, with the
remaining loans fall into three categories: foreclosure, return, and bankrupt.
Table 3.2: Sample Loan Statistics by Workout Strategy
Workout No. of Sum of Average % by No. of % by Cutoff
Strategy Loans Cutoff Balance Cutoff Balance Loans Balance
Foreclosure 48 $265,017,274 $5,521,193 9.7% 9.3%
Modified 122 $811,761,552 $6,653,783 24.7% 28.5%
Return 53 $295,271,563 $5,571,162 10.8% 10.4%
Bankrupt 36 $186,395,154 $5,177,643 7.3% 6.6%
Unidentified 234 $1,285,553,494 $5,493,818 47.5% 45.2%
Total 493 $2,843,999,036 $5,768,761 100.0% 100.0%
Real estate market data include occupancy rates for the hotel sector and
rfy
vacancy rates for the remaining property types. In addition, NCREIF Property
Index (NPI) is used to proxy for the market-level value indices and NOI indices53.
5 2 The author is grateful for Property & Portfolio Research, Inc. (PPR) for providing these real estate
market data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
IV. Empirical Analysis
This section presents empirical analysis on the behavior of both servicers and
borrowers. The first part applies multinomial logit model to analyze the one-time
decision-making process of the servicers, and the second part applies a proportional
hazards model with time-varying covariates to capture the repeated decision-making
process of the borrowers in the special service category. A Heckman style two-stage
approach is employed in the second part to correct for the potential sample selection
bias that may arise.
A. Multinomial Logit Analysis o f Lenders’ Workout Strategy
Of the 493 special serviced loans in the final sample, 217 loans have clear
identification of servicers’ workout strategy. Among these 217 loans, servicers
intend to bring 52 loans back to “current” status, to foreclose 47 loans, and to modify
the terms of the remaining 118 loans. Remember that servicers’ intention does not
guarantee the success of each strategy, in fact, loans could still fail to perform even
though servicers intend to bring them back to “current” or have modified the loan
terms. The first part of the analysis focuses on the reasons behind servicers’ choice
of a particular workout strategy over alternatives. The ultimate outcome of these
strategies will be examined in the second part of the analysis using a proportional
hazard approach. The measurable variables that have the potential to influence the
5 3 NCREIF Property Index (NPI) publishes data series at several aggregation levels. Here I use the
property-type/MSA level indices.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
83
servicers’ choice of workout strategy are mainly related to loan characteristics and
real estate market conditions. Unfortunately, there is not enough information on
borrower characteristics although they certainly matter.
Both option theory and empirical evidence suggest that a loan’s current
equity level (measured by one minus the current loan-to-value ratio, i.e. LTV) has a
dominant effect on the probability of loan default. We expect servicers would be
more likely to foreclose high LTV loans due to their high default option value. To
cut the carrying cost and interest payment advance, the sooner the loans are
foreclosed, the lower loss severity would be. For the loans with middle-tier LTV
(that is, LTV is not too high so immediate foreclosure is justified and LTV is not too
low hence there is no need for servicers to modify loan term5 4 ), we expect servicers
would be more willing to modify the loan terms in order for them to stay “current”.
For this type of loans, a little bit payment reduction could be enough for the
borrowers to remain solvent. Therefore we expect LTVs should be positively related
to servicers’ choice of foreclosure strategy and to a lesser extent to servicers’ choice
of loan term modification strategy.
When borrowers are insolvent and run into trouble (that’s the likely reason
why they enter the special service category), the net operating cash flows are critical
since it is the net cash flows that affect the immediate financial stress to the
5 4 Instead of loan term modification that is long term, servicers could offer forbearance, which is short
term, to help borrowers overcome temporary cash flow problems for low LTV borrowers. See Capone
(1996).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
borrowers of commerci al mortgages. Because commercial properties are very
illiquid and involves substantial amount of transaction cost (both tangible and
intangible), borrowers are very unlikely to dispose their properties quickly to meet
the cash payment requirements even if the market value of collateral is higher than
the mortgage principal amount. We expect the net operating cash flows (proxied by
debt-service-coverage-ratio, i.e. DSCR) have a negative relationship with servicers’
choice of foreclosure.
While commercial properties are illiquid assets, we should also realize that
rational servicers would take a forward-looking approach in their decision making
process. They would examine the property market condition in order to determine
whether the performance of a particular collateral would get better or worse in the
future, and whether the property would be eventually sold at a higher price or a
lower price. Because all these property market conditions ultimately affect the
possibility of the borrowers’ regaining financial solvency through either improved
cash flows and/or profitable sales of the properties, we expect that higher rental
growth rates in the real estate space market (proxied by the market-level NOI growth
rates) and higher value appreciation rates in the property asset market (proxied by the
market-level value appreciation rates) would have a negative relationship with
servicers’ choice of foreclosure5 5 . Also, in an improving commercial real estate
5 5 Note we implicitly assume that servicers do not intend to profit by foreclosing a property in a “hot”
market in order to sell the property at a higher price than the principal loan amount. This assumption
is reasonable given the fact that most servicers have no intention to take advantage of the temporary
hardship of borrowers so that foreclosure is always the last and least preferred strategy of lenders
facing defaults.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
85
market, servicers are less likely to modify the loan terms so that the NOI growth
rates and property value appreciation rates should have a negative relationship with
servicers’ choice of loan term modification.
The change of market-level occupancy rates is used as another variable
proxying for real estate market condition. It is well known by commercial real estate
participants, the vacancy rates (or the occupancy rates) serve as an excellent leading
indicator of future cash flows and property value growth potential5 6. If the occupancy
rates in a market are getting higher, the servicers would expect improving cash flow
and would be less likely to foreclose the property. We therefore expect a negative
relationship between the change of occupancy rates and lenders’ choice of
foreclosure.
Empirical mortgage research literature has also identified the seasoning effect
in loan default probability. That refers to the default seasoning pattern that default
probabilities steadily increase in the initial years after loan origination and then level
off between the third and the seventh year and then gradually decline (see Goldberg
and Capone 2002 for recent evidence). We expect servicers would consider the
seasoning of troubled loans in their decision making process. For both financial and
psychological reasons, we expect servicers are more likely to tolerate payment delay
and more likely to workout a modification strategy after the loans are in good
5 6 It should be noted that vacancy rates are traditionally used in the commercial real estate studies in
the sectors of apartment, office, retail and warehouse, while occupancy rates are preferred measure for
hotel properties.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
standing for a long time period. A positive relationship is thus expected between loan
age and servicers5 choice of modification strategy. Riddiough (2000) presents
another possibility. He argues that the borrower’s bargaining power in renegotiating
the loan may be reduced in the CMBS market because the special servicer may view
financial distress as an isolated occurrence instead of an ongoing business
relationship. This impersonal relationship between the borrower and the special
servicer may restrict the ability to arrive at a mutually agreeable outcome. This
hypothesis is empirically tested in the following analysis.
Studies by Clauretie (1987), Ciochetti (1997) and Ambrose, Capone and
Deng (2001) also documented the importance of state foreclosure laws on the
probabilities of default because foreclosure is more costly in states that require
lengthy legal process. In this study, states are grouped by two categories: judicial
foreclosure and power-of-sale, the assignment of each state to these categories
follows Ciochetti (1997).
In all, seven variables are identified to represent the various dimensions that
rational servicers are likely to take into consideration in making workout strategic
decisions. Before turning to the statistical model, I also performed a simple
correlation analysis of these explanatory variables (Table 3.3) and find mostly
insignificant correlations between the independent variables. It suggests that the
independent variables indeed represent different dimensions that are likely to be
orthogonal. The three real estate market variables - value growth, NOI growth and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
e n
occupancy change - have positive yet less than significant correlation , suggesting
that several dimensions of the commercial real estate market should be
simultaneously examined.
Table 3.3: Correlation Matrix of the Variables Used in Multinomial Logit Analysis
LTV DSCR Value
Growth
(Market)
NOI
Growth
(Market)
Occupancy
Change
(Market)
Loan
Age
LTV (Loan)
DSCR (Loan) (0.23)
Value Growth (Market) (0.16) 0.30
NOI Growth (Market) (0.14) 0.16 0.31
Occupancy Change (Market) (0.13) 0.26 0.22 0.11
Loan Age (0.17) (0.05) (0.15) (0.02) (0-05)
Mean 75.8% 1.28 -2.7% -6.0% 1.21 40.5
Standard Deviation 38.1% 0.56 6.3% 15.4% 0.32 20.8
No. of Observations 217 214 217 217 217 217
Once the potential explanatory variables are identified, we further assume a
loss severity function where lenders maximize a linear utility function Uj over j
workout strategies:
Uj = a j + P jX + JjZ + Bj, y = 1,2,3. (3.1)
where X is a vector of loan and property characteristics (LTV, DSCR, and loan age),
Z is a vector of real estate market variables. The possible workout strategies are: (1)
foreclosure, (2) modification, and (3) return to “current”, which are all conditional on
the mortgage being specially serviced. The workout strategy j is chosen whenever
the servicers expect the lowest future loss severity conditional upon that strategy. For
5 7 This is because these three variables are correlated through lagged relationships, see the first and
the second chapters of this dissertation for their relationships.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
example, if the servicer finds that the real estate market is drastically improving, he
would neither foreclose the loan nor modify the loan term. Instead, he would simply
push the borrower to make timely payments so that he wouldn’t realize any loss.
Although the expected loss severity function is unobservable, we do observe the
choices servicers made under varying conditions, and these choices directly reflect
the least loss severity expectations for the servicers. The probability of each workout
strategy Pj can therefore be modeled as a multinomial logit function5 8:
Oj+PjX+YjZ
P r(P . = 1) = _ r -------- , j = 1,2,3. (3.2)
X ea i+ P k X + riZ
The expected sign of the coefficients are explained earlier in the section. The
multinomial logit analysis is performed using SAS CATMOD procedure. Table 3.4
shows the results from the maximum likelihood estimation with “return to current”
as the base case.
It is interesting to note that only three explanatory variables show up as
significant in affecting lenders’ workout choice. The negative relationship between
market NOI growth rates and foreclosure strategy is strongly supported by the logit
analysis. The magnitude of the impact of market NOI growth rates on servicers’
workout strategy is also confirmed. Everything else being equal, in a real estate
market where rents are increasing (NOI growth rate is positive), servicers prefer to
5 8 Among many others, similar multinomial logit analysis has been used by Campbell and Detriech
(1983) in examining the termination of residential mortgage default, and by Ambrose and Capone
(1998) in modeling the conditional foreclosure probability of single-family mortgages.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
89
bring the loans back to “current” and are least likely to foreclose on that property.
The negative coefficient of market value growth rates appear to support the
hypothesis, however the insignificance of covariate in both foreclosure and
modification also seem to suggest that servicers pay more attention to cash flow
variables (NOI growth rates) than to property value variables (value growth rates),
possibly because cash flow is tangible and easily measurable at the time of decision
making while property value is subject to error-prone value appraisals and less
accurate in practice. Another real estate market proxy, the change of market
occupancy rates, has the wrong sign and is insignificant. The possible reason is that
the market vacancy rates (occupancy rates) exert indirect influence on loan
performance through affecting the cash flows of the underlying collateral, servicers
have no immediate need to understand the more complex real estate market if they
have property cash flow information at hand.
Table 3.4: Multinomial Logit Analysis of Workout Strategy
Foreclosure Modified
Parameter Estimate Standard Chi- Pr > Estimate Standard Chi- Pr >
Error Square ChiSq Error Square ChiSq
Intercept -3.0108 1.3441 5.02 0.0251 -1.8902 1.0741 3.10 0.0784
LTV (Loan) 1.0368 0.6403 2.62 0.1054 0.4908 0.6053 0.66 0.4175
DSCR (Loan) 0.5506 0.4310 1.63 0.2014 0.4471 0.3383 1.75 0.1863
Value Growth (Market) -2.4174 4.1440 0.34 0.5596 -3.6360 3.4628 1.10 0.2937
NOI Growth (Market) -5.1921 1.7572 8.73 0.0031 -1.4455 1.3784 1.10 0.2943
Loan Age 0.0048 0.0124 0.15 0.7017 0.0214 0.0100 4.58 0.0324
Occupancy Change (Market) 0.7282 0.7683 0.90 0.3433 0.6926 0.6174 1.26 0.2619
Foreclosure Law (Judicial) 0.4359 0.2206 3.90 0.0482 0.1063 0.1801 0.35 0.5552
Log Likelihood Value:_________-198.80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
The significant positive relationship between loan age and servicers’ choice
of loan term modification strategy suggests that servicers do seem to be more
tolerable to borrowers who have been performing for a long period.
Two loan-specific financial variables, LTV and DSCR are not significant,
with LTV has the correct sign and DSCR has the incorrect sign. This is possible
because the loans must have some type of idiosyncratic problems (could be some
type of trigger events as in residential mortgages) before they enter the special
service category. Since both variables are largely estimated from market-level
indices, they may not reflect the true financial conditions for these properties. In
other words, both LTV and DSCR in the empirical model are imperfect proxies.
Another possibility could be that, even if LTV and DSCR are correctly estimated,
servicers might still pay more attention to the general market condition rather than
focusing on individual property performance. Because rational lenders would focus
more on the possibility of curing the problem in the future, which is mostly
dependent upon the general market condition, rather than upon the past financial
situation that is very likely a reflection of idiosyncrasy.
The results show significant positive impact of judicial foreclosure law on
servicers’ choice of foreclosure strategy. This seems puzzling at the first look,
because judicial foreclosure is more costly than power-of-sale, one might expect the
servicers not to prefer foreclosure in the states where judicial foreclosure is required.
However, as suggested by Riddiough and Wyatt (1994b), servicers may not want to
reveal their unwillingness to foreclose in these states because doing that would
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
encourage more defaults. Actually, as shown from the statistical results, servicers
may purposely become tougher in states with judicial foreclosure laws in order to
discourage future defaults.
The significant coefficients of both intercepts suggest that, either the
empirical model misses some explanatory variables, or servicers prefer foreclosure
the least and prefer the “return to current” strategy the most. Both are equally likely
reasons, while the later explanation seems to corroborate with the lenders’ rationale
as examined earlier.
In summary, the results of multinomial logit analysis appear to suggest that
special servicers make workout strategic decisions based largely upon the real estate
space market condition - proxied by market-level NOI growth rates. This is
understandable since space market conditions (rental growth and NOI growth rates)
are easily observable and measurable. The forward-looking component of current
space market condition is also helpful in the decision-marking process. Another
finding is that servicers are more willing to modify loan term for more seasoned
commercial mortgages and are more likely to foreclose loans in states where judicial
foreclosure is required.
B. Proportional Hazard Analysis ofDefault Probability o f Special Serviced Loans
Before turning into the proportional hazard analysis of default outcomes of
special serviced loans, recall we define loans being “bad” as the “90 days late” in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
mortgage payment or worse, so “bad” also includes “foreclosure” or “REO”5 9. Since
loans enter special service due to various payment problems, “30 days late” and “60
days late” are considered as “good” in the sample. Hence “good” loans in the sample
include “current” loans and those loans in minor delinquency. Among the 493
special serviced loans in the final data sample, 183 are identified as “bad” since they
became “90 days late” or worse by the end of the data collection date, and 310 still
remain in “good” standing by the end of the data collection date. These 310 loans are
stamped as censored observations. Because special-serviced loans are counted as
non-performing status in many industry reports, it is important to realize that not all
special-serviced loans end up in default and the percentage of non-defaults is
actually not trivial6 0.
Once the problem loans are transferred to the special servicer, the special
servicer must decide the most effective (lease cost) solution to the problems. The
decision must be made repeatedly until the loans terminate or drop out of the special
service category. The loans may remain in special service for varying length of time.
If the loans remain current while they are special serviced, it would imply the
effectiveness of special service. While the results certainly depend upon various
conditions, the ideal goal of special service is to cure the problems of the loans and
5 9 Defining defaults as 90-days-late or more is consistent with many other studies, e.g. Archer et al.
(2002). Loans that are delinquent for 90 days or more are also called “serious delinquency” in the
mortgage industry. Foreclosure becomes a viable option only until this stage. See Capone (1996) for
details.
6 0 We should not conclude from the sample data that the majority of special serviced loans would not
default because our data sample is censored.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
make them current (to maximize the present value for the lenders/investors). The
special servicer also makes decisions regarding whether to modify the loan term
would be the least-cost alternative. The survival probability of special serviced loans
is a function of various characteristics, observable at the time when loans became
special serviced and during the special service period.
The Cox proportional hazards model is employed to analyze the probability
of loans becoming “bad” since they enter the special service category. The Cox
model has recently become the most popular technique in mortgage performance
studies (Green and Shoven 1986, Schwartz and Torous 1989 are among the first to
apply hazard model, and Deng, Quigley and Van Order 2000 presents more recent
applications with increased realism and sophistication). The model was primarily
developed and extensively used in the biomedical sciences to predict survival of
patients (e.g., patients who have had heart transplants or cancer diagnoses) based on
patient and treatment characteristics. Because mortgage default (becoming “bad”)
can also be considered as a survival failure, the model has been conveniently
borrowed by mortgage researchers to estimate the effects of explanatory variables on
the commercial mortgage’s time to default. In particular, the model estimates the
probability that a mortgage with certain characteristics will default in a given period
given the fact the mortgage is still alive at the beginning of the period, which is also
called the conditional probability of default. Cumulative default probability can then
be easily computed from the conditional default rate (CDR).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
Assuming the probability density function of duration of the loan to first
default at t is fit), and the cumulative probability distribution is F(t), the hazard
function is defined as the probability density of default at time t, conditional on its
being active before time t:
m = a n ( 3 3 )
a - > o A 1 — F(t)
This hazard function, h(t\ represents the conditional default probability in the
next period given that loan was current at time t. The proportional hazard assumption
of Cox (1972) assumes a vector of covariates, z,{t), either time-constant or time-
varying, affect the baseline hazard function, hrft) proportionally in exponential form.
Thus the hazard function for subject i at time t can be specified as:
k(ti; z(0 ) = ho(ti)exp(z(ttyf3) (3.4)
where j 8 is the vector of constant coefficients. Note that the baseline hazard function
is the hazard rates over the time for average loan in the sample, and the
proportionality factor is the exponential function of the time varying or time constant
covariates z and the coefficient vector /3 . A popular estimation approach is Cox’ s
Partial Likelihood specification, which only requires the existence of a common
stationary baseline hazard function, ho, for all subjects. The Cox approach estimates
the coefficients for the proportional factors based on rank and order statistics (hence
called Partial Likelihood). So p can be identified without parametric restrictions on
the baseline function since ho(t) is concentrated out as a nuisance number. Note the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
proportional hazard model is parametric in the specifications of proportional change
while the baseline hazard function can be either parametric or non-parametric.
Figure 3.2: Survival Functions by Property Type
Survivor Function by Property Type
1.00
-A partm ent
-H otel
-O ffice
- Ratal
• W areh o u se
0.90 -
0.80 -
0.70
3 .
0.60 -
0.50
0.40
0.30
0.20 -
0.10
0.00
6 12 15 27 30 0 3 S 18 21 24
Duration (in months)
Before proceeding to the Cox hazard model, I first examine the empirical
survivor functions from the unadjusted sample by property type. Figure 3.2 shows
that survival probabilities vary substantially by property type. The graph clearly
suggests that hotel loans are the most likely to become default, followed by retail
loans. Only about 37% of the hotel loans are still alive by month 12 since they are
special serviced. Retail loans also have high default rates. The performance of
apartment, office and warehouse loans looks similar considering the sample size.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
This observation seems to reflect the recent property market conditions, that is,
during the recent economic slowdown, the hotel sector was hit the hardest due to
reduced traveling, and the retail sector was also hit very badly due to heightened
competition and increased bankruptcies of many retailers.
Table 3.5: Descriptive Statistics
At the Date Loans Were First
Transferred To Speciiil Servicer
At the Date Loans either
Went "Bad" or Were Censored
Variable Loan Status
Total
Loan Status
Total Bad8 Good Bad Good
Loan Age 41.9 42.9 42.5 45.5 50.9 48.9
(18.1) (20.7) (19.8) (18.1) (19.9) (19.4)
LTV 83.2% 68.9% 76.1% 81.9% 67.7% 73.0%
(53.5%) (19.6%) (56.0%) (53.1%) (19.8%) (36.5%)
DSCR0 1.24 1.31 1.29 1.22 1.29 1.26
(0.72) (0.61) (0.65) (0.71) (0.59) (0.64)
Value Change (yr-to-yr) -4.8% -2.9% -3.6% -5.0% -3.6% -4.1%
(7.0%) (7.3%) (7.2%) (7.2%) (6.2%) (6.6%)
NOI Change (yr-to-yr) -7.4% -4.4% -5.5% -8.0% -4.8% -6.0%
(18.8%) (18.9%) (18.9%) (15.4%) (12.3%) (13.6%)
Cutoff Occupancy*1 88.2% 92.2% 90.8% 77.3% 83.7% 81.3%
(14.7%) (11.4%) (12.8%) (22.6%) (19.2%) (20.8%)
M arket Occupancy6 77.9% 83.5% 81.4% 78.0% 83.3% 81.3%
(14.6%) (11.8%) (13.2%) (14.1%) (11.1%) (12.5%)
Annual Payment 511,935 531,071 523,977
(481,950) (788,483) (690,414)
Initial Note Rate 8.50% 8.26% 8.35%
(0.86%) (0.84%) (0.85%)
No. of Loans 183 310 493 183 310 493
Note: Standard deviations are in parentheses
8 "Bad" is defined in this table as having entered "90 days late" or worse condition.
b "Good" is defined in this table as having not met the definition of "Bad".
c DSCR: Debt-service-coveiage ratio.
d Cutoff Occupancy is the occupancy dan obtained d irectly from the loan files.
e Market Occupancy is the market-level occupancy data supplied by PPR.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
Table 3.5 shows the summary statistics both at the time loans first enter the
special service status and at the time loans either become “bad” or censored at the
end of the data collection date. There appears to be big differences between “bad”
loans and “good” loans in terms of average LTV and the market-level occupancy
rates. There is also slight difference in the initial coupon rates, “bad” loans have
relatively higher coupon rates, yet the difference is not that big. The differences of
year-to-year value appreciation, DSCR, the NOI (year-to-year) growth rate, and
property-level cutoff occupancy rates are also as expected, but the differences do not
appear to be as pronounced as in LTV. There doesn’t seem to be meaningful
differences between the two categories in terms of loan age and annual loan
payment, which are used as a proxy for the financial obligation of the borrowers.
Table 3.6: Descriptive Statistics at the Date Loans either W ent "Bad" or Were Censored
Prop Type Apartment Office Retail Warehouse Hotel
Standing Bad Good Bad Good Bad Good Bad Good Bad Good
Loan Age 37.8 49.1 41.5 44.8 44.7 56.4 41.5 45.0 51.0 54.1
LTV 74.5% 65.5% 62.3% 65.0% 97.6% 69.3% 60.5% 64.4% 83.1% 72.6%
DSCR 1.15 1.33 1.36 1.50 1.42 1.33 1.39 1.44 1.03 0.94
Current 89.9% 88.9% 86.7% 86.1% 86.2% 87.2% 96.1% 96.8% 58.9% 62.3%
Occupancy
Market 92.7% 91.7% 82.8% 83.8% 87.1% 86.6% 90.8% 89.7% 61.4% 62.8%
Occupancy
Value Change 1.2% 0.6% -2.3% -4.5% -2.0% -1.7% 0.9% -1.0% -11.8% -12.8%
(yr-to-yr)
NOI Change -5.5% -6.9% 0.5% 3.4% -3.1% -1.4% 2.1% -0.5% -16.8% -15.1%
(yr-to-yr)
Initial Note 8.25% 8.05% 8.07% 8.27% 8.35% 8.28% 8.24% 8.22% 8.87% 8.57%
Rate
Annual 361,078 256,252 524,574 1,012,517 538,691 672,653 571,392 348,614 535,961 484,225
Payment
No. of Loans 29 89 16 46 51 80 16 34 71 61
Note: All the variables are measured at loan level except Market Occupancy.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
Table 3.6 reports the summary statistics by property type. It is striking to
notice that the big differences of LTV come mainly from retail, hotel and apartment
sectors. The difference of LTV does not appear to be significant in both office and
warehouse sectors. The major difference of DSCR comes from apartment and office
sectors while not in the others. The differences ofNOI and value growth rates are not
significant in all the sectors. Closer observation of Table 3.6 also suggests that the
marked performance differences between property types could be explained by more
fundamental variables. For example, the whole hotel sector appears to have suffered
the greatest cash flow drain (the biggest negative NOI growth) and largest value
decline (more than 10% value decline on annual basis). We can also observe that
“bad” retail loans have exceedingly high LTV based on the estimation. These
observations lead one to suspect that more fundamental variables rather than
property type determine the default probabilities.
As widely known, the biggest advantage of proportional hazard model over
the regular multinomial logit model is its ability to examine the dynamics of the
time-varying decision making process. In so doing, we should incorporate time-
varying explanatory variables in the proportional hazard model to capture the time-
dependent financial conditions of the commercial mortgages and time-dependent real
estate market conditions. This is a very nice feature because we know that borrowers
constantly evaluate their financial situation and constantly monitor the market
condition before they make the decision to either continue the mortgage payment or
to withhold the payments. The empirical model incorporates the following time-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
dependent explanatory variables: PeriodicLTV, which is calculated based on the
estimated property value and the calculated unpaid mortgage principal balance at
each point in time before they either become “bad” or are censored. The property
value is estimated by first taking the initial appraised property value in the loan file
and then applying the market-level value growth rates moving forward period to
period. In cases where the loan file contains a recent property value, I compare that
value to the initial value, if the two values are the same, I assume the recent value is
simply a carry-over from the initial value and is disregarded61. If the recorded recent
value is different from the initial value, I then assume either lenders or property
owners re-appraised the property and that value is taken as the new value at the
current value recording date. I then continue to apply market-level value growth rates
to this new value going forward period to period. The variable, VaiueGrowthMkt is
the market-level year-to-year value appreciation rates. Because the market-level
value indices used here are NCREIF indices that are known to be sticky and affected
by the infrequent appraisals, I feel it is the best choice to use year-to-year change as a
proxy for the market property value change. Since most properties in the NCREIF
index are re-appraised at least once a year, the year-to-year market value change
should have overcome some of the weakness in this market value index. The
variable, NOIGrowthMkt is also the market-level year-to-year NOI growth rates. I
use the variable, Vacancy ChangeMkt to represent the leading indicator of the space
6 1 It is quite common that property owners only appraise the property value once in a long while. Even
in the institutional real estate industry, property owners don’t re-appraise very often.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
market condition, which is also measured as the year-to-year vacancy change.
Because Table 3.4 has shown that hotel sector experienced the largest value and NOI
declines while the other property sector performed relatively better, I test an
alternative model including a dummy variable HotelFlag that takes value 1 if the
collateral is hotel and takes value 0 if otherwise. As in the previous section, a dummy
variable JudicialForeclosure is used to indicate the states that have judicial
foreclosure laws.
Finally, following Lekkas, Quigley and Van Order (1993) and Ambrose,
Capone and Deng (2001), an inverse Mills ratio is included as an additional
explanatory variable in the hazard model to correct the sample selection bias. This
Heckman-style approach consists of two steps. The first step is to estimate a simple
binary probit model of commercial mortgages falling into the special serviced pool
using the full sample that consists of the event history of both performing and non
performing loans, and the second step is to add the inverse Mills ratio from the first-
stage probit model as a covariate into the second stage hazard model. The Mills ratio
is calculated a s/(l-F ), w here/is the probability density function and F is the
cumulative density function. Heckman (1979) shows that including the inverse Mills
ratio in the second-stage estimation corrects the sample selection bias and provides
more consistent estimates of the behavioral parameters. The Heckman two-stage
approach is the appropriate estimation when dealing with truncated samples (in our
case, non-special serviced loans are truncated).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
Amemiya (1985) points out that the inverse Mills ratio can be explained as
hazard rate. Therefore by adding the inverse Mills ratio in the second-stage
estimation, the model also explores the possible correlation between the efforts of
special service screening process and the default risk of the special serviced loans.
Tables 3.7 Panel A and Panel B show the results of Cox proportional hazard model
using SAS PHREG procedure. Table 3.7 Panel A shows the model without inverse
Mills ratio (Model 1). The coefficients behave mostly as we expected, and the
significance level is much higher than that from the multinomial logit model. The
most significant variable is PeriodicLTV, suggesting that the equity effect is
dominant in affecting borrowers’ decision to continue or withhold the payments.
Higher LTV leads to more defaults, which is exactly as option pricing theory would
suggest, and appears to conform with that has been observed in other mortgage
default studies, both residential and commercial. Two other variables,
NOIGrowthMkt and VacancyChangeMkt, are significant at the 10% and 5% level
respectively, suggesting that market-wide cash flow increase makes default less
likely, and that the market-wide decline in vacancy rates has a positive effect on the
borrowers’ willingness to continue the mortgage payments and therefore reduce the
default probability. JudicialForeclosure does not show up as significant, suggesting
that borrowers do not consider foreclosure laws in their default decision. In other
words, the results do not provide significant evidence to the hypothesis by Archer,
Elmer, Harrison and Ling (2002) that states “judicial” states should have higher
default incidence, reflecting a tendency for mortgagors to risk default more readily if
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
foreclosure is more difficult to enforce. HotelFlag is significant at the 10% level,
probably because the hotel sector experienced the largest value decline in the last
few years therefore captures a large chunk of the variation in ValueGrowthMkt,
which does not appear to be significant at all.
Table 3.7: Proportional Hazard Model Analysis Results
Panel A. Hazard Model 1
Variable Parameter
Estimate
Standard
Error
Chi-
Square
Pr >
ChiSq
Hazard
Ratio
PeriodicLTV 0.613 0.20 9.85 0.002 1.85
V alueGrowthMkt 0.235 1.86 0.02 0.900 1.26
NOIGrowthMkt -0.927 0.51 3.30 0.069 0.40
VacancyChangeMkt 0.320 0.16 3.93 0.048 1.38
JudicialForeclosure 0.216 0.18 1.52 0.218 1.24
HotelFlag 0.427 0.26 2.72 0.099 1.53
inverse Mills ratio
-2 Log Likelihood Value:
Schwartz B.LC.
981.2
1012.4
Panel B. Hazard Model 2
Variable Parameter
Estimate
Standard
Error
Chi-
Sqnare
Pr >
ChiSq
Hazard
Ratio
PeriodicLTV 0.874 0.29 9.12 0.003 2.40
ValueGrowthMkt -0.638 2.56 0.06 0.804 0.53
NOIGrowthMkt -1.105 0.53 4.38 0.036 0.33
VacancyChangeMkt 0.334 0.16 4.16 0.041 1.40
JndicialForeclosure 0.249 0.18 1.96 0.161 1.28
HotelFlag 0.602 0.27 5.08 0.024 1.83
inverse Mills ratio -2.968 2.67 1.24 0.266 0.05
-2 Log Likelihood Value:
Schwartz B.I.C.
957.2
993.4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
Table 3.7 Panel B reports the estimated proportional hazard model including
inverse Mills ratio (Model 2). The inclusion of inverse Mills ratio increases the
significance and the magnitude of the coefficients of PeriodicLTV, NOIGrowthMkt,
VacancyChangeMkt and HotelFlag. This indicates that model 2 yields more efficient
estimates by inclusion of inverse Mills ratio. The robustness of the variables
representing a loan’s LTV, the market-level NOI growth rates and market-level
vacancy change is very encouraging, as these variables make perfect theoretical
sense.
Tables 3.8 Panel A and Panel B present two alternative models. Table 3.8
Panel A shows the results from Model 3 that includes LoanAge, PeriodicDSCR and
LTVJudicial in addition to the variables included in Model 2 (Table 3.7 Panel B).
LoanAge is measured as the months that a loans remains outstanding since the first
payment due date. PeriodicDSCR is the current DSCR based on the estimated
current property NOI and mortgage payment. The methodology in estimating current
property NOI using market-level NOI indices is similar to that in estimating
PeriodicLTV, as explained earlier. Following Ambrose, Capone and Deng (2001),
the model also includes LTVJudicial, the interaction term of PeriodLTV and
JudicialForeclosure. The results show that both LoanAge and PeriodicDSCR are not
significant. The big change of the coefficient of ValueGrowthMkt also confirms that
this variable does not possess explanatory power. The interaction term LTVJudicial
is not significant, confirming the earlier conclusion that state foreclosure law is not a
significant factor in the borrower’s default decision making process.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
Table 3.8: Proportional Hazard Model Analysis Results
Panel A. Hazard Model 3
Variable Param eter
Estimate
Standard
Error
Chi-
Square
Pr >
CMSq
Hazard
Ratio
PeriodicLTV 0.715 0.31 5.34 0.021 2.04
ValueGrowthMkt 1.251 1.96 0.41 0.523 3.49
NOIGrowthMkt - 1.000 0.52 3.64 0.056 0.37
VacancyChangeMkt 0.347 0.17 4.40 0.036 1.42
JudicialForeclosure 0.285 0.36 0.64 0.425 1.33
HotelFlag 0.526 0.27 3.88 0.049 1.69
PeriodicDSCR 0.048 0.13 0.14 0.709 1.05
LoanAge 0.004 0.00 0.71 0.401 1.00
LTVJudicial -0.052 0.40 0.02 0.896 0.95
inverse Mills ratio
-2 Log Likelihood Value:
Schwartz B.LC.
960.9
1007.4
Panel B. Hazard Model 4
Variable Parameter
Estimate
Standard
Error
Chi-
Square
P r >
ChiSq
Hazard
Ratio
PeriodicLTV 1.210 0.40 9.15 0.003 3.35
ValueGrowthMkt -3.302 3.19 1.07 0.301 0.04
NOIGrowthMkt -1.189 0.54 4.91 0.027 0.30
VacancyChangeMkt 0.320 0.17 3.64 0.056 1.38
JudicialForeclosure 0.234 0.36 0.42 0.518 1.26
HotelFlag 0.614 0.27 5.30 0.021 1.85
PeriodicDSCR -0.227 0.20 1.29 0.256 0.80
LoanAge 0.009 0.01 3.04 0.081 1.01
LTVJudicial 0.098 0.41 0.06 0.812 1.10
inverse Mills ratio -8.102 4.39 3.41 0.065 0.00
-2 Log Likelihood Value:
Schwartz B.I.C.
954.0
1005.7
Model 4 in Table 3.8 Panel B extends Model 3 by including the inverse Mills
ratio variable. The inclusion of inverse Mills ratio not only increases the significance
and the magnitude of the coefficients of the key variables, such as of PeriodicLTV,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
NOIGrowthMkt and LoanAge, the inverse Mills ratio itself is significant at the 10%
level. This suggests that the more likely a loan is special serviced, the less likely the
loan will end up in default. In other words, sending a problem loan to the special
servicers does have a positive impact on the performance of the problem loan, and
the special servicers appear to be functioning in their expected role.
Table 3.9: Logit Model Analysis Results Using Event History Data
A. Event History Model 1 B. Event History Model 2
Variable Parameter Standard Chi- Pr > Parameter Standard Chi- Pr >
Estimate Error Square ChiSq Estimate Error Square ChiSq
Intercept -3.144 0.31 105.94 <.0001 -2.393 0.33 53.74 <.0001
PeriodicLTV 0.682 0.24 8.40 0.004 0.680 0.25 7.17 0.007
ValueGrowthMkt -0.406 2.02 0.04 0.840 -0.108 2.14 0.00 0.960
NOIGrowthMkt -0.690 0.74 0.88 0.350 -0.921 0.77 1.43 0.231
VacancyChangeMkt 0.298 0.20 2.27 0.132 0.321 0.21 2.32 0.128
JudicialForeclosure 0.127 0.11 1.32 0.251 0.147 0.12 1.60 0.206
Period 0.046 0.09 0.27 0.603 -0.117 0.07 2.63 0.105
Period*Period -0.014 0.01 3.10 0.078 0.000 0.00 0.01 0.930
3rd Month Dummy -1.068 0.12 78.42 <.0001
Because the hazard model does not output a default seasoning curve, as the
last test, I apply a logit model to the event history data of the 493 sample loans, a
methodology consistent with Goldberg and Capone (2002). A squared duration term
Period*Period is included in the model to capture the potentially nonlinear default
seasoning pattern. Table 3.9 shows the results from the estimation on the event
history data. It is interesting to see that the most significant variable, PeriodicLTV,
has almost the same coefficient as in Model 3, and VacancyChangeMkt also reports
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
106
similar coefficient. This is very encouraging and suggests the robustness of the
empirical estimation.
In summary, a borrower is very likely to make his payment decision based
largely upon his equity position in the mortgage and the potential cash flow
condition as indicated by the current space market movement. The borrower also
looks at the space market vacancy (occupancy) movement to aid his estimation of
potential cash flows from the collateral. State foreclosure laws do not seem to have
significant impact on the borrower’s default process. In addition, the result from the
fully-specified model seems to confirm the positive role of special service.
The two hypothesis regarding residential mortgage defaults: negative equity
hypothesis and ability to pay (cash flow) hypothesis, seem to co-exist in commercial
mortgage defaults. The proportional hazard model appears to validate the importance
of both negative equity effect and cash flow effect. The results also highlight the
significance of real estate market-wide variables, such as market-wide vacancy
movement, as excellent proxies for the default determinants.
V. Conclusions
All the existing literature in commercial mortgage defaults studies the default
process for loans in the current status to the default status where default is either
defined as foreclosure (e.g. Vandell et al. 1993 and Ciochetti et al. 2002) or as 90-
days-late or worse (e.g. Archer et al. 2002). This study recognizes that commercial
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
mortgage default is not a one-step process and examines a previously unexplored
aspect in the whole default process, that is the stage between the initial delinquency
to default, which is defined as 90-days-late or worse. The servicers’ behavior is
distinguished from the borrowers’ behavior in the default process, where the
servicers mainly make the initial workout strategic decisions that are expected to
minimize the potential losses meanwhile the borrowers make the repeated decisions
on the default put option exercise during the course of being special serviced.
Because most problem loans become special serviced in the CMBS market, the study
empirically examines the probability of special servicers’ choosing one workout
strategy versus others and the conditional probability of default after problem loans
become special serviced.
The empirical results show that special servicers make initial workout
strategic decisions based largely upon the real estate space market condition -
proxied by market-level NOI growth rates. In other words, cash flow condition is the
most significant factor in the servicers’ decision making process. The model also
shows that borrowers are likely to make default decisions based upon both the equity
position in the mortgage as suggested by the option theory and the cash flow
condition as indicated by the space market movement, therefore negative equity
hypothesis and ability to pay hypothesis appear to co-exist in the default process of
commercial mortgages. In addition, key real estate space market variables, such as
market-level vacancy rates, provide very useful information in explaining
commercial mortgage defaults. State foreclosure laws do not have empirically
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
108
significant relationship with the borrowers’ default process. Finally, special service
seems to be functioning as it reduces the probability that a troubled loan will default.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
109
Bibliography
Abraham, Jesse M., and Patric H. Hendershott. 1996. Bubbles in metropolitan
housing markets. Journal o f Housing Research 7(2): 191-207.
Ambrose, Brent W., and Richard J. Buttimer, Jr.. 2001. Embedded options in the
mortgage contract. Journal o f Real Estate Finance and Economics 21 (2): 95-111.
Ambrose, Brent W., and Charles A. Capone. 1998. Modeling the conditional
probability of foreclosure in the context of single-family mortgage default
resolutions. Real Estate Economics 26(3): 391-429.
Ambrose, Brent W., Charles A. Capone, and Yongheng Deng. 2001. Optimal put
exercise: An empirical examination of conditions for mortgage foreclosure.
Journal o f Real Estate Finance and Economics 23(2): 213-234.
Ambrose, Brent W., and Anthony B. Sanders. 2003. Commercial mortgage-backed
securities: Prepayment and default. Journal o f Real Estate Finance and
Economics 26(2-3): 179-196.
Amemiya, Takeshi. 1985. Advanced Econometrics. Boston: Harvard University
Press.
Archer, Wayne R., Peter J. Elmer, David M. Harrison, and David C. Ling. 2002.
Determinants of multifamily mortgage default. Real Estate Economics 30(3):
445-473.
Archer, Wayne R., and David C. Ling. 1997. The three dimensions of real estate
markets: Linking space, capital, and property markets. Real Estate Finance
(Fall): 7-14.
Black, Fischer, and Myron Scholes. 1973. The pricing of options and corporate
liabilities. Journal o f Political Economy 81(3): 637-672.
Blank, David M., and Louis Winnick. 1953. The structure of the housing market.
Quarterly Journal o f Economics 67(2): 181-208.
Campbell, Tim S., and J. Kimball Dietrich. 1983. The determinants of default on
insured conventional residential mortgage loans. Journal o f Finance 38(5): 1569-
1385.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
110
Capone, Jr., Charles A. 1996. Providing alternatives to mortgage foreclosure: A
report to congress. Washington, DC: U.S. Department of Housing and Urban
Development, August (HUD-1611-PDR).
Case, Karl E., and Robert J. Shiller. 1989. The efficiency of the market for single
family homes. American Economic Review 79(1): 125-137.
Case, Karl E., and Robert J. Shiller. 1990. Forecasting prices and excess returns in
the housing market. AREUEA Journal 18(3): 253-273.
Chen, Jun, and Yongheng Deng. 2003. Commercial mortgage workout strategy and
conditional default probability: Evidence from special serviced CMBS loans.
Working paper.
Chen, Jun, Ruijue Peng, and Susan Hudson-Wilson. 2002. Is there momentum in
office rental growth - An empirical investigation and test for space market
efficiency. Working paper.
Childs, Paul D., Steven H. Ott, and Timothy J. Riddiough. 1996. The pricing of
multiclass commercial mortgage-backed securities. Journal o f Financial and
Quantitative Analysis 31(4): 581-603.
Cho, Man. 1996. Housing price dynamics: A survey of theoretical and empirical
issues. Journal o f Housing Research 7(2): 145-172.
Ciochetti, Brian A. 1997. Loss characteristics of commercial mortgage foreclosures.
Real Estate Finance 14(1): 53-69.
Ciochetti, Brian A., Yongheng Deng, Bin Gao, and Rui Yao. 2002. The termination
of mortgage contracts through prepayment and default in the commercial
mortgage markets: A proportional hazard approach with competing risks. Real
Estate Economics 30(4): 595-633.
Ciochetti, Brian A., and Kerry A. Vandell. 1999. The performance of commercial
mortgages. Real Estate Economics 27(1): 27-62.
Ciochetti, Brian A., Rui Yao, Yongheng Deng, Gail Lee, and James Shilling. 2003.
A proportional hazards model of commercial mortgage default with originator
bias. Forthcoming in Journal o f Real Estate Finance and Economics 27.
Clapp, John M., and Carmelo Giaccotto. 1994. The influence of economic variables
on local house price dynamics. Journal o f Urban Economics 36: 161-183.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I ll
Clapp, John, Henry O. PollakowsM, and Lloyd Lynford. 1992. Intrametropolitan
location and office market dynamics. AREUEA Journal 20(1): 229-257.
Clauretie, Terrence M. 1987. The impact of interstate foreclosure cost differences
and the value of mortgages on default rates. AREUEA Journal 15(3): 152-167.
Deng, Yongheng. 1997. Mortgage termination: An empirical hazard model with a
stochastic term structure. Journal o f Real Estate Finance and Economics 14(3):
309-331.
Deng, Yongheng, Jeffrey D. Fisher, Anthony B. Sanders, and Brent Smith. 2003.
Estimation of NOI growth, volatility and clustering by MSA, Working paper.
Deng, Yongheng, John M. Quigley, and Robert Van Order. 1996. Mortgage default
and low downpayment loans: The cost of public subsidy. Regional Science and
Urban Economics 26(3-4): 263-285.
Deng, Yongheng, John M. Quigley, and Robert Van Order. 2000. Mortgage
terminations, heterogeneity and the exercise of mortgage options. Econometrica
68(2): 275-307.
DiPasquale, Denise, and William C. Wheaton. 1996. Urban economics and real
estate markets. Englewood Cliffs, NJ: Prentice-Hall, Inc.
Downing, Chris, Richard Stanton, and Nancy Wallace. 2001. An empirical test of a
two-factor mortgage prepayment and valuation model: How much do house
prices matter?. Working Paper.
Dunn, Kenneth B., and John J. McConnell. 1981a. Valuation of GNMA mortgage-
backed securities. Journal o f Finance 36(3): 599-616.
Dunn, Kenneth B., and John J. McConnell. 1981b. A comparison of alternative
models for pricing GNMA mortgage-backed securities. Journal o f Finance
36(2): 471-487.
Eubank, Jr., Arthur A., and C.F. Simians. 1979. The price adjustment mechanism for
rental housing in the United States. Quarterly Journal o f Economics 93(1): 163-
168.
Fathe-Aazam, Dale. 1995. A comparison for prospective investors. Real Estate
Finance 12(1): 40-47.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
Fisher, Jeffrey D. 1992. Integrating research on markets for space and capital.
AREUEA Journal 20(1): 161-180.
Fisher, Jeffrey D. 2000. Trends in capitalization rates from the NCREIF database:
Twenty years of sold properties. Real Estate Finance 2000(Spring): 35-40.
Fisher, Jeffrey D., Susan Hudson-Wilson, and Charles H. Wurtzebach. 1993.
Equilibrium in commercial real estate markets: Linking space and capital
markets. Journal o f Portfolio Management 1993(Summer): 101-107.
Foster, Chester, and Robert Van Order. 1984. An option-based model of mortgage
default. Housing Finance Review 3(4): 351-372.
Foster, Chester, and Robert Van Order. 1985. FHA terminations: A prelude to
rational mortgage pricing. AREUEA Journal 13(3): 273-291.
Gabriel, Stuart A., and Frank E. Nothaft. 1988. Rental housing markets and the
natural vacancy rate. AREUEA Journal 16(4): 419-429.
Gabriel, Stuart A., and Frank E. Nothaft. 2001. Rental housing markets, the
incidence and duration of vacancy, and the natural vacancy rate. Journal o f
Urban Economics 49: 121-149.
Goldberg, Lawrence, and Charles A. Capone, Jr.. 2002. A dynamic double-trigger
model of multifamily mortgage default. Real Estate Economics 30(1): 85-113.
Grundy, Bruce D. and J. Spencer Martin. 2001. Understanding the nature of risks
and the sources of rewards to momentum investing. Review o f Financial Studies
14(1): 29-78.
Han, Jun. 1996. To securitize or not to securitize? The future of commercial real
estate debt markets. Real Estate Finance 1996(Summer): 71-80.
Harding, John P., and C.F. Sirmans. 2002. Renegotiation of trouble debt: The choice
between discounted payoff and maturity extension. Real Estate Economics 30(3):
475-503.
Heckman, James J. 1979. Sample selection bias as a specification error.
Econometrica 47(1): 153-162.
Hekman, John S. 1985. Rental price adjustment and investment in the office market.
AREUEA Journal 13(1): 32-47.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
Hendershott, Patric H. 1996a. Rental adjustment and valuation in overbuilt markets:
evidence from the Sydney office market. Journal o f Urban Economics 39: 51-67.
Hendershott, Patric H. 1996b. Valuing properties when comparable sales do not exist
and the market is in disequilibrium. Journal o f Property Research 13: 57-66.
Hendershott, Patric H. 2000. Property asset bubbles: Evidence from the Sydney
office market. Journal o f Real Estate Finance and Economics 20(1): 67-81.
Hendershott, Patric H., and Edward J. Kane. 1995. U.S. office market values during
the past decade: How distorted have appraisers been?. Real Estate Economics
23(2): 101-116.
Hendershott, Patric H., Colin M. Lizieri, and George A. Matysiak. 1999. The
working of the London office market. Real Estate Economics 27(2): 365-387.
Hendershott, Patric H., Bryan D. MacGregor, and Raymond Y.C. Tse. 2002.
Estimation of the rental adjustment process. Real Estate Economics 30(2): 165-
183.
Hendershott, Patric H., Bryan D. MacGregor, and Michael White. 2002. Explaining
real commercial rents using an error correction model with panel data. Journal o f
Real Estate Finance and Economics 24(1/2): 59-87.
Hendershott, Patric H., and Robert Van Order. 1987. Pricing mortgages: An
interpretation of the models and results. Journal o f Financial Services Research
1:77-111.
Jackson, Jerry R., and David L. Kaserman. 1980. Default Risk on Home Mortgage
Loans: A Test of Competing Hypothesis. Journal o f Risk and Insurance 47(4):
678-690.
Jegadeesh, Narasimhan, and Sheridan Titman. 1993. Returns to buying winners and
selling losers: Implications for stock market efficiency. Journal o f Finance 48:
65-91.
Jegadeesh, Narasimhan, and Sheridan Titman. 2002. Cross-sectional and time-series
determinants of momentum returns. Review o f Financial Studies 15(1): 143-157.
Kau, James B., and Donald C. Keenan. 1995. An overview of the option-theoretic
pricing o f mortgages. Journal o f Housing Research 6(2): 217-244.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
Kau, James B., Donald C. Keenan, and Taewon Kim. 1994. Default probabilities for
mortgages. Journal o f Urban Economics 35(3): 278-296.
Kau, James B., Donald C. Keenan, Walter J. Muller III, and James F. Epperson.
1987. The valuation and securitization of commercial and multifamily
mortgages. Journal o f Banking and Finance 11: 525-546.
Kau, James B., Donald C. Keenan, Walter J. Muller III, and James F. Epperson.
1990. Pricing commercial mortgages and their mortgage-backed securities.
Journal o f Real Estate Finance and Economics 3(4): 333-356.
Kuo, Chiong-Long. 1995. Serial correlation and seasonality in the real estate market.
Journal o f Real Estate Finance and Economics 12(2): 139-162.
Kuo, Chiong-Long. 1996. Housing price dynamics and the valuation of mortgage
default options. Journal o f Housing Economics 5(1): 18-40.
de Leeuw, Frank, and Nkanta F. Ekanem. 1971. The supply of rental housing. The
American Economic Review 61(5): 806-817.
Lekkas, Vassilis, John M. Quigley, and Robert Van Order. 1993. Loan loss severity
and optimal mortgage default. AREUEA Journal 21(4): 353-371.
Mankiw, N. Gregory, and David H. Weil. 1989. The babyboom, the baby bust, and
the housing market. Regional Science and Urban Economics 19(2): 235-258.
McConnell, John J., and Manoj Singh. 1994. Rational prepayments and the valuation
of collateralized mortgage obligations. Journal o f Finance 49(3): 891-921.
Meese, Richard, and Nancy Wallace. 1994. Testing the present value relation for
housing prices: Should I leave my house in San Francisco?. Journal o f Urban
Economics 35(3): 245-266.
Merton, Robert C. 1973. The theory of rational option pricing. Bell Journal o f
Economics and Management Science 4(1): 141-183.
Merton, Robert C. 1974. On the pricing of corporate debt: The risk structure of
interest rates. Journal o f Finance 29(2): 449-470.
Pollakowski, Henry O., Susan M. Watchter, and Lloyd Lynford. 1992. Did office
market size matter in the 1980s? A time-series cross-sectional analysis of
metropolitan area office markets. AREUEA Journal 20(1): 303-324.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
Quercia, Roberto G., and Michael A. Stegman. 1992. Residential mortgage default:
A review of the literature. Journal o f Housing Research 3: 341-379.
Quigley, John M., and Robert Van Order. 1990. Efficiency in the mortgage market:
The borrower’s perspective. AREUEA Journal 18(3): 237-252.
Quigley, John M., and Robert Van Order. 1995. Explicit tests of contingent claims
models of mortgage default. Journal ofReal Estate finance and Economics
11(2): 99-117.
Richard, Scott F., and Richard Roll. 1989. Prepayments on fixed rate mortgage-
backed securities. Journal o f Portfolio Management 15(Spring): 73-82.
Riddiough, Timothy J. 2000. Forces changing real estate for at least a little while:
Market structure and growth prospects of the conduit-CMBS market. Real Estate
Finance 2000(Spring): 52-61.
Riddiough, Timothy J., and Howard R. Thompson. 1993. Commercial mortgage
default pricing with unobservable borrower default costs. AREUEA Journal
21(3): 256-291.
Riddiough, Timothy J., and Steve B. Wyatt. 1994a. Strategic default, workout, and
commercial mortgage valuation. Journal o f Real Estate Finance and Economics
9(1): 5-22.
Riddiough, Timothy J., and Steve B. Wyatt. 1994b. Wimp or tough guy: Sequential
default risk and signaling with mortgages. Journal o f Real Estate Finance and
Economics 9(3): 299-321.
Rosen, Kenneth T. 1984. Toward a model of the office building sector. AREUEA
Journal 12(3): 261-269.
Rosen, Kenneth T., and Lawrence B. Smith. 1983. The price-adjustment process for
rental housing and the natural vacancy rate. American Economic Review 73(4):
779-786.
Sanders, Anthony B. 1999. Commercial mortgage-backed securities. In The
Handbook o f Fixed-Income Securities. Edited by Frank J. Fabozzi.
Schwartz, Edwardo S., and Walter N. Torous. 1989. Prepayment and the valuation of
mortgage-backed securities. Journal o f Finance 44(2): 375-392.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
Shilling, James D. 1995. Rival interpretations of option-theoretic models of
commercial mortgage pricing. Real Estate Finance 12(3): 61-72.
Shilling, James D., C.F. Sirmans, and John B. Corgel. 1987. Price adjustment
process for rental office space. Journal o f Urban Economics 22: 90-100.
Sivitanides, Petros S. 1997. The rent adjustment process and the structural vacancy
rate in the commercial real estate market. Journal o f Real Estate Research 13(2):
195-209.
Sivitanides, Petros, Jon Southard, Raymond G. Torto, and William C. Wheaton.
2001. The determinants of appraisal-based capitalization rates. Real Estate
Finance 2001(Summer): 27-37.
Sivitanidou, Rena, and Petros Sivitanides. 1999. Office capitalization rates: Real
estate and capital market influences. Journal o f Real Estate Finance and
Economics 18(3): 297-322.
Sivitanidou, Rena Mourouzi-. 2002. Office rent processes: The case ofU.S.
metropolitan markets. Real Estate Economics 30(2): 317-344.
Smith, Lawrence B. 1969. A model of the Canadian housing and mortgage markets.
Journal o f Political Economy 77: 795-816.
Smith, Lawrence B. 1974. A note on the price adjustment mechanism for rental
housing. American Economic Review 64(3): 478-481.
Springer, Thomas M., and Neil G. Waller. 1993. Lender forbearance: Evidence from
mortgage delinquency patterns. AREUEA Journal 21(1): 27-46.
Titman, Sheridan, and Walter Torous. 1989. Valuing commercial mortgages: An
empirical investigation of the contingent claims approach to pricing risky debt.
Journal o f Finance 44(2): 345-373.
Tu, Charles C., and Mark J. Eppli. 2002. Extension risk in commercial mortgages.
Real Estate Finance 2002(Winter): 53-62.
Vandell, Kerry D. 1984. On the assessment of default risk in commercial mortgage
lending. AREUEA Journal 12(3): 270-296.
Vandell, Kerry D. 1992. Predicting commercial mortgage foreclosure experience.
AREUEA Journal 20(1): 55-88.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
Vandell, Kerry D. 1993. Handing over the keys: A perspective on mortgage default
research. AREUEA Journal 21(3): 211-246.
Vandell, Kerry D. 1995. How ruthless is mortgage default? A review and synthesis
o f the evidence. Journal o f Housing Research 6(2): 245-264.
Vandell, Kerry D., Walter Barnes, David Hartzell, Dennis Kraft, and William
Wendt. 1993.Commercial mortgage defaults: Proportional hazards estimations
using individual loan histories. AREUEA Journal, 21(4): 451-480.
Voith, Richard, and Theodore Crone. 1988. National vacancy rates and the
persistence of shocks in U.S. office markets. AREUEA Journal 16(4): 437-458.
Wheaton, William C. 1987. The cyclic behavior of the national office market.
AREUEA Journal 15(4): 281-299.
Wheaton, William C., and Lawrence Rossoff. 1998. The cyclic behavior of the U.S.
lodging industry. Real Estate Economics 26(1): 67-82.
Wheaton, William C., and Raymond G. Torto. 1988. Vacancy rates and the future of
office rents. AREUEA Journal 16(4): 431-436.
Wheaton, William C., and Raymond G. Torto. 1990. An investment model of the
demand and supply for industrial real estate, AREUEA Journal 18(4): 530-547.
Wheaton, William C., and Raymond G. Torto. 1994. Office rent indices and their
behavior over time. Journal o f Urban Economics 35(2): 121-139.
Wheaton, William C., Raymond G. Torto, and Peter Evans. 1997. The cyclic
behavior of the Greater London office market. Journal o f Real Estate Finance
and Economics 15(1): 77-92.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Intra-metropolitan variation in residential mortgage prepayment risks: Unobserved factors and estimation bias

PDF

Essays on exchange rates, prices, and corporate behavior during the Asian currency crisis

PDF

An essay on Korean reunification: Spatial effects of regional integration and its implications for regional and transportation policies

PDF

Infrastructure investment and regional productivity of the manufacturing industries in Mexico

PDF

GAC63 is a transcriptional coactivator for nuclear receptors, aryl hydrocarbon receptor, and LEF1/beta-catenin

PDF

Economic analysis of ground lease-based land use system

PDF

Estimation of origin -destination matrices from link traffic counts and user equilibrium link information

PDF

Redlining revisited: spatial dependence and neighborhood effects in mortgage lending

PDF

Evaluation of policy alternatives to alleviate transportation-related air pollution

PDF

Immigrants and housing attainment: Different forms of residential assimilation

PDF

Three essays on real estate risk and return

PDF

Dietary fats, fat metabolizing genes, and the risk of breast cancer

PDF

Essays on technological evolution and financial returns to innovation

PDF

Leasehold, ownership, and urban land use

PDF

Macroeconomic conditions, systematic risk factors, and the time series dynamics of commercial mortgage credit risk

PDF

Decentralizing of public finance: Centralizing forces in developing countries

PDF

Health care finance reform and market failure at King/Drew Medical Center, Los Angeles: An analysis of pediatric social outcomes in an urban public safety -net hospital

PDF

Evaluating input data for DEM-based environmental analysis and classification

PDF

Androgyny and transformational leadership: Effects of gender and sex -role identity in the collectivistic context of Taiwan, R.O.C.

PDF

Essays on housing market behavior analysis within the international context

Asset Metadata

Creator Chen, Jun (author)

Core Title Essays on commercial real estate and commercial mortgages

School Graduate School

Degree Doctor of Philosophy

Degree Program Planning

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag business administration, banking,Economics, Finance,OAI-PMH Harvest,Urban and Regional Planning

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Deng, Yongheng (committee chair), Dale-Johnson, David (committee member), Gabriel Stuart (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-630273

Unique identifier UC11334989

Identifier 3116677.pdf (filename),usctheses-c16-630273 (legacy record id)

Legacy Identifier 3116677.pdf

Dmrecord 630273

Document Type Dissertation

Rights Chen, Jun

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA