Real-Estate Risk Effects on Financial Institutions’ Stock Return Distribution: a Bivariate GARCH Analysis

Real-Estate Risk Effects on Financial Institutions’ Stock
Return Distribution: a Bivariate GARCH Analysis

Elyas Elyasiani & Iqbal Mansur & Jill L. Wetmore

Published online: 9 May 2008
# Springer Science + Business Media, LLC 2008
Abstract This paper examines two relationships using the bivariate generalized
autoregressive conditionally heteroskedastic (GARCH) methodology. First, the
relationship between equity returns of commercial banks, savings and loans
(S&Ls) and life insurance companies (LICs), and those of the real-estate investment
trusts (REITs), a proxy for the real-estate sector performance. Second, the
relationship between conditional volatilities of the stock returns of these financial
intermediaries (FIs) and that of REITs. The former relationship allows the spillover
of returns between the real-estate and the financial intermediation sector to be
analyzed. The latter allows an investigation of the prevalence, direction and strength
of inter-sectoral risk transmission to be carried out. Several interesting results are
obtained. First, the equity returns of the FIs considered follow a GARCH process
and should be modeled accordingly. Second, as found in the literature, returns on
REITs should be modeled using the Fama-French multiple factor model. However,
this model has to be extended to incorporate a GARCH error structure. Third, all FI
returns considered are highly sensitive to REIT returns and the effects are both
statistically and economically significant. This is an indication that shocks to REITs
returns spillover to the former markets. Fourth, spillover of increased volatility in the
real-estate sector to S&Ls and LICs is significant but not to commercial banks.

Keywords Financial institutions . Real-estate . REITs . Bivariate GARCH
J Real Estate Finan Econ (2010) 40:89–107
DOI 10.1007/s11146-008-9125-3
E. Elyasiani (*)
Fox School of Business and Management, Temple University, Philadelphia, PA, USA
e-mail: elyas@temple.edu
I. Mansur
Widener University, Chester, PA, USA
e-mail: imansur@widener.edu
J. L. Wetmore
University Center, Saginaw Valley State University, Saginaw, MI, USA

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Introduction
Sensitivity of financial institution (FI) stock returns to interest rates and foreign
exchange rate is well established. (See, e.g., Choi et al. (1992), Flannery et al.
(1997), Elyasiani and Mansur (1998, 2003), Wetmore and Brick (1994), and
Elyasiani et al. (2007)). Sensitivity of FI stocks to the real-estate sector, however, is
investigated to a more limited extent, in spite of the fact that changes in real-estate
values can have significant effects on the risk and profitability of FIs. For example,
Mei and Saunders (1995) demonstrate the sensitivity of bank stock returns to realestate
risk by showing that the time variation of bank risk premiums is determined
partly by real-estate market conditions. Similarly, He et al. (1996, 1997) provide
evidence that bank stock returns are sensitive to real-estate loan returns for all types
of real-estate loans, except farmland loans.
The sensitivity of FI stock returns, and in particular bank stock returns, to realestate
has become more important in the recent decades because since 1989, banks
have shifted more of their assets from commercial loans to real-estate loans in
response to the implementation of risk-based capital requirements, and increased use
of commercial paper by corporations as a substitute for bank loans. This asset
substitution has created a reduction in bank credit risk due to the collateralized
nature of real-estate loans but it has also generated a potential for serious problems
for banks in the event of an unanticipated increase in interest rates or a decline in
real-estate prices (Blaško and Sinkey 2006).1
Our contribution includes the following. First, we examine the stock return
behavior of commercial banks (BNK), saving and loans (S&Ls) and life insurance
companies (LICs) within the same framework. These financial intermediaries are
considered to be the main FI participants in the mortgage market and are highly
active in both consumer and commercial mortgage sectors.2 Second, we use a
bivariate generalized autoregressive conditionally heteroskedastic (GARCH) model
to investigate the relationship between FI stock returns and stock return volatilities
with their counterparts in the real-estate investment trusts (REITs) return distribution,
where the latter are used as proxies for the performance of the real-estate sector. An
advantage of the bivariate GARCH framework is that it offers a unique opportunity
1 Most recently, this problem has manifested itself with the turmoil in the sub-prime mortgage markets
resulting in huge losses to commercial and investment banks, hedge funds, and others, and threatening the
stability of the world financial system. As fallout from this crisis, in December 2007, Washington Mutual,
the nations’ largest thrift, slashed its dividend payment, laid off more than 3,000 workers, and set aside $1.6
billions for loan losses in the quarter. Similarly, Citigroup had to take a $7.5 billion investment from Abu
Dhabi to shore up its finances. Freddie Mac and Fannie Mae also announced sales of $6 billion and $7 billion
in preferred stocks, respectively, to deal with the turmoil. Source: CNNFN.Com December 11, 2007.
2 Government sponsored enterprises (GSEs, Fannie Mae, Ginnie Mae, Freddie Mac), mortgage bankers
and brokers, and real-estate agents and brokers also play a role in the mortgage market. GSEs specialize in
loan securitization by creating mortgage-pass-through securities. Mortgage bankers and brokers originate
loans, fund them, and subsequently bundle and sell them to GSEs and institutional investors. Real-estate
agents and brokers bring buyers and sellers of properties together and suggest financing alternatives. In
some markets, these firms buy property to sell at a later date. Nationally, there are currently about two
million active real-estate agents and brokers associated with about 100,000 firms (White 2006). All of
these institutions are affected by changes in the real-estate market, though in different ways and by
different degrees, depending on the extent and the nature of their real-estate exposure and market activity.

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to simultaneously determine the effects of the changes in the real-estate sector on FI
portfolio returns and return volatilities (risk). In addition, this approach produces
more efficient parameter estimates than a univariate GARCH or the conventional
asset pricing models, because it allows for the interaction of the error terms, thus
producing more powerful test results. Third, we examine a longer and more recent
sample period than earlier studies. Advances in technology have increased mortgage
market liquidity, widened its geographic scope, and integrated it with stock and bond
markets to a larger extent than before. This is likely to have altered the spillover
dynamics among these three sectors. The paper is organized as follows. In “Interest
Rate and Real-Estate Return Sensitivity”, the literature on the sensitivity of FIs to
real-estate is reviewed. “Model, Methodology, and Data” describes the model,
methodology and data collection, and “Empirical Results” presents the results,
followed by the conclusions in “Conclusions”.
Interest Rate and Real-Estate Return Sensitivity
Before we focus on the relationship between FI and real-estate returns, we briefly
discuss the literature on the relationship between FI returns and changes in interest
and exchange rates. Stone (1974) argues that stocks of certain types of firms such as
banks and S&Ls are sensitive to interest rate changes. According to Stone, interest
rate risk is a part of the systematic risk, which is not captured by the market beta of
the stock, and cannot be diversified away. Hence, both debt and equity markets
should be included in the model in order to avoid the noise and parameter instability
likely to be present in estimation of a single index model.
Empirical findings of interest rate risk of FIs in the 1970s and 1980s show mixed
results, depending on model specification, measures of interest rate used and the
time period studied.3 The general consensus is that commercial bank stock returns
are negatively related to changes in interest rates and the sensitivity to the long-term
rate, though small, is stronger than to the short-term rate. Bae (1990), Yourougou
(1990), Akella and Chen (1990), Kane and Unal (1988), Kwan (1991) and Akella
and Greenbaum (1992) provide additional evidence reinforcing this conclusion.
Song (1994), and Elyasiani and Mansur (1998, 2003, 2004), reach similar
conclusions using ARCH and GARCH methodologies. Studies of interest rate
sensitivity of the LICs, e.g., Brewer et al. (1993), Lee and Stock (2000), Brewer et
al. (2007), also support the use of long-term interest rates.
Recent evidence points to the strengthening of the effect of real-estate markets on
FI stock returns. Due to high levels of liquidity in the US lending markets in the
recent decade, credit standards in the real-estate markets have been relaxed (Herring
and Wachter 1999). Moreover, to increase their lending, FIs have introduced a wide
variety of innovative products to the mortgage market, including 0% down-payment,

3 Elyasiani and Mansur (1998) review the literature on interest rate sensitivity of U.S. bank stock returns.
For a comparative analysis of interest rate sensitivities of US, German and Japanese bank stock returns see
Elyasiani and Mansur (2003). For a study on rate sensitivity of European bank stock returns, see
Stevenson (2002a).

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interest-only, layering, adjustable rate loans, etc.4 Nevertheless, research on the
effect of real-estate on FIs remains limited.
Eisenbeis and Kwast (1991) find that earnings performance of banks specializing
in real-estate lending over 1978–1988 was similar to other commercial banks,
possibly because the former were able to identify high-yielding, low-risk lending
opportunities and to adjust their real-estate loans quickly. Moreover, the loan
portfolios of the real-estate-focused banks were less concentrated in mortgages than
the thrifts (these banks held 47% while thrifts held 56% of their assets in mortgage
loans). Allen et al. (1995) use the seemingly unrelated regression procedure and
monthly data for 1979–1992 to estimate a three-index model, relating bank stock
returns to market, interest rate, and real-estate. The main finding is that stock returns
on money-center, large and medium-size bank portfolios are positively related to
returns on real-estate. Moreover, bank stock sensitivity to real-estate market
conditions is positively and significantly related to the level of real-estate investments
and the (loans/capital) ratio, with bank sensitivity increasing in the post 1987
stock market crash period.
He et al. (1996) use a three-index model to measure sensitivity of bank stock
returns to real-estate returns over 1986–1991 and find significant positive results
regardless of whether weekly or monthly data are used. Banks with large
components of construction and development loans, one-to-four family residences,
five or more family residential loans, non-residential real-estate, and total real-estate,
demonstrate a higher level of sensitivity to changes in real-estate returns. Farmland
loans show no sensitivity to real-estate risk. He et al. (1997) use a two-step
regression to examine how different types of real-estate loans affect bank stock
returns over the 1986–1991 period. Commercial real-estate loans are found to be
high-risk loans while farm loans serve to diversify risk. The quality of mortgage
portfolios significantly changes the sensitivity of bank stocks to real-estate returns.
He and Reichert (2003) investigate the relationship between changes in stock returns
of a portfolio of FIs (the S&P Financial Sector Stock Index), and the stock market,
bond market, and REIT indexes over 1972–1995 using monthly data. They find the
REIT coefficient to be positive and significant, except for 1972–1973 and 1979–
1980, which are periods of oil price shocks and political upheaval.

Model, Methodology, and Data
Bivariate GARCH Model
The following multifactor capital asset pricing model (CAPM) with a GARCH error
structure forms the theoretical foundation of the FI and REIT return generating
processes.

The following multifactor capital asset pricing model (CAPM) with a GARCH error structure forms the theoretical foundation of the FI and REIT return generating processes.

$$R_{1,t}  = \beta _{10}  + \beta _{11} {\text{ }}RM_t  + \beta _{12} {\text{ }}R_{2,\;t}  + \beta _{13} \Delta I_t  + \beta _{14} {\text{ Time}} + \varepsilon _{1,t}$$
(1)

$$h_{1,t}  = \nu _{10}  + \nu _{11} {\text{ }}h_{1,\,t - 1}  + z_{11} \;\varepsilon _{1,\;t - 1}^2  + \kappa _{12} {\text{ }}h_{2,{\text{ }}t - 1}  + \omega _{11} {\text{ }}D$$
(2)

$$R_{2,{\text{ }}t}  = \beta _{20}  + \beta _{21} {\text{ RM}}_t  + \beta _{22} {\text{ SMB}}_t  + \beta _{23} {\text{ HML}}_t  + \varepsilon _{2,t}$$
(3)

$$h_{2,t}  = \nu _{20}  + \nu _{22} {\text{ }}h_{2,{\text{ }}t - 1}  + z_{22} \;\varepsilon _{2,t - 1}^2  + \omega _{22} {\text{ }}D$$
(4)

$$h_{12,{\text{ }}t}  = \rho _{12} {\text{ }}h_{1,t} {\text{ }}h_{2,t} \left( { - 1{\text{ $<$ }}\rho _{12} {\text{ $<$ }}1} \right)$$
(5)

$$\begin{aligned}  & {\text{ }} \\ & \varepsilon _{{i,t}} |\Omega ^{\prime }_{{t - 1}}  \sim N{\left( {0,h_{{i,t}} } \right)}{\text{        }}{\left( {i = 1,2} \right)} \\  \end{aligned}$$

4 E.g., interest only loans were about 23% of all mortgages in the first half of 2005 (Olszowy 2006).

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In this specification, Eqs. 1 and 2 represent the mean return (R1) and the
conditional volatility (h1,t), for each type of FI (Banks, S&Ls, or LICs). Equations 3
and 4 represent the mean return (R2) and volatility (h2,t) of the REITs returns. The
conditional covariance between each FI type and REITs returns (h12,t) is presented
by Eq. 5, and the error distribution (ei,t) is described by Eq. 6. Among the
determinants of the FI returns, RM is the return on the S&P500 market index; ΔI is
the change in Long-term interest rate (10-year treasury constant maturity); and Time
is a time trend intended to capture the changes in technology and regulation (Time =
1 for January 1972, 2 for February, 1972,…, and 396 for December 2004).5 The
time-trend coefficient reflects the effect on stock returns due to technological and
deregulatory changes during the sample period.
Following Chan et al. (1990), Peterson and Hsieh (1997) and Chiang et al. (2004,
2005), REIT returns are specified as a three-factor Fama-French model with the
market return (RM), the difference between the returns on portfolios of small and big
stocks (SMB), and the difference between the returns on portfolios of high and low
book-to-market ratio stocks (HML) serving as the three factors (Fama and French
(1993)). While the small cap return component in REITs has long been established,
the recognition of the value stock returns is relatively recent (see, Chan et al. (1990),
Stevenson (2002b)). Chiang et al. (2004) analyze the return-based styles sensitivities
of REITS using a moving window of 36 months. Their findings strongly suggest that
the growth style exposures of REITs are the aggregation of small growth and big
growth exposures. In addition, the value stock exposure consistently represents a
large component of equity exposure of REITs. Therefore, Chiang et al. (2004)
conclude that the above Fama-French three factor model is the proper return
generating process for REITs. The GARCH system model described above is
estimated simultaneously once for each type of FI and REITs. Three types of FIs are
considered; Banks, S&Ls, and LICs. An advantage of GARCH type models is that

5 To avoid spurious results due to misspecification, the Augmented Dickey–Fuller and Phillips–Perron
tests of stationarity are performed. The findings indicate that all variables, except long-term interest rate,
follow an integrated process of order zero (I (0)), and thus are considered to be stationary. The long-term
interest rate series follows an I (1) process, but its first difference series DI is an I (0) process and is,
therefore, used in estimation.

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they discard some of the restrictive assumptions maintained in the conventional asset
pricing models including linearity, error independence, and constant conditional
variance (homoskedasticity). In addition, the extended GARCH model employed
here allows for return and volatility feedback effects from the real-estate sector to
FIs, and possible shifts in volatility in different phases of the financial cycle
accounted for by introducing a dummy variable. The cyclical dummy (D) takes the
unit value for periods of real-estate downturns and zero otherwise.
GARCH models specify the conditional variance of returns as a function of
the past shocks (lagged squared errors, e2i
;t1, hi,t−1, i=1,2), allowing volatility to
evolve over time and permitting volatility shocks to persist (Eqs. 2 and 4). The
inclusion of squared error terms implies that if current shocks are large (small) in
absolute value, future innovations are likely to be large (small) as well. The
magnitudes of the GARCH and ARCH parameters (3ii, zii) determine the weights
attached to the lagged innovations. The sum of these parameters (3ii+zii)
determines the degree of persistence in the shocks introduced (Engle and
Bollerslev (1986)). To ensure a well defined process, the GARCH and ARCH
parameters (3ii, zii, i=1, 2) must be non-negative and must satisfy the second-order
stationarity conditions such that (0<3ii+zii<1). If the sum of these coefficients is
unity, the model is integrated of order 1 in variance, and the persistence of shocks
to the system will be never-ending.
It is notable that the specification adopted here is rather general and nests a
variety of simpler conventional models. In particular, if all the coefficients in Eq. 2,
except the intercept term (310), are zero (311=z11=κ12=w1=0), the model will reduce
to the traditional constant variance specification. The parameter 310 is the time
independent component of risk but can vary across different FIs. The conditional
covariance matrix between the REITs and FIs can be specified in several ways. The
specification chosen here (Eq. 5) is a constant correlation model frequently used in
the literature (e.g., Bollerslev (1990), Baillie and Bollerslev (1990), and Kroner and
Sultan (1993)). This specification allows the variances to change but requires the
correlation between the series to remain the same over the sample period. The
constant correlation coefficient, ρ12, has to be estimated.6
Choice of Variables and the Direction of Spillover
Extant banking studies, e.g., Elyasiani and Mansur (2004), show that commercial
bank stock returns are more sensitive to the long-term than the short-term interest
rate. Similarly, Browne, Carson, and Hoyt (1999) find that in modeling life insurer
solvency, long-term interest rates are more important than short-term rates. Based on
these studies, among others, a long-term interest rate (10-year treasury constant
maturity) is used in our model specification.
In this study, the REIT return changes, used as the proxy for the dynamics of the
real-estate sector, are calculated using the National Association Of Real Estate
Investment Trust (NAREIT) ALLINDEX measure. While a number of other realestate
indices such as appraisal-based valuation and market-based residential price

6 For further explanation of GARCH models and their properties see Elyasiani and Mansur (1998, 2003).

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do exist, the findings by Mei and Lee (1994) and its application by Mei and
Saunders (1997), He (2002), and others suggest that the REIT returns serve as a
good proxy for returns on the underlying real-estate assets.7 It is plausible that the
changes in the regulatory environment in the financial sector, and changes in the
availability of hedging instruments produce a bidirectional return spillover. To
establish the proper direction of spillover of shocks between FI and REIT returns,
Granger causality tests are performed between these two variables using lag
structures of 2, 4, 8, and 12 months. The results (not reported) show that, for all lag
structures, the unidirectional causality from REIT to all FIs is significant indicating
that REITs do affect Banks, S&Ls and LICs. Regarding the effect of FIs on REITs,
no causality is found from S&Ls and LICs to REITs. However, for Banks, although
the causality is insignificant for lags 2 and 12, it is significant for lags 4 and 8. To
verify the validity of the proposed FI-REITs model (Eqs. 1–6), an additional model
which adds bank returns in the mean equation for the REITs (Eq. 3) is also
estimated. The results show that the coefficient pertaining to bank stock return is
statistically insignificant in this model.8
The Effect of the Real-Estate Cycle
It is important to determine whether the cyclical character of the real-estate market
adds to the strength of the real-estate risk effects on FIs by increasing their
volatilities. As more and more real-estate assets are securitized and traded in liquid
markets, real-estate return volatility becomes more and more subject to the same
macroeconomic influences as those of the other securities, exacerbating the
cyclicality of the overall FI return volatility. Sagalyn (1990) has demonstrated that
securitization indeed amplifies the real-estate risk over the course of the business
cycle, with REITs showing higher returns, lower volatility and lower systematic risk
during the periods of high growth in the real gross national product.
Although the cyclical movements in commercial and residential real-estate have
been a traditional source of distress for FIs, real-estate cycles are difficult to
characterize because of their varying severity across different sectors and/or
asynchronous cyclical behavior within the same sector in various geographical
markets. For example, it has been observed that the residential construction cycles
tend to be counter-cyclical while the commercial construction cycles tend to be
7 There is a debate on whether the performance of REITs follows that of the real estate market closely.
Some authors have indicated that REITs tend to behave like stocks, rather than real estate. For example,
Peterson and Hsieh (1997) use the model employed by Fama and French (1993) to analyze monthly
returns on NYSE, ASE, and NASDAQ traded REITs. They find that over the 1976–1992 period, the risk
premiums between REITs and equity markets were indeed significantly related. Alternative measures of
real estate sector performance include the Morgan Stanley Capital International and the SNL US REIT
indexes. However, data on these indexes are available only sine 1995 and 1989, respectively, and do not
cover most of our sample period. The OLS estimates of the coefficients for the latter index are positive and
significant for banks and S&Ls but insignificant for the LICs. We would like to thank Ms. Elizabeth
Schoen of the SNL Financial LC for providing these data.
8 As yet an additional step, a likelihood ratio (LR) test is also conducted to determine the validity of the
proposed model. In the LR test statistic specified below, L refers to the log of the likelihood function. The
χ2 value of -1.14 rejects the bidirectional causality model in favor of the maintained model

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coincidental with macroeconomic cycles (Dokko et al. 1999). Along the same lines,
Heckman (1985) has shown that the office construction cycle follows the national
economic cycle closely.
Given the complexity of these forces, and the difficulty to properly recognize the
start and the ending of the physical real-estate cycles, Mueller (2002) separates the
physical cycles, that describe only the demand and supply of physical space, and
financial cycles, that are based on the capital flows into real-estate for both the
existing properties and new construction. This separation helps to explain the lag
that appears to exist between the market occupancy and real-estate prices. In the
current study, we use a financial cycle indicator because it appears to be better suited
to capture the return volatility movements of FIs. The financial cycle dummy takes
the unit value for the downturns and zero otherwise. Based on the financial cycles
calculated by Mueller (2002), the cycle dummy is defined to take the unit value over
1974–1976, 1986–1992, and 2001–2004, and zero for the remaining periods.9
Modeling REIT Returns
The literature in the REIT modeling can be divided into three groups of studies. First, the
CAPM-based or multi index studies where the focus is to determine the proper
relationship between REITs and the broadermarket index, and to assess the sensitivity of
REITs returns to market and interest rate indices. These studies include Ross and Zisler
(1991), Ennis and Burik (1991), and Gyourko and Keim (1992). The finding is that
REIT returns are highly correlated with those of the overall stock market. The interest
rate sensitivity of REIT is analyzed by Chen and Tzang (1988), Liang et al. (1995),
Sanders (1996) and He et al. (2003). With the exception of Liang et al. (1995), other
authors confirm the interest rate sensitivity of REIT returns. Second, a number of
authors have applied the Fama-French factors to the REIT return analysis.10 These
include Peterson and Hsieh (1997) and Chiang et al. (2004, 2005). The findings
provide strong evidence that the Fama-French factor model explains the REIT pricing
9 Mueller (2002) does not specify the status of the real-estate cycle in 2003 and 2004. However, based on his
assessment of the real-estate cyclical behavior in the 1990s and 2000s, it can be argued that the downward
trend in the real-estate financial cycle continued in 2003 and 2004. This conclusion can be supported by the
following market conditions: (a) the demand for office spaces in 1999 and 2000 were higher than the long
term U.S. trend, due to the growth of the technology industry. With the technology bubble burst in 2001,
annual office employment declined by over 1% and office demand declined by over 2% (Mueller 2002). This
contributed adversely to the “physical market cycle”; (b) Muller predicted that the office employment would
return to its average growth rate by 2004 and that the overall office demand would follow suit by the middle
of the decade; (c) there is a substantial lag between the historical movement in the office physical market and
the corresponding movements in the financial cycle. This lag amounted to 1 to 5 years over the last 20 years
(Mueller 2002). Due to the built-in lag between the physical and financial cycles and the obvious decline in
the demand for physical assets in early 2000, it is reasonable to conclude that the downward financial trend
that started in 2001 continued into 2003 and 2004.
10 Chan et al. (1990) develop a model and identify a set of pre-specified macroeconomic risk factors that
explain REIT returns. Their findings suggest that REITs behave in a similar fashion to small capitalization
stocks, rather than large capitalization stocks. Furthermore, the term and risk premiums and changes in
industrial production are found to be important factors in explaining the average variation in REIT returns.
96 E. Elyasiani et al.
better than the CAPM framework. Additional evidence for superiority of the Fama-
French factor model for REITs is provided by Chiang et al. (2004, 2005). Chiang et al.
(2004) test the robustness of the asymmetric beta under a variety of asset pricing
specifications and determine that the asymmetry in market betas in advancing and
declining markets virtually disappears when the three factor Fama-French model is
utilized. Evidence of a temporal decline in equity REIT market beta, found in the
CAPM-based models, is addressed by Chiang et al. (2005). This study reveals that the
declining trend in equity REIT betas also disappears under the three-factor Fama-
French specification. The Fama-French factor model is also used within the framework
of event study methodology by Sahin (2005) to identify the long-run performance of
acquiring and target REITs. Third, although limited in extent, a number of papers
address the volatility of REIT returns. Devaney (2001) and Stevenson (2002b)
examine the linkages of REIT volatility within a univariate GARCH framework.
Devaney (2001), using a GARCH-M model, finds significant ARCH and GARCH
effects for Mortgage-REITs (MREITs) and only significant GARCH effect for Equity-
REITs (EREITs). The only significant GARCH-M parameter for MREIT indicates that
there is a positive tradeoff between conditional variance and excess returns of
Mortgage-REITs, but not so for Equity-REITs.
Stevenson (2002b) reports two interesting results. First, the volatility of small cap
and value stocks exert strong influences on REIT volatility. Second, the volatility of
the stock market (S&P 500) influences the volatility of the Mortgage-REIT returns
far more so than that of the fixed income sector. Cotter and Stevenson (2006), using
a multivariate GARCH model and daily data attempt to determine the return and
volatility linkages among various REIT returns as well as between REITs and other
US equity return series. The linkages measured based on daily data are found to be
weaker than those found using monthly data, both between and within the REIT
sector. Because of the superiority of the Fama-French factor model, demonstrated in
the above studies, the current study models the REIT return-generating process
accordingly, but extends this model to account for GARCH errors.
Data Description
Monthly data from January 1972 to December 2004 are analyzed.11 The FI
portfolios are formed based on the standard industrial classification (SIC) codes.12
Three portfolios of FIs are examined. They include BNK (SIC 6021 and 6022), S&L
(SIC 6035, 6036), and LIC (SIC 6310). The return on the REIT portfolio is
calculated using the NAREIT ALLINDEX. The long-term interest rate variable is the
change in the 10-year Treasury constant maturity (ΔI). All return data, with the
exception of the Fama-French factors (SMB and HML) are collected from the Center
for Research in Security Prices database. The data on the two Fama-French factors
are obtained from Kenneth R. French website at: www.mba.tuck.dartmouth.edu.
11 The advantage of using monthly data is that the noise caused by settlement and clearing delays, which
are found to be a significant determinant of returns in high frequency data, is less influential.

12 Alford (1992) and Lie and Lie (2002) find that SIC-based portfolio disaggregation maintains much of
the portfolio characteristics compared to non-industry grouping techniques based on size or profitability.
Real-Estate Risk Effects on Financial Institutions’ Stock Return Distribution

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better than the CAPM framework. Additional evidence for superiority of the Fama-
French factor model for REITs is provided by Chiang et al. (2004, 2005). Chiang et al.
(2004) test the robustness of the asymmetric beta under a variety of asset pricing
specifications and determine that the asymmetry in market betas in advancing and
declining markets virtually disappears when the three factor Fama-French model is
utilized. Evidence of a temporal decline in equity REIT market beta, found in the
CAPM-based models, is addressed by Chiang et al. (2005). This study reveals that the
declining trend in equity REIT betas also disappears under the three-factor Fama-
French specification. The Fama-French factor model is also used within the framework
of event study methodology by Sahin (2005) to identify the long-run performance of
acquiring and target REITs. Third, although limited in extent, a number of papers
address the volatility of REIT returns. Devaney (2001) and Stevenson (2002b)
examine the linkages of REIT volatility within a univariate GARCH framework.
Devaney (2001), using a GARCH-M model, finds significant ARCH and GARCH
effects for Mortgage-REITs (MREITs) and only significant GARCH effect for Equity-
REITs (EREITs). The only significant GARCH-M parameter for MREIT indicates that
there is a positive tradeoff between conditional variance and excess returns of
Mortgage-REITs, but not so for Equity-REITs.
Stevenson (2002b) reports two interesting results. First, the volatility of small cap
and value stocks exert strong influences on REIT volatility. Second, the volatility of
the stock market (S&P 500) influences the volatility of the Mortgage-REIT returns
far more so than that of the fixed income sector. Cotter and Stevenson (2006), using
a multivariate GARCH model and daily data attempt to determine the return and
volatility linkages among various REIT returns as well as between REITs and other
US equity return series. The linkages measured based on daily data are found to be
weaker than those found using monthly data, both between and within the REIT
sector. Because of the superiority of the Fama-French factor model, demonstrated in
the above studies, the current study models the REIT return-generating process
accordingly, but extends this model to account for GARCH errors.
Data Description
Monthly data from January 1972 to December 2004 are analyzed.11 The FI
portfolios are formed based on the standard industrial classification (SIC) codes.12
Three portfolios of FIs are examined. They include BNK (SIC 6021 and 6022), S&L
(SIC 6035, 6036), and LIC (SIC 6310). The return on the REIT portfolio is
calculated using the NAREIT ALLINDEX. The long-term interest rate variable is the
change in the 10-year Treasury constant maturity (ΔI). All return data, with the
exception of the Fama-French factors (SMB and HML) are collected from the Center
for Research in Security Prices database. The data on the two Fama-French factors
are obtained from Kenneth R. French website at: www.mba.tuck.dartmouth.edu.
11 The advantage of using monthly data is that the noise caused by settlement and clearing delays, which
are found to be a significant determinant of returns in high frequency data, is less influential.
12 Alford (1992) and Lie and Lie (2002) find that SIC-based portfolio disaggregation maintains much of
the portfolio characteristics compared to non-industry grouping techniques based on size or profitability.

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Descriptive statistics for respective series are presented in Table 1. They include
the first four moments of each series along with the test results for serial correlations
of the return series of orders 8, 16, and 24. The results show that the average
monthly returns of FIs and REITs range from 0.7% to 0.8% with returns on
commercial banks, LICs and REITs exceeding those of the S&Ls. It is noteworthy
that REITS also exhibit the a lower unconditional volatility (standard deviation of
4.40%) compared to commercial banks, S&Ls and LICs with similar or better
returns. This finding is consistent with Cotter and Stevenson (2006) who also report
that REITs have provided one of the best return profiles in recent years due to their
asset backing and high potential income. Among the FIs, the bank portfolio has the
lowest unconditional risk (4.70%) while the corresponding figures for LICs and
S&Ls are, respectively, 5.80% and 6.70%. The correlation coefficients, presented in
Table 2, show REITs to have a much higher correlation with FI returns than with the
long-term interest rate, and to be also highly correlated with the market.
Skewness and kurtosis are significant for all of the series. Consequently, the
unconditional distributions of returns are non-normal, as evidenced by significant
Bera and Jarque (1981) statistics, and demonstrate leptokurtosis as evidenced by the
significant kurtosis values. The Ljung and Box (1978) test statistics for the return
series for the S&L portfolio reject the null hypothesis of no autocorrelation, though
not for the bank and LIC portfolios. These findings are to be expected because the
time period studied covers some rather extreme economic situations of record high,
as well as record low interest rates, and record high stock prices, followed by
corrections. The high sensitivity of the mortgage market to economic conditions
strengthens these patterns. The non-normality, serial correlation, skewness, and
kurtosis results suggest that a GARCH-type process is indeed appropriate for
modeling FIs and REIT returns.

Empirical Results
Systematic Risk and Interest Rate Sensitivity
The bivariate-GARCH model (Eqs. 1–6) is estimated simultaneously once for each
type of FI and REITs. This procedure produces three sets of estimates for the three
FIs considered. The estimated coefficients and the related t-statistics are presented in
Table 3. The magnitudes of market betas (β11) for all FIs are found to be less than
1.0 with the highest risk attributable to the Commercial Bank portfolio (0.34)
followed by S&L portfolio (0.28), followed by the LIC portfolio (0.12). This
indicates that these financial institutions are less risky than the market portfolio. He
et al. (1996), using monthly and weekly data, value-weighted and equally-weighted
indices, and various specifications also find market betas for commercial banks to be
less than unity. Elyasiani et al. (2007) find the magnitude of market beta for FIs
(commercial banks, securities firms, and LICs) to be size-dependent, with larger FIs
displaying greater market beta values. The dissimilarity in betas may be due to the
fact that larger FIs tend to be more highly leveraged, less liquid, and oriented toward
non traditional banking activities such as derivatives, which can be highly risky. For
S&Ls, Schrand (1997) finds the market beta to be of larger magnitude than that

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found here, but still below the unit value, during the flattening of the yield curve
period. Brewer et al. (2007) also find LICs’ market beta to be size-dependent but in
all cases less than unity.13,14
The interest rate sensitivity (β13) is found to be negative and significant for
commercial banks and S&Ls, but positive for LICs. These findings suggest that
these institutions are exposed to the risk of interest rate fluctuations depending on
the duration gaps that they maintain as well as the off balance sheet positions such as
interest rate derivatives that they have taken. This result is consistent with much of
the literature cited earlier in the literature review section but stands in contrast to He
et al.’s (1996) finding that the long-term interest rate sensitivity for commercial
banks is insignificant and with Schrand (1997) who finds that the S&L returns are
not significantly affected by the changes in interest rate during the periods of upward
movements in interest rates. The financial cycle dummy and the time variable are
found to exert statistically insignificant influences on the volatility of the portfolios.

13 Presence of multicollinearity is investigated by examining the Conditional Index (CI) values calculated
for Eqs. 1 and 3. The CI values are 15.37 and 1.88, respectively. A Conditional Index is defined as the
ratio of ((Maximum Eigenvalue)/(Minimum Eigenvalue))1/2. Although statistical significance of the
Conditional Indexes can not be tested, index values greater than 30 are understood to indicate severe
multicollinearity (Gujarati 2003, p. 362). The index values calculated for our model suggest that
multicollinearity is not a serious problem. It is notable, however, that given the magnitude and significance
of the correlation coefficient between contemporaneous market and REITs portfolio returns (ρ=.54), it is
difficult to completely separate their effects on the bank portfolio returns.
14 Schrand (1997) estimates the market and interest rate sensitivities over three time periods: flattening of
the yield curve, steepening of the yield curve, and all periods. For the period of steepening of the yield
curve, and all period, the market beta is found to be greater than one.

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Sensitivity of FI Returns to Real-Estate Returns
The effect of real-estate on FI return distribution is the issue of most interest to this
study. The results presented in Table 3 provide evidence that, REIT returns have a
positive and significant impact on commercial bank, S&L, and LIC stock returns
(b12>0). At least, three channels can be identified through which the effect of a
boost in real-estate returns can be transmitted to the FIs. First, as a result of
enhancement in the real-estate sector, the level of credit risk faced by the FIs falls,

because the value of the mortgage loans held by FIs and collateralized by real-estate
increases. Second, FIs benefit from the increase in value of the real-estate that they
directly hold in the form of office buildings, or other property that they have
received in loan default cases. Third, the wealth of the borrowers from the bank, and
possibly their revenues from rent, increase in response to improved real-estate
market conditions. This is likely to curtail the probability of loan default that the
bank faces and the scale of its losses on uncollateralized loans.
In terms of magnitude of the effect, the coefficients for FI sensitivities to REITs
returns range from 0.63 to 1.00 with the LIC portfolio displaying the highest level of
sensitivity (b12=1.00), followed by the S&L portfolio (b12=0.98), and commercial
bank portfolio (b12=0.63). The levels of FI sensitivities to REITs found here appear
reasonable given their large extent of exposure to mortgage or mortgage-related
activities, with possible accounting for interest rate derivative positions. These
results are consistent with the findings of He et al. (1996) who report that
commercial banks with larger real-estate loan exposure are more sensitive to changes
in the real-estate returns, with the exception of farmland loans.
Economic significance is examined by measuring the impact of one standard
deviation change in an explanatory variable (here, the REITs returns) on the
explained variable (here, the FI returns). Specifically, the figures on economic
significance are obtained by multiplying the standard deviation of an explanatory
variable by its coefficient. Based on the figures in Tables 1 and 3, a one standard
deviation change in REIT returns results in a change of 2.7% for banks, 4.13% for
S&Ls and 4.4% for LICs returns, less than equiproportionately for banks and S&Ls
and equiproportionately for LICs. These figures indicate that not only the association
between the FI returns and REITs returns is statistically significant, but that the
magnitudes of the effects are also economically significant.
The figures in Tables 1 and 3 also show that S&Ls and LICs are more heavily
affected by the real-estate sector than commercial banks, with the effect being
strongest on the LICs. Securitization of mortgages by banks and to a lesser degree by
S&Ls and the purchase of these securitized instruments by LICs, among other
institutional investors, are consistent with these findings. It is noteworthy that
although the association between FI returns and interest rates has received much
more attention in the literature and regulatory circles, the effect of changes in the
real-estate on FIs is also very strong both statistically and economically. This calls
for increased attention by banks and bank regulators as well as bank borrowers and
depositors to the subject.
Results on REITs Return and Volatility Models:

The coefficient estimates for the REITs return equation (Eq. 3) pertaining to market
return (β21), and the two other Fama-French factors, SMB returns (β22) and HML
return (b23), are all positive and highly significant, indicating a clear co-movement
between REITs returns and the latter three variables. The coefficient values for SMB
and HML vary over the 0.50–0.66 range. These values are similar in magnitude to
those obtained by Chiang et al. (2005) using a three-factor model.
The results on the conditional volatility of FI and REIT returns, described by Eqs. 2
and 4 in the model, are also presented in Table 3. The volatility variables (hit, i=1,2)

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statistically significant influence on the volatility (risk) of any of the financial
institutions considered. The statistical significance and the magnitude of the intersectoral
spillover effects should serve as an alert to the FI regulators to pay serious
attention to the developments in the real-estate market and to include them in the
policy deliberations such as those of the Federal Open Market Committee meetings.
The differential model parameter values found here for different FI portfolios
indicate that pooling different institutions may produce unreliable results. In other
words, the intra-sample dissimilarity of the effects highlights the importance of
group homogeneity in econometric estimation and testing of the hypotheses.
Concerning the appropriate model of REITs return distribution, the fact that both
the GARCH and ARCH coefficients are found to be significant for REIT returns,
strongly suggest that the second moment of the REIT return distribution should be
modeled accordingly. The volatility of REIT returns is not associated with the realestate
financial cycles. It appears that REITs are able to attract capital flows at all
times and remain unaffected in terms of stock return volatility by changes in
availability of capital for real-estate construction during the two phases of the cycle.
Conclusions
This paper examines the relationship between the equity returns and return
volatilities of three categories of financial institutions (commercial banks, S&Ls,
and LICs) with the corresponding moments of the REITs return distribution using
the bivariate GARCH methodology. Several interesting results are obtained. First, FI
returns follow a GARCH process and should be modeled within this general
framework. Second, the findings here reinforce the conclusion reached in the earlier
studies that the REITs returns should be modeled using the Fama-French factor
model. However, this model needs to be extended to allow for the time-varying
nature of REITs return volatility. Third, the stock returns of all three FIs considered
are highly sensitive to changes in the REIT returns and the magnitude of the effects
exhibit statistical as well as economic significance. Fourth, volatility in the realestate
sector does get transmitted into S&L and life insurance company markets
demonstrating the exposure of the latter to the former.
Acknowledgements Earlier versions of the paper were presented at the Financial Management
Association meeting of 2007 and the Mid Atlantic Regional Conference at Villanova University in
2007. The authors would like to thank Mingming Zhou and Shawn Howton, the respective discussants for
comments and suggestions. Thanks are due also to Paul Asabere, Yan Hu, and Arun Upadhyay for
comments and suggestions and to Yan Hu for excellent research assistance. Any remaining errors are ours.

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