financial crises and contagion_ evidence for bric stock markets
TRANSCRIPT
Electronic copy available at: http://ssrn.com/abstract=1087282
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Financial Crises and Contagion: Evidence for BRIC Stock Markets
Dimitris Kenourgios* Department of Economics, University of Athens, 5 Stadiou Str., 10562 Athens, Greece, Tel.: +30 210 3689449, e-mail: [email protected] Aristeidis Samitas Department of Business Administration, Business School, University of the Aegean, 8 Michalon Str., 82100 Chios, Greece, e-mail: [email protected]
Nikos Paltalidis
Faculty of Finance, Cass Business School, City University London, 105 Westbourne Terrace, W2 6QT, Paddington, UK, e-mail: [email protected]
Abstract
This paper proposes a new multivariate copula regime-switching model to capture non-linear relationships in four emerging stock markets, namely Brazil, Russia, India, China (BRIC) and two developed markets (U.S. and U.K.), during five recent financial crises (the Asian crisis, the Russian crisis, the tech bust and the two episodes in Brazil). We also investigate the presence of asymmetric responses in conditional variances and correlations during these periods of negative shocks, applying the asymmetric generalized dynamic conditional correlation (AG-DCC) approach. These methods go beyond a simple analysis of correlation breakdowns, analyze the second moment dynamics of stock market returns, and enable us to overcome problems arising in the existing empirical research of financial contagion. Results provide evidence that there is an asymmetric increase in dependence among stock markets during all five crises. The jump in correlations and volatilities between stable and crisis periods supports financial contagion when crises are spread to other markets. Moreover, the differences in the magnitudes of the dependence changes show that the industry-specific tech bust appears to have a larger impact than country-specific crises. Furthermore, increases in tail dependence imply that the probability of markets crashing together is higher during periods of financial turmoil. Our findings imply that policy responses to a crisis are unlikely to prevent the spread among countries, making fewer domestic risks internationally diversifiable when it is most desirable. A further finding of this study is that the multivariate regime-switching copula model captures higher level of dependence than the AG-DCC approach, possibly due to econometric reasons.
Keywords: Financial crises, stock market contagion, BRICs, multivariate regime-switching copula, AG-DCC model. JEL classification: F30, G15
* Corresponding author: Dimitris Kenourgios, 5 Stadiou Street, 10562 Athens, Greece, e-mail: [email protected]
Electronic copy available at: http://ssrn.com/abstract=1087282
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1. Introduction
The global extent of recent crises and the potential damaging consequences of being
affected by contagion continuously attract attention among economists and
policymakers. The transmission of shocks to other countries and the cross-countries
correlations, beyond any fundamental link, has long been an issue of interest to
academics, fund managers and traders, as it has consequences to international
portfolio investment with important implications for portfolio allocation and asset
pricing. The past decade was marked by the Asian stock market crisis in 1997, the
Russian default in 1998, the Internet bubble collapse in 2000 and the Brazilian stock
market crash in 1997-1998 and 2002. According to Boyer et al. (2006), crisis is
spread from one country to the other generating the “contagion phenomenon”.
The existence of financial contagion has been studied by many researchers,
mainly around the notion of “correlation breakdown” (a statistically significant
increase in correlation during the crash period). However, the existing literature
suffers from certain limitations. First, there is a heteroskedasticity problem when
measuring correlations caused by volatility increases during the crisis. Second, there
exists a problem with omitted variables (such as economic fundamentals, risk
perception and preferences) in the estimation of cross-country correlation coefficients
due to the lack of availability of consistent and compatible financial data, especially in
emerging markets. Third, contagion must involve evidence of a dynamic increment in
the regressions, affecting at least in the second moments correlations and covariances
(Pesaran and Pick, 2006). Otherwise, a continued market correlation at high levels is
considered to be «no contagion, only interdependence» (Forbes and Rigobon, 2002).
This study focuses on four major emerging stock markets, namely Brazil,
Russia, India and China (BRICs) and two developed stock markets, U.S. and U.K.
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BRICs could become the larger force in the world economy over the next fifty years.
The relative importance of the BRICs as an engine of new demand growth and
spending power seems to shift more dramatically and quickly than expected. Higher
growth in these emerging market powerhouse economies could offset the impact of
greying population and slower growth in the advanced economies. The aim of this
paper is to investigate stock market contagion during five financial crises occurred the
last ten years: (i) the Asian stock market crisis in 1997, (ii) the Russian default in
1998, (iii) the collapse of the internet bubble of developed markets in 2000, (iv) the
Brazilian stock market crash in 1997–1998 and (v) the Brazilian crisis in 2002.
To avoid the limitations found in the existing literature, this paper proposes a
new multivariate copula function with Markov switching parameters. This approach
goes beyond a simple analysis of correlation breakdowns, analyses the second
moment dynamics of financial time-series, and enables us to overcome the
heteroskedasticity problem raised by Forbes and Rigobon (2002). This enables us to
analyze the behaviour among stock markets when at least one of them is under
financial crisis. Following the methodology of Patton (2006a, b) and Bartram et al.
(2007), we employ a GJR-GARCH-MA-t specification for the marginal distributions
and the Gaussian copula for the joint distribution. Based on their work on time-
varying copula dependence model, we extend it to a multivariate model with Markov
switching parameters. The dependence parameters in the copula function are modeled
as a time-varying process conditional on currently available information, allowing for
time-varying, non-linear relationships and asymmetries.
We also apply a recently developed GARCH process, the asymmetric
generalized dynamic conditional correlation (AG-DCC) model (Cappiello et al.,
2006). This process allows for series-specific news impact and smoothing parameters,
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permits conditional asymmetries in correlation dynamics and accounts for
heteroskedasticity directly by estimating correlation coefficients using standardized
residuals. Moreover, this specification enables us to overcome the problem with
omitted variables and is well suited to investigate the presence of asymmetric
responses in conditional variances and correlations during periods of negative shocks.
Furthermore, this model interprets asymmetries broader than just within the class of
GARCH models, since does not assume constant correlation coefficients over the
sample period. Ignoring the asymmetric frictions lead to overestimating the benefits
of international portfolio diversification in falling markets.
Similar to other studies in the literature (Forbes and Rigobon, 2002; Bekaert et
al., 2005; Boyer et al., 2006), we maintain an equivalently strict definition of
contagion as the increase in the probability of crisis, beyond the linkages in
fundamentals, and the rapid increase in co-movements among markets during a crisis
episode. Given this definition, both methodologies applied in this paper allow us to
determine whether cross-market correlation dynamics (contagion effects) are driven
by behavioral reasons or by changes in macroeconomic fundamentals1. This is in
contrast to the traditional asset pricing theory, according to which co-movement in
prices reflects co-movement in fundamentals in an economy with traditional
investors.
This paper contributes to the existing literature by: i) proposing a new
multivariate copula regime switching model for testing the contagion hypothesis; ii)
examining asymmetric contagion effects during the five extreme market downturns
applying the recently developed AG-DCC approach; iii) comparing the level of
dependence among stock markets obtained by using the above two methodologies; iv) 1 There is considerable disagreement regarding the definition of the fundamentals (for discussion on this issue, see Bekaert et al. 2005). Our research uses multi-parameters that accommodate various degrees of market co-movements.
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shedding new light in the area of financial crises focusing our research on four major
emerging stock markets (BRICs) and two of the most dominant international stock
markets (U.S. and U.K.).
Results provide evidence that there is an asymmetric increase in dependence
among stock markets during crises periods. Furthermore, the industry-specific tech
bust appears to have a larger impact than country-specific crises. Comparing the
results provided by the two methodologies, the multivariate regime switching copula
captures higher levels of dependence than AG-DCC model. Finally, results provide
support to the contagion phenomenon due to behavioral reasons rather than due to
changes in macro fundamentals.
The structure of the paper is organized as follows. Section 2 briefly presents
the literature review. Section 3 presents multivariate regime-switching copula
methodology and the AG-DCC model, both applied to examine stock market
contagion. The data used for the empirical analysis is presented in Section 4. Section
5 reports the empirical results. Finally, conclusions are stated in Section 6.
2. Literature Review
Most financial decisions are based on the risk and return trade-off. A central issue in
asset allocation and risk management is whether financial markets become more
interdependent during financial crises. This issue has acquired great importance
among academics and practitioners in the last decade where five major crises were
obtained. Common to all these events was the fact that the turmoil originated in one
market extended to a wide range of markets and countries, in a way that was hard to
explain on the basis of changes in fundamentals (Rodriguez, 2007).
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Generally, contagion refers to the spread of financial disturbances from one
country to others. Forbes and Rigobon (2002) define contagion as “a significant
increase in cross-market linkages after a shock to one country (or group of countries).
The study of financial contagion was conducted mostly around the notion of
“correlation breakdown”. Bertero and Mayer (1989) and King and Wadhwani (1990)
find evidence of an increase in stock returns’ correlation in 1987 crash. Calvo and
Reinhart (1996) report correlation shifts during the Mexican crisis. Baig and Goldfajn
(1999) find significant increases in correlation for several East Asian markets and
currencies during the East Asian crisis, supporting the contagion phenomenon.
The studies of contagion based on structural shifts in correlation are
challenged by Boyer et al. (1999), who point to biases in tests of changes in
correlation that do not take into account conditional heteroskedasticity. They argue
that the estimated correlation coefficient between the realized extreme values of two
random variables will likely suggest structural change, even if the true data generation
process has constant correlation. Forbes and Rigobon (2002) generalize the approach
of Boyer et al. (1999) and apply it to the study of three major crises (the 1987 crash,
the Mexican devaluation, and the East Asian crisis). They are unable to find evidence
of correlation breakdown in any of these crises after adjusting for heteroskedasticity
and conclude that the phenomenon that has been labelled as “contagion” is non-
existent.
Evidence that equity returns have a dependence structure that is not consistent
with multivariate normality is presented by Lognin and Solnik (2001). They provide a
method based on extreme value theory and find that correlation generally increases in
periods of high-volatility of the U.S. market. Also, they find that correlation is
essentially affected in bear markets when it increases significantly. As an alternative
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approach, Rachmand and Susmel (1998) and Ang and Bekaert (2002) estimate a
multivariate Markov-switching model and test the hypothesis of a constant
international conditional correlation between stock markets. They report that: (i)
correlation is generally higher in the high-volatility regime than in the low-volatility
regime; (ii) equity returns appear to be more correlated during downturns than during
upturns.
Boyer et al. (2006) use both regime switching model and extreme value theory
to gauge the cross-market transmission mechanism of financial crises for numerous of
accessible and inaccessible stock indices. They identify that there is greater co-
movement during high volatility periods, suggesting that crises spread through the
asset holdings of international investors rather than through changes in fundamentals.
However, Markov switching models have been limited to analyze the case of bivariate
normality. Consequently, they have missed a potentially important dimension of the
contagion phenomenon, such as non-linear dependence.
Copulas have recently become increasingly popular in various finance
applications (e.g., modeling default correlations, portfolio allocation, time-varying
dependence and pricing foreign exchange rate quanto options and multivariate
contingent claims)2. Patton (2006a) pioneers the study of time-varying copulas for
modelling asymmetric exchange rate dependence, while Bartram et al. (2007)
estimate time-varying copula dependence models for 17 European stock market
indices, following the methodology of Patton (2006a). Rodriquez (2007) uses a mixed
copula using returns from five East Asian stock indices during the Asian crisis and
from four Latin American stock indices during the Mexican crisis, and finds evidence
of changing dependence during periods of turmoil.
2 Cherubini et al. (2004) presents copulas applications in finance, while Bartram et al. (2007) provide selective and recent international references.
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A large literature investigate asymmetric effects in conditional covariances for
individual stocks, bonds, equity portfolios and stock market indices using different
approaches (e.g., Koutmos and Booth, 1995; Kroner and Ng, 1998; Christiansen,
2000)3. Recently, Engle (2002) develops a dynamic conditional correlation (DCC)
GARCH model capable of allowing for conditional asymmetries in both volatilities
and correlations. Chiang et al. (2007) apply a DCC model to nine Asian stock markets
from 1990 to 2003, confirming a contagion effect. Cappiello et al. (2006) extend the
original model of Engle (2002) along two dimensions: on the one hand, they allowed
for series- specific news impact and smoothing parameters and on the other hand,
permitted conditional asymmetries in correlations. Including into their analysis three
group of countries (Europe, Australasia and North America), they provide evidence
on that equity returns show strong evidence of asymmetries in conditional volatility,
while little is found for bond returns.
Overall, the existing literature only partially explains the reaction of stock
markets to crashes originated in other countries. Moreover, correlations between U.S.
stocks and the aggregate U.S. market, computed by Ang and Chen (2002), are
especially large during market downturns, suggesting that contagion may be
“asymmetric” (stronger during market downturns). As Bae et al. (2003) point out:
“The concerns (about contagion) are generally founded on the presumption that there
is something different about extremely bad events that leads to irrational outcomes,
excess volatility, and even panics. In the context of stock returns, this means that if
panic grips investors as stock returns fall and leads them to ignore economic
fundamentals, one would expect large negative returns to be contagious in a way that
small negative returns are not”. 3 These studies account for asymmetric effects in conditional covariances, although they parameterize time-varying covariances in the spirit of Bollerslev (1990) where correlation coefficients are assumed to be constant over the sample period.
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3. Methodology: Conditional Copula and AG-DCC model
3.1 Conditional Copula
Copula functions permit flexible modeling by enabling the construction of
multivariate densities that are consistent with the univariate marginal densities.
Hence, they allow separation of the marginal distributions from the dependence
structure that is entirely represented by the copula function. This separation enables
researchers to construct multivariate distribution functions, starting from given
marginal distributions that avoid the common assumption of normality for either
marginal distributions or their joint distribution function (Bartram et al., 2007).
Copulas have certain properties that are very useful in the study of
dependence. First, copulas are invariant to strictly increasing transformations of the
random variables. Second and most important in the study of financial contagion,
asymptotic tail dependence is also a property of the copula. A switching copula can
capture increases in tail dependence, reflecting for example, that the probability of
markets crashing together is higher in periods of financial turmoil, while a model
based on multivariate normality imposes tail independence.
In this paper, we employ a multi-parameter conditional copula to represent the
dependence between two equity index returns, conditional upon the historical
information provided by previous pairs of index returns (parameter 1) and cross–
country differences in volatilities (parameter 2). When we test for dependence, we
employ the copula function with the return and volatility from one country against the
other. We estimate the univariate distributions and then the joining distributions. The
parameters of the conditional copula depend upon the conditioning information.
Important conditional theory and time-varying conditional copulas methodology have
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been developed and applied to financial market data by Patton (2006a, b) and Bartram
et al. (2007).
Let Xt and Yt be random variables that represent two returns for period t and
let their conditional cumulative distribution functions (c.d.f.s) be Ft(xt|Φt-1) and
Gt(yt|Φt-1) respectively, with Φt-1 denoting all previous returns, i.e. {xt-1, yt-1, i>0}.
Moreover, let Mt and Nt be random variables that represent two volatilities for period
t and their c.d.f.s are Ft*(mt|Λt-1) and Gt
*(nt|Λt-1) respectively, with Λt-1, denoting all
previous volatilities, i.e. {mt-i, nt-I,,i>0}. Define two further random variables by Ut =
Ft(Xt|Φt-1) and Vt = Gt(Yt|Φt-1), whose marginal distributions are uniform on the
interval from zero to one. Then the conditional copula density function, denoted by
ct(ut,vt|Φt-1), is defined by the time-varying, bivariate density function of Ut and Vt.
Also, the conditional bivariate density functions of Xt , Yt, and Mt, Nt are given by the
product of their copula density and their two marginal conditional densities,
respectively denoted by ft and gt.:
Ht(xt,yt|Φt-1) = ct(Ft(xt|Φt-1), Gt(yt|Φt-1)|Φt-1)ft(xt|Φt-1)gt(yt|Φt-1) (1)
Ht(mt,nt|Φt-1) = ct(Ft(mt|Φt-1), Gt(nt|Φt-1)|Φt-1)ft(mt|Φt-1)gt(nt|Φt-1) (2)
3.1.1 Regime switches in copula
Introducing regime switches in variance, ut is modeled as stgu = * −
tu and
−
tu follows a GJR-GARCH-MA- t specification process (Glosten et al., 1993). The
level of the variance can occasionally change, depending on the values of gst, where
gst is a scaling parameter that changes in time as a function of a latent variable st. This
latent variable is assumed to take values 1,2,…,K and to be described as a Markov
Chain:
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p11 p12….pk1
P= p12 p22…pk2 ,
… … …
p1k p2k…pkk
where, pij= p(st=i|st-1=j) and st is regarded as the regime that the process is in at date t.
Hence, variable st can be in any K states at time t and q is the number of lags in the
conditional variance. Therefore, the variable ut is multiplied by √g1 in state 1, √g2 in
state 2, and so on. Hamilton (1989) describes how to estimate the parameters in
through the maximization of a likelihood function and also how to do inference about
the state in which the process has been at date t. Inferences based on information up to
time t are called “filtered probabilities”, while inferences based on information from
the full sample are called “smoothed probabilities.”
The model selected to investigate the presence of different volatility regimes
in the markets considered in this paper follows a (2, 1) process. Although the selection
of the number of states and lags has been based on practical reasons of avoiding
overparameterization and cumbersome computation in the multivariate case,
specification tests on the copulas suggest that the GJR-GARCH-MA-t −switching (2,
1) performs well in describing the structure of the marginals.
3.1.2 Estimation of parameters
In the first stage, the parameters of the marginal distributions parameters are
estimated from univariate time series as follows:
^
1
arg max log (n
ttt
f xχθ=
≡ ∑ |1, )t xθ−Φ
(3)
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^
1arg max log (
n
y t tt
g yθ=
≡ ∑ |1, )t yθ−Φ
The second stage then estimates the dependence parameters as:
^
,1
arg max log (n
c t t tt
c u vθ=
= ∑ | ^ ^
1, , ,t c x yθ θ θ−Φ ) (4)
According to Patton (2006a), the two stage ML estimates
⎥⎦⎤
⎢⎣⎡= cyx
^^^^;; θθθθ (5)
are asymptotically as efficient as one-stage ML estimates. The variance-covariance
matrix of ^θ has to be obtained from numerical derivatives.
3.1.3 Models for marginal distributions
The conditional densities of equity index returns are leptokurtic and have variances
that are asymmetric functions of previous returns. Therefore, we obtain our marginal
distributions by fitting appropriate ARCH models that have conditional Gaussian
distributions.
We let Ri,t and hi,t denote the return from equity index i and its conditional
variance for period t. Also, Li,t and λi,t denote the actual volatility from equity index i
and its conditional variance for period t. The ARCH model for the returns from index
i is defined by:
Ri,t = μi + εi,t + Θiεi,t-1,
hi,t = ωi + βihi,t-1 + αi,1ε 2i,t-1+αi,2 si,t-1 ε2i,t-1, (6)
εi,t|Φt-1 ~ tvi (0,hi,t),
and for the volatility:
Li,t = μi + εi,t + Θiεi,t-1,
λi,t = ωi + βiλi,t-1 + αi,1ε 2i,t-1+αi,2 si,t-1 ε2i,t-1, (7)
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εi,t|Φt-1 ~ tvi (0,λi,t),
with si,t-1 = 1 when εi,t-1 is negative and otherwise si,t-1 = 0. In the first stage of
parameters estimation, all of the parameters, including the degrees of freedom vi, are
estimated separately for each equity index by maximizing the log-likelihood for each
time series of index returns.
3.1.4 Specifying the dependence parameter
Patton (2006a) proposes that current dependence between markets is explained by the
previous dependence and the historical average difference of cumulative probabilities
for the two assets. Following Patton (2006a) and Bartram et al. (2007), we suppose
that pt depends on the previous dependence pt-1 to capture persistence, and historical
absolute differences, |ut-i – vt-i|, i>0, to capture variation in the dependence process.
We estimate the following dependence process:
(1-β1L)(1-β2L)ρt = ω + γ|ut-1 – vt-1| (8)
The intuition for the use of |ut-1 – vt-1| is the smaller (larger) the difference between the
realized cumulative probabilities, the higher (lower) is the dependence. So, equation
(8) describes an AR (2) model when extra assumptions are made, namely that a linear
function of the previous absolute difference, |ut-1 – vt-1|, provides a white noise
innovation term. We model the dependence structure as a mixture of copulas, with
parameters changing over time according to a Markov switching model.
Our approach is different from Patton (2006a), since we use all historical
information about the absolute differences, rather than arbitrarily truncating the
historical information. Furthermore, instead of a logistic transformation function, we
use a constraint in the estimation procedure to keep the dependence process within
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zero and plus one. The use of a logistic transformation function would unhelpfully
restrict the volatility of the dependence term when it is near its limiting values.
3.2 AG-DCC Model
Volatilities and correlations measured from historical data may miss changes in risk.
Thus, Cappiello et al. (2006) investigate properties of international equity returns
generalizing the DCC-GARCH model of Engle (2002) by introducing two
modifications: asset-specific correlation evolution parameters and conditional
asymmetries in correlation dynamics.
Following Cappiello et al. (2006), we let rt be a k x 1 vector of asset returns,
which is assumed to be conditionally normal with mean zero and covariance matrix
Ht:
rt|Ћt-1~N(0,Ht) (9)
where, Ћt-1 is the time t-1 information set. All DCC class models use the fact that Ht
can be decomposed as follows:
Ht = DtPtDt (10)
where, Dt is the k x k diagonal matrix of time-varying standard deviations from
univariate GARCH models with √hit on the ith diagonal and Pt is the time-varying
correlation matrix.
As the DCC model is designed to allow for three-stage estimation of the
conditional covariance matrix, any univariate GARCH process that is covariance
stationary and assumes normally distributed errors (irrespective of the true error
distribution) can be used to model the variances (Engle and Sheppard, 2001). In this
paper, we estimate univariate volatility using α GARCH (1,1) model (Bollerslev,
1986), and the standardised residuals, εi,t = ri,t / √hi,t, are used to estimate the
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correlation parameters4. The evolution of the correlation in the standard DCC model
(Engle, 2002) is given by:
1'
11
_)1( −−− ++−−= tttt bQaPbaQ εε (11)
1*1* −−= tttt QQQP (12)
where, ]'[ ttEP εε=−
and α and b are scalars such that α+b<1. [ ] [ ]iitiitt qqQ == ** is a
diagonal matrix with the square root of the ith diagonal element of Qt on its ith
diagonal position. As long as Qt is positive definite, *tQ is a matrix which guarantees
1*1* −−= tttt QQQP is a correlation matrix with ones on the diagonal and every other
element≤1 in absolute value. The model described by equations (11) and (12),
however, does not allow for asset-specific news and smoothing parameters or
asymmetries.
Cappiello et al. (2006) modify the correlation evolution equation as:
BQBGnnGAAGNGBPBAPAPQ tttttt 11111
_''''')'''( −−−−−
−−−
+++−−−= εε (13)
where, A, B and G are k x k parameter matrices, [ ] ttt In εε op 0= ( [ ]⋅I is a k*1
indicator function which takes on value 1 if the argument is true and 0 otherwise,
while “o ” indicates the Hadamard product) and [ ]'tt nnEN =−
. Equation (13) is the AG-
DCC model. In order the Qt to be positive definite for all possible realizations, the
intercept, GNGBPBAPAP−−−−
−−− ''' must be positive semi-definite and the initial
covariance matrix Q0 positive definite. The scalar A-DCC model has the following
form:
4The first stage of the DCC model building consists of fitting univariate GARCH specifications to each of the return series and selecting the best one according to the Bayesian information criterion. For a description of the three-stage estimation procedure, see Cappiello et al. (2006).
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12
112
11222
_2 '')( −−−−−
−−−
+++−−−= tttttt QbnngaNgPbPaPQ εε (14)
A sufficient condition for Qt to be positive definite is that the matrix in parentheses is
positive semi-definite. A necessary and sufficient condition for this to hold is
α2+b2+δg2<1, where δ is the maximum eigenvalue ][2/1__2/1_ −−
PNP . If the matrices A,
B and G are assumed to be diagonal, the AG-DCC model reduces to the following
form:
1'
11'
11''''' '')( −−−−−
−−
+++−−−= tttttt QbbnnggaaggNbbaaiiPQ ooooo εε (15)
where, i is a vector of ones and a, b and g are vectors containing the diagonal
elements of matrices A, B and G, respectively.
4. Data
The data employed consist of stock indices for four developing countries, namely
Brazil, Russia, India and China and two developed (U.S. and U.K.) The stock indices
are the following: Bovespa index (Brazil), RTS index (Russia), BSE Sensex index
(India), Shanghai index (China), S&P500 (U.S.) and FTSE-100 (U.K.). We construct
weekly log returns, in U.S. dollar terms, dividend un-adjusted, and cross–country
differences in volatilities. This paper uses all historical information generated from
equity index returns, rather than arbitrarily truncating the historical information. This
point makes our approach different from Patton (2006a, b). Non-synchronous trading
can cause a bias in the estimation of correlations. Therefore, weekly data provide the
best trade-off to avoid the market microstructure biases at daily frequencies.
The sample period is from January, 2, 1995 till October, 31, 2006 and
excludes holidays. We split our data as follows: (i) Asian crisis: 1997; (ii) Brazilian
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crisis: 1997-1998; (iii) Russian crisis: 1998; (iv) Internet collapse in developed
markets: 2000; (v) Brazilian crisis: 2002. Then, we compare the difference in returns,
actual and asymmetric volatilities and correlations between stable and crisis periods.
One difficulty in testing for contagion during these periods is that there is no a
single event to act as a definite catalyst behind the turmoil periods. For instance, the
Thai market declined sharply in June 1997, the Indonesian market fell in August
1997, and the Hong-Kong market crashed in mid-October 1997. Moreover, the
collapse of the Long Term Capital Management (LTCM) played an important role in
the Russian and the Brazilian crisis in 1998. Finally, the bust of the tech bubble in
2000 seems that began in March. However, a review of American and British
newspapers and periodicals during this period shows that there was a belief that the
market will recover soon to its all time high. It is obvious that contagion possibly
occurred during other periods of time. Therefore, this study takes into account a
period before and after the actual crash, using all historical information contained in
pre and post-crash data5.
5. Empirical Results
5.1 Dependence using Conditional Copula
Appropriate specifications for marginal densities are required when modeling
dependence by conditional copula densities. We use diagnostic test of Berkowitz
(2001) to evaluate the goodness-of-fit of our marginal densities, specified by the GJR-
GARCH-MA-t model given by (6) and (7). The residual series pass the goodness-of-
fit test at the 10% level for all 6 equity indices.
5 Following Forbes and Rigobon (2002), a sensitivity analysis shows that period definition does not affect the central results.
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Table 1 reports the summary statistics for the data which exhibit the standard
properties of financial returns. All markets exhibit a positive mean return for the
whole sample period. As for equity returns, all are negatively skewed and leptokurtic
and have variances with asymmetric functions.
Table 2 shows estimates of the copula dependence model equity index returns.
The time-varying dependence model is estimated for each country index. Across all
equity indices, parameter β1 is always larger than 0.5, and even as high as 0.92,
implying high dependence persistence. The other autoregressive parameter, β2, is also
larger than 0.5, but smaller than β1. Comparing the parameters during normal and
crises periods, β1 and β2 appear to increase significantly during turmoil periods. This
is a prerequisite for contagion to occur. Higher correlation during crises times
provides support on contagion effects. Also, as expected, the parameter γ is always
negative and highly significant, indicating that the latest absolute difference of returns
is consistently a relevant measure when modeling market dependence. Investors need
to adjust their portfolios accordingly, since markets share higher correlation during
market crashes. Portfolio diversification across markets might be less useful than
anticipated if based on correlations in tranquil times.
Results provide clear evidence of “jumps” in dependence levels from stable to
crises periods. However, the differences in the magnitudes of the dependence changes
are quite interesting. Specifically, the changes in dependence among emerging
countries are much larger than those between BRICs and the developed U.S. and
U.K., suggesting that the emerging countries are more prone to financial contagion.
However, in the case of China, the jump in dependence is higher with the developed
markets. This may be due to the convergence of market consensus and index returns.
It seems that, given the increasing uncertainty in the markets, investors in the Chinese
19
market preferred to follow information and financial movements from developed
markets rather than other emerging markets.
Furthermore, the industry-specific tech bust appears to have a larger impact
than country-specific crises. During the industry-specific episode, the proportion of
the valuation in the other markets that is driven by movements of the S&P500
increases significantly. The dependence between the U.S. and U.K. is the higher
shared during all crises examined (0.92). The bust of the tech bubble in 2000 makes
dependence among all markets to be constantly higher than 0.8. This implies that
stock market co-movements increased dramatically in 2000. One reason for this is the
leading role of the U.S. market, since is considered as a “global factor” influencing all
countries. Analyzing the crisis in the U.K. market over the same period, we also
observe high co-movements among stock markets. However, dependence between
U.K. and BRICs is lower when compared to the effect of the U.S. market on the
emerging markets, ranging from 0.584 (China) to 0.724 (Brazil).
On the contrary, the Asian crisis in 1997 does not spread with the same
magnitude. Correlations between the Chinese and all other stock markets range from
0.53 (U.K.) to 0.643 (Brazil). However, the co-movement with its neighbored Indian
market is higher than 0.78, implying that the crisis spreads with a larger magnitude
due to regional factors. The Brazilian crisis in 1997-1998 also spreads with a large
magnitude, ranging from 0.783 (Russia) to 0.813 (U.S.). During the Brazilian crisis in
2002, stock market correlations are also high, but to a lesser extent compared to the
crisis in 1997-1998. During the Russian crisis (1998), co-movements between Russia
and other countries increase significantly. Spread of contagion is higher with the U.S.
(0.728) and Brazil (0.723). However, the correlation between Russia and Brazil may
be misleading since the Brazilian stock market was in crisis during 1998.
20
Table 3 shows results for the multivariate copula with switching regime
parameters during all five crises periods. At least two regimes exist (s11 and s22)
during each of the five crises periods. The maximum value of the restricted likelihood
(LF) shows that a crisis in one market affects the movement to the other markets.
Also, all variances (v) are significantly different from one. The shifts in variances
during crisis periods affect the value of a market portfolio, since betas become time-
varying accommodated with various degrees of market integration. Increases in tail
dependence imply that the probability of markets crashing together is higher during
periods of financial turmoil. Figure 1 shows the regimes listed in Table 3. The higher
regime among stock markets observed during the 1997-1998 Brazilian crisis
(smoothed prob. 0.868), implying that this turmoil affected strongly the movements of
other markets.
The findings for dependence changes between stable and crises periods
suggest that all crises drive higher market dependence. While different economies
follow different economic policies, contagion is supported regardless any changes in
macro fundamentals. Equally, the policy responses to a crisis depend on the perceived
nature of transmission of shocks across the financial markets. Hence, it seems that
policymakers are unlikely to prevent spread of crisis since changes in fundamentals
do not help to avoid a crisis. Contagion effects result when pessimism for stocks in
one market brings a similar behavior in other markets, regardless of economic
fundamentals’ development.
5.2 Dependence using AG-DCC model
Table 4 summarises information about the distribution of the unconditional
correlations between stock markets. Results show that unconditional correlations
21
increase significantly during all crises, supporting the contagion hypothesis.
Furthermore, stock markets share the higher correlated level during the bust of the
tech bubble, supporting the results of the copula regime-switching model.
The magnitude of the tech bust spread is higher between the U.S. and U.K.
markets (0.896). Furthermore, the effect of U.S. stock returns on BRIC stock markets
is significant and consistently large in magnitude, ranging from 0.754 (Russia) to
0.872 (Brazil). Correlations between the U.K. and BRICs are also significantly high
but to a lesser extent compared to the U.S. effect. The Asian turmoil appears to be
spread with a large magnitude between India and China (0.896), though not
surprisingly. On the contrary, low correlations appear between China and Russia
(0.523), India and Russia (0.539) during the Asian crisis, as well as between Russia
and India (0.527) and Russia and China (0.536) during the Russian turmoil. These
stock markets seem to follow weaker co-movements during the above two episodes.
Finally, the Brazilian crisis in 2002 spreads with a larger magnitude than the crisis
during 1997-1998. This result comes in contrast to copula findings regarding those
two country-specific episodes.
Table 5 shows nonparametrically the presence of asymmetries in conditional
second moments. Results indicate that covariances are higher during negative shocks
than stable periods, supporting the contagion phenomenon6. During the more volatile
periods, conditional covariances and correlations are substantially greater than
unconditional correlations, supporting the presence of asymmetric responses to
negative shocks. Overall, comparing the levels of dependence during normal and
crises periods, this paper finds, consistent with the existing literature and the findings
6 Conditional correlations between equity index returns, not presented here, are also highly increased during crises periods. Results are available upon request.
22
of Cappiello et al. (2006), that during crises, stock market dependence is heightened
and there are clear asymmetric effects.
Table 6 reports results for testing whether we should adopt the symmetric or
the asymmetric DCC model. Four different parameterizations are estimated for the
dynamics of correlation. The first model is a standard scalar DCC model with no
asymmetric terms (Equation 11). Second, a symmetric diagonal version is estimated
(Equation 13, where matrices A and B are diagonal and matrix G is set equal to zero).
Next, two asymmetric specifications are considered, an asymmetric scalar DCC
model (Equation 14) and the full diagonal version of a scalar A-DCC (Equation 15).
All parameters are significantly different from zero. The g2i term in the asymmetric
model is always higher than zero, implying the presence of asymmetric movements.
Furthermore, the asymmetric b2i term is always higher than the symmetric b2
i,
providing further evidence to support the use of the asymmetric model in the study.
Therefore, results show that correlations among stock markets are much greater
during extreme downside moves than upside moves.
Figure 2 presents a comparison of the level of dependence among the stock
markets obtained by the two methodologies. Although both models provide results
supporting the contagion hypothesis, they report different level of dependence. One
interpretation of this result is that the models may fail under specific circumstances to
capture fully asymmetric volatility and its potential effects on covariances and
correlations during periods of crisis. Alternatively, this difference could be explained
by the different perspectives on stock market dependence during financial crises
captured by different methodologies. Comparing the AG-DCC model with the
multivariate regime switching copula, we find that the latter captures higher levels of
dependence. This may be due to its ability to connect the multivariate distribution to
23
its marginals in such a way that it captures the entire dependence structure in the
multivariate distribution, disregard to normality assumptions and tail dependence
increases. As a result, the multivariate copula manages to separate out the temporal
dependence from the marginal behavior of the time series capturing higher levels of
dependence than the AG-DCC model.
6. Conclusions
The financial crises of the late 1990s prompted extensive empirical studies on
contagion. However, the existing literature suffers from certain limitations caused
mainly by heteroskedasticity and omitted variables when measuring correlations
during the crisis. This paper applies two methodologies to investigate stock market
contagion, using returns for BRIC countries as well as for the U.S. and U.K., during
five recent financial crises (the Asian, Russian, Tech bust and the two episodes in
Brazil). These methods model time-variations in the dependence structure between
pairs of sample countries, account for asymmetries in the second moments of stock
market returns and enable us to overcome the problems arising in the existing
empirical research of financial contagion.
First, we propose and apply a time-varying regime-switching copula
dependence model in order to examine cross-market linkages. Specifically, we search
whether there are significant changes in the time-varying dependence structure of
markets during crises periods. We find that conditional correlations among stock
markets increase significantly during crises periods. Structural changes spread to
other markets with a big order of magnitude, while increases in tail dependence imply
that the probability of markets crashing together is higher during periods of financial
turmoil. Furthermore, the changes in dependence between BRICs are larger than those
24
between BRICs and the developed U.S. and U.K., suggesting that emerging markets
are more prone to financial contagion.
Second, we investigate asymmetries in conditional variances and correlation
dynamics for all countries during crises periods, applying the AG-DCC model.
Conditional volatilities of equity indices show widespread evidence of asymmetry.
The AG-DCC results provide further evidence for higher joint dependence during
stock market crashes. When bad news hit stock markets, conditional equity
correlations increase dramatically among BRIC and developed markets.
Overall, results using both methodologies provide support to the contagion
phenomenon. This implies that policy responses to a crisis are unlikely to prevent the
spread among countries since cross-market correlation dynamics are driven by
behavioural reasons. Moreover, the jump in correlations is higher during the tech
bubble crash implying that the industry–specific turmoil has a larger impact than the
country–specific crises. Finally, comparing the results obtained by the two
methodologies, this paper finds that the multivariate copula regime switching model
captures higher level of dependence than the AG-DCC approach. This may be due to
the fact that the multivariate copula captures the entire dependence structure in the
multivariate distribution, managing to separate out the temporal dependence from the
marginal behavior of the time series.
This study shows that a crisis episode spreads with a large magnitude even
though some countries belong in different regional blocks. This finding has important
implications for international investors, as the diversification sought by investing in
multiple markets is likely to be lower when it is most desirable. In other words,
returns and volatilities exhibit higher correlations among stock markets (i.e. contagion
spreads with a large magnitude), leaving international investors exposed to unhedged
25
risks. As a result, an investment strategy focused solely on international
diversification seems not to work in practice during turmoil periods.
A possible explanation for the contagion effect during recent crises is that
investors retrenched from many emerging markets after the series of crises in the late
1990s, causing significant changes in the countries’ financial structures. Commercial
banks reduced their volume of short-term loans to emerging markets, while portfolio
investors also reduced their exposure to emerging markets due to the shift in their
attitudes generated from the loss of confidence. This created a “domino effect”,
causing the “contagion phenomenon” in global markets.
Acknowledgement
The authors would like to thank an anonymous referee and the participants of the
European Financial Management Association Annual Conference, 27th – 30th June
2007, Vienna, Austria, for their valuable comments in an earlier version of this paper.
All remaining errors are the sole responsibility of the authors. Dimitris Kenourgios
would like to acknowledge financial support through the Operational Programme for
Education and Initial Vocational Training (O.P. "Education"), in the framework of the
project “Reformation of undergraduate programme of the Department of Economics /
University of Athens”.
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29
Table 1
Descriptive statistics
Country Mean St. Deviation Skewness Kurtosis
Brazil 0.093 2.85 -0.624 7.24
Russia 0.096 2.97 -0.747 6.39
India 0.081 2.80 -0.603 16.33
China 0.062 2.86 -1.215 19.27
U.S. 0.046 1.69 -0.880 6.83
U.K. 0.054 1.71 -1.114 12.79
This table reports summary statistics for the 6 equity index returns (at weekly frequency, dividend un-adjusted) during the period 1995-2006. All of the indices are denominated in USD.
30
Table 2
Estimates of the multivariate regime-switching copula dependence model for stock
market indices
Country ω β1 β2 γ LLF(c)
Crisis period Brazil 1997-1998 Russia 0.0468** 0.783** (0.639)* 0.702** (0.612)* -0.0371** 385.19 India 0.0392** 0.794** (0.608)* 0.715** (0.572)* -0.0316** 347.11 China 0.0386** 0.785** (0.539)* 0.710** (0.518)* -0.0349** 321.17 U.S. 0.0472 0.813** (0.697)** 0.802** (0.625)** -0.0303** 390.06 U.K. 0.0419 0.791** (0.630)** 0.784** (0.592)** -0.0455** 418.77 Russia 1998 Brazil 0.0374** 0.723** (0.639)* 0.680** (0.612)* -0.0347** 385.99 India 0.0348** 0.631** (0.544)* 0.607** (0.493)* -0.0388** 401.42 China 0.0365** 0.627** (0.537)* 0.601** (0.491)* -0.0479** 314.60 U.S. 0.0421 0.728** (0.642)** 0.716** (0.583)** -0.0597** 396.12 U.K. 0.0480 0.683** (0.611)** 0.628** (0.587)** -0.0521** 402.71 India 1997 Brazil 0.0368** 0.623** (0.608)* 0.597** (0.572)* -0.0738** 631.43 Russia 0.0372** 0.629** (0.544)* 0.615** (0.493)* -0.0583** 431.00 China 0.0829** 0.782** (0.679)* 0.751** (0.615)* -0.0694** 579.42 U.S. 0.0548 0.587** (0.511)** 0.560** (0.476)** -0.0428** 468.93 U.K. 0.0620 0.564** (0.503)** 0.540** (0.428)** -0.0676** 350.04 China 1997 Brazil 0.0576** 0.643** (0.539)* 0.619** (0.518)* -0.0686** 578.93 Russia 0.0527** 0.628** (0.537)* 0.620** (0.491)* -0.0517** 476.31 U.S. 0.0479 0.527** (0.409)** 0.516** (0.370)** -0.0438** 495.47 U.K. 0.0468 0.530** (0.428)** 0.518** (0.388)** -0.0691** 416.30 U.S. 2000 Brazil 0.0942** 0.874* (0.697)* 0.826* (0.625)* -0.0807** 682.22 Russia 0.0752 0.839* (0.642)** 0.810* (0.583)* -0.0641** 529.03 India 0.0740 0.816* (0.511)* 0.793* (0.476)* -0.0431** 368.89 China 0.0781 0.827** (0.409)** 0.798** (0.370)** -0.0588** 402.36 U.K. 0.104** 0.920* (0.587)* 0.845* (0.542)* -0.0836** 814.74 U.K. 2000 Brazil 0.089** 0.724* (0.630)* 0.718* (0.592)* -0.0732** 527.90 Russia 0.064 0.674* (0.611)** 0.639* (0.587)* -0.0613** 498.86 India 0.052 0.619* (0.503)** 0.600* (0.428)** -0.0539** 471.55 China 0.047 0.584* (0.428)** 0.566 * (0.388)** -0.0526** 470.03 Brazil 2002 Russia 0.0376 0.721** (0.639)* 0.689** (0.612)* -0.0582** 361.47 India 0.0437 0.708** (0.608)* 0.682** (0.572)* -0.0544** 421.73 China 0.0482 0.693** (0.539)* 0.658** (0.518)* -0.0371** 366.19 U.S. 0.0475 0.724* (0.697)** 0.700* (0.625)** -0.0466** 385.42 U.K. 0.0439 0.711* (0.630)** 0.695* (0.592)** -0.0427** 437.88 This table reports estimates of the multivariate copula dependence model during crises periods. The correlation parameter pt is given by Equation 8. Estimates of parameters β1 and β2 during stable periods are reported in parentheses. LLF(c) is the maximum of the copula component of the log-likelihood function. * and ** indicate significance at the 1% and 5% level, respectively.
31
Table 3
Results from multivariate regime-switching copula dependence model
Brazilian crisis Russian default Asian crisis Tech bust Brazilian crisis
(1997-98) (1998) (1997) (2000) (2002)
Brazil Russia India China U.S. U.K. Brazil
LF -1347.9 -1474.1 -1186.2 -1495.5 -1082.4 -1107.3 -1265.0
p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00
v 4.377 4.806 4.129 4.900 2.065 2.131 4.279
s11 0.868 0.739 0.744 0.645 0.672 0.680 0.632
s22 0.733 0.712 0.686 0.619 0.620 0.627 0.608
This table reports results using the multivariate regime-switching copula for each stock market against all others when at least one of them is under financial crisis. LF is the restricted likelihood function, v is the variance, while s11 and s22 are two regimes. P-value shows the statistical significance of the results.
32
Table 4
Unconditional correlations between equity index returns
Country Crisis period Stable Period Period Brazil 1997-1998 Russia 0.648* 0.584* India 0.612* 0.579* China 0.639* 0.503* U.S. 0.682* 0.674* U.K. 0.627* 0.591* Russia 1998 Brazil 0.624* 0.584* India 0.527* 0.518 China 0.536* 0.483 U.S. 0.618* 0.586* U.K. 0.614* 0.571* India 1997 Brazil 0.589* 0.579* Russia 0.539* 0.518 China 0.896* 0.644* U.S. 0.630* 0.581* U.K. 0.613* 0.539* China 1997 Brazil 0.582* 0.503 Russia 0.523 0.483 U.S. 0.627* 0.527 U.K. 0.615* 0.534 U.S. 2000 Brazil 0.872* 0.674* Russia 0.754* 0.586* India 0.783* 0.581* China 0.789* 0.527 U.K. 0.896* 0.722* U.K. 2000 Brazil 0.715* 0.584* Russia 0.638* 0.571* India 0.642* 0.539*
China 0.627* 0.534 Brazil 2002 Russia 0.682* 0.584* India 0.653* 0.579* China 0.671* 0.503 U.S. 0.720* 0.674* U.K. 0.691* 0.591* This table reports unconditional correlations of equity index returns during crises and stable periods. * indicates significance at the 5% level.
33
Table 5
Conditional partial covariances
Country Crisis period Stable Period Period Brazil 1997-1998 Russia 0.732* 0.671* India 0.697* 0.620* China 0.684* 0.562* U.S. 0.795* 0.706* U.K. 0.741* 0.619* Russia 1998 Brazil 0.706* 0.671* India 0.645* 0.600* China 0.630* 0.524 U.S. 0.679* 0.662* U.K. 0.648* 0.583* India 1997 Brazil 0.629* 0.620* Russia 0.658* 0.600* China 0.918* 0.827* U.S. 0.677* 0.634* U.K. 0.635* 0.587* China 1997 Brazil 0.633* 0.562* Russia 0.658* 0.524 U.S. 0.629* 0.577* U.K. 0.625* 0.576* U.S. 2000 Brazil 0.905* 0.706* Russia 0.870* 0.662* India 0.842* 0.634* China 0.818* 0.577* U.K. 0.936* 0.789* U.K. 2000 Brazil 0.734* 0.619* Russia 0.662* 0.583* India 0.650* 0.587*
China 0.644* 0.537* Brazil 2002 Russia 0.727* 0.671* India 0.671* 0.620* China 0.695* 0.562* U.S. 0.759* 0.706* U.K. 0.782* 0.619* This table reports conditional partial covariances during crises and stable periods. * indicates significance at the 5% level.
34
Table 6
DCC GARCH models
Country Symmetric model Asymmetric model
2ia 2
ib 2ia 2
ig 2ib
Brazil 0.0019* 0.9627* 0.0015* 0.0012* 0.9649*
Russia 0.0017* 0.9603* 0.0012* 0.0009* 0.9678*
India 0.0022* 0.9634* 0.0015* 0.0011* 0.9642*
China 0.0016* 0.9682* 0.0011* 0.0008* 0.9695*
U.S. 0.0084* 0.9243* 0.0057* 0.0051* 0.9420*
U.K. 0.0079* 0.9286* 0.0034* 0.0025* 0.9461*
This table reports parameter estimates for the symmetric and asymmetric DCC GARCH models. Four different parameterizations are estimated: a) a standard scalar DCC model with no asymmetric terms (Equation 11); b) a symmetric diagonal version (Equation 13, where matrices A and B are diagonal and matrix G is set equal to zero; c) an asymmetric scalar DCC model (Equation 14); d) the full diagonal version of a scalar A-DCC (Equation 15). * indicates significance at the 5% level.
35
Figure 1
Copula regimes during crises periods
00,10,20,30,40,50,60,70,80,9
1Ja
n. 1
995
Jan.
199
6
Jan.
199
7
Jan.
199
8
Jan.
199
9
Jan.
200
0
Jan.
200
1
Jan.
200
2
Jan.
200
3
Jan.
200
4
Jan.
200
5
Jan.
200
6smoo
thed
pro
babi
lity
for r
egim
es
Brazilian crises
Russian crisis
Asian crisis - India
Asian crisis - China
Developed marketscrisis - U.S.Developed marketscrisis - U.K.
36
Figure 2
Comparison between copula and AG-DCC results
Copula vs. AG-DCC
0
0,2
0,4
0,6
0,8
1
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Date
Dep
ende
nce
AG-DCC
Copula Switchingregime parameters