International stock markets interactions and conditional correlations
Christos S. Savva
*
Economics Research Centre, University of Cyprus
This version: 03 November 2008
Abstract
This paper investigates the transmission of price and volatility spillovers across
the US and European stock markets in bivariate combinations. The framework used
encompasses the most popular multivariate GARCH models, with News Impact Surfaces
employed for interpretation. By using synchronous data the Dynamic Conditional
Correlation model (Engle, 2002) is found to best capture the relationships for over half of
the bivariate combinations of markets. Other findings include volatility spillovers from
the US to European markets, and a reverse spillover. In addition, the magnitude of the
correlation between markets is higher not only for negative shocks in both markets, but
also when a combination of shocks of opposite signs occurs.
JEL Classification: C32; F36; G15
Keywords: Multivariate garch models; News impact surfaces; Asymmetric volatility
*
Corresponding author: Tel.:+357 22 892407; fax: +357 22892426.
E-mail address: christos.savva@ucy.ac.cy
1. Introduction
The extent of price spillovers, volatility spillovers and correlations between
international stock markets has received much attention in recent years. It has been
argued and generally accepted that multivariate models are appropriate for studying the
transmission mechanism and correlation dynamics (Martens and Poon, 2001).
A brief review outlines the most popular multivariate GARCH models suggested
in the literature. The first attempt was made by Bollerslev, Engle, and Wooldridge (1988)
who proposed the VECH specification. However, the major drawbacks of the VECH
model are the difficulty to guaranty a positive definite variance covariance matrix and the
rapid increase of the parameters to be estimated for any additional dependent variable.
This model was followed by the Constant Conditional Correlation (CCC) model,
proposed by Bollerslev (1990) with the only critique being the assumption of constant
correlations which is often unrealistic in empirical applications. In 1995 Engle and
Kroner suggested the BEKK model which overcomes the problem of positive definite
variance-covariance but not the problem of dimensionality.1
Alexander proposed the Factor-GARCH (with Chibumbu, in 1997) and
Orthogonal-GARCH (2001) respectively. Recently, an extension of the CCC model, the
Dynamic Conditional Correlation (DCC) model was proposed by Engle (2002). Under
the DCC specification, the correlation is time-varying and is able to capture the changes
over time. For further details about various multivariate models, refer to Bawens, Laurent
and Rombouts (2006), and Palandri (2005).
Although each of the above models has its own characteristics with some
advantages and disadvantages, it will be very beneficial to have a model that
encompasses at least the major multivariate models. In a seminal paper, Kroner and Ng
1
The acronym comes from synthesised work on multivariate models by Baba, Engle, Kraft and Kroner.
(1998) attempt to do so. Their model, the Generalized Asymmetric Dynamic Correlation
(GADC) encompasses a number of major multivariate models. They apply this
generalized model to study the dynamic relation between large and small firm returns and
they show that it behaves better than the specific multivariate GARCH models. However,
the GADC model does not encompass one of the most recent and popular models, the
DCC model.
By following a suggestion of Bawens et. al. (2006), we extent the GADC model
to include the DCC specification. Under this Extended Generalized Asymmetric
Dynamic Correlation framework (hereafter EGADC) we examine the price and volatility
spillovers as well as the correlations between five important European stock markets (the
UK, Germany, France, Italy and Spain) along with the US.2
Many other studies have tried to examine similar relationships (for instance see
Cappiello, Engle and Sheppard, 2006; Baele, 2004; Bartham, Taylor and Wang, 2007;
Billio and Pelizzon, 2003; Kim, Moshirian and Wu, 2006; Hardouvellis, Malliaropoulos
and Priestly, 2006; Savva, Osborn and Gill, 2005 among others). Although concerned
with similar issues, each study employs a different model and as Martens and Poon
(2001) point out, conditional correlations may have different signs depending on the
model and data type used.
Therefore, on the one hand this study examines similar relationships to the
previous studies (i.e. whether evidence for price and/or volatility spillovers from one
market to another exists, the direction of influence, and the changes in conditional
correlations). On the other hand it differs from others by using a general framework
(which encompasses the most popular multivariate GARCH models), thereby providing
2
These European markets account for more than 80% of total stock market capitalisation in Europe and
four of them have adopted a common currency, the Euro. Therefore, it is very important to monitor whether
there are any changes in their conditional correlations. Furthermore, the inclusion of the US and the UK
allows capturing international influence since both countries are home to many of the world’s largest
companies.
evidence on which model fits the data better. Furthermore, news impact surfaces analysis
is employed for the investigation on the pattern of shock transmissions.
Our findings suggest that for around half of the bivariate combinations of markets
in this study; the Dynamic Conditional Correlation model adequately captures the
relationships between stock markets, whereas a more general asymmetric model is
required for the remaining cases. Furthermore, there are price and volatility spillover
effects not only from US to European stock markets but also from Europe to US,
supporting previous evidence of Martens and Poon (2001). Finally, we observe an
increase in correlation in all markets before the launch of the Euro, which became less
volatile after the introduction of the common currency, especially for the Euro Area
countries.
The rest of the paper is organized as follows: Section 2 discusses the methodology
of the study; section 3 analyses the data and the empirical findings; section 4 presents the
specification tests and section 5 summarizes the study and concludes.
2. Methodology
2.1. The model
A model that nests a number of popular multivariate GARCH models (VECH,
CCC, BEKK and F-ARCH) is the general asymmetric dynamic covariance (GADC)
model proposed by Kroner and Ng (1998). This study uses an extension of that model,
proposed by Bauwens et al. (2006) to cover the dynamic conditional correlation model
(DCC) of Engle (2002). Under the framework of EGADC we investigate interdependence
and volatility transmission between stock markets in different countries.3 To the best of
our knowledge this model has not previously been applied to observed data.
3
We investigate interdependence by considering two markets each time.
To model the short-run dynamic relationships between stock markets, we use the
following bivariate Vector Autoregressive (bi-VAR) model:
2
yi ,t = ψ i ,0 + ∑ψ iρ, j yi ,t − ρ + ε i ,t
(1)
j =1
The conditional mean daily return in each market, yi ,t (i=1,2) is a function of own
past returns yi ,t − p and cross-market past returns, y j ,t − p (i≠j). Te VAR lag order p, is
determined by the Schwartz Information Criterion using a maximum of 10 lags. ψ iρ, j ,
captures the lead-lag relationship between returns in different markets, for i ≠ j . Market j
leads market i when ψ iρ, j is positive and significant.
We also assume that ε t ~ N (0, H t ) , where ε t = [ε1,t , ε 2,t ]' and H t = [hij ,t ] is the
2 × 2 conditional variance-covariance matrix of the unexpected returns.
Following Kroner and Ng (1998) and Bauwens et al. (2006) the conditional
variance-covariance matrix of EGADC model is defined as follows:
H t = Dt Rt Dt + Φ : Θt
where
:
(2)
denotes the element-by-element matrix multiplicator (Hadamard product
operator).
⎡h
H t = ⎢ 11t
⎣ .
Dt = (dijt ),
diit = θiit
h12t ⎤
θ12t ⎤
⎡θ
and Θ t = ⎢ 11t
⎥
⎥
h22t ⎦
⎣ . θ 22t ⎦
d ijt = 0 ∀ i ≠ j
Θt = (θijt )
Rt is specified as in Engle’s DCC model, i.e.
Rt = (diag (Qt ))
−1
2
Qt (diag (Qt ))
−1
2
(3)
and Qt is a 2 × 2 symmetric positive definite matrix described by the following equation:
Qt = (1 − α − β )Q + α ut −1ut −1 '+ β Qt −1
(4)
with ui ,t = ε it / hiit , Q the unconditional 2 × 2 correlation matrix of ut , α and β scalars
satisfying (α ≥ 0), ( β ≥ 0) and α +β <1 .
Φ = (φij ), φii = 0 ∀ i, φij = φ ji
θij ,t = ωij + Ai ' ε t −1ε t −1 ' Aj + Gi 'ηt −1ηt −1 ' G j + bij hij ,t −1
(5)
Ai = [a1i , a 2i ]' and Gi = [ g1i , g 2i ]' are 2 ×1 vectors of parameters, Ω = (ωij ) is positive
definite and symmetric while ε t is the T × 2 vector of disturbances (where T denotes the
number of observations) and ηt = max[0, − ε t ] .
Elementwise (2) implies:
hii ,t = θii ,t
hij ,t = ρij ,t θii ,tθ jj ,t + φijθ ij ,t ∀ i ≠ j
where ρij ,t is the i,jth element of Rt .
The correlation ρ12,t indicates to what extent the covariance between two assets is
related to the market’s individual variances. The coefficient α in (4) captures the impact
of recent comovents on the correlation while the coefficient β captures the persistence in
correlation. The parameter φ12 captures the asymmetry in the covariance that is not driven
by the asymmetry in variances. Variance asymmetry is captured by the coefficients of Gi
and G j in (5).
Although the parameters φ12 , α and β, are easily interpreted, this is not the case for
the rest of the parameters. A positive (or a negative) value of a ij cannot be interpreted as
a positive (or a negative) impact, due to the complicated product terms in (5). However
the magnitude and the combination of the parameters can give us useful information. In
addition a ij , gij , a ji and g ji (i≠j) give information about spillover effects.
As noted before, the EGADC model nests several multivariate GARCH models. It
reduces to: (i) the DCC model of Engle (2002) if φij = 0 , (ii) the CCC model of
Bollerslev (1990) if a = β = φij = 0 with some restrictions also imposed on the vectors Ai
and Gi, (iii) the BEKK model in Engle and Kroner (1995) if α = β = 0 , Q = I N and
φij = 1 , (iv) the VECH model of Bollerslev et. al. (1988) if α = β = 0 with some imposed
restrictions to the vectors Ai , Gi and the values of bij , and (v) F-ARCH model of Engle,
Ng and Rothschild (1990) if α = β = 0 , φij = 1 with some imposed restrictions to the
vectors Ai , Gi and the values of bij . More details can be found in Bauwens et al. (2006).
2.2. Model estimation
The model is estimated by pseudo maximum likelihood, using
L=−
1 T
(n log(2π ) + log | H t | +ε t ' H t−1ε t )
∑
2 t =1
which is maximized over all parameters of the model. Therefore, we maximize the loglikelihood function in a single step. To obtain the estimates for the parameters, we use a
combination of the standard gradient search algorithms Broyden-Fletcher-GoldfarbShanno (BFGS) and Brendt-Hall-Hall-Hausman (BHHH). All computations were carried
out using GAUSS. To allow for non-normality of the disturbances conditioning on all
available information at time t-1, robust “sandwich” standard errors (Bollerslev and
Wooldridge, 1992) are used for the inference.
3. Data and empirical findings
3.1. Data and preliminary statistics
The data consist of daily prices recorded at 16:00 London time (pseudo-closing
prices) of S&P-500 (USA), FTSE-100 (UK), DAX-30 (Germany), CAC-40 (France),
MIBTEL-30 (Italy) and IBEX-35 (Spain) indices. Where available we use 16:00 London
time closing prices in order to avoid the problems of non-synchronous data.4 The period
is from August 3, 1990 to April 12, 2005 for all markets except Italy. The period for the
Italian market spans from October 17, 1994 to April 12, 2005. At the time of collecting
the data this was the longest series available.5
We analyze returns, defined as the difference of the logarithm of the price index,
scaled by 100. Since the data comes from different countries, it is unavoidable to have
different holidays for each market. We side-step this problem by taking the holiday
(pseudo) closing price as being the same as the previous day. Hence the sample for each
country contains all days of the week except weekends.
All markets show positive average returns over our sample, with IBEX-35 and
S&P500 possessing the highest values both at 0.032 percent per day and the remaining
three between 0.02 and 0.03. On the other hand, the Eurozone markets of Milan,
Frankfurt, Paris and Madrid have substantially higher (unconditional) volatility, between
1.32 and 1.43, compared with London and New York, with values of 1.017 and 1.021
4
As Martens and Poon (2001) show, using non-synchronous data leads to underestimation of conditional
correlations between the markets. Although, for the markets of Italy and Spain pseudo-closing prices are
not available, their closing time is close to 16:00 London time.
5
The data for this study is extracted from DataStream. The above indices are basically designed to reflect
the largest firms. The DAX-30 is a price-weighted index of the 30 most heavily traded stocks in the
German market, while the FTSE-100 is the principal index in the UK and consists of the largest 100 UK
companies by full market value. CAC-40 is calculated on the basis of the 40 largest French stocks based on
capitalization on the Paris Bourse. The MIBTEL-30 is a capitalization-weighted index and is based on the
30 most highly capitalized stocks listed on the Italian Stock Exchange. IBEX-35 is composed of the 35
securities quoted on the Joint Stock Exchange System of the four Spanish Stock Exchanges. Finally S&P500 is a value weighted index representing approximately 75 percent of total market capitalization in New
York.
respectively. Although detailed univariate descriptive statistics are not presented to
conserve space, it may be noted that daily returns are negatively skewed (except for
London) and, as usual for high frequency stock market data, highly leptokurtic with
respect to the normal distribution. Furthermore, Ljung-Box statistics for squared returns
show strong evidence of second moment (nonlinear) dependencies.
Table 1 reports the values for (unconditional) cross-correlations of returns over
the whole sample period and also separately for the sub-periods before and after the
introduction of the Euro.6
Table 1. Unconditional Cross-market correlations of daily returns
S&P500
S&P500
FTSE100
1
FTSE100
0.676
0.630
0.712
1
DAX30
0.642
0.538
0.719
0.695
0.578
0.787
DAX30
CAC40
MIBTEL30
IBEX35
1
CAC40
0.664
0.593
0.722
0.742
0.667
0.804
0.758
0.619
0.872
1
MIBTEL30
0.591
0.551
0.626
0.679
0.612
0.732
0.685
0.535
0.790
0.767
0.654
0.848
1
IBEX35
0.595
0.539
0.646
0.650
0.570
0.722
0.682
0.574
0.783
0.755
0.668
0.840
0.736
0.637
0.811
1
Notes:
Correlations for the whole period are in black.
Correlations for the pre-Euro period are in grey.
Correlations for the post-Euro period are in italics.
Measured over the whole sample, the highest unconditional returns correlation are
between French and the rest of the European stock markets, with values varying from
0.72 to 0.767. The lowest correlation is between US and Italy at 0.59, US and Spain at
0.60 followed by US and Germany, at 0.64. However, these values conceal substantial
differences over time, with all correlations increasing after the launch of Euro. The most
6
The introduction of the Euro is used as a reference point. Whether this event has caused alterations in
correlations remains an open question for further research.
marked effect is between the European stock markets and especially between French
stock market with German and Spanish and Italian with Spanish.
3.2. Estimation of EGADC model
Since we use bivariate combinations we have fifteen combinations of the
aforementioned indices. Table 2 summarizes the results from estimating the EGADC
model.
When the model was estimated, it became obvious that almost all correlations
have undergone a structural break around the period of the introduction of the Euro. The
same result is supported by the analysis of Cappiello et. al. (2006) and Savva et. al.
(2005). For that reason dummy variables were included in the mean, volatility and
correlation equations (1, 4 and 5). However, the model with the dummies revealed that
only the dummy in the correlation equation is significant. Hence, the model is estimated
by using a dummy only in the correlation equation.
To include the structural break into the correlation equation we substitute Q by
Qt which is defined as:
Qt = Q1 I [t ≤ τ ] + Q2 I [t ≥ τ ]
(7)
where Q1 = E[ut ut' ], for t ≤ τ , Q2 = E[ut ut' ], for t ≥ τ and I [ K ] is the indicator function
for the event K and τ denotes the break point (van Dijk, Munandar and Hafner, 2006).
The empirical findings are discussed in the following sub-sections.
Table 2. EGADC Model Estimation Results
S&PFTSE
S&PDAX
S&PCAC
S&PMIBTEL
S&PIBEX
FTSEDAX
FTSECAC
FTSEMIBTEL
FTSEIBEX
DAXCAC
DAXMIBTEL
DAXIBEX
CACMIBTEL
CACIBEX
MIBTEL
-IBEX
Mean Equations Results
ψ10
ψ(1)11
ψ(1)12
ψ(2)11
ψ(2)12
ψ20
ψ(1)21
ψ(1)22
ψ(2)21
ψ(2)22
0.026**
-0.039**
0.018
0.017*
0.030***
-0.045**
0.017
0.037**
0.028**
-0.054***
0.019
-0.026
0.028
0.027*
0.033**
-0.062***
0.004
-0.026
0.027
0.039**
0.029**
-0.040**
0.017
-0.032*
0.004
0.046***
0.0158
0.050***
-0.024*
0.033**
0.014
-0.012
0.043***
0.018
0.015
0.013
0.020
0.031*
0.015
0.007
0.004
-0.025
0.002
0.04***
0.030**
-0.153***
0.250***
0.024*
0.047**
-0.114***
0.183***
0.047***
0.038**
-0.110***
0.210***
0.047***
0.038**
-0.015
0.025
0.042**
0.031**
0.021
0.007
0.043***
0.048***
-0.011
0.033
0.059***
0.021
0.006
-
0.153***
-0.058***
-
0.018
-0.003
-0.036**
0.012
0.011
-0.018
0.032**
0.029*
-0.009
0.057***
0.026**
0.002
0.201***
-0.082***
-
-0.021
0.019
-
0.003
-0.005
-
-0.006
0.090***
-0.052**
0.020
-0.056***
0.061***
-
-0.053***
0.030
-
-0.079***
0.110***
-
0.010
-0.007
-
-0.023
0.073***
-
0.005
0.043*
-
w11
w22
w12
a11
a21
a12
a22
g11
g21
g12
g22
b11
b12
b22
α
β
φ12
0.007**
0.006**
-0.171
0.195***
-0.105***
-0.186***
0.178***
0.194***
0.102*
-0.029
0.308***
0.932***
0.361
0.930***
0.026**
0.851***
0.091
0.008***
0.023**
-0.031
0.149***
-0.063**
-0.038
0.187***
0.218***
0.053*
0.054
0.209***
0.938***
-0.047
0.927***
0.031***
0.951***
-0.076
0.007***
0.011***
-0.265
0.130***
-0.025**
-0.173***
0.173***
0.207***
0.050***
0.044*
0.252***
0.945***
0.147
0.936***
0.023***
0.947***
-0.020
0.008**
0.008
-0.089
0.103***
-0.049**
-0.169***
0.299***
0.294***
0.044
0.199***
0.102***
0.923***
0.196
0.910***
0.015
0.978***
0.191**
0.006**
0.013**
-0.197
0.157***
-0.045***
-0.227***
0.231***
0.195***
0.061**
0.112**
0.221***
0.942***
0.234
0.912***
0.016*
0.963***
0.034
0.015**
0.008**
-0.417
0.165***
0.070***
-0.110***
0.298***
0.281***
-0.060
0.170***
0.073*
0.916***
0.688
0.913***
0.026**
0.964***
0.024
0.024**
0.022**
-0.014
0.194***
-0.015
-0.107***
0.216***
0.147***
0.104***
0.122***
0.159***
0.924***
-0.075
0.921***
0.031***
0.942***
-0.211*
0.015**
0.008*
-0.186
0.184***
-0.053
-0.133***
0.292***
0.195***
0.064***
0.203***
0.041
0.937***
0.290
0.923***
0.022**
0.970***
0.050
0.024***
0.022**
-0.134
0.164***
-0.063
-0.076
0.210***
0.180***
0.087***
0.128***
0.130***
0.936***
0.031
0.927***
0.042***
0.924***
-0.126*
0.011**
0.013**
-0.298
0.286***
-0.110***
-0.047
0.228***
0.075*
0.167***
0.145***
0.104*
0.919***
0.430
0.924***
0.028***
0.961***
0.017
Conditional Variance - Covariance Equations Results
Notes:
* represents 10% significance level.
** represents 5% significance level.
*** represents 1% significance level.
0.0067***
0.016**
-0.076
0.058
-0.129***
-0.101**
0.206***
0.368***
-0.088*
0.135**
0.149***
0.930***
0.213
0.935***
0.033***
0.940***
0.107
0.0060*
0.018**
-0.049
-0.046*
0.132***
-0.158***
0.197***
0.318***
-0.030
0.193**
0.145*
0.932***
0.049
0.933***
0.025***
0.946***
0.190***
0.0050**
0.005
-0.127*
0.125***
-0.068***
-0.235***
0.277***
0.265***
0.025
0.223***
0.102***
0.942***
0.249*
0.923***
0.025***
0.960***
0.164**
0.009***
0.016***
-0.215***
0.177***
-0.053**
0.255***
-0.182***
0.176***
0.093***
0.122**
0.236***
0.930***
0.274**
0.914***
0.032***
0.910***
0.176***
0.024***
0.024***
-0.092
0.116***
0.063**
-0.085**
0.191***
0.238***
-0.009
0.134***
0.140**
0.931***
-0.051
0.930***
0.035***
0.948***
-0.165**
3.3. Mean equations
The results from estimating the mean equations reveal that there are some
interdependencies between the stock markets.7 The S&P500 is correlated with its
previous day’s returns with no effects from other markets. There are no effects from
S&P500 to the FTSE100 while there are previous day’s effects to the German market
(DAX30). Two days ago S&P500’s returns influence the rest of the markets. A possible
explanation is attributed to the fact that historically these markets have been considered
less important than the other markets analysed, and hence international investors may
take longer to react to information from these markets.
In contrast to the US market, FTSE100 is predicted by its previous day’s returns
only in the combination with DAX30. It is also predicted by DAX30 and CAC40 and
affects DAX30 and IBEX35.
The case of DAX30 appears to be an interesting one. While in all combinations
DAX30 is negatively correlated with its previous day’s returns, it is also positively
affected by the returns of all other markets. The magnitude and significance of the
(negative) autoregressive coefficient for Frankfurt, together with the size and significance
of the (positive) other markets’ coefficient in the equations where Frankfurt appears,
indicate some inefficiencies in this market. The interaction among other markets and
Frankfurt, and the apparent inefficiencies in the Frankfurt market, may reflect difficulties
experienced by the German economy in the period after reunification.
Moreover, the French stock market (CAC40) influences the UK and German
stock markets with feedback effects only from the German stock market. There are no
effects to or from the Italian and Spanish stock markets. Similar behaviour holds for the
case of Italian (MIBTEL30) and Spanish (IBEX35) stock markets.
7
The market used in the “first equation” of the model is the one referred first in column heading of Table 2.
3.4. Conditional variance – covariance equations
Turning to conditional second moment parameters, the estimated coefficient φ12
in (2) is insignificant for eight combinations (although the magnitude of the coefficient is
not always close to zero). The insignificance of φ12 supports that any asymmetry in
covariance is purely driven by the asymmetry in the conditional variance in the markets
of the respective combinations. For the rest of the combinations φ12 is significant and
indicates asymmetry in the covariance of two markets. A negative sign of φ12 denotes a
negative correlation between the covariance and θ12,t while a positive sign denotes the
opposite.
Furthermore, the parameter β, is highly significant for all markets, with a value
varying from 0.85 to 0.99, showing that the correlation between two markets is time
varying with high level of persistency.8 Similarly, the recent comovements in correlation
(captured by the parameter, α) are highly significant for all markets except from the
combination of S&P500 with MIBTEL30.9
All the above suggest that for the cases where φ12 is insignificant ( φ12 = 0 )the
DCC model of Engle (2002) is adequate to describe the relationship between those
markets (for further details see subsection 2.1).10 For the rest of the combinations, the
EGADC model is the most appropriate.
As far as the conditional variances are concerned it can be seen that the estimates
of b11 and b22 parameters vary from 0.91 to 0.95 and they are highly statistically
significant, indicating that conditional stock returns variances are highly persistent. b12
8
However, the persistency in conditional correlations is lower when we include the structural break since
the estimate of β declines if a break is included.
9
Using a likelihood ratio test, various models discussed in section 2.1 (such as BEKK, CCC etc) have been
tested. They are all rejected at the 1% significance level.
10
Note that if φ12 = 0 then θ12,t is irrelevant to the model. Hence b12 and ω12 will not be identified.
captures effects additional to those captured through the conditional variances and
correlations. However, it is insignificant for all combinations, indicating that there is no
any further information in the conditional covariance from this term.11
In addition, the majority of a ij and gij coefficients are highly significant, with the
latter indicating that asymmetric effects for shocks on conditional variances exist among
the markets, supporting the results of Martens and Poon (2001). By inspecting the
estimates for the parameters a ij and gij we infer whether there are volatility spillover
effects from market i to j and vice versa. Many of a ij coefficients are negative, implying
that some of the shocks in one market have negative impact on the volatility of the other.
The latter holds for the combinations between European markets and the US,
showing that there are volatility spillovers from Europe to the US. This finding is
attributed to the data we use (pseudo closing prices). Many studies (including Chan, Chan
and Karolyi, 1991) show that the volatility in US stock market is higher during opening
and closing periods than at other times of the day. Our pseudo closing prices correspond
to 11:00 in New York, when S&P500 volatility is at its lowest level, whereas the
European markets are near to their close when their volatility is relatively high. It is
possible that these differences play a role in the volatility spillover results we obtain in
relation to the US.12
Furthermore, for five combinations an insignificant coefficient for g 21 is
combined with a significant coefficient for φ12 .13 A possible explanation might be that the
11
Except from the combination between FTSE100 and MIBTEL30 where b12 is marginally significant (at
10%).
12
In addition, for the case of New York with the London market, Susmel and Engle (1994) show that when
the returns are calculated over a specific intra-day intervals, then volatility spillovers occur from one
market to the other last only for a brief period after the opening of the New York market. Therefore, the
method used to allow for the time difference between the US and Europe might be an important factor in
the results obtained.
13
Those are the combinations of S&P500 with MIBTEL30, DAX30 with CAC40 and FTSE100 with
CAC40, MIBTEL30 and IBEX35 respectively.
asymmetry in volatility in market 1 is indirectly driven in market 2 through their
covariance.
Nevertheless, as noted previously the interpretation of each parameter
individually is a difficult task, and it is easier to interpret the complete model intuitively
by using news impact surfaces, firstly introduced by Kroner and Ng (1998).
3.5. News impact surfaces
The news impact surfaces for the variance show the impact of the previous day’s
shocks of market i and j on the conditional variance of market i, conditional variance of
market j and conditional correlation.14 Following Kroner and Ng (1998) each surface
region is evaluated in the region ε i ,t = [−5,5] for i=1,2. The following figures (1 – 3)
represent the most common patterns arising from combinations between two markets.
The news impact surface of the conditional variance depicted in Figure 1a and b
represents the patterns from the combinations between US with French and UK with
French stock markets respectively. However, one of these patterns holds for the majority
of combinations. The first one shows a situation where the conditional variance in one
market is more sensitive to shocks coming from its own market regardless of the sign and
magnitude of the shocks coming from the other market, while the second shows a case
where the conditional variance is more sensitive to the negative shocks in both markets,
and to the combination of negative with positive shocks.
14
News impact surfaces have also been calculated for the conditional covariance. Since they do not present
much useful and incremental information compared to the conditional correlations, we do not report them.
Plots are available upon request.
Figure 1. News Impact Surface for the Conditional Variance.
(a)
(b)
More specifically, the conditional variance of S&P500 is described better by
Figure 1a for all combinations except the case of FTSE100. Similar patterns to Figure 1a
also hold for the combinations of FTSE100 with the DAX30, CAC40, MIBTEL30, and
IBEX35. However, in the case of the combination of FTSE100 with DAX30, negative
shocks in FTSE100 do not have such a great impact on the conditional variance of
FTSE100. The conditional variance of FTSE100 with S&P500 is more sensitive to the
combination of positive with negative shocks (Figure 1b).
Moreover, the combinations of DAX30 with S&P500, CAC40, MIBTEL30, and
IBEX35 have very similar patterns to Figure 1a, while the conditional variance of
DAX30 resulting from the combination of the German market with the British market is
more sensitive to any combination of opposite shocks (Figure 1b with an increased edge
for the combination of positive shocks).
In the case of the French market the combinations of CAC40 with the markets of
MIBTEL30, and IBEX35 have very similar pattern to Figure 1a while the combinations
of CAC40 with S&P500, FTSE100 and DAX30 are similar to Figure 1b.
The conditional variances of MIBTEL30 arising from the combinations between
MIBTEL30 with the rest of the markets (S&P500, FTSE100, DAX30, CAC40 and
IBEX35) are more sensitive only to the combinations of opposite shocks in two markets
as in Figure 1b. A similar pattern appears in the combinations of IBEX35 with the rest of
the markets.
The news impact surfaces for the conditional correlations ( ρ12,t ) reveal some
interesting results.15 Figure 2 depicts the pattern of US with UK, which is the most
common for all combinations. The correlation appears to be more sensitive to the
combination of positive or negative shocks with negative shocks having a slightly greater
15
The News Impact Surfaces of the conditional correlations are estimated by using h12, t /
h11,t h22,t .
impact (asymmetry in correlation). However, for some combinations (e.g. FTSE100 and
DAX30 with CAC40) it appears to be more sensitive to the combinations of opposite
shocks (supporting the findings of Martens and Poon, 2001 and Bekaert and Wu, 2000),
while for some cases (e.g. S&500 and FTSE100 with DAX30 and CAC40 with
MIBTEL30) the combination of positive shocks has the same impact with the
combinations of negative shocks (no asymmetry in correlation).
Figure 2. News Impact Surface for the Conditional Correlations
Although the finding that opposite shocks affects correlations more than any other
combination of shocks is surprising, it has to be interpreted with caution. The
simultaneous occurrence of a large positive shock in one market and negative in the other
is very unlikely. In order to illustrate of the above, we plot (available upon request) the
scatter plots of the synchronised returns between FTSE100 with CAC40 and DAX30
with CAC40. Indeed, there are no cases where the returns in one market are large and
negative and in the other are large and positive.16 Hence, this finding includes
extrapolations in areas for which there are no observations.
16
Martens and Poon (2001) have also found a similar result.
3.6. Conditional correlation plots
As mentioned above, one of the purposes of this paper is to investigate whether
the correlations of the stock markets under investigation alter during our sample period.
Figure 3 plots some indicative daily conditional correlations while Table 3 presents the
average correlations of the pre-Euro and post-Euro period based on the coefficient
estimates of Table 2.17 The introduction of the Euro on 1st January 1999 is given by a
vertical line in Figure 3.
Table 3. Average Correlation for Pre and Post Euro Period
S&P500
FTSE100
DAX30
S&P500
1
FTSE100
0.594
0.701
1
DAX30
0.459
0.716
0.502
0.764
1
CAC40
CAC40
0.560
0.712
0.642
0.787
0.573
0.863
1
MIBTEL30
IBEX35
MIBTEL30
0.453
0.626
0.540
0.693
0.477
0.764
0.613
0.815
1
IBEX35
0.478
0.640
0.516
0.697
0.493
0.773
0.618
0.825
0.571
0.768
1
Notes: The average correlations of each combination for the post-Euro period are in italics.
Given the increased average levels of conditional correlations in the post-Euro
period it is not surprising that these daily conditional correlations trend upwards over
time. A similar pattern is well documented in the literature (for instance Cappiello et. al.,
2006, Bartram et. al. 2007, Savva et. al., 2005, Kim et. al., 2006, among others). The
smallest increase in Table 3 is for the combination of S&P500 and FTSE100 (from 0.59
to 0.70). The highest increase is observed in correlations concerning the European
markets. More specifically the correlation between DAX30 with CAC40 increased
dramatically (from 0.57 to 0.86), followed by the correlation of DAX30 with MIBTEL30
and IBEX35 (with an increase around 50% compared to the pre-Euro period). A similar
increase appears in correlations of CAC40 with MIBTEL30 and MIBTEL30 with
IBEX35 (33% compared to the pre-Euro period).
17
As in the case of descriptive statistics, the introduction of the Euro is used as a reference point.
A notable pattern appears in the correlations of MIBTEL30 with the rest of the
European markets. More specifically, a large increase is observed from the beginning of
1997 until the end of 1998. For the following 8-12 months there is a decrease in
correlations, while for the rest of the sample period it is trending upwards.
Although, there is an increase in correlations after the introduction of the Euro,
this cannot be attributed exclusively to that event. During the period of this study many
incidents took place and influenced the interrelations between financial markets. For
instance, Asian crisis in 1997 (for more details on its impacts to international stock
markets we refer to Lafuente and Fernadez, 2004), various terrorist attacks (Chulia et. al.,
2006), technology boom (Brooks and del Negro, 2005) may be some of the factors that
caused increase in international financial market correlations.
Another interesting implication of Figure 3 is the stability in the dynamic
conditional correlation between the European markets that adopted the Euro for the postEuro period.18 After the introduction of a common currency, the correlation has not only
increased but also remained high (around 0.8-0.9) and substantially less volatile than in
the preceding period.19 This high and relatively constant correlation points towards the
increased integration of these Euro Area markets which may be attributed to the
reduction of the currency risks across these markets. These findings are in line with other
studies in that area (Cappiello et. al., 2006, Bartram et. al. 2007, Savva et. al., 2005, Kim
et. al., 2006) who found an increase in correlations, especially between European
markets. Also the stability noted by Savva et. al. (2005), here applies also for other Euroarea markets.
18
Examining whether the Euro was the main factor for the increase in correlations is beyond the scope of
this study. We refer to Kim et. al. (2006), for an extensive analysis on that issue.
19
This is also supported by Figure 3, suggesting that the dynamics of the conditional correlations have
changed as well. However, the model we employed in this paper only allows for a change in the
unconditional correlation. Therefore, the question whether a more general specification, which allows the
dynamics to change, is more appropriate remains open for further investigation.
Figure 3. Conditional Correlation Plots
4. Specification test
In order to asses the adequacies of the EGADC model we use the robust
conditional moment test of Wooldridge (1990). To perform this test we define a
generalised covariance residual vij ,t (a generalised residual is a constructed residual, such
as vij ,t = ε i ,t ε j ,t − hij ,t , which should have conditional expectation zero). If the model is
correctly specified, then Et −1{vij ,t } = 0 , thus vij ,t should be uncorrelated with any of
variable known at time t-1. These variables are referred as misspecification indicators. As
Kroner and Ng (1998) state “knowing that a major difference between the models is their
asymmetric property, a beneficial approach is to partition the (ε i ,t −1 , ε j ,t −1 ) space in a way
that can highlight the asymmetric property. Misspecification indicators can then be built
based on this partition”.
Hence, we partition the (ε i ,t −1 , ε j ,t −1 ) space into four quadrants: (-,-), (-,+), (+,-),
and (+,+) and let I(.) be the indicator function that equals one if the argument is true and
zero otherwise. The misspecification indicators corresponding to such a partition are:
x1, t − 1 = I ( ε i , t − 1 < 0; ε
j ,t −1
< 0)
x 2 , t − 1 = I ( ε i , t − 1 < 0; ε
j ,t −1
> 0)
x 3 , t − 1 = I ( ε i , t − 1 > 0; ε
j ,t −1
< 0)
x 4 , t − 1 = I ( ε i , t − 1 > 0; ε
j ,t −1
> 0)
We also define the following “sign indicators”,
x 5 , t −1 = I ( ε i , t −1 < 0 )
x 6 ,t −1 = I ( ε
j ,t −1
< 0)
Moreover, the magnitude of the shocks along with the sign and size of shocks can
also play an important role and influence the size of the effect on variances and
covariance (Engle and Ng, 1993). To measure these effects, we define the following
indicators:
x 7 , t −1 = ε i2,t −1 I ( ε i , t −1 < 0)
x8 , t −1 = ε i2,t −1 I ( ε j ,t −1 < 0)
x 9 , t −1 = ε 2j ,t −1 I ( ε i , t −1 < 0)
x10 ,t −1 = ε 2j ,t −1 I ( ε j ,t −1 < 0)
Wooldridge (1990) presents a test statistic that is robust to the conditional
distribution used when testing the multivariate GARCH model. This test statistic is
defined as C m = ( 1
T
T
∑v
t =1
ij , t
λ g , t −1 ) 2 (
1
T
T
∑v
t =1
2
ij , t
λ g2, t −1 ) − 1
where λg ,t −1 is the residual from a regression of the misspecification indicator xg ,t −1 on the
derivatives of hij ,t with respect to the parameters of the model. Under a general regularity
condition, Wooldridge (1990) shows that Cm has an asymptotic χ12 distribution.
The robust conditional moment test statistics can be computed easily from two
auxiliary regressions. First, we regress xg ,t −1 on the derivatives of hij ,t with respect to all
the parameters of the null model. Next, we regress a vector of ones on the product
vij ,t λg ,t −1 . The test statistic Cm is then equivalent to T times the uncentered R 2 from the
second regression.
The test statistics for the covariance between market i and market j are reported in
Table 4 along with the Ljung-Box tests for serial correlation in the normalized crossproduct of residuals, ε i ,t ε j ,t / hij ,t .
From Panel A of Table 4 we observe that the EGADC model is able to capture
asymmetries within the covariances for the most of the combinations. The only
exceptions are the cases of some combinations that include the Italian stock market
(MIBTEL30). This result leads to the conclusion that a better model might exist for
capturing the asymmetries for these combinations. In addition, the sample of these
combinations is smaller than the other cases and this might be one of the reasons for this
appearance of misspecification. Although the EGADC model has difficulty in capturing
some asymmetries in the covariances between the stock markets, generally it performs
very well.
Panel B reports the normalised cross-product of residuals, ε1t ε 2t / h12t . As can be
seen, the Ljung-Box tests do not reject any of combinations under the EGADC model
suggesting that the model is well specified.
Table 4. Diagnostic Tests for Covariance Specification for EGADC Model
PANEL A: Robust conditional moment tests
I (ε
I (ε
1 , t −1
2 , t −1
< 0)
< 0)
I (ε 1, t −1 < 0, ε 2 , t −1 < 0)
S&PFTSE
S&PDAX
S&PCAC
S&P-
S&PIBEX
FTSEDAX
FTSECAC
FTSE-
DAXCAC
MIBTEL
CACIBEX
MIBTEL
MIBTEL
DAXIBEX
CAC-
MIBTEL
FTSEIBEX
DAX-
MIBTEL
1.259
1.580
1.321
2.867
2.005
0.177
0.001
3.248
0.009
1.746
0.252
0.990
2.005
2.764
2.612
0.100
2.550
0.512
0.021
0.069
1.747
1.487
0.837
0.751
3.198
3.960**
2.569
0.727
1.302
2.709
-IBEX
0.163
1.394
0.529
0.084
0.730
1.144
0.046
0.917
0.007
1.318
0.977
1.139
0.797
1.789
2.629
I (ε 1, t −1 < 0, ε 2 , t −1 > 0)
2.883
0.055
0.181
5.837**
2.487
0.796
0.146
1.444
0.011
0.037
0.605
0.775
0.858
0.005
0.013
I (ε 1, t −1 > 0, ε 2 , t −1 < 0)
0.011
0.094
0.126
0.069
0.430
0.170
0.816
0.006
0.523
1.414
1.673
0.213
0.017
1.741
0.001
I (ε 1, t −1 > 0, ε 2 , t −1 > 0)
1.962
3.713
1.121
4.327**
2.281
1.368
1.411
3.816
1.076
4.898**
2.412
3.007
2.112
2.236
2.953
ε 1,t −1 I (ε 1,t −1 < 0)
2.787
0.805
1.213
0.238
0.427
0.011
0.046
0.216
0.066
1.155
0.089
0.060
0.005
0.465
3.026
ε 1,t −1 I (ε 2,t −1 < 0)
2.052
1.791
0.098
0.409
0.236
0.705
1.491
0.127
0.042
1.014
0.304
0.257
0.031
1.418
1.305
ε 2, t −1 I (ε 1,t −1 < 0)
0.471
0.012
1.334
2.988
0.473
1.428
0.027
5.449**
0.127
0.053
0.298
0.201
3.879**
0.034
0.155
0.171
0.054
1.588
3.211
0.392
2.182
0.031
6.156**
0.013
0.321
1.634
1.996
3.557
0.028
0.848
2
2
2
2
ε 2,t −1 I (ε 2, t −1 < 0)
PANEL B: Ljung-Box tests for serial correlation in ε1ε2/h12
Q(6)
3.322
1.713
1.313
10.541
1.786
1.638
2.201
10.442
2.395
0.629
11.447
0.664
4.438
0.297
6.489
Q(12)
7.806
5.214
11.001
16.779
3.228
3.101
6.255
14.237
3.718
1.662
19.371
1.124
8.595
0.674
13.420
Q(18)
14.456
6.711
13.658
18.487
3.933
4.754
7.570
18.748
5.254
3.945
39.01**
1.658
11.152
1.189
15.118
Notes:
Panel A gives the robust conditional moment test statistics for each combination under the EGADC model. The misspecification indicators are listed in the first column and
the remaining columns give the test statistics for each of the fifteen combinations. This statistic is distributed χ21 and has a 95% critical value of 3.84.
Panel B gives the Ljung-Box test statistic for serial correlation in the standardized cross-product of residuals from these combinations. The 5% critical levels for Q(6), Q(12),
and Q(18) are 12.6, 21.0, and 36.4, respectively.
*** denotes significance at the 1% level.
** denotes significance at the 5% level.
5. Main findings and conclusions
This paper employs the EGADC to estimate the price, volatility spillovers and
correlations between the US and the major European stock markets. This model
encompasses the most popular multivariate GARCH models suggested in the literature.
The data consists of daily pseudo closing prices (prices recorded at 16:00 London time)
where applicable, to avoid the problem of non-synchronous closing times. It covers the
period from August 3, 1990 to April 12, 2005, except from the case of Italy where the
period is from the October 17, 1994.
The estimates from a bivariate VAR specification for the return equations show
that there are price spillover effects from US to Europe without any feedback effects. As
far as the volatility spillover effects are concerned, we find effects not only from US to
Europe but also from Europe to US, supporting previous findings of Martens and Poon
(2001). To assess the impact of the shocks in each market on the conditional volatilities
and covariance we employ News Impact Surfaces. The patterns of conditional volatilities
vary with the combination of markets while the conditional correlation of each
combination is not only higher in the case of negative shocks in both markets but also in
the combination of negative shocks in one market and positive shocks in the other.
Generally, according to the parameter estimates, for around half of the bivariate
combinations of the markets under investigation, the Dynamic Conditional Correlation
specification of Engle (2002) is found to be appropriate. For the rest of them, the
EGADC specification is preferred, as the DCC model does not fully capture the dynamics
of the cross-market covariances.
As far as the changes in the patterns of the conditional correlations are concerned,
the results of the paper indicate an increase in the correlations between returns across
markets. While this increase is not confined to the Euro Area French, Italian, Spanish and
German stock markets, the increase is most marked for the correlation between these
markets. For the period since the launch of the Euro dynamic correlations of shocks
between countries that adopted the Euro is not only high (at around 08 to 0.9), but is
relatively constant, indicating that these markets are substantially integrated and subject
to common shocks.
All the above findings motivate further research. For instance, we can extend the
DCC model specification to include different dynamics for each market along with
asymmetry (for more details see Cappiello et. al., 2006). In addition, it will be interesting
to analyze relations within industry across different regions (see for instance Soriano and
Climent, 2006). Moreover, since under the bivariate structure of the model we lose useful
information about the spillovers coming from other markets, it would be useful to modify
the EGADC specification (although a difficult task) to include more than two markets
each time.
Acknowledgment
The author is very grateful to Denise Osborn, Len Gill and two anonymous
referees for their helpful comments and suggestions. He is also indebted to Martin
Martens and Olan Henry for providing the Gauss routines, which were modified and used
for the estimations.
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