Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
The Transmission of Volatility between the CDS Spreads and
Equity Returns Before, During and After the Global Financial
Crisis: Evidence from Turkey
Sinem Derindere Köseoğlu
The aim of this study is to investigate the transmission of volatility between
the Credit Default Swap spreads (CDS spreads) and equity returns in
Turkey. In recent years, credit related instruments have been developed
rapidly and since then their effect on equity markets has become the
research subject. The existed literature generally concentrates on
conditional means rather than conditional volatility. However, in the
theoretical background, it is highly possible that the volatility in any of the
two markets is usually conveyed to the other two markets. Therefore, a
multivariate GARCH model is applied to data to analyze volatility contagion
effect of the global financial crisis on Turkey. Although, there is not any
consensus on the contagion definition, it usually refers to the markets
which move more closely together during crisis periods. Thus, the data has
been divided into three sub-periods; before, during and after the global
financial crisis in order to show the crisis effect more clearly and if there is
a volatility contagion effect during the crisis and normal periods between
the CDS spreads and equity markets.
Key Words: CDS spreads, equity markets, financial crisis, multivariate GARCH
JEL Codes: C58, G01, G10
1. Introduction
This paper examines the transmission of volatility between the CDS spreads and equity
returns in Turkey for the period of January 03, 2005 to June 30, 2012. To investigate this
relation, we fit VAR-GARCH BEKK model to the daily logarithmic return series of ISE 100
stock index as an aggregate equity returns and 5 year CDS spreads as a country credit
risk measure for Turkey. In another words, these markets have been analyzed at the index
(market) level.
In the last two decades, derivative markets have developed significantly both in size and
liquidity. Particularly, the credit default swap market has grown enormously and is leading
one in the derivative markets currently. The spread or prices of credit default swaps
theoretically represent the credit risk of a country or an entity. As a consequence of the
rapid development of CDS markets, CDS spreads in particular have attracted much
attention as a guide to the credit risk. On the other hand, the equity returns is probably the
most vital market indicators all around the world. Thus, variety of empirical studies has
investigated the relations between CDS spreads and equity returns recently. There is also
a theoretical background to the argument that there exist an empirical relation between the
equity returns and the CDS spreads. Merton (1974) argues that there exists close relations
between the default probability and volatility of equity returns. Since the most important
determinant of CDS spreads is the default probability, the possibility of the close relations
between the equity returns and the CDS spreads is extremely high.
___________________________________________________________
Dr. Sinem Derindere Köseoğlu, Istanbul University, Turkey. Email:sderin@istanbul.edu.tr
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
Firstly, many of the empirical studies in this field concentrate on the first moments of CDS
spreads and equity returns. In another words, they examine mean spillovers rather than
volatility spillovers between the variables. (Longstaff et al., 2003; Norden and Weber,
2004, 2009; Bystrøm, 2004; Hafer and Dynes, 2008; Fung et.al., 2008; Forte and Peña,
2009; Lake and Apergis, 2009; Kikuchi and Uomoto, 2009; Fonseca and Gottschalk,
2012). A common conclusion of those is that the first moments of the variables are
negatively related. Since then some studies starts to concentrate on second moments of
the variables whereas these studies are very rather. (Meng et al., 2009; Lake and Apergis,
2009; Schreiber et.al., 2009; Belke and Gokus, 2011; Fonseca and Gottschalk, 2012). In
addition, these studies in general investigate the Europe, the USA and Asia Pacific
markets. Thus, further research should be done in this field and as far as we know there is
no study to investigate volatility contagion between these variables for Turkey. The
volatility patterns of CDS spreads and equity returns have become more important during
the recent financial crisis. The common evident is that the volatility of these variables is
higher during the crisis. The value of correlation and covariance coefficients between them
also increase in times of crisis. Therefore, in this study, the data has been divided into
three sub-periods before, during and after the global financial crisis in order to show the
crisis effect more clearly and if there is a volatility contagion effect during these periods
between the CDS spreads and equity markets of Turkey.
The rest of the paper is organized as follows. Section 2 provides a brief review of the
literature on the relations between CDS spreads and equity returns. Section 3 discusses
the econometric methodology. Section 4 presents the data and Section 5 gives the
empirical results from the VAR-MGARCH model. Section 6 concludes.
2. Literature
Most of the empirical studies in the field of relations between CDS spreads and equity
returns generally concentrate on modeling the conditional mean, whereas the studies in
this field focused on modeling the time-varying conditional variance and covariance
structure is very rather. This study particularly is in line with second literature, therefore the
result of those has been reported only. Since the credit market has been represented by
bond market as well as CDS market, it is also mentioned the results of the studies about
the volatility transmission between bond and equity returns here. In practice, the CDS
spreads are very close to bond spreads. (Blanco et al.,2005; Forte and Peña, 2009)
Steeley (2006) used the multivariate GARCH-CCC framework to examine volatility
transmission between short term bond, long term bond and stock markets in the UK for the
period 1984-2004. The empirical findings showed that volatility spillover exists from longterm bond yields to short term bond yields and stock returns and from short term bond
yields to stock returns.
Chulia and Torró (2008) investigated the volatility transmission between equity and bond
markets in Europe by using Dow Jones Euro Stoxx 50 index futures and Euro Bond
futures as a proxy for equity market and bond market respectively. They fit VAR-GARCH
models to the weekly data to investigate this relation and they found that volatility
spillovers are two directional.
Meng, Gwilym and Varas (2009) investigated the volatility transmission among the bond,
CDS, and equity markets for ten large US companies by using a multivariate GARCHBEKK approach over the period 2003-2005. They found almost reciprocal volatility
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
spillover among these markets. On the other hand, empirical results support the
conception that as investors search for high yield across different asset categories, the link
between the CDS, bond, and equity markets strengthens. In addition, innovation in any of
the three markets can cause trading activity to increase in the other two markets. Their
study should also try to shed light on the efficiency of the markets. The result of
bidirectional volatility transmission implies that none of these three markets is relatively
more efficient than the other two.
Lake and Apergis (2009) conducted an empirical study in this field for the US and
European (German, UK and Greek) equity markets. They used multivariate GARCH in
mean modeling to investigate the volatility spillover between CDS spreads and equity
returns in the period 2004 to 2008. They reported that equity returns volatility and CDS
spreads volatility reinforce each other.
Schreiber et al. (2009) investigates the volatility contagion between aggregate CDS
spreads, equity returns and implied equity volatility by fitting VAR-GARCH models. They
investigate the conditional variance and covariance structure by using daily data of the
iTraxx Europe, Dow Jones Euro Stoxx 50 and Dow Jones VStoxx index for the period 23
June 2004 to 30 April 2009. They used this period to shed light on the recent crisis effect
on the related markets. Five year maturity iTraxx Europe index has been taken as an
aggregate credit risk measure of Europe, Dow Jones Euro Stoxx 50 has been taken as a
representative for Europe equity and lastly Dow Jones VStoxx indices has been taken as
implied equity volatility. They found that the correlations between the iTraxx Europe and
the Euro Stoxx 50, and the Euro Stoxx and the VStoxx to be negative. A positive
correlation exists between the iTraxx and the VStoxx. In addition, they provided evidence
of strongly time varying conditional variances and correlations, with the rising dependency
after the start of the latest global financial crisis.
Belke and Gokus (2011) examined the volatility structure of equity returns, CDS spreads
and bond spreads for four large US banks by employing multivariate GARCH approach.
Their time period is from 2006 to 2009 to be accounted for the recent global crisis. The
empirical findings support the view that volatility levels increase after the start of the crisis.
Fonseca and Gottschalk (2012) analyzed the volatility spillover effects among CDS
spreads, realized volatility and equity returns for Australia, Japan, Korea and Hong Kong
markets, which are the most liquid countries in Asia Pacific region. Their sample was
weekly data between September, 2007 and December, 2010. They illustrated that realized
volatility is the main supplier to aggregate market volatility.
All studies about the volatility spillovers display typical results. The volatility transmission
between CDS spreads and equity returns is in general reciprocal. In addition, the
conditional variances, covariances and correletions of the variables are significantly timevarying and absolute values of them increases particularly during the crisis, which shows
the volatility contagion in these markets. However, these findings belong to the studies
analyzed the US, Europe and Asia Pacific markets. To the best of our knowledge, there is
no this kind of study for the high growth emerging market of Turkey and therefore it is not
obvious if these results are valid for Turkey. To fill this gap, it is conducted this study in this
field for Turkey as a high growth emerging market. We thus widen the results known for
the US, European and Asia Pacific markets to a high growth emerging market of Turkey.
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
3. Methodology
In this study, it is followed a two step approach of a vector autoregressive generalized
conditional heteroskedastic VAR-GARCH model. First step a VAR model has been fitted
to the data series for the conditional mean equations. Then, the standard VAR approach
has been extended by admitting time coefficients, which is specified by a multivariate
GARCH model.
First stage, a two dimensional VAR(p) model have been used to analyze the dynamic
relations between CDS spreads and equity returns.
(1)
(2)
Where xt,1 and xt,2 represent two different time series variables; equity returns and CDS
spreads respectively in this study. The structure is that each variable is a linear function of
past lags of itself and past lags of the other variables. α and w symbols represent
intercepts and residuals respectively. The number of lags (p) included in each equation is
estimated by using a test of system reduction. The lag length of VAR model has been
chosen with respect to the AIC (Akaike Information Criterion), HQ (Hannan Quinn
Information Criterion), SC (Schwarz Information Criterion) and FPE (Final Prediction Error)
information criteria.
Second stage, a multivariate GARCH model is fitted to the VAR system that has been
estimated at first step. Multivariate GARCH models are very similar to univariate GARCH
models except that they also allow to measure dynamic relationships. Several multivariate
GARCH models have been proposed including BEKK, VECH and DCC. The BEKK model,
which was proposed by Engle and Kroner (1995), has some simple solutions for the
problems of previous models like VECH and DCC models (Syriopoulos and Roumpis,
2008). The conditional variance of each equation in BEKK model is denoted as below:
(3)
where C is a 2x2 lower triangular matrix with intercept parameters, and A and G are 2x2
square matrices of parameters. This model requires estimation of only 11 parameters in
the conditional variance-covariance structure and ensures that the variance-covariance
matrix (Ht) is always positive definite. Also, the BEKK model implies that only the
magnitude of past return innovations is important in determining current conditional
variances and covariances. Because of this performance, the BEKK parameterization is
adopted for the purposes of this analysis.
In the equations, the series are ISE100 index and CDS spreads of Turkey. We can
express Equation 3 in the form of matrix:
[
-
-
][
-
-
-
][
]
[
]
-
[
]
(4)
-
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
Where shows the ARCH parameter, is the GARCH parameter and is the error term.
If
representation is enlarged by matrices multiplications following equations can be
obtained.
(5)
(6)
(
)
(
)
(7)
Particularly, the Diagonal BEKK is well organized in estimating than the full BEKK model,
when the number of samples is a constraint. Namely, the matrices, A and G, are diagonal
and the elements of the variance covariance matrix Ht, depend only on its own lagged
values and those of ε1t and ε2t. Hence, both
,
,
and
are equalized to zero.
Then, representation of the bivariate DBEKK model can be shown as below by following
simple form of multivariate GARCH (Chou, Wu and Liu, 2009):
(8)
(9)
(10)
This form allows measuring volatility spillovers between equity returns and CDS spreads in
variance equations. This variance modeling allows us to see dynamic or time varying
conditional variances and correlations.
4. Data
Our data set consists of daily quotes of two time series; ISE100 stock index and 5 year
CDS spreads of Turkey. ISE100 consists of closing index numbers while CDS spreads
has been expressed in basis points (bps). The whole time period covered is January 03,
2005 to June 30, 2012. As it can be seen from Figure 1, ISE 100 index and CDS spreads
of Turkey move in opposite directions due to the fact that increased credit risk increases
the CDS spreads and reduces the equity. As mentioned before, CDS spreads represent
the credit risk of a country or a firm and this credit risk is also present in equities. It is
expected that when the credit risk of a country or a firm increases, in another words the
probability of default risk raises, the CDS spreads will increase. This increase will affect
the stock index of a country or the equity price of a firm in a negative way. Thus, there
should be a negative relationship between the CDS spreads and the stock index of a
country or equity price of a firm.
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
Figure 1. Daily closing quotes of ISE100 stock index and 5 year CDS spreads of Turkey between January 03, 2005 and
June 30, 2012
90000
900
80000
800
70000
700
60000
600
50000
500
40000
400
30000
300
20000
200
10000
100
0
0
ISE100
CDSspreads
The data has been divided into three sub-periods; before, during and after the global
financial crisis in order to show the crisis effect more clearly. Pre-crisis, crisis and after the
crisis periods are from January 2005 to March 2008, from March 2008 to May 2009 and
from May 2009 to June 2012 respectively. These divisions have been made according to
the Figure 1. Although the global financial crisis, which is originated from the USA, started
in 2007, Turkey affected from it particularly in 2008. Thus, volatile period starts in 2008 for
Turkey as can be seen from Figure 1. Basic characteristics of whole and sub-periods of
the data have been summarized in Table 1.
Table 1. Summary statistics of ISE100 stock index and 5 year CDS spreads for whole and sub-periods.
Whole period
Pre-crisis period
Crisis period
After crisis period
Jan 2005- June 2012
Jan 2005 - March 2008 March 2008 - May 2009 May 2009 - June 2012
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Observations
ISE100
45646.30
44891.25
71543.26
21228.27
12724.93
-0.011071
1.971830
83.24384
0.000000
1889
CDSs
227.3387
202.9000
824.6100
116.5500
84.11556
2.026854
9.604423
4726.510
0.000000
1889
ISE100
39556.29
39635.43
58231.90
23285.94
8928.196
0.004871
2.170041
22.96423
0.000010
800
CDSs
202.4579
190.8350
374.1300
116.5500
52.35867
0.917719
3.252618
114.4216
0.000000
800
ISE100
34828.74
35829.40
48364.83
21228.27
7460.004
-0.112867
1.709046
28.26750
0.000001
395
CDSs
327.0243
284.6600
824.6100
188.2600
107.2452
1.432266
5.608300
247.0195
0.000000
395
ISE100
58823.45
58821.20
71543.26
45230.95
5847.708
0.027661
2.288628
14.72179
0.000636
694
CDSs
199.2824
183.3700
344.0000
118.6100
49.08508
0.753254
2.603919
70.16471
0.000000
694
In general, skewness and kurtosis values of the CDS spreads are higher than the equity
index. All series present significant kurtosis and all the Jarque Bera tests reject the
normality. Kurtosis and skewness values show that the series are heavy tail and excess
skewed, which is common for financial time series and indicates the series are suitable for
ARCH type modeling.
The CDS spreads have a sample mean of 327 bps during the crisis period, which is the
highest level compared to other periods. In contrast to CDS spreads, mean value of
ISE100 stock index has the lowest level during the crisis period at 34,828. This also
indicates the negative relations between CDS spreads and equity returns for the sample
period. Standard deviation of the CDS spreads is especially extremely high during the
crisis period.
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
The return series are obtained by using the logarithmic differences of the equity index and
CDS spread values with 1889 daily observations using equation 11.
returnt  ln( Pt / Pt 1 )
(11)
Figure 2. Daily logarithmic returns of ISE100 and CDS spreads between January 03, 2005 and June 30, 2012
0.15
0.30
0.10
0.20
0.05
0.10
0.00
0.00
-0.05
-0.10
-0.10
-0.20
-0.15
ISE100return
-0.30
CDSspreads
Both return series display typical stylized features such as volatility clustering. (see Figure
2). Thus, the assumption of homoscedasticity has not met and the series show time
varying variance feature, which also implies that ARCH type models are suitable for these
return series.
Table 2. Covariance of daily logarithmic returns of CDS spreads and ISE100 Index for the whole period and
sub periods.
CDSs
Whole period
Jan 2005- June 2012
ISE100
Pre-crisis period
Jan 2005 - March 2008
ISE100
Crisis period
March 2008 - May 2009
ISE100
After crisis period
May 2009 - June 2012
ISE100
-0.000078
-0.000135
-0.000326
-0.0000473
Covariance between equity returns and CDS spreads for the whole and sub-periods can
be seen in Table 2. This preliminary analyze shows the volatility patterns of the variables.
As expected, the covariance between equity returns and CDS spreads are negative and
higher in absolute values during the crisis period. In addition, second highest absolute
value belongs to the pre-crisis period, since the effects of the crisis started to be felt in
Turkey just before the crisis.
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
Table 3. Stationary, Autocorreletaion and Heteroscedasticty Test Results
test
Whole period
Jan 2005- June
2012
trend
-13.46230(0.0000)
trend and intercept
-13.46179(0.0000)
trend
-12.49802(0.0000)
trend and intercept
-12.49889(0.0000)
Pre-crisis period
Jan 2005 - March
2008
trend
-27.48140 (0.0000)
trend and intercept
-27.50189 (0.0000)
trend
-8.233541(0.0000)
trend and intercept
-7.334639(0.0000)
Crisis period
March 2008 - May 2009
trend
-17.88117 (0.0000)
trend and intercept
-18.05005 (0.0000)
trend
-7.174463(0.0000)
trend and intercept
-7.291495(0.0000)
After crisis period
May 2009 - June
2012
trend
-25.70584 (0.0000)
trend and intercept
-25.70167 (0.0000)
trend
-14.55096 (0.0000)
trend and intercept
-14.55007(0.0000)
ISE100
-0.003 (0.009)
-0.023 (0.010)
-0.001 (0.021)
-0.001 (0.020)
CDS
spreads
-0.036 (0.000)
-0.070 (0.000)
-0.050 (0.000)
-0.018 (0.034)
ISE100
0.173 (0.000)
0.041 (0.000)
0.231 (0.000)
0.024 (0.034)
variable
ISE100
ADF
CDS
spreads
Q(12)
2
Q (12)
CDS
0.109 (0.000)
0.024 (0.000)
0.154 (0.000)
0.030 (0.000)
spreads
Akaike Information Criteria has been used to conduct ADF tests. Parenthesis shows probabilities of test statistics.
To investigate the stationary of the data the most commonly used Augmented Dickey
Fuller (ADF) test has been applied to the data series. The results of ADF tests are
presented in Table 3. The null hypothesis of the unit root is tested against the alternative
of no unit root (stationary). The results depict that all daily return data series are stationary
(having no unit root), creating no need for data transformation. For detecting the presence
of autocorrelation and heteroscedasticty in return series, we have employed Ljung-BoxPierce-Q and Ljung-Box-Pierce-Q2 tests. Autocorreletaion and heteroscedasticty test
results indicate that all data have significant autocorrelation and ARCH effect.
5. Estimation and Empirical Findings
First, the empirical results are analyzed to answer the following research hypothesis:
H0= The level of conditional variances and covariances computed for equity returns and
CDS spreads are equal over the whole period and sub-periods.
In order to test the null hypothesis above, it is followed a two step approach of vector
autoregressive generalized conditional heteroskedastic VAR-GARCH model. First, a pair
wise VAR model has been fitted to generate the conditional mean equations of CDS
spreads and equity returns. The lag length of VAR model has been chosen with respect to
AIC, HQ, SCI and FPE information criteria. All criteria suggest a model order of one.
Therefore, it is fitted a VAR (1) model to the data set. (see Table 4.)
Table 4. Different Criteria Results for choosing lag length of VAR model
Lag
FPE
AIC
SC
HQ
0
4.41e-07
-8.957846
-8.951956
-8.955676
1
2.66e-07*
-9.462324*
-9.444654*
-9.455816*
2
2.67e-07
-9.459548
-9.430098
-9.448701
3
2.68e-07
-9.456499
-9.415269
-9.441313
4
2.69e-07
-9.454226
-9.401216
-9.434701
5
2.67e-07
-9.460414
-9.395624
-9.436551
6
2.68e-07
-9.457763
-9.381193
-9.429561
7
2.68e-07
-9.457104
-9.368754
-9.424563
8
2.68e-07
-9.455816
-9.355686
-9.418936
* indicates lag order selected by different criterions
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Proceedings of 8th Asian Business Research Conference
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We then fit a BEKK-GARCH model to the residuals obtained from VAR(1) model. In the
next step, VAR(1) model equations are used to set up systems with two dimensions under
multivariate GARCH methodology. Depending on the aforementioned methodology,
VAR(1)-GARCH (1,1) BEKK model is found the best fitting model between ISE100 and
CDS spread data. Most of the dependence structure is captured by our VAR(1)-GARCH
BEKK(1,1) model. In our aggregation model, we have focused on the variance and
covariance estimations. The results of VAR(1) GARCH-(1,1) BEKK Models for whole
period and sub-periods can be seen in Table 5.
The validity of the model has been checked by using the residuals of square root of
covariances. Residual Portmanteau test for autocorrelation indicate that there are no
autocorrelations up to 6 and 12 lag lengths. The iteration number is an important criteria
for the reliability of the model and they are under 100 for all the models. The correlogram
of both residuals and squared residuals have been examined and then concluded that
there are no significant auto correlations and arch effects left.
The first panel of the Table 5 shows the conditional mean equation coefficients and the
lower panel presents the conditional variance equation coefficients for the whole period
and sub-periods. Some coefficients of φii and αi are not significant; for the whole period for
example three out of six coefficients are insignificant. The conditional mean equations
coefficients are indeed ignored in the empirical literature. However, it still gives the
information about the negative relations between CDS spreads and equity returns in
Turkey.
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Proceedings of 8th Asian Business Research Conference
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Table 5. VAR(1)-GARCH (1,1) BEKK model result for the whole and sub-periods.
Whole period
Pre-crisis period
Crisis period
After crisis period
Conditional Mean Equation Coefficients VAR(1) model
Coefficient
Prob.
Coefficient
Prob.
Coefficient
Prob.
Coefficient
Prob.
φ11
0.031413
0.2342
0.014688
0.7014
0.047408
0.4382
0.034055
0.3999
φ12
-0.013340
0.2746
-0.029503
0.0987
0.000325
0.9900
-0.000121
0.9948
α1
0.001138
0.0003
0.001399
0.0249
0.001575
0.1399
0.000808
0.1482
φ21
-1.068278
0.0000
-1.086816
0.0000
-1.101277
0.0000
-1.027179
0.0000
φ22
0.083295
0.0000
0.091496
0.0014
0.112260
0.0032
0.049791
0.1393
α2
-0.000123
0.5979
-0.000176
0.8319
-0.000297
0.8513
-0.000143
0.8774
Conditional Variance Equation Coefficients GARCH BEKK (1,1) model
Coefficient
Prob.
Coefficient
Prob.
Coefficient
Prob.
c11
0.000012
0.0000
0.000022
0.0051
0.000013
0.0395
c12
-0.000002
0.1218
0.000006
0.0104
0.000000
c22
0.000030
0.0000
0.000037
0.0000
0.000064
Coefficient
Prob.
0.000030
0.0015
0.9411
0.000000
0.9293
0.0217
0.000020
0.0012
a11
0.288962
0.0000
0.279194
0.0000
0.265376
0.0000
0.349994
0.0000
a22
0.260555
0.0000
0.288033
0.0000
0.302749
0.0000
0.237576
0.0000
g11
0.939182
0.0000
0.925202
0.0000
0.950177
0.0000
0.870444
0.0000
g22
0.946274
0.0000
0.933412
0.0000
0.921248
0.0000
0.952195
0.0000
Q(6)
17.37573
0.8303
11.50641
0.9843
25.52788
0.3637
20.27154
0.6738
Q(12)
35.29097
0.9110
35.42932
0.9036
44.99464
0.5669
40.78599
0.7447
a11* a22
g11* g22
(covar. coef.)
(a11*a22)+(g11*g22)
a11+g11
a22+g22
LOG Li.
Iterations
0.075291
0.080417
0.080342
0.08315
0.888724
0.964014
1.228144
1.206829
9197.928
20
0.863595
0.944012
1.204396
1.221445
3908.127
37
0.875349
0.955691
1.215553
1.223997
1764.443
19
0.828832
0.911983
1.220438
1.189771
3543.569
16
Our main focus is on the conditional variance equations. Looking at Table 5, the dynamic
structures in the conditional variance and covariance equations are stronger for all indices
and all periods as it is seen in probability values. All of the parameters in the conditional
variance and covariance equations of the indices are significant at 1% level. a11 and g11
measure the dependence of the conditional equity return volatility on its own lagged
residuals and own lagged volatility and a22 and g22 measure the dependence of the
conditional CDS spreads volatility on its own lagged residuals and own lagged volatility.
ARCH parameters (a11, a22) for equity returns and CDS spreads are significant, indicating
the presence of significant arch effects. The values of a11 and a22 range from 0.237 to
0.350 and the highest value of a22 is 0.30 belonged to the crisis period. News or shocks in
the previous period of CDS spreads during the crisis play more important role in
determining the conditional variances and covariances compared to other periods.
However, the value of a11 has the lowest level at 0.265 during the crisis period, which
implies that news or shocks in the previous period of equity returns play a minor role in
determining the conditional variance and covariances during the crisis period. When we
examine the g11 and g22 values, the result is opposite of a11 and a22 values. The highest
value of g11 belongs to the crisis period, whereas the lowest value of g22 belongs to the
crisis period. Therefore, we can say that lagged equity volatility and previous CDS spread
shocks are important during the crisis period on the conditional variances and
covariances. On the other hand, all the lagged volatilities (g11, g22) are much larger in
magnitude, indicating the presence of high level Garch effects in any situation.
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
As a presentation, the whole period conditional mean and variance equations are as
follow;
Conditional Mean Equations; (see also equations 1 and 2);
Rise100 = 0.03141*Rise100(-1) - 0.013340*CDSs(-1) + 0.001138
CDSs = -1.06827*Rise100(-1) + 0.083295*CDSs(-1) - 0.0001228
Conditional Variance and Covariance Equations: (see also equations 8, 9 and 10);
Variance equation of ISE100;
=0.000012+0.083499
Variance equation of CDSs;
=0.000030+0.067889*
Covariance equation between ISE100 and CDSs;
= -0.000002+ 0.075291*
+0.88206*
+0.895435*
+ 0.888724*
The last coefficient in the conditional covariance equation presents the covariance
coefficient, which is calculated by multiplying of Garch parameters (cov12=g11*g22) and
range from 0.8288 to 0.8887. Between the sub-periods, the crisis period has the highest
value of covariance coefficients between CDS spreads and equity returns at 0.8753. The
null hypothesis that the level of conditional covariances computed for equity returns and
CDS spreads are equal is rejected. This implies that there is a contagion effect between
CDS spreads and equity returns during the crisis.
Figure 3. Conditional Covariance Coefficients between ISE100 and CDS spreads for the whole period.
0.0004
0.0002
-0.0001
-0.0004
-0.0006
-0.0009
-0.0011
-0.0014
-0.0016
Figure 3 also displays the covariance coefficients for the whole period. There is a strong
time varying conditional volatility. Volatility range is particularly very high during the crisis
period. The global financial crisis effect is clearly visible here. Conditional covariance value
reached the highest level during the crisis period. There is a volatility contagion effect
between CDS spreads and equity returns during the crisis. In addition the covariances
have a tendency of being higher during the high volatility periods, which is a similar result
of Schreiber et al. (2009) and Belke and Gokus (2011).
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Proceedings of 8th Asian Business Research Conference
1 - 2 April 2013, Bangkok, Thailand, ISBN: 978-1-922069-20-7
Figure 4. Conditional Variance of ISE100 and CDS spreads for the whole period.
0.003
0.012
0.002
0.010
0.008
0.002
0.006
0.001
0.004
0.001
0.002
0.000
Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12
Var(ISE100)
0.000
Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12
Var(CDS)
Figure 4 displays the conditional variances of equity returns and CDS spreads for the
whole period. The conditional variances show the similar results with conditional
covariances. There is a significant time varying volatility and after the crisis both variances
have higher absolute values with a stronger varying. The volatility range is particularly
large for CDS spreads during the crisis period. Both conditional covariances (Figure 3) and
conditional variances (Figure 4) show the crisis effect clearly.
6. Conclusion
Knowledge about the link between equity returns and CDS spreads at a country level is
important especially for risk managers using credit default swaps for hedging purposes. In
this paper, a vector autoregressive generalized conditional heteroskedastic VAR-GARCH
BEKK model has been estimated with the aim of understanding volatility patterns of equity
returns and CDS spreads of Turkey before, during and after the global financial crisis. The
empirical findings indicate that there are significant arch and garch effects of equity returns
and CDS spreads for all the periods and variances and covariances are all time varying.
In addition both conditional variances and covariances have higher values during the crisis
period, which implies a volatility contagion effect between the variables
Acknowledgements
This work was supported by Scientific Research Projects Coordination Unit of Istanbul
University. Project Number: 26812 (YADOP)
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