Are natural disasters also contagious? Tsunami of Japan evidence from DCC
GARCH model
Najam us Sahar1
Dr. Syed Zulfiqar Ali Shah2
Zuee Javaira3
Abstract:
This paper uses a Dynamic Conditional Correlation Model to examine financial contagion
phenomenon following the Japan tsunami 2011. Conditional volatility transmission models like
Engle (2001, 2002), and Tse and Tsui (2002) as an original specification of multivariate
models’ conditional correlations, permit to follow correlation advancement between different
stocks returns asymmetries. Our sample consists of Nikkei 225 and KSE 100 index from Jan
2008 to Nov 2011. The obtained results Confirms the financial Contagion and an amplification
of dynamic conditional correlations during the natural disaster period which stretches from 11th
March 2011 to 25th March 2011. The results show the convergence in the correlation and
variance of market returns internationally which infer that when there is disaster, there is little
usefulness of portfolio diversification, portfolio managers should incorporate these uncertain
events.
Keywords: Conditional correlation; MGARCH; Contagion, Natural disaster
JEL Classification: F15, G11, G12, G15
1
Lecturer, Riphah International University, Islamabad
Ph.D Scholar.
[email protected]
2
Chairman Higher studies and Research,
International Islamic University, Islamabad
[email protected]
3
Lecturer, Federal Urdu University of Arts Science and Technology, Islamabad
1
Introduction:
As markets are more interlinked, interconnected and interdependent with the advent of
globalization and global financial linkages, so in financial research domain there is a bandwagon
especially dedicated to explore these phenomena, its effects and implications. Contagion is one
of those phenomenon, which can be defined as
“the spread of markets” turmoil from one
country to other financial markets”.
There are three types of contagion described in literature, one is where several countries are
effected in chorus due to a crises in common stock known as Moosonal effect (Masson, 1998,
1999). The second type of contagion is known as spillover effect in which crises in one country
cause crises in fundamental variables of other countries, mainly interdependent through trade and
financial means. Whereas the third form of contagion is pure contagion or shift contagion
(Forbes & Rigobon, 2000), which is the spread of crises to other countries without any
fundamental reason, rather this propagation of crises can be justified by investor’s behavioral
factors or psychology. Investors intensify the crises first by following the news and at second
stage the behavior become public by herding phenomenon, and the turmoil spreads in other
countries.
On 11th March2011 Tsunami hit Japan’s Fukushima- Daiichi Aomori, Yamagata, Miyagi and
other cities, as a result 20319 were killed and 405719 were affected and it caused an estimated
dollar loss of 210 Billion as reported by natural disaster data. There was enormous selling around
the world stock markets. The FTSE 100 index lost £47 billion and Nikkei 225 index was down 1.72%
of its value in London as it shed more than 180 points in early trading. Shares in New York and Europe
also suffered heavy losses.
Uptill now Contagion is measured majorly in different financial crises like Asian Financial
Crises (Caporale, et al., 2003, Baig and Goldfajn, 1999), Subprime debt crises (Naoui, Liouane
& Brahim, 2010) and at one instance Lee (2005) measured contagion for the World War. This
research attempts to measure whether natural disasters are also contagious in nature and take into
account 11th march Tsunami of 2011.
2
Contagion is measured through correlations enormously in economics literature. This concept of
contagion illustrates that during crises period the correlations between the securities tend to
increase. This study first finds the simple Pearson correlation between the Nikkei 225 index and
KSE 100 index of pre and post disaster period. Then the analysis is improved by estimates of
Constant Conditional Correlation (CCC) by Bollerslev (1990), than Dynamic Conditional
Correlation (DCC) of Engle (2002) and Dynamic Conditional Correlation (DCC) of Tse and Tsui
(2002), stepwise. The aim of this method is to show how market correlations vary in time and
especially to point at their amplifications during and post disaster period. This study estimates
time varying conditional asymmetries by using Multivariate GARCH on cross country model,
which will surmount the limitations of model and will consider the heteroskedasticity problem
addressed by
Forbes and Rigobon (2002). The endogeneity Bias is covered with dividing the
sample data into two sub periods that is pre and post disaster.
The main rationale behind the research is to investigate the impact of natural disaster as a case
of contagion, verily this phenomena is only researched in financial turmoil and crises, this
research is believe to be first study in this regard. The paper is organized as follow. Section 2
contains literature review Multivariate GARCH models capturing conditional Volatilities and
contagion as phenomenon. Section 3 describes details of models and data used results achieved
from application of methodology are captured in section 5.Section 5 presents concluding
remarks.
Related Literature:
Investor’s expectations may be “stigmatized” and shift from stable pattern to bad volatility or
equilibrium in one country due to a shock or market turmoil in other country, the real economic
links don’t cause this shift rather these are expectation linkages of investors and they cause the
liquidity too be less (Masson, 1999). There is a difference between fundamental or real contagion
and behavioral contagion (Calvo & Reinhart, 1996 and Kaminsky & Reinhart, 2000). Forbes and
Rigobon (2002) consider that trade and finance links are the main cause of contagion. Calvo
(1999) states that when there is information asymmetry the endogenous liquidity increases due to
the abnormal situation. The informed forces in the market start selling their assets and the un
informed follow and form a herd without knowing the reason, this all phenomenon when
transfers to other markets is known as contagion.
3
Many scholars started working on multivariate GARCH models after the huge usage of
univariate ARCH and GARCH models to illustrate the time varying asymmetries in stock returns
(Tse & Tsui 2002) . For multivariate GARCH models the conditional variance matrix must
have the property of positive definiteness (Engle et al., 1984). Bollerslev (1990) overcome this
limitation in his model CCC that is Constant Conditional Correlation in Multivariate GARCH
model. This model is widely used to test the contagion but in some cases the empirical research
showed denial of the model (Tse & Tsui 2002). Longin and Solnik (1995)used GARCH
specification with constant Conditional correlations, it also showed the factors behind the
conditionality with limitation of one parameter at one time, wihich make the model too complex
to use. There is a strand of more advance models (Engle and Rodrigues, 1989, Nerlov. 1989,
Engle et al. 1990, Engle & Kroner 1995 ) after CCC but they had the same problem of complex
and un interpretable parameters. Engle and Sheppard (2001) using significantly large securities
data of S&P 500 and Dow Jones, they extended the model to include considerable number of
matrixes. Tse and Tsui (2002) solved the problem of complex parameters and yet retained the
positive definiteness and checking through Log-likelihood(MLE) with some significant Monte
Carlo results. All the models derived either only correlation or including in regression has an
assumption of Null hypothesis beta remains constant during the time of crises in verifying
contagion (Forbes & Rigobon 2001-2002).
The very first work on contagion as increase in correlation among the securities after a market
crisis was done by King and Wadhwani (1990), they took the point of 1987 market crash and
tested with Japan, United States and United Kingdom and found convergence in the markets
after the crash, there study was folloed by a large empirical literature on the model proposed.
Data and Methodology:
In this section the sample data and model will be discussed. Only secondary data is used for the
study, data of KSE-100 index Nikkei 225 is taken for the period of 2008-2011 on daily basis.
We obtain the data Index price data from Yahoo Finance. To test for DCC we have to define
two regimes one with low and other with high volatility and the heteroskedasticity assumption
must be satisfies, for this reason data is divided in two period one is pre disaster period or
stable period with low volalitility and other is post disaster which starts from 11th March 2011
after tsuenami. May studies have tries to divide the data set into two pairwise correlation to test
4
the difference between normal and crises period (Forbes & Rigobon, 2002, Corsetti et al. 2002).
Instead of taking dates the data is sampled as number of observations. A total of 713
observations are taken from which 681 observations are from non crises period.
After CCC model Engle (2002) presented a simpler version of DCC-GARCH with two steps.
One Step Involves the estimation of univariate-GARCH analysis of the involved returns, so the
conditional asymmetries of stock return is presented in following GARCH equation
where
is the error term of a d-dimensional model, and t is a sequence of
independently and identically distributed random variables with zero mean and variance of
one, ,Hit is the conditional variance of returns on stock i at time t, and α and β are ARCH
and GARCH effects respectively (Manera, et al. 2006,).
Following the first step, the residual term εt is typified as diagonal matrix and time varying
correlation. As presented below using asymptotic theory.
where Ht denotes a positive definite conditional covariance matrix,
Rit is normally
distributed with zero mean, Ψ1-t denotes information set available at 1- t , and Dt is a
Kx K diagonal matrix of time-varying residuals obtained from step 1 with under root Hit on
the Ith diagonal,
5
All the estimations are done by Gaussian log likelihood.
The descriptive analysis are presented with all graphics. All the analysis are presented pairwise
with two countries for KSE-100 index and Nikkie225 with two periods in considersation one is
pre disaster and other is during and post disaster,
Table 1 shows the difference in normality of data in variances and it can be clearly notices that
the variance increased in returns after the natural disaster of Tsunami as skewness deviated more
from zero and kurtosis Excess to value 3 also increased sharply. So the stock return distribution
has leptokurtic properties.
Fig 1:
Figure 1 represents the individual market returns of both countries pre and post disaster. And we
can neatly note strong convergence in returns trend after tsunami 2011.
Table1: Normality in variances
6
Pre-Disaster
Post disaster
Statistic
P-value
Statistic
P-Value
Skewness
-0.27765
0.0030534
-0.34914
0.065490
Excess Kurtosis
0.35328
0.059114
0.76970
0.041142
Jarque-Bera
12.273
0.0021626
7.3802
0.024970
Figure 2 plots the conditional correlation series pre and post disaster and we can clearly see the
difference in variances and increased correlation after the tsunami. Which reflect a pattern in the
investor’s behavior after crisis in one country, how dynamically investors response to news and
innovations.
Fig 2:
Pre-disaster
Post-Disaster
Table 2 presents the results of three tests that are CCC, DCC by Engle(2001), and DCC by Tse
and Tsui (2002) pre and post tsunami situation. Here the objective of the study is not to compare
the three models but to check for the contagious effect between Pakistan and Japan during
Tsunami by three methods available.
7
Analysis shows strong convergence of equity returns in all three models. As we can see the pre
disaster correlation coefficient is 0.1127 in CCC, 0.113235 in DCC of Engle and 0.112784 in
DCC of Tse and Tsui at significance level of 0.05. And when we see the post disaster
correlations these are 0.2420 in CCC, 0.204804 in DCC of Engle and 0.243866 in DC of Tse and
Tsui at 95% confidence interval. At first step of analysis we can see significant co-efficient of
ARCH and GARCH term for both sets of data.
From earlier studies these parameters have an approximate size of α=0.01 and Β=0.97 .
Tables 2 contain estimates of DCC values δ2 and δ1 respectively. We used Berndt, et al
(1974) algorithms to obtain quasi-maximum likelihood estimates of δ1 and δ2.
Table2: Pre Disaster tests
CCC
Rho
P-value
ARCH(Alpha1)
P-value
GARCH(Beta1)
P-value
Log Likelihood
Estimated Parameters
Vector :
Post disaster:
Rho
P- Value
ARCH(Alpha1)
P-value
GARCH(Beta1)
P-value
Log Likelihood
Estimated Parameters
Vector :
DCC (Engle)
DCC (Tse &Tsui)
0.113235
0.0147
0.112784
0.0073
0.136304
0.0000
0.136304
0.0000
0.136304
0.0000
0.831816
0.0000
0.831816
0.0000
0.831816
0.0000
3874.150
3874.46
3874.150
0.000902; 0.064338;
0.136304; 0.831816
0.000902; 0.064338;
0.136304; 0.831816
0.000902; 0.064338;
0.136304; 0.831816
0.2420
0.0026
0.204804
0.0546
0.243866
0.0151
0.224961
0.000
0.224961
0.000
0.332623
0.000
0.566820
0.000
0.566820
0.000
0.571020
0.000
1014.695
0.000191; 20.971084;
0.224961; 0.566820
1017.569
0.000191; 20.971084;
0.224961; 0.566820
1019.399
0.000191; 20.971084;
0.224961; 0.566820
0.112784
0.0073
Conclusion:
This research look into relationship of stock markets of Pakistan KSE 100 index and Japanese
Stock Market Nikkei 225 during the great tsunami, the natural disaster of Japan, in March 2011.
8
Contrary to the findings of Forbes and Rigobon (2002) of No Contagion, this study finds the
evidence of contagion by three types of correlation analysis, one Constant Conditional and two
Dynamic Conditional Correlation analyses.
All the results are significantly supporting the hypothesis that Natural disaster can also be
contagious. These indicate the dependency of local market on international environment. In this
arena of globalization even if we can’t define the trade and fundamental economic linkages
among the countries but still disaster in one country do effect the returns in stock of other
countries through contagion. Analysis shows that the stock market of Pakistan is structurally
conditional dependent on other markets like Japanese in the case in both level and variability of
returns.
The results show the convergence in the correlation and variance of market returns
internationally which infer that when there is disaster, there is little usefulness of portfolio
diversification. This inculcation of natural disasters in the paradigm of contagion literature and
empirical study will be facilitate the decision making process in portfolio formation, risk
diversification and asset allocation.
Yet there is a couple of limitations to the approach one is
that multi assets and multi market analysis of Correlation and Covariance require long periods to
generalize the results but disaster and crises are in nature for small periods. We cannot forecast
on the basis of Conditional models, we can’t structure the factors behind the contagion. To
investigate the phenomenon of contagion of natural disaster, we can test for most devastating
disasters with multi-country model.
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