Contagion between Islamic and Conventional Banking : A GJR DCC-GARCH and VAR Analysis

This study aims testing the presence of contagion through Islamic and conventional banking systems during the subprime crisis. Specifically, we examine how far a shock striking conventional or Islamic banks is exported from one group to another or remain limited. Therefore, we adopt a GJR DCC-GARCH model to study the dynamic conditional correlation and the vector auto-regression VAR model in order to identify causality direction and the impact of a shock on the returns of each banking index. Hence, our results indicate that Islamic banks are not isolated from conventional banks while there is a contagion phenomenon between these two financial systems. Furthermore, we determined that during the crisis, Islamic banks could not absorb this effects and ensure stability because these banks were also affected by the crisis. JEL Classification: G21, G32, G33


Introduction
While Islamic banking system has improved throughout these years, the level of competition with conventional system has intensified too.Regarding the co-existence of Islamic and conventional banking and such differences in their foundations, the question of contagion risk between them in case of shocks become a major concern.The period of financial crises are a perfect experimental context to identify the relationship between these two industries in the event of financial distress.The series of crises faced by international financial institutions have raised several questions about the ability of each banking system (Islamic and conventional) to withstand financial and economic shocks.Most studies in the literature have compared Islamic to conventional banking separately and assume that there is no interaction between them.In this study, we try to fill in this gap by examining contagion risk between Islamic and conventional banks so as to see how far a shock that strikes conventional or Islamic banks is exported to the other system, or remain constrained.
Thereby, our paper is structured as follows.We first present a theoretical overview of banking contagion focusing on the different definitions proposed in the literature and the methods of its detection.Then, we present the methodology used to test the presence of this phenomenon on domestic and cross-country levels.Finally, we report the results.

Theoretical Context
In fact, the concept of contagion has been defined in several ways.According to Masson (1998), Kamisnsky and Reinhart (2000), contagion can be defined as the spread of financial market disturbances from one country to financial markets of other countries.This definition is used very frequently insofar as it takes into account shock transmission mechanisms.Other definitions have been proposed in the literature such as that of Pericoli and Sbracia (2001).For these authors, contagion is defined as a significant increase in co-movement of prices and quantities across markets following a crisis in a market or a group of markets.This definition places contagion as an excessive increase in co-movements against a certain standard.It is important to distinguish between normal co-movements due to simple excessive interdependences and co-movements due to financial turbulence.In the same way, Forbes and Rigon (2002) stated that contagion is explained by a change in transmission mechanisms during financial turbulence.Consequently, this change can be expressed as a significant increase in correlation across markets.Under this perspective, contagion is detected through investors' and speculators' behavior.
Indeed, financial crises are a relevant experiment to test the presence of financial or banking contagion.In late of 2007, the global economy experienced a severe financial crisis produced in the American real estate market and then spread to the rest of the world.This financial turbulence caused the failure and bankruptcy of several financial institutions in many countries.Therefore, there are two main channels contributed to the spread of this crisis.The first one is the direct exposure of financial institutions around the world to the mortgage market, through securitization transactions.The second one is the common shocks on asset markets, particularly real estate markets.
The presence of the interbank market was the source of banking contagion.The mission of an interbank market is to transfer liquidity between banks.Contagion risk is said to be triggered by liquidity shocks to the market, enabling the transmission of crises.According to Van and Weder (2001), in the presence of liquidity shocks or a financial crisis, investors rally to reconstruct their portfolios.Through share purchases and sales, they transfer risk from one institution to another or from one market to another.It is this kind of behavior that triggers contagion.According to Forbres and Rigobon (2001), this process causes an increase in correlation between financial assets.Worth noting is that this mechanism does not occur during financial stability but only during crisis periods.Nevertheless, Van Rijckeghen and Weder (2000) examined the notion of liquidity in the banking system.Indeed, banks react to a crisis in a country by a generalized reduction in credit granting depending on the borrowing countries.Therefore, investors will rebalance their portfolios, causing the spread of crises.
According to Hartmann et al (2004), bank contagion may be possible through two channels.The first leads to the bank's direct exposure to the interbank market.The second is information dissemination.In fact, banks resort to financial markets for liquidity if needed and for risk management too.Consequently, failure of a bank may have negative repercussions on the liquidity of other banks.
Banking contagion has been the subject of several studies.Furfine (2003) examined a database reflecting bilateral exposure to the US banking market and studied the impact of individual banking failures on other banks.This study proved that the concept of systemic risk exceeds that of interconnection of the interbank market.Upper and Worms (2004), who studied contagion in the German banking market, found that contagion risk in the interbank market mainly affects small German banks.
To study the vulnerability of the German banking system, Memmel and Stein (2008) examined data on bilateral exposure between all banks.They assumed that the interbank market itself is a contagion mechanism since contagion occurs when a bank fails.The results indicate that banking contagion depends in large part on the size of the failing bank and its interrelationships with other banks.Moreover, among the factors behind banking contagion, the literature identifies information asymmetry.Information asymmetry is a very important factor in triggering contagion.During banking panics, depositors worry about their deposits, and they start to retain their deposits causing banking failures.Indeed, bankruptcy of a large number of banks suggests that dissemination of information to financial markets has deteriorated.
Finally, contagion may depend on the structure of interbank links.According to Allen and Gales (2000), the interbank market may take three structures.First is, the entire structures, in which banks are symmetrically related to any other bank.Second, the incomplete structure is where banks are related only to neighboring banks.Third, there is the incomplete and offline market structure.Several studies agree on the importance of the interbank market structure.Indeed, Elsinger and al (2002) used a model of complex networks for interbank market exposure and examined the consequences of macroeconomic shocks on the Austrian banking system.Interbank market structure and exposure size are important elements in determining contagion risk.Specifically, degree of completeness and heterogeneity of the interbank market are closely linked to contagion risk.

Method
To meet our research objectives, we use GJR-DCC model to identify the presence of contagion across these two banking industries on a domestic scale.We follow Forbes and Rigobon (2002) to identify contagion in that correlation which is a measure of contagion during a crisis.Indeed, an increase in correlation coefficient indicates contagion.These authors compared the intensity of financial links, before and after the crisis, between different markets.We do the same to examine co-movements between these two banking industries (Islamic and conventional) at the domestic level during the study period.
To identify contagion across the two banking systems during the crisis period, we introduce a return index for Islamic and conventional banking industries for each country.This index represents the weighted average returns of banks according to their market capitalization to see the effect of bank size on the banking system.
Then we use the GJR-DCC model to examine dynamic conditional correlation between the return index of Islamic banks and that of conventional banks during the entire study period.We opted for the GJR-DCC model because the DCC-MGARCH model has been criticized for its symmetrical nature and its non-accountability of the asymmetric reaction of past shocks for current volatility.However, such researchs in the 1970s indicated that negative past returns increase volatility more strongly than past positive returns.Hence, reasons explaining this phenomenon come with a lot of controversy.According to Black (1976), decrease in the stock price of a leveraged firm worsens its solvency ratio.This increases intrinsic risk and therefore stock volatility.This is leverage theory.
To overcome this critical appraisal, we propose to use the GJR-GARCH model introduced by Glosten, Jagannathan and Runkle (1993).This is a nonlinear GARCH model to account for asymmetry in the conditional variance of a response to innovation.The principle of the GJR-GARCH model is the dynamics of conditional variance which admits a change regime and depends on the sign of past innovation.The difference between these two models lies in conditional variance.For the GJR-GARCH model, variance is written as: Where The model can also be written as follows: In what follows, we try to apply analysis tools recently introduced in applied finance.These are the family of Dynamic Conditional Correlation models (DCC), which allow for the correlation matrix to be dynamic over time while retaining few parameters.GJR-DCC introduces equations describing the evolution of correlation coefficients between the banking index (Islamic or conventional) with that of the market index.Through this model, we can deduce dynamic conditional correlation between Islamic and conventional banking indices.
This model is proposed by Engle (2002) and Tse and Tsui (2002) and is written as follows: Where - =   represents the variance and covariance matrix of the two assets.- is a diagonal matrix of time-varying standard deviations collected from the estimated two univariate GJR -GARCH, -The elements contained in  are generated by a GJR-GARCH (p, q), which also gives: = [   ] represents the matrix of constant conditional correlation coefficients,  = [   ] is the covariance matrix of standardized residuals, of (N x N)dimension, symmetric and positive definite.In what follows, we use VAR developed by Christopher Sims, to examine dependence between the two banking industries in the different countries studied.(Cross-country contagion risk analysis) The VAR (p) model is presented by: Or equivalently: Where c, (n, 1) dimension, is a vector of constants, or matrices   , whatever i [0, p] of (n, n) dimension, fulfill  =   and   ≠ 0  .The vector (n, 1) of innovations   is i.i.d.
In general, for x jt , whatever j ϵ [1, n], we have: This model captures interdependencies between multiple time series since the variables are treated symmetrically so that each series is explained by its own past values and the past values of the other variables.This allows us to examine the causal link between returns of Islamic banks and those of conventional banks and also to study the impulse response function to see whether the impact of a shock on the returns of conventional banks will instantly impact the returns of Islamic banks and vice versa.

Data
Our sample consists of ( 51 The figures below report the various indices' return series for conventional and Islamic banks.We notice that the two banking industries were affected by the subprime crisis, as there is a higher fluctuation of returns during the crisis period in each of the countries studied.   1 and 2, return series are not normally distributed, hence the null hypothesis of normality is rejected because the probability of Jarque Bera test is less than 0.05.Skewness coefficients show that the marginal distributions are asymmetric; skewed to the right when values are positive and to the left when values are negative.We note first that kurtosis is very high, well above 3.Such a high kurtosis indicates that these banks have fat-tailed distributions.This phenomenon of excess kurtosis confirms the strong leptokurtic character of stock returns series.Similarly, the stationarity analysis shows that all return series are stationary.In addition, the heteroscedasticity test points to some ARCH effects, and that the null hypothesis of no autocorrelation is accepted because probability levels are greater than 5%, except for the Saudi Arabia conventional banking index.

Results
After estimating the univariate GJR-GARCH model for the Islamic and conventional banking indices in the presence of asymmetry effects, we found the parameters (λ + α) and (α), which represent respectively the impact of the negative and positive shocks on variance.In other words, the more important they are, the more volatility increases after the shock.The results show that returns of Islamic banks are more volatile than those of conventional banks, whether the impact is positive or negative.Similarly, for the (β) coefficient, which represents return speed to minimum volatility, the results indicate that this coefficient is higher for conventional banks than for Islamic banks.Therefore, we can conclude that returns of conventional banks are less volatile than those of Islamic banks and conventional banks are more resistant to shocks than Islamic banks.
The results on dynamic conditional correlation between returns of Islamic and conventional banks using the GJR-DCC model present a positive correlation for the entire period of study for the different countries in our sample.Moreover, we also found that correlation between these two banking industries differs from one country to another with an unstable trend over time.This difference depends on co-movement between the two banking systems in each country.After a filtering test, we note that during the crisis correlation between returns of Islamic and conventional banks increased significantly in all studied countries, providing evidence of contagion between these two banking industries during the crisis period.However, after the crisis, correlation records a downward trend.We also found that the estimated parameters of the univariate GJR-GARCH models check the validity conditions of the model [c>0, α>0, α+ λ>0, β>0 and theta (1) + theta (2) < 1].Moreover, the parameters are statistically significant, suggesting that the adoption of a GJR-GARCH model is appropriate.

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Step 2: Es According lagged ter convention Step

VAR satisfies the stability condition
Step 4: Causality Analysis The causality analysis will allow us to determine the statistically significant interaction of the variables in the model.This analysis is a necessary prerequisite to study the dynamics of the model.Causality tests, being bivariate, are two types that should be Granger tested.We therefore proceed to a Granger causality test using the previously-estimated VAR (1).Recall that Granger considers that a variable causes another if predictability of the former is improved when information on the latter is incorporated into the analysis.We obtained the following results.0.0260 0.0000 0.7443 0.3397 0.0000 0.0001 0.6539 0.8097 0.6557 0.4153 0.5901 0.1286 IQC 0.8335 0.1567 0.0182 0.1600 0.1103 0.0589 0.0000 0.0002 0.4619 0.5286 0.8267 0.4295 IQI 0.8510 0.2895 0.2349 0.8132 0.5620 0.0591 0.9038 0.0000 0.1208 0.6819 0.0992 0.5479 ISC 0.0017 0.4603 0.0192 0.0027 0.0635 0.0645 0.0000 0.0382 0.0005 0.0226 0.0106 0.0094 ISI 0.3038 0.3677 0.3289 0.5442 0.7397 0.2962 0.0452 0.0013 0.1892 0.0238 0.1370 0.3362 ITC 0.5569 0.9341 0.0670 0.1856 0.2885 0.0084 0.3802 0.3105 0.1359 0.9301 0.2919 0.5135 ITI 0.3931 0.2609 0.2974 0.1365 0.2869 0.0551 0.8717 0.9186 0.0226 0.0319 0.0937 0.4483 All 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0030 0.0221 0.0688 Hypothesis testing: The Granger causality analysis of returns of conventional and Islamic banks operating in the different countries studied indicates that causality is bidirectional across the different banking markets, whether Islamic or conventional.Accordingly, the null hypothesis of no causality between Islamic banks and conventional banks is rejected and the opposite is true as well.Under GRANGER and with a threshold of 1 to 5% and during the studied period, reverse causality is statistically accepted.This allows us to conclude that Islamic banks are not isolated from conventional banks and there is contagion across these two industries since one depends on the other. http://ibr.cc

Conclusion
Regarding two types of banking industries which are Islamic and conventional banking, and with take into account different activities and different foundations, a special focus should be given to this field in order to analyze the effect of the two banking systems on financial stability and the relationship between them in case of distress.Thus, We obtained the following main results: First, we estimated the univariate GJR-GARCH model on Islamic and conventional banking index in the presence of an asymmetry effect, we found that the returns of Islamic banks are more volatile than those of conventional banks, whether the shock is positive or negative.Similarly, for the (β) coefficient, which represents the return speed to minimum volatility, the results show that this coefficient is higher for conventional banks than for Islamic banks.Therefore, we may conclude that the returns of conventional banks are less volatile than those of Islamic banks and those conventional banks are more resilient to shocks than Islamic banks.
Second, we used the GJR-DCC model and the VAR model to examine contagion risk on a domestic and cross-country scale and analyze the effect of a shock to each banking system and its repercussions on the other in the different countries studied.The results pointed to the presence of contagion risk across both systems.We notice that during the crisis, correlation between the returns of Islamic banks and those of conventional banks increased significantly in all countries studied and providing evidence of contagion across these two banking systems during the crisis period.Similarly, the analyses cross-country contagion risk and the results of the VAR Granger causality test argue that there is a bilateral relationship between both systems in different banking markets.
In conclusion, during the crisis period, Islamic banking was not able to absorb its effects and ensure stability because it was also affected by the crisis.

Figure 1 .
Figure 1.Evolution of indices' returns for conventional and Islamic banks by country * Blue represents returns of conventional banks, red represents returns of Islamic banks. Figure if the following hypothesis is accepted H0 : b 11 = b 12 = … = b 1P Y 1t does not cause Y 2t , if the following hypothesis is accepted H0 : a 12 = a 22 = … = a 2P Decision rule at α = 5%: If p > 5%, then H0 is accepted.

Table 1 .
Distribution of the sample according to type of bank ) listed banks in six Middle Eastern countries.These are Bahrain, Saudi Arabia, Kuwait, Qatar, Egypt and Turkey, with (12) Islamic banks and (39) conventional banks.The study period stretches from 04/09/2006 until 04/12/2013.We eliminate from the sample countries with no listed Islamic banks.Individual bank data are collected from the Datastream database.

Table 2 .
Descriptive statistics of the indices returns for conventional banks by country

Table 3 .
Descriptive statistics of the indices returns for Islamic banks by country

Table 4 .
Dynamic Conditional Correlation between Islamic and conventional banking indices GJR-DCC