The main aim of this paper is to compare the stability, in terms of systemic risk, of conventional and Islamic banking systems. To this aim, we propose correlation network models for stock market returns based on graphical Gaussian distributions, which allows us to capture the contagion effects that move along countries. We also consider Bayesian graphical models, to account for model uncertainty in the measurement of financial systems interconnectedness. Our proposed model is applied to the Middle East and North Africa (MENA) region banking sector, characterized by the presence of both conventional and Islamic banks, for the period from 2007 to the beginning of 2014. Our empirical findings show that there are differences in the systemic risk and stability of the two banking systems during crisis times. In addition, the differences are subject to country specific effects that are amplified during crisis period.
The late 2007-2008 global financial crisis has assured the importance of financial systems’ stability and soundness under a systemic risk event. The crisis also highlighted the difference between Islamic and conventional banks in terms of their stability. Even though Islamic banks faced the challenges encountered by their conventional peers during the financial crisis, they managed to achieve an average growth rate of 20% after 2009 ( [
Usually, Islamic banks stability is inferred through comparative risk analysis with conventional banks. [
In addition to the previous stability inference based on the z-score measure, Islamic banks stability is also assessed based on market risk. [
From the previous discussion, we note that the literature does not directly consider the measurement of Islamic banks systemic risk. In addition, and to our knowledge, the issue of evaluating Islamic banks systemic risk, through modelling their interconnectedness within the financial system, has not yet been addressed, and has overlooked the process of systemic risk assessment that considers the financial system as a network of institutions with linkages, which allows the systemic risk and the financial distress to be transfered and magnified during crisis times, as applied by [
Our contribution tries to take into consideration the two prevailing research view- points present in the literature of Islamic banking stability. The first questions if there is a real difference between the Islamic and conventional banking systems (see e.g. [
The main aim of this paper is to investigate whether including Islamic banking activities within a country’s banking system supports the financial performance and stability at the country level. To achieve this purpose, we compare countries that operate either conventional or Islamic banking systems with those that operate both. We apply this study on the publicly trade banks located within the countries of the Middle East and North Africa (MENA) region, as the majority of the Islamic banking activities are settled there. The MENA region is found to hold 78.57% of the total global Islamic banking assets, with the GCC countries holding 38.19% of this total ( [
The methodological contribution of this paper is aimed at providing a statistical model that allows to compare banking systems in terms of their systemic implications using financial networks, based on graphical Gaussian models. Graphical Gaussian models were introduced in multivariate statistics to model complex relationships between many variables (see e.g. [
Country level Graphical models allow us to avoid the heterogeneity of the results at the individual banks level, especially that the available literature assess Islamic banks’ stability based on the individual bank level, whether using z-score or other risk indicators, which captures the idiosyncratic effects, but misses the systemic interconnectedness component, and overlooks the definition of systemic risk as a macroeconomic event that causes simultaneous severe losses for market participants as it diffuse through the system ( [
We believe that the implications of our research results can be beneficial to regulators and central banks in terms of Islamic banking activities effect on the countries’ financial and economic stability during a crisis period. Conventional banks can gain insight regarding the effect of diversifying their services with Islamic banking activities on the bank’s risk profile, especially that in the last years several conventional banks from Europe, UK and the USA are being involved in Islamic banking activities. Finally, fund providers and investors may benefit from the research in making portfolio allocation decisions.
The paper is organized in five sections. The second section provides the proposed methodology, based on graphical Gaussian models and the centrality measures obtained from them. The third section describes the data and the application of the proposed models. And the final section provides the research conclusions.
The research field of systemic risk has emerged after the recent financial crisis. Several empirical studies have been carried out to determine the degree of contagion between conventional banks and the related financial systems.
Specific measures of systemic risk have been proposed by [
Trying to address this aspect of systemic risk, researchers have recently introduced financial network models. In particular, [
Network models, albeit elegant and visually attractive, are based on the assumption of full connectedness among all institutions, which makes their estimation and interpretation quite difficult, especially when a large number of them is being considered. To tackle the previous limitation, [
Our contribution follows the latter perspective, and employs graphical network models to understand and compare the different banking systems in terms of systemic risk and its transmission mechanisms. To achieve this aim we use the closing price for the corresponding banks’ shares, and we measure how such prices correlate. The data is assumed to be generated by a stationary process, with the mean
Formally, if
In our framework, we consider a cross-sectional perspective to understand the change in systemic risk transmission mechanism in relation to the presence and absence of the financial crisis, in which the systemic risk can be depicted by a network that describes the mutual relationships between the different banking systems involved. Correlation based networks are suitable to visualize the structure of pairwise marginal correlations among a set of nodes N that corresponds to the investigated banking systems. Each banking system represents a node in the network, and each pair of nodes can be connected by an edge, which has a weight related to the correlation coefficient between the two nodes. Furthermore, the banking systems that comprise a network of N nodes can be described by an associated
Another issue that relates to correlation networks initialization is the specification of the correlation itself, as being marginal against being partial. It is known that the use of pairwise marginal correlations will measure both the direct and the indirect effect of one network node on another. On the other hand, the use of pairwise partial corre- lations will measure only the direct effect between the two network nodes, excluding the mediation of others, which better servers our purpose of modelling the systemic risk of each node, or in other words, the systemic risk of each banking system.
From a statistical viewpoint, marginal correlations can be estimated on the basis of the observed N time series, in which each time series contains the return data of a specific banking system, under the assumption that the observations follow a multi- variate Gaussian model, with unknown variance-covariance matrix
More formally, let
The network model is represented by an undirected graph G, such that
this indicates that, the absence of an edge between two vertices, i and j, is equivalent to the independence between the random variables
In our context, all random variables are continuous and are assumed to be normally distributed, with each
where
In practice, the available data will be used to test which partial correlations are different from zero at the chosen significance level threshold
To summarize the systemic risk form the network that we estimated on the basis of the graphical Gaussian model, network centrality measures are used. The most important summary measure that has been proposed in financial network modeling, to explain the capacity of an agent to cause systemic risk, as a large contagion loss on other agents, is eigenvector centrality (see e.g. [
More formally, for the i-th node, the eigenvector centrality score
where
where
A different, and simpler to interpret, measure of systemic risk is node degree, which is a measure of the number of links that are significantly present in the selected model, between a node and all others. For a node
Both the previously introduced measures are based on the adjacency matrix of a correlation network and depend, therefore, only on the presence or absence of a link between two nodes, and not on the actual (direct) dependence between them. To introduce such dependence we can extend the node degree measure
In the application section, we compare node degree, partial correlation degree and eigenvector centrality measures. Before moving to the application, we remark that the measures are conditioned on the chosen graph and, therefore, may be quite unstable, depending on the results of the selection procedure.
To check the robustness of our results, a Bayesian approach can be followed so that the centrality measures can be estimated without being conditioned on the chosen graph, as in the classical approach, but rather as a model average between different graphs, each with a weight that corresponds to its posterior probability, and is repeated on a yearly base rolling window.
To achieve this aim, the first task is to recall the expression of the marginal likelihood of a graphical Gaussian model, and specify prior distributions over the parameter
When the graph G is decomposable, the likelihood of the data, under the graphical Gaussian model specified by P, nicely decomposes as follows (see e.g. [
where C and S respectively denote the set of cliques and the set of separators for the graph G, and:
the same representation holds for
A convenient prior for the parameters of the above likelihood is the hyper inverse Wishart distribution. It can be obtained from a collection of clique specific marginal inverse Wisharts as follows:
where
It can be shown that, under the previous assumptions, the posterior distribution of the variance-covariance matrix
where
In addition, the proposed prior distribution can be used to integrate the likelihood with respect to the unknown random parameters, obtaining the so-called marginal likelihood of a graph, which will be the main metric for structural learning, that in- volves choosing the most likely graphical structures. Such marginal likelihood is equal to:
in which
where
By Bayes rule, the posterior probability of a graph is given by:
and, therefore, since we assume a uniform prior over the graph structures, maximizing the posterior probability is equivalent to maximizing the marginal likelihood. For graphical model selection purposes we shall thus search in the space of all possible graphs for the structure such that
The Bayesian approach does not force conditioning inferences on the (best) model chosen. The assumption of G being random, with a prior distribution on it, allows any inference on quantitative parameters to be model averaged with respect to all possible graphical structures, with weights that correspond to the posterior probabilities of each graph. This is due to Bayes’ Theorem:
However, in many real problems, the number of possible graphical structures could be very large and we may need to restrict the number of models to be averaged. This can be done efficiently, for example, following a simulation-based procedure for model search, such as Markov Chain Monte Carlo (MCMC) sampling.
In our context, given an initial graph, the algorithm samples a new graph using a proposal distribution. To guarantee irreducibility of the Markov chain, we follow [
We have selected all the publicly traded banks in the MENA region from Bureau Van Dijk’s Bankscope database. The banks that have data availability limitations where dis- carded which resulted in a total sample size of 81 listed banks that belong to 14 different countries. The country list along with the corresponding percentage of bank- ing assets for each bank type from MENA region total assets is described per year in
Country | Bank Type | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |
---|---|---|---|---|---|---|---|
AE | CB | 0.11 | 0.1 | 0.13 | 0.16 | 0.15 | 0.15 |
CB.win | 1.3 | 1.22 | 0.96 | 0.87 | 0.67 | 0.69 | |
CB.sub | 7.54 | 7.86 | 7.91 | 7.68 | 7.77 | 7.47 | |
IB | 1.6 | 1.63 | 1.66 | 1.57 | 1.59 | 1.66 | |
SA | CB.win | 5.74 | 6.03 | 5.71 | 5.32 | 5.4 | 5.21 |
CB.sub | 0.96 | 1.01 | 1 | 0.98 | 1.06 | 1.02 | |
IB | 1.67 | 1.85 | 2 | 2.26 | 2.56 | 2.6 | |
IL | CB | 8.65 | 8.76 | 9.03 | 8.81 | 8.36 | 8.15 |
KW | CB | 0.84 | 0.77 | 0.9 | 0.86 | 0.88 | 0.89 |
CB.win | 1.41 | 1.46 | 1.32 | 1.27 | 1.28 | 1.25 | |
CB.sub | 1.49 | 1.4 | 1.38 | 1.35 | 1.42 | 1.49 | |
IB | 1.81 | 1.83 | 1.82 | 1.99 | 1.94 | 1.79 | |
QA | CB.win | 0.89 | 0.75 | 0.81 | 0.81 | 0.88 | 0.99 |
CB.sub | 1.66 | 1.77 | 1.96 | 2.37 | 2.8 | 3.06 | |
IB | 0.86 | 0.75 | 0.8 | 0.94 | 1.09 | 1.07 | |
IR | IB | 1.44 | 1.89 | 1.97 | 2.17 | 2.34 | 2.85 |
BH | CB.win | 0.5 | 0.36 | 0.34 | 0.37 | 0.38 | 0.36 |
CB.sub | 1.72 | 1.7 | 1.56 | 1.51 | 1.42 | 1.32 | |
IB | 0.69 | 0.72 | 0.74 | 0.72 | 0.65 | 0.63 | |
MA | CB | 1.03 | 1.09 | 1.06 | 1.08 | 1.02 | 0.82 |
CB.win | 0.41 | 0.39 | 0.43 | 0.48 | 0.26 | 0.4 | |
CB.sub | 1.08 | 1.14 | 1.1 | 1.12 | 0.72 | 0.92 | |
LB | CB | 0.17 | 0.17 | 0.2 | 0.25 | 0.27 | 0.27 |
CB.sub | 2.03 | 2.1 | 2.05 | 1.93 | 1.83 | 1.79 | |
JO | CB | 0.19 | 0.17 | 0.24 | 0.26 | 0.25 | 0.23 |
CB.sub | 1.08 | 0.93 | 0.87 | 0.88 | 0.85 | 0.79 | |
OM | CB | 0.21 | 0.09 | 0.08 | 0.08 | 0.14 | 0.15 |
CB.win | 1.04 | 0.72 | 0.76 | 0.75 | 0.82 | 0.82 | |
EG | CB.win | 0.4 | 0.36 | 0.37 | 0.38 | 0.39 | 0.36 |
IB | 0.24 | 0.14 | 0.14 | 0.15 | 0.15 | 0.15 | |
MT | CB | 0.42 | 0.31 | 0.19 | 0.23 | 0.23 | 0.23 |
CB.win | 0.34 | 0.24 | 0.22 | 0.14 | 0.17 | 0.18 | |
TN | CB | 0.48 | 0.31 | 0.28 | 0.28 | 0.27 | 0.25 |
The banks in the sample are also classified according to four banking types: CBs group, which includes conventional banks that do not provide any type of Islamic financial services; CB-Win group, which includes conventional banks that provide Islamic financial services within their operations but do not operate a fully Islamic banking subsidiary; CB-Sub group, which includes conventional banks that provide Islamic financial services and operate an Islamic banking subsidiary; and IBs group, which includes fully fledged Islamic banks in all its services and subsidiaries. The 81 banks in the sample are distributed between the different banking groups to 19 CBs, 24 CB-win, 17 CB-sub, 21 IBs, a more detailed distribution by country is shown in
We use a dataset that represents market data on equities that extends over 89 months from January 2007 to May 2014. The data set is split into two main parts, the first is
Country | Country code | Gulf countries | CBs | CB-Win | CB-Sub | IBs |
---|---|---|---|---|---|---|
Kuwait | KW | Yes | 2 | 3 | 1 | 4 |
United Arab Emirates | AE | Yes | 1 | 4 | 6 | 4 |
Oman | OM | Yes | 1 | 3 | - | - |
Qatar | QA | Yes | - | 3 | 2 | 3 |
Saudi Arabia | SA | Yes | - | 6 | 1 | 4 |
Bahrain | BH | Yes | - | 2 | 2 | 2 |
Iran | IR | Yes | - | - | - | 3 |
Total Number of Banks = 57 | 4 | 21 | 12 | 20 | ||
Israel | IL | No | 6 | - | - | - |
Morocco | MA | No | 3 | 1 | 1 | - |
Lebanon | LB | No | 1 | - | 2 | - |
Jordan | JO | No | 1 | - | 2 | - |
Malta | MT | No | 2 | 1 | - | - |
Tunisia | TN | No | 2 | - | - | - |
Egypt | EG | No | - | 1 | - | 1 |
Total Number of Banks = 24 | 15 | 3 | 5 | 1 | ||
Total Number of Banks = 81 | 19 | 24 | 17 | 21 |
during the crisis period, which extends from January 2007 to December 2009, and the second is after the crisis period, from January 2010 to May 2014.
Before studying systemic risks, we describe the systematic effects of countries on bank performances.
Returns per Country | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
IL | KW | MA | MT | TN | AE | OM | LB | JO | SA | QA | BH | EG | IR | |
Mean | 0.539 | 0.187 | 1.530 | 0.378 | 1.154 | 0.046 | −0.107 | 0.675 | 0.966 | 0.713 | 0.963 | −0.236 | 0.527 | −0.482 |
Standard Deviation | 0.103 | 0.294 | 0.040 | 0.108 | 0.091 | 0.121 | 0.122 | 0.054 | 0.074 | 0.086 | 0.092 | 0.249 | 0.115 | 0.570 |
Kurtosis | 2.084 | 10.100 | −0.874 | 21.714 | −1.208 | −0.917 | −0.072 | −0.441 | 1.975 | −0.336 | 0.704 | 0.711 | −0.042 | −1.247 |
Skewness | −1.559 | −3.135 | 0.241 | −3.106 | −0.443 | 0.773 | 0.908 | −0.199 | 1.530 | 0.732 | −0.925 | 1.363 | −0.424 | 0.375 |
Minimum | 0.210 | −0.960 | 1.450 | −0.340 | 0.980 | −0.100 | −0.280 | 0.560 | 0.870 | 0.550 | 0.680 | −0.590 | 0.240 | −1.380 |
Maximum | 0.670 | 0.480 | 1.620 | 0.550 | 1.320 | 0.280 | 0.220 | 0.780 | 1.200 | 0.930 | 1.150 | 0.400 | 0.740 | 0.480 |
Count | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 | 89 |
high portion of conventional banks, such as Tunisia. Having seen the systematic effects of countries, we examine if this volatility is transmitted by assessing the impact in terms of systemic risk, the main focus of our paper.
To achieve this aim we present the graphical Gaussian model obtained on the basis of the partial correlations between aggregate country returns, separately for the crisis period (2007-2009) and the post-crisis period (2010-2014). We have chosen the best model by means of a backward selection procedure that, starting from the fully con- nected model, progressively tests for edge removal using a significance level of
In the above figure for the crisis and post crisis periods, the nodes with the highest number of edges are the most interrelated, we can determine the capacity of the corre- sponding countries as agents for systematic risk using centrality measures, and rank countries from the most to the least contagious.
The centrality measures in
As for the dual banking systems, weak economies such as JO and LB are in relatively high ranks during and after the crisis, with the other weak economies moving upward in the ranks for the post crisis period. On the other hand, strong economies are rela- tively stable, as they have a moderate change in their ranks, except for KW, which seems to follow the behavior of the full conventional system in both its rank and its returns variability through time. These findings suggest that the impact of the dual hybrid systems strongly depends on the country in which they are based.
Node Degree | Node Partial Correlation Degree | Eigenvector Centrality | ||||
---|---|---|---|---|---|---|
Country | During-Crisis | Post-Crisis | During-Crisis | Post-Crisis | During-Crisis | Post-Crisis |
IL | 7 | 5 | 3.69 | 2.22 | 0.52 | 0.43 |
KW | 1 | 4 | 0.43 | 2.23 | 0.06 | 0.31 |
MA | 0 | 2 | 0 | 0.78 | 0 | 0.14 |
MT | 1 | 3 | 0.43 | 1.19 | 0.08 | 0.2 |
TN | 2 | 4 | 0.86 | 1.52 | 0.24 | 0.28 |
AE | 4 | 4 | 1.95 | 1.94 | 0.37 | 0.35 |
OM | 2 | 3 | 1.17 | 1.27 | 0.12 | 0.2 |
LB | 4 | 4 | 2.13 | 1.64 | 0.3 | 0.28 |
JO | 3 | 3 | 1.75 | 1.31 | 0.29 | 0.21 |
SA | 5 | 2 | 2.43 | 0.92 | 0.42 | 0.14 |
QA | 3 | 4 | 1.38 | 1.43 | 0.22 | 0.33 |
BH | 3 | 3 | 1.62 | 1.7 | 0.24 | 0.22 |
EG | 3 | 4 | 1.55 | 1.64 | 0.23 | 0.3 |
IR | 0 | 3 | 0 | 1.42 | 0 | 0.19 |
We now consider the full time evolution of the eigenvector centrality measure by means of the Bayesian approach, which provides a stable averaged model inference on yearly basis as shown in
The Bayesian model eigenvector centrality measure in
In terms of the dual banking systems, weak economies such as MA, MT, TN, JO and LB are in relatively high ranks during the crisis and remain there after the crisis (except for JO). On the other hand, strong economies with a high concentration of Islamic banks, as in the case of SA, start in low ranks during the crisis, move to higher ranks upon its materialization in 2009, and progress towards lowering their ranks after. Similarly, the Bayesian model shows that KW starts from a high contagion rank and progresses towards a lower one after the crisis.
The dispersion in the eigenvector centrality measure estimated from the Bayesian model around its yearly average, from 2007 to 2013, is provided in
Eigenvector Centrality per Year | |||||||
---|---|---|---|---|---|---|---|
Country | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |
IL | 0.35 | 0.399 | 0.269 | 0.313 | 0.021 | 0.279 | 0.331 |
KW | 0.001 | 0.399 | 0.269 | 0.313 | 0.021 | 0.193 | 0.144 |
MA | 0.35 | 0.399 | 0.269 | 0.313 | 0.356 | 0.279 | 0.331 |
MT | 0.35 | 0.418 | 0.269 | 0.313 | 0.356 | 0.279 | 0.331 |
TN | 0.35 | 0.022 | 0.269 | 0.036 | 0.356 | 0.223 | 0.135 |
AE | 0.06 | 0.001 | 0.269 | 0.313 | 0.356 | 0.279 | 0.331 |
OM | 0.001 | 0.023 | 0.269 | 0.313 | 0.098 | 0.245 | 0.115 |
LB | 0.35 | 0.399 | 0.271 | 0.008 | 0.098 | 0.353 | 0.372 |
JO | 0.35 | 0.022 | 0.001 | 0.313 | 0.058 | 0.204 | 0.103 |
SA | 0.009 | 0.024 | 0.269 | 0.313 | 0.374 | 0.231 | 0.135 |
QA | 0.06 | 0.114 | 0.027 | 0.324 | 0.098 | 0.368 | 0.307 |
BH | 0.365 | 0.399 | 0.006 | 0.324 | 0.133 | 0.076 | 0.139 |
EG | 0.35 | 0.005 | 0.058 | 0.072 | 0.364 | 0.279 | 0.331 |
IR | 0.062 | 0.11 | 0.586 | 0.036 | 0.414 | 0.322 | 0.343 |
Yearly Average | 0.215 | 0.195 | 0.221 | 0.236 | 0.222 | 0.258 | 0.246 |
higher conventional banking concentration, and reflects a lower extent of high dis- persion during 2009 that is led by countries of higher Islamic banking concentration. For both systems, the dispersion around the mean is reduced in the following years. Overall,
To summarize, our findings suggest that there is a difference between the con- ventional and the Islamic banking systems impact on systemic risk, not only in mag- nitude but also in timing as there is a one year time lag for the crisis effect on Islamic banks. In addition, a hybrid system within a strong economy may in general support a lower systemic risk which may be consistent with a diversification effect on the country’s systemic level portfolio. Finally, we remark that the eigenvector centrality dispersion measure in
The main aim of this paper is to investigate whether and how Islamic financial services support financial stability, based on how they affect the country level systematic risk. To achieve this aim, we have proposed a correlation network approach based on graphical Gaussian models, both classical and Bayesian, with a set of related centrality measures, which may describe the systemic risk of each country.
Our results support the ability of the Islamic banking model to enhance financial and economic stability, but also the presence of a strong cross-country variability. These results confirm the findings provided by the literature. Our findings also clearly describe the different impact of the recent financial crisis on the systemic risk levels of each country.
Suggestions for future research involve further studying systemic risk in dual systems combining graphical models with standard bivariate measures such as MES, SRISK and DCoVaR. Furthermore, it would be important to let systemic risk to depend on variables such as the leverage and the size of the banking sectors and the market share of different banking types.
The authors acknowledge the financial support from the PRIN project MISURA: multivariate models for risk assessment, and of the PhD programme in Economics and management of technology at the University of Pavia. The paper has been written by Shatha Hashem, with the supervision of Professor Paolo Giudici.
Hashem, S.Q. and Giudici, P. (2016) Systemic Risk of Conventional and Islamic Banks: Comparison with Graphical Network Models. Applied Mathematics, 7, 2079-2096. http://dx.doi.org/10.4236/am.2016.717166