Abdelkader Derbali
email: derbaliabdelkader@outlook.fr

Slaheddine Hallara

Systemic risk of European institutions: estimation and ranking by Marginal Expected Shortfall

Keywords: Systemic risk, MES, euro zone, DECO-GARCH JEL Classifications: D53, E02, E44, G21, G32

The task of processing a systemic event and its negative externalities requires approaches to measure systemic risks and break it down into contributions of different institutions. The objective of this paper is to assess systemic risk in European banks during the period following the 2007 financial crisis. To do so, we estimated the systemic risk of a sample of 281 European institutions from January 01, 2006 to December 31, 2012. We used the Marginal Expected Shortfall (MES) to measure systemic risk. The results showed that the total systemic risk supported by European banks is very high. Moreover, the contribution of financial institutions in the risk of their system is very important. This prompted the international authorities to intervene, as the case of the countries of the Euro zone, where the IMF, the ECB and the WB intervened but lead to a permanent solution to the accumulation of systemic risk.

Introduction

The failure of some financial institutions such as Lehman Brothers, Northern Rock and HRE after the financial crisis of 2007 showed that the failure of a single firm may have a negative and significant impact on the financial system as a whole. Therefore, the approach of specific firm or micro-prudential is not sufficient to promote the financial stability. Careful evaluation of the contribution of a financial company in the systemic risk should be an important part in the macro-prudential financial supervision (Puzanova and Duellmann, 2013).

The risk which refers to a financial system as a whole is often treated as a systemic risk. This term was defined as the risk of financial collapse with loss in the overall system.

The task of processing a systemic event and its negative externalities requires approaches to measure systemic risks and break it down into contributions of different institutions. In addition, the macro-prudential approach will be based on measurements of the magnitude of the potential loss or the cost associated with systemic events on procedures for the establishment of an adequate capital base in the financial system absorbs this cost.

The systemic risk measures took into account the risk of extreme losses for a financial company in the event of market disruption. Many methods of assessing systemic risk and the contribution of risk were discussed in the financial literature. Several recent approaches have been developed to detect the extreme risk of a financial system by examining the direct and indirect links of the financial sector. The market prices of financial instruments and credit risk modeling have already been used in the literature to measure systemic risk. Acharya et al. (2012) and [START_REF] Brownlees | Volatility, Correlation and Tails for Systemic Risk Measurement[END_REF] proposed an economic and statistical approach to measuring systemic risk of banks. The externality that generates systemic risk is the tendency of a financial institution to be undercapitalized when the financial system as a whole is undercapitalized (Acharya et al., 2012).

The CoRisk analysis is based on the analysis developed by Adrian CoVaR andBrunnermeier (2008, 2011). This analysis is introduced by Chan-Lau (2010), in which he studied the risk of interdependence between the various financial institutions. The CoRisk analysis can be defined as a risk measurement Codependency between financial institutions. In his study, [START_REF] Chan-Lau | Regulatory Capital charges for connected-Too-To-Tail institutions: A Practical Proposal[END_REF] measured the default risk of the transmission of a bank to another bank or the entire financial system. The risk of Codependency (CoRisk) can be estimated by the quantile regression method developed for the first time by Koenker and Basset (1978).

Chan-Lau used the VaR to measure systemic risk. The estimation method is the bivariate quantile regression. The data used in this study are the values of CDS spreads. The inputs used to measure systemic risk are implied default probabilities CDS. Chan-Lau measured in his study the default probabilities for 26 banks. The study period is from May 2, 2003to February 27, 2009. The main idea of this study is to calculate the impact of the bankruptcy of a bank in the probability of default of other banks. [START_REF] Brownlees | Volatility correlation and tails for systemic risk measurement[END_REF] proposed a new model of systemic risk. The model developed by its two authors is named the SRISK (ShortRISK). The SRISK measures the contribution of a financial institution to systemic risk and systemic risk across the financial system as a whole.

The SRISK index of an institution is determined by the projected shortage of capital of this company in the event of a systemic event that defined as a substantial decrease in the market in a given time horizon. The shortage depends on the level of indebtedness of a firm, its size and its loss of such conditional capital, which is defined as the expected deficit marginal (Marginal Expected Shortfall (MES)). [START_REF] Brownlees | Volatility correlation and tails for systemic risk measurement[END_REF] proved that companies with a high SRISK are those that have a strong contribution to the underfunding of the financial market in times of crisis. Its companies are considered those most systemically risky. The sum of SRISK of the entire financial system is the potential shortage of capital that the government is under pressure to recapitalize its policy in this capital. Conceptually this type of calculation is similar to the fault tests that are consistently applied to financial institutions. This type of calculation is based on publicly available information and is inexpensive.

Brownless and Engle (2011) used the same sample used by [START_REF] Acharya | Measuring Systemic Risk[END_REF]. They split the sample into four groups of US firms that have a market capitalization of more than 5 billion dollars at the end of June 2007. The four groups are repositories (29 institutions), brokers (32 institutions), companies Insurance (10 institutions) and non-depository institutions (23 institutions). The study period began in June 3, 2000 to June 30, 2010.

Its two authors measured the systemic risk by Expected Shortfall technique. Their results are obtained using two methods for estimating the conditional correlation (Conditional Correlation: DCC-GARCH) and simulation Monte Carlo (Monte Carlo Simulation). The inputs of their approach are virtually asset returns that are obtained from the data on stock prices and balance sheet data. [START_REF] Acharya | Measuring Systemic Risk[END_REF][START_REF] Acharya | Measuring Systemic Risk[END_REF]Acharya et al. ( , and 2012) ) have developed a new model for measuring systemic risk. This model is named the Systemic Expected Shortfall (SES) or the expected systemic deficit. [START_REF] Acharya | Measuring Systemic Risk[END_REF][START_REF] Acharya | Measuring Systemic Risk[END_REF]Acharya et al. ( , and 2012) ) showed that the SES is measurable and it can observe the level of indebtedness of an institution, its volatility, and the volatility of the financial system, the correlation between the financial system and the institution and appearance finally a systemic crisis. [START_REF] Acharya | Measuring Systemic Risk[END_REF][START_REF] Acharya | Measuring Systemic Risk[END_REF]Acharya et al. ( , and 2012) ) proposed a measure of systemic risk for 102 American firms grouped into four groups. They used to estimate the expected shortfall systemic risk.

Their empirical validation is done on the basis of balance sheet data and stock prices.

Operated the study period is almost one year (June 2006 to June 2007). Moreover, they used the law of Gaussian and Power law as estimation methods following a sampling and made empirical scale. The authors have proposed a simple and intuitive method to measure the contribution of each bank systemic risk and thus, to propose some means of limiting this risk.

Their studies have verified the importance of the debt level of firms in their contributions to systemic risk.

The objective of this paper is to assess systemic risk in European banks. This objective is only a quantification of the propagation of default in European banking systems mainly during the period following the 2007 financial crisis. Then, we used the Marginal Expected Shortfall (MES) to estimate the systemic risk of a sample of 281 European institutions of 16 countries for the period from January 01, 2006 to December 31, 2012. Also, we proceed in ranking of European institutions based on the level of their contributions on the systemic risk.

The rest of this paper is organized as follow. Section 2 presents econometric methodology.

Section 3, summarizes data characteristics used in our study. In section 4, we analyze and interpret the empirical results. Finally, section 5 concludes.

Methodology

The MES is the marginal contribution of an institution to systemic risk i system. This contribution is measured by the Expected Shortfall (ES). MES The measure was proposed for the first time by [START_REF] Acharya | Measuring Systemic Risk[END_REF] and it was developed to a conditional release by [START_REF] Brownlees | Volatility, Correlation and Tails for Systemic Risk Measurement[END_REF].

By definition The Expected Shortfall (ES) or deficit under the threshold %  is expected to return %  , but, it can be beneficial when it exceeds a given threshold C. Expected Shortfall conditional of a system is given by:

    11 1 () N mt t mt mt it t it mt i ES C r r C w r r C          (2)
Then the MES is the partial derivative of ES system relative to the proportion of the company i in the economy.

  1 () () mt it t it mt it ES C MES C r r C w        (3)
The MES can be considered an extension to the concept of marginal VaR proposed by [START_REF] Jorion | Bank trading risk and systemic risk[END_REF] to the expected shortfall is a risk measure introduced by Artzner et al. (1999).

The measurement MES the increased risk for the system (measured by ES) induced a slight increase in the value of the firm i in the system. More MES of a firm, the higher its individual contribution to the financial system risk is high.

MES template extension is the expected systemic deficit (Systemic Expected Shortfall). The SES is the reduction of the amount of a bank's capital below its target level (defined as a fraction of the assets k) in the case of a global systemic crisis:  

1 it it it i it SES kL MES W       (5)
Where,  and i  are constants.

The calculation is made by the MES the DECO-GARCH art proposed by [START_REF] Brownlees | Volatility, Correlation and Tails for Systemic Risk Measurement[END_REF]. Documentation for DECO models will be formulated for many performance series. Consider a vector N series different return The DECO-GARCH model assumes a specific parametric assumption for the conditional correlation matrix. Then, at a given date DECO-GARCH model assumes that all pairwise correlations are identical. It turns out that, despite the appearance of strong restrictions, the DECO model can provide consistent estimates of DCC parameters in large systems. The correlation matrix is defined as an equi-correlation matrix and evolves as:

  1 t t N t N R I J     (10) ,, , , , , 2 ( 1)
i j t t ij i i t j j t q NN qq      (11) , , , , 1 , 1 , , , 1 , ( ) ( )
i j t i j DECO i t j t i j DECO i j t i j qq                (12)
Where , ij  is the unconditional correlation between , it  and , jt  . The complete specification GARCH-DECO is therefore obtained partner after the modeling of the univariate return series have individual GARCH processes and their standardized residual series as a DECO process.

The complete specification of DECO-GARCH is obtained after modeling univariate performance series by an individual GARCH process and their residual normalized set as a process DECO.

All parameters   1,2 ;; To implement the maximum likelihood, we assume that the accumulated performance series

    ' 1 ' ' 1 , log 2 c DECO DECO t t t t t t t L R R             (13)
As in the GARCH models require that 0, 0, 1

DECO DECO DECO DECO         .
After estimating the correlations (DECO), we can present the SRISK model used for the calculation of systemic risk.

The return of firm i and procurement are as follows:

mt mt mt r   (14) 2 1 it it it mt it it it r          (15)
For any event conditioned by a threshold C:

  1 1 2 1 () 1 mt t mt mt it it t mt mt mt it it t it mt mt ES C r r C C C                                (16)
Based on the hypothesis that mt  and it  are independent, we get:

  1 1 2 1 0 1 () 1 mt t mt mt it it t mt mt mt it it t it mt mt it it t mt mt mt ES C r r C C C C                                             (17)
You can also write,

  1 () mt it it t mt mt ES C r C        (18)
In addition, the volatility of the beta of firm i over time is expressed by equation ( 19):

    cov , var it mt it it it mt mt rr r     (19)
By combining the equation beta to equation ( 18) returns:

      1 1 1 () mt it it t mt mt it mt t mt mt it t mt mt ES C r C rC r r C                    ( 20
)
The MES is expressed as the product of the beta that varies in time and the expected return of the market at a given threshold C.

The deficit anticipated market performance ()

mt ES 
matches the expected market return for a given threshold equal to the conditional VaR [START_REF] Jorion | Bank trading risk and systemic risk[END_REF] (

) mt C VaR   :   1 ( ) ( ) mt t mt mt mt ES r r VaR      (21)
Thus, the MES a firm i at a given threshold ()

mt C VaR   , Is denoted () it MES 
and expressed by the product between the beta and the expected deficit market performance.

( ) ( )

it it mt MES ES     (22)
The expected deficit systemic (SES) is given by:

    ( ) 1 ( ) 1 ( ) it it it i it it it mt i it SES kL MES W kL ES W                (23)
The expression of ES and SS for the market performance can be expressed while assuming that mt  is characterized by a normal standard distribution. Thus, we obtain:

1 ( ) ( ) mt mt VaR      (24) Therefore, 1 ( ( )) () mt mt ES         (25)
Where, (.)  and (.)  mean respectively the normal standard distribution function and probability and function of the cumulative distribution. The ESM is expressed as follows:

1 ( ) ( ( )) it it mt MES          (26)
Where, () () ()

z z z    
noted the Mills ratio.

The determination of the MES has two consequences main. First, on a given date, systemic risk ranking of financial institutions based on the ESM (in absolute value) is strictly equivalent to the rankings that would be produced by the sort of businesses based on their betas.

Indeed, the higher return of a company is sensitive to market performance over its systemic risk. Therefore, to identify companies that have the greatest systemic risk, simply resort to their highest betas.

Secondly, for a given financial institution, the time profile of the systemic risk measured by its MES can be different from the evolution of its systematic risk measured by its beta conditional. For an ES variable market over time, predicting the systematic risk of the firm i can not be sufficient to predict the future evolution of its contribution to systemic risk.

Data

The sample used in this article is made up of 281 European financial institutions belong to the 16 countries of the euro zone. The structure of our sample is homogeneous since it is composed only of banks. The choice of these banks is justified by the availability of data and the context of deficit of European financial institutions. In addition, we have retained in our work only banks that exist in the financial market during the study period chosen in our research work.

Different countries used in our doctoral thesis as well as the number of banks in each country are given in Table 1. The study period is from January 1, 2006 to December 31, 2012. This period was characterized by the declaration of the bankruptcy of several banks following the outbreak of the financial crisis of 2007.

In Appendix 1, we presented a list of different libraries used in our research. The choice of its banks is justified by the level of systemic risk in European countries.

In Figure 1 In Figure 3, we presented the systemic risk contribution in the GDP of each European country. From this figure, we found that France (11.5%), Britain (10%) and Greece (10%)

have the ratio SRISK/highest GDP compared to other European countries.

In Figure 4, we presented the contribution of systemic risk in the market capitalization of individual banks in each European country. From this figure, we found that Greece (147%),

France (88%) and Germany (60%) have the ratio SRISK/Market capitalization highest compared to other European countries.

In Figure 5, we presented the systemic risk contribution in the total assets of individual banks in each European country. From this figure, we found that Greece (4.2%), France (3.7%) and Germany (2.9%) showed the ratio SRISK/Total Assets highest compared to other European countries.

According to this preliminary analysis, we found that Greece and France are the most affected by the 2007 financial crisis by analyzing the level of systemic risk of financial institutions of his country.

Results

We estimated the systemic risk measured by MES technique for different banks used in this paper for a period of 7 years (from January 1, 2006 to December 31, 2012). We used the methodology DECO-GARCH to estimate the correlation between the performance of a bank and the return the market to which it belongs.

In table 2, we presented descriptive statistics for the correlation between each bank and the system in which it operates. This correlation is estimated by maximum likelihood using the methodology DECO-GARCH (1,1).

According to Table 2, we observed that on average banks of Germany (0.73), Belgium (0.68), Norway (0.68), Sweden (0.68), and Italy (0.67) have the highest dynamic equicorrelation with their systems which they operate. This level reflects the correlation dependence between banks returns of its country and the performance of their markets. Furthermore, this correlation is positive. From this positive sign, we can define the risk factors relating to the market is one of the main factors of the performance of banks in our sample. Thus, this high level of correlation can justify the spread of systemic risk of European banks. The level of risk measured by the standard deviation of the correlation between the performance of banks and the system efficiency is low since it is less than 1.

In Table 3, we presented the descriptive statistics for the MES variable which is the expected loss for each dollar invested in the capital of a bank when the market down 2% for one day.

The capital of each bank marginal loss compared to the total loss of the system evolves with a fairly significant rate because of the dependency relationship between the banks of the euro zone and systems which they operate. According to this Have the volatility of the higher leverage compared to other banks in our sample. For the evolution of systemic risk, we noticed that the SRISK peaked during 2008 (11.38) especially after the outbreak of the subprime crisis of 2007. After that date and after the recovery plan and implemented reforms by national and international regulatory authorities, the capital loss for all EU institutions has been reduced to only two years. This loss increased again after the outbreak of the sovereign debt crisis in the Euro zone in 2011 and mainly in 2012.

We also conducted a ranking of the top 50 banks according to the measure of systemic risk MES. This ranking was presented in Appendix 3 to 7 years of study (01/01/2006-01/12/2012).

So, we will only concentrate on the top 50 banks since the remaining banks in our sample have a very low level of systemic risk compared to those previously classified. The classification of financial institutions according to the evolution of systemic risk allows good control authorities choose and fully exploit their stimulus plan against triggering a systemic crisis. This ranking allows regulators of financial and banking system to distinguish between banks by degree of risk and according to their degree of contribution to the risk of the entire system.

Conclusion and remarks

Measuring the contribution of a bank in the systemic risk of a banking system has the objective of this paper. This contribution is reflected in the presence of the specific characteristics of a bank which in turn may affect the transmission of the defect to other banks. Most approaches and theories concerning the measurement of systemic risk focus on the quantification and monitoring of it. In our paper, we estimate the systemic risk for European banks included. This estimate is based on the exposure of a literature review regarding the estimation of systemic risk for financial institutions. Then, we used the MES approach to analyze the existence of systemic risk in the banking systems in the euro area during the period of study in our research ranging from January 01, 2006 to December 31, 2012. We found that there are systemic events in European banking systems mainly after the outbreak of the financial crisis of 2007 and after the outbreak of the sovereign debt crisis in 2010. Similarly, we did a ranking of the different financial institutions based on the marginal loss in investment (MES). Based on this classification, we noticed that there is a high level of contribution from European banks in the risk of their systems. We've broken down systemic risk for the first 20 European banks.

Figure 1 :Figure 2 :Figure 3 :Figure 4 : 2012 Figure 5 :

 123420125 Figure 1: The evolution of systemic risk (as measured by SRISK) of the European institutions (billion USD)

  It can be shown that the probability function can be decomposed into a volatile component and a correlation component, which naturally leads to an estimation procedure in two stages. First, we estimate univariate GARCH models to each series of performance. Then, using the estimated residuals

	t r	'   is normally with a conditional multivariate covariance 1, 2, , t t r r 
	Thus, it is assumed that		0,	
						t	'   1, 2, , t t   	1 t t Dr 

t H as defined above. tt r N H leads to the natural definition of the function of maximum likelihood. . We can estimate the correlation parameters DECO  and DECO  by maximizing the following function:

  , we presented the evolution of systemic risk in European banks. From this figure, we noticed that the systemic risk in the euro zone peaked in the fourth quarter of 2008 and the first quarter of 2009. This period corresponds to the early onset of the liquidity crisis and debt in Euro zone. The maximum value of the European Systemic Risk financial institutions is equal to USD 2.3 trillion in late 2008. Following the stimulus applied by the authorities of European international and national regulations, the risk decreased to the beginning of the year 2011 it equals 1.4 trillion USD. After that period and following the outbreak of the sovereign debt crisis in Europe, systemic risk has increased that he reach 2 trillion USD in the second half of 2011 until the end of the second half of 2012.

	In Figure 2, we presented the level of systemic risk, measured by the SRISK, each European
	country in the late fourth quarter of 2012. According to this figure, we noticed that France
	(320 billion USD), Britain (270 billion USD), Germany (USD 150 billion), and Italy (80
	billion USD) have high levels of systemic risk compared to other European countries.

Table 1 : The sample Country Number of bank

 1

  table, we noticed that on average banks of Turkish (3.070197), Sweden (3.059716), Poland (2.903542), Italy (2.81945), and Austria (2.766458) have the highest values in the MES. Thus, we noticed that the banks of values of the highest MES during the period of study. This proves that the expected loss of the amounts invested in the capital of European banks is high. Thus, the presence of a positive and strong correlation and accumulation expected losses in the capital of European financial institutions justify the spread of systemic events and subsequently the beginning of a systemic crisis.Descriptive statistics on the volatility of the equity of the different banks in the Euro zone are presented in Table5. The results presented in this table, we found that on average equity of

	Belgium (10.82), Austria (9.06), Greece (7.74), Italy (7.5), Norway (7.06), and Spain (6.98)
	are the maximum banks that belong to banking systems of Turkish (50.60789), Greece (47.33462), Austria
	(47.00208), Spain (41.33), Finland (39.6725), Poland (39.41979), Sweden (38.58977), and
	Norway (38).

In Table

5

, we presented the descriptive statistics of the average leverage of banks in each European country. In fact, the leverage is equal to a book value of liabilities of a bank divided by the market value of equity. From this table, we noticed that on average banks of Greece (45.01981), Belgium (43.29625), Germany (26.0219), Italy (16.7135), Norway (14.61071), and Spain (14.40863) have the highest leverage among banks of the other countries mentioned in our research. In addition, banks in

Belgium (279.1939) And Greece (101367)

Table 2 : Descriptive Statistics of the DECO-GARCH (1,1) of European banks

 2

	(The sample is composed of 281 European banks during the period 01/01/2006 -31/12/2012)
	Country	Average	Maximum Minimum	Standard deviation	Skewness	Kurtosis
	Austria	0.3222917	0.56	0.09	0.1195068	0.0441881	2.518637
	Belgium	0.3399167	0.68	0.11	0.1263947	0.4327894	2.570271
	Denmark	0.34325	0.52	0.14	0.0979112 -0.3860333	2.438524
	Finland	0294	0.59	-0.01	0.1654334 -0.0125083	2.03088
	France	0.3020066	0.65	-0.08	0.1581898	0.1688845	2.311402
	Germany	0.3490476	0.73	0	0.1759125 -0.0686187	2.261896
	Greece	0.2470192	0.41	0.04	0.0824018 -0.2931751	2.315121

Table 3 : Descriptive Statistics of the MES of European banks

 3

	(The sample is composed of 281 European banks during the period 01/01/2006 -31/12/2012)
	Country	Average	Maximum Minimum	Standard deviation	Skewness	Kurtosis
	Austria	2.766458	9.06	0.34	1.944617	0.8870127	3.609788
	Belgium	2.231167	10.82	0.49	1.382215	2.860596	15.41821
	Denmark	2.1255	3.57	1.01	0.6945832	0.0866083	2.419143
	Finland	2.49	4.71	0.8	1.101696	0.1489401	2.065372
	France	2.120888	6.65	-1.11	1.376048	0.8819277	3.372464
	Germany	2.457738	6.08	0.1	1.25853	0.3565158	2.947593
	Greece	2.668846	7.74	0.96	1.293998	1.47902	5.543549
	Italy	2.81945	7.5	0.29	1.196275	0.7722942	3.536127
	Netherlands	2.687125	6.68	0.89	1.26026	0.8730286	3.495332
	Norway	2.454286	7.06	0.81	1.164546	1.228678	5.772229
	Poland	2.903542	5.42	1.06	0.8824857	0.0098557	2.583673
	Spain	2722	6.98	0.45	1.230254	0.6990796	4.134667
	Suede	3.059716	5.6	0.95	0.8891514	0.1111578	3.226727
	Switzerland	1.820972	5.35	0.06	1.137915	0.6166923	2.462693
	Turkish	3.070197	6.97	1.04	0.8917387	1.157841	5.803076
	Great Britain	2.591582	5.64	0.29	1.044397	0.2419493	2.637012

Table 5 : Descriptive Statistics of the volatility of the equity of European banks

 5

	(The sample is composed of 281 European banks during the period 01/01/2006 -31/12/2012)
	Country	Average	Maximum Minimum	Standard deviation	Skewness	Kurtosis
	Austria	47.00208	201.7	10.8	40.52518	2.488944	9.309743
	Belgium	30.3025	202	13.8	22.43014	4.664988	31.91066
	Denmark	28.3475	73.9	14	12.39508	2.032348	7.047098
	Finland	39.6725	77.7	17.4	15.7856	0.9272932	2.850177
	France	31.86349	138.3	11.7	15.58517	2.290562	11.74178
	Germany	36.58929	195.5	14.3	21.93389	3.084249	19.06761
	Greece	47.33462	130.7	11.8	23.67891	1.384762	4.849449
	Italy	33.0985	98.3	0	16.51254	1.056053	5.240987
	Netherlands	31.6725	122.7	14.3	17.88367	2.308222	10.48209
	Norway	38	105.4	18.1	19.42417	1.846391	6.101873
	Poland	39.41979	92.8	13.7	11.94431	1.273677	6.776303
	Spain	41.33	176.8	16.4	22.73188	3.364764	18.90316
	Suede	38.58977	284	16.2	26.28356	5.367002	45.85579
	Switzerland	1.820972	5.35	0.06	1.137915	0.6166923	2.462693
	Turkish	50.60789	284.2	26.4	23.48447	6.698511	65.72769
	Great Britain	35.60791	151.3	11	19.85293	2.154533	9.165913

Table 6 : Descriptive Statistics of the leverage effect of European banks

 6

	(The sample is composed of 281 European banks during the period 01/01/2006 -31/12/2012)
	Country	Average	Maximum Minimum	Standard deviation	Skewness	Kurtosis
	Austria	13.97167	41.1	1.92	9.917049	1.171049	3.803583
	Belgium	43.29625	2974.42	1	279.1939	9.891269	103.2634
	Denmark	14.2425	94.41	2.06	18.16811	2.567477	10.7721
	Finland	7.49325	31.44	1.83	6.725169	1.828884	6.393586
	France	16.61526	159.35	1.03	22.62948	2.840167	14.22862
	Germany	26.0219	434.15	1.01	44.3914	5.398256	44.95648
	Greece	45.01981	623.58	1.03	101367	3.925989	19.77729

Similarly, table 8 summarizes the classification of European banks according to the systemic risk level measured by the MES. In this table, we presented the first 10 banks for each year those are ranked in descending order according to the systemic risk value measured by the MES. From this table, we noticed that among the bank list will change from one year to another.

Table 8 : The classification of European banks by the MES

 8

	(The sample is composed of 281 European banks during the period 01/01/2006 -31/12/2012)
	Institution	MES	Rank
	31/12/2006
	Yapi Kredi Finansal Kiralama AO	3.88	1

Classification of European banks by the MES  31/12/2006

	Banca Profilo SpA Aareal Bank AG Credit Agricole SA Danske Bank A / S UBS Group AG Deutsche Boerse AG	1.71 2.69 3.97 3.30 3.43 3.38	IVG Immobilien AG Lloyds Banking Group PLC 35 31 32 37 39 41
	Credito Valtellinese SC Legal & General Group PLC Swiss Life Holding AG Svenska Handelsbanken AB Standard Life PLC UBS Group AG	1.71 2.64 3.87 3.24 3.40 3.32	MLP AG London Stock Exchange Group PLC 36 32 33 38 40 42
	Credito Artigiano SpA Lloyds Banking Group PLC Allied Irish Banks PLC DNB ASA Swedbank AB Svenska Handelsbanken AB	1.57 2.62 3.85 3.22 3.28 3.26	Muenchener Rueckversicherungs-Gesellschaft AG in Man Group PLC 37 33 34 39 41 43
	Danske Bank A / S Erste Group Bank AG CNP Assurances Deutsche Postbank AG Deutsche Boerse AG London Stock Exchange Group PLC	1.51 2.60 3.68 3.06 2.91 3.07	Muenchen Old Mutual PLC 38 34 35 40 42 44
	Bank of Greece Svenska Handelsbanken AB Lloyds Banking Group PLC CNP Assurances Nordea Bank AB Friends Life Group Ltd	1.48 2.58 3.66 2.99 2.82 2.77	Oldenburgische Landesbank AG Paragon Group of Cos PLC / The 39 35 36 41 43 45
	Landesbank Berlin Holding AG Allied Irish Banks PLC Deutsche Postbank AG Intesa Sanpaolo SpA Svenska Handelsbanken AB HSBC Holdings PLC	1.22 2.52 3.61 2.93 2.79 2.73	Wuestenrot & Wuerttembergische AG Provident Financial PLC 40 36 37 42 44 46
	Greece Italy Generali Deutschland Holding AG Banca Monte dei Paschi di Siena SpA Danske Bank A / S Banca Monte dei Paschi di Siena SpA Danske Bank A / S Danske Bank A / S SpareBank 1 SMN SNS REAAL NV Svenska Handelsbanken AB Swiss Life Holding AG HSBC Holdings PLC CIC Vaudoise Assurances Holding SA Deutsche Postbank AG SNS REAAL NV Generali Deutschland Holding AG Friends Life Group Ltd Bank of Greece Fonciere Massena DNB ASA HSBC Holdings PLC Bank of Greece Bank of Greece Deutsche Postbank AG Banque Cantonale de Geneve Swiss Life Holding AG Intesa Sanpaolo SpA CIC CIC National Bank of Belgium Danske Bank A / S Banca Monte dei Paschi di Siena SpA Espirito Santo Financial Group S.A. Landesbank Berlin Holding AG ABC Arbitrage SpareBank 1 SR-Bank ASA Wuestenrot & Wuerttembergische AG Generali Deutschland Holding AG Assicurazioni Generali SpA Landesbank Berlin Holding AG Landesbank Berlin Holding AG National Bank of Belgium  31/12/2012 Alandsbanken Abp Wuestenrot & Wuerttembergische AG Hannoversche Hypothekenbank AG Berlin Bank of Valletta PLC Caisse Regionale de Credit Agricole Bank of Greece SpareBank 1 SR-Bank ASA CIC CIC National Bank of Belgium  31/12/2011 Institution Dexia SA Landesbank Berlin Holding AG  31/12/2010 Institution Banco Popolare SC National Bank of Belgium Dexia SA Commerzbank AG  31/12/2009 Institution ING Groep NV National Bank of Greece SA Bank of Ireland Societe Generale SA Deutsche Bank AG Mutuel d'Ille-et-Vilaine HSBC Bank Malta PLC  31/12/2008 Institution Allied Irish Banks PLC SNS REAAL NV UniCredit SpA Allied Irish Banks PLC Societe Generale SA KBC Groep NV Societe Generale SA	Agricultural Bank of Greece Alpha Bank AE Attica Bank SA Bank of Greece Emporiki Bank SA Eurobank Ergasias SA Grivalia Properties REIC Hellenic Exchanges -Athens Stock Exchange SA Holding Lamda Development SA Marfin Investment Group Holdings SA National Bank of Greece SA Piraeus Bank SA TT Hellenic Postbank SA Assicurazioni Generali SpA Azimut Holding SpA Banca SpA Intermobiliare Prudential PLC 41 37 38 43 45 47 Quintain Estates & Development PLC 38 39 42 44 46 48 Rathbone Brothers PLC 39 40 43 45 47 49 Royal Bank of Scotland Group PLC 40 41 44 46 48 50 RSA Insurance Group PLC 41 42 45 47 49 Savills PLC 42 43 46 48 50 Schroders PLC SEGRO PLC 43 44 44 45 47 48 49 50 Shaftesbury PLC Songbird Estates PLC St James's Place PLC ST Modwen Properties PLC Standard Chartered PLC UNITE Group PLC / The Willis Group Holdings Plc 45 46 47 48 46 47 49 MES Rank 1.16 2.46 3.57 2.89 2.68 2.63 1.13 2.46 3.51 2.75 2.61 1.76 1.06 2.23 3.45 1.90 2.05 1.54 0.94 2.05 3.15 1.71 2.04 1.41 0.94 1.98 3.13 1.33 1.85 0.92 1.90 2.72 1.27 1.32 0.87 0.81 1.84 1.38 2.56 1.34 1.21 1.02 0.80 0.70 0.66 0.52 1.23 1.18 1.01 1.31 1.24 50 10.82 1 48 0.84 MES Rank 5.54 2 49 0.72 6.88 1 5.42 3 50 MES Rank 6.68 2 4.96 4 0.19 49 8.36 1 6.65 3 4.86 5 0.06 MES Rank 6.62 2 6.40 4 4.85 6 50 5.97 1 5.36 3 6.37 5 4.78 7
	Netherlands Norway  31/12/2007 Institution Institution Irish Bank Resolution Corp. Ltd. / Old Bank of Ireland AXA SA Bank of Ireland ING Groep NV Permanent TSB Group Holdings PLC Barclays PLC KBC Groep NV AXA SA UniCredit SpA Credit Agricole SA Commerzbank AG AXA SA Aegon NV Credit Agricole SA * KBC Groep NV Credit Agricole SA * Unione di Banche Italiane SCPA Erste Group Bank AG Appendix 2: Institution Paragon Group of Cos PLC / The KBC Groep NV Erste Group Bank AG ING Groep NV BNP Paribas SA Natixis SA * Yapi Kredi Finansal Kiralama AO Banca Italease SpA HBOS PLC Aegon NV Assicurazioni Generali SpA Natixis SA * UBS Group AG AXA SA Prudential PLC Prudential PLC Credit Agricole SA Banco Bilbao Vizcaya Argentaria SA UniCredit SpA Banco Popular Espanol SA Turkiye Sinai Kalkinma Bankasi AS Permanent TSB Group Holdings PLC Deutsche Bank AG KBC Groep NV BNP Paribas SA Unione di Banche Italiane SCPA ING Groep NV Yapi Kredi Sigorta AS IKB Deutsche Industriebank AG Skandinaviska Enskilda Banken AB Commerzbank AG Dexia SA Raiffeisen Bank International AG Credit Suisse Group AG ING Groep NV Standard Life PLC Credit Suisse Group AG AXA SA Erste Group Bank AG Erste Group Bank AG Bank of Ireland Prudential PLC Natixis SA * Aegon NV Prudential PLC Unione di Banche Italiane SCPA Deutsche Bank AG Intesa Sanpaolo SpA Anadolu Anonim Turk Sigorta Sirketi AXA SA BNP Paribas SA Deutsche Bank AG Banco Santander SA Barclays PLC Prudential PLC Skandinaviska Enskilda Banken AB Premafin Finanziaria SpA Standard Chartered PLC Societe Generale SA Intesa Sanpaolo SpA Banco Popolare SC Banca Monte dei Paschi di Siena SpA Credit Suisse Group AG Skandinaviska Enskilda Banken AB Aviva PLC Dexia SA Barclays PLC Allianz SE AXA SA BNP Paribas SA Barclays PLC Banco Popolare SC Royal Bank of Scotland Group PLC Deutsche Bank AG Bank of Ireland Barclays PLC Deutsche Bank AG Societe Generale SA ING Groep NV Natixis SA Royal Bank of Scotland Group PLC Lloyds Banking Group PLC SNS REAAL NV Allianz SE Deutsche Bank AG Swedbank AB Banco Popolare SC Banco Popolare SC Intesa Sanpaolo SpA Bankia SA Aegon NV Allianz SE DNB ASA Old Mutual PLC Deutsche Postbank AG Banca Monte dei Paschi di Siena SpA Aegon NV Societe Generale SA Credit Suisse Group AG Legal & General Group PLC Skandinaviska Enskilda Banken AB Aegon NV Royal Bank of Scotland Group PLC BNP Paribas SA IKB Deutsche Industriebank AG UBS Group AG Societe Generale SA Credit Suisse Group AG Natixis SA DNB ASA Banco de Sabadell SA CNP Assurances Credit Agricole SA Barclays PLC Allianz SE Banco Espanol de Credito SA Assicurazioni Generali SpA London Stock Exchange Group PLC DEPFA Bank PLC Old Mutual PLC Standard Life PLC Banco Bilbao Vizcaya Argentaria SA Prudential PLC Banco Bilbao Vizcaya Argentaria SA Assicurazioni Generali SpA UBS Group AG Irish Bank Resolution Corp. Ltd. / Old Erste Group Bank AG Swedbank AB Banco Popular Espanol SA Aviva PLC CaixaBank SA Credit Agricole SA Bank of Ireland Dexia SA UBS Group AG London Stock Exchange Group PLC Skandinaviska Enskilda Banken AB Aviva PLC Aviva PLC BNP Paribas SA UBS Group AG Banco Santander SA Banca Monte dei Paschi di Siena SpA Swedbank AB Skandinaviska Enskilda Banken AB Deutsche Postbank AG Commerzbank AG Allianz SE Legal & General Group PLC SNS REAAL NV Prudential PLC Lloyds Banking Group PLC Commerzbank AG CNP Assurances Old Mutual PLC SNS REAAL NV Skandinaviska Enskilda Banken AB Banco Santander SA CNP Assurances Sekerbank TAS Dexia SA Natixis SA Nordea Bank AB Credit Suisse Group AG Credit Suisse Group AG Standard Life PLC Barclays PLC Swedbank AB Royal Bank of Scotland Group PLC Aviva PLC Lloyds Banking Group PLC Nordea Bank AB Banco Bilbao Vizcaya Argentaria SA ICAP PLC Aegon NV UniCredit SpA Lloyds Banking Group PLC Aviva PLC CaixaBank SA Banco Santander SA Legal & General Group PLC Aviva PLC Nordea Bank AB Assicurazioni Generali SpA Allianz SE Standard Life PLC Allianz SE Aareal Bank AG HBOS PLC Commerzbank AG BNP Paribas SA Commerzbank AG CNP Assurances Nordea Bank AB Svenska Handelsbanken AB Royal Bank of Scotland Group PLC Banco Santander SA UniCredit SpA CNP Assurances Old Mutual PLC Royal Bank of Scotland Group PLC Dexia SA ING Groep NV Banco Bilbao Vizcaya Argentaria SA Standard Life PLC Legal & General Group PLC Legal & General Group PLC DNB ASA Swiss Life Holding AG Nordea Bank AB Swiss Re AG HSBC Holdings PLC Old Mutual PLC Swiss Life Holding AG Legal & General Group PLC	Banca Monte dei Paschi di Siena SpA Banca Popolare dell'Emilia Romagna SC Banca Popolare di Milano Scarl Banca Profilo SpA Banco di Desio e della Brianza SpA Banco di Sardegna SpA Beni Stabili SpA SIIQ Credito Bergamasco SpA Credito Emiliano SpA Credito Valtellinese SC DeA Capital SpA Immobiliare Grande Distribuzione SIIQ SpA Intesa Sanpaolo SpA Mediobanca SpA Mediolanum SpA Milano Assicurazioni SPA Prelios SpA Societa Cattolica di Assicurazioni SCRL UniCredit SpA Unione di Banche Italiane SCPA Unipol Gruppo Finanziario SpA UnipolSai SpA Aegon NV Corio NV Eurocommercial Properties NV HAL Trust ING Groep NV Kardan NV NSI NV Van Lanschot NV Vastned Retail NV Wereldhave NV ABG Sundal Collier Holding ASA DNB ASA Gjensidige Forsikring ASA Olav Thon Eiendomsselskap ASA SpareBank 1 SMN MES Rank MES Rank 11.38 1 5.97 2 5.65 3 5.94 2 5.47 3 5.32 4 5.08 5 5.25 4 5.23 5 5.19 6 4.97 7 6.03 6 5.96 7 5.92 8 5.89 9 4.69 8 4.68 9 4.64 10 4.49 11 5.14 1 5.57 4 4.85 6 4.95 8 5.86 10 4.34 12 MES Rank 3.88 4.93 2 5.57 5 4.75 7 4.80 9 5.76 11 4.30 13 1 3.54 4.17 3 5.48 6 4.75 8 4.71 10 5.75 12 4.26 14 2 3.37 4.10 4 5.42 7 4.65 9 4.65 11 5.74 13 4.25 15 3 3.34 4.01 5 5.41 8 4.58 10 4.61 12 5.59 14 4.23 16 4 3.18 3.80 6 5.35 9 4.53 11 4.28 13 5.59 15 4.21 17 5 3.09 3.78 7 5.22 10 4.39 12 4.21 14 5.31 16 4.18 18 6 3.01 3.77 8 5.15 11 4.39 13 4.18 15 5.27 17 4.11 19 7 2.99 3.72 9 5.03 12 4.30 14 4.04 16 5.14 18 4.08 20 8 2.98 3.53 10 5.03 13 4.15 15 4.04 17 4.90 19 4.07 21 9 2.95 3.46 11 5.00 14 4.10 16 4.00 18 4.78 20 4.07 22 10 2.88 3.43 12 4.96 15 4.04 17 3.97 19 4.76 21 4.04 23 11 2.85 3.38 13 4.95 16 4.01 18 3.95 20 4.74 22 4.01 24 12 2.81 3.35 14 4.88 17 3.98 19 3.95 21 4.65 23 3.93 25 13 2.80 3.28 15 4.75 18 3.96 20 3.91 22 4.62 24 3.85 26 14 2.73 3.18 16 4.75 19 3.94 21 3.88 23 4.50 25 3.81 27 15 2.66 3.17 17 4.73 20 3.78 22 3.82 24 4.42 26 3.80 28 16 2.52 3.16 18 4.70 21 3.70 23 3.75 25 4.41 27 3.71 29 17 2.48 3.12 19 4.62 22 3.66 24 3.66 26 4.27 28 3.64 30 18 2.42 3.12 20 4.43 23 3.64 25 3.66 27 4.24 29 3.56 31 19 2.25 3.12 21 4.42 24 3.62 26 3.63 28 4.18 30 3.53 32 20 2.21 3.10 22 4.41 25 3.62 27 3.62 29 4.08 31 3.52 33 21 2.12 3.05 23 4.32 26 3.58 28 3.60 30 4.07 32 3.46 34 22 2.11 3.04 24 4.30 27 3.55 29 3.59 31 4.03 33 3.32 35 23 2.11 3.00 25 4.27 28 3.55 30 3.59 32 3.97 34 3.32 36 24 2.09 2.95 26 4.25 29 3.55 31 3.58 33 3.88 35 3.32 37 25 2.08 2.92 27 4.22 30 3.54 32 3.53 34 3.83 36 3.26 38 26 2.07 2.88 28 4.20 31 3.54 33 3.51 35 3.81 37 3.18 39 27 2.05 2.87 29 4.15 32 3.53 34 3.50 36 3.72 38 3.15 40 28 1.80 2.82 30 4.08 33 3.51 35 3.48 37 3.69 39 3.11 41 29 1.78 30 2.74 31 4.04 34 3.43 36 3.45 38 3.48 40 3.05 42


Dr Abdelkader Derbali
email: derbaliabdelkader@outlook.fr

Slaheddine Hallara

Dr Slaheddina Hallara

Day of the week effect on the Tunisian stock market return and volatility

Keywords: day of the week, volatility, returns, GARCH, T-GARCH, E-GARCH, TUNINDEX. JEL Classification: C22, G10, G12

In this paper, we examine empirically the day of the week effect on the Tunisian stock exchange index (TUNINDEX) return and volatility. We use three multivariate General Autoregressive Conditional Heteroscedasticity models (GARCH (1,1), EGARCH (1,1) and TGARCH (1,1)) to examine the presence of daily anomalies in the TUNINDEX returns and volatilities during the period from December 31, 1997 to April 07, 2014. The empirical results of GARCH (1,1), EGARCH (1,1) and TGARCH (1,1) model indicate the existence of a significance and positive effect for Thursdays and for the return at (t-1) on the return and volatility of TUNINDEX in a threshold of 1%. Additionally, we find the presence of a significance and negative effect for Tuesday in the TUNINDEX return and volatility. Also, we can show the persistence of volatility in the case of Tunisian stock market index.

Introduction

The Hypothesis of efficiency of markets (HEM) postulates that the stock exchanges must effectively reflect all information available on their fundamental value. The assumption of efficiency of the market was contradicted by anomalies such as the calendar of the anomalies, the fundamental anomalies and the technical anomalies. The calendar of the anomalies refers to the tendency of the titles to behave differently over a particular day of the week, or month of the year. Among these anomalies, the effect of the day of the week was seen like one of the most important models and it was noted in several actions on several financial markets [START_REF] French | Stock Returns and the Weekend Effect[END_REF][START_REF] Jaffe | The week-end effect in common stock returns: The international evidence[END_REF][START_REF] Balaban | Day of the Week Effects: New Evidence from an Emerging Stock Market[END_REF][START_REF] Lian | Seasonal Anomalies of Stocks in ASEAN Equity Markets[END_REF]).

The effect of the day of the week indicates that the returns are abnormally high over certain days of the week that the other days. More precisely, the results resulting from several empirical studies showed that the average return of Friday is abnormally raised, and the average return of Monday is abnormally low. Moreover, the rational investor must take account of the risk or the volatility of the returns while making decisions of investment.

However, the investors could buy actions with abnormal daily returns and sell actions with high abnormal daily return. This phenomenon was developed in several former work such as; [START_REF] French | Stock Returns and the Weekend Effect[END_REF], [START_REF] Gibbons | Day of the week effects and asset returns[END_REF][START_REF] Gibbons | Day of the week effects and asset returns[END_REF]Aggarwal &Rivoli (1989). However, all studies above concentrates only on the equations of the average returns of the stock exchange markets and uses the methods of ordinary least squares (OLS) like method of estimate to regress the outputs on five daily dummy variables.

In this paper, we investigate empirically the effect of the day of the week on the stock returns and volatility of the Tunisian stock exchange market. We use daily returns of the Tunisian index (TUNINDEX) over the period from December 31, 1997 to April 07, 2014. For the econometric methodology, we employ a General Autoregressive Conditional Heteroscedasticity models based in the GARCH (1,1), EGARCH (1,1), and TGARCH (1,1).

The empirical findings of estimated GARCH models indicate the existence of the impact of the day of the week on the stock returns and volatility of the TUNINDEX. Then, the results of GARCH (1,1), EGARCH (1,1) and TGARCH (1,1) models show the existence of a highly and positive effect for Wednesday, Thursdays, Friday and the past return at date (t-1) on the stock returns and volatilities. However, Tuesday have a negative effect. The estimation results of EGARCH (1,1) and TGARCH (1,1) models indicate the highly impact of the returns observed at date (t-1) and a significance and positive impact of Thursdays on the TUNINDEX returns.

The rest of this paper is organized as follows: section 2 provides a review of the related literature. In section 3, we present the econometric methodology based on the GARCH models. We expose the data used in our paper in the section 4. Section 5 shows and analysis the empirical results of the estimation of the conditional heteroscedasticity models. Section 5 concluding remarks.

Literature review

Many empirical works on the effect of the day of the week in the outputs of the actions was undertaken so much on the developed and emergent markets as; [START_REF] French | Stock Returns and the Weekend Effect[END_REF] and [START_REF] Gibbons | Day of the week effects and asset returns[END_REF]. All these studies have obtained different conclusions on the effect of the day from the week on the stock returns and volatility. [START_REF]The day of the week anomaly: the Toronto stock exchange experience[END_REF] and [START_REF] Dubois | The day of the week effect: the international evidence[END_REF] examine the effect of the day of week for the emerging developed markets. Their empirical results show that Monday has a negative effect on the stock exchange returns for the United States, the European markets, and in Hong Kong, Tuesday has a negative effect on the stock returns for Australia, Japan, and South Korea.

The studies made by [START_REF] Kato | Weekly patterns in Japanese stock returns[END_REF] show that Tuesday has a weak effect but Wednesday has a highly effect on the stock returns for Japan.

The study developed by [START_REF] Poshakwale | Modelling volatility in East European emerging stock markets: evidence on Hungary and Poland[END_REF] show that Monday has a negative and significant effect while Friday has a positive effect on the stock returns in the stock exchange markets of Hungary and Poland. [START_REF] Brooks | Seasonality in Southeast Asian Stock Markets: Some New Evidence on the day-of-the-week effects[END_REF] evaluate the elements of proof of the day of the week for five countries of the South Asia: Malaysia, South Korea, Philippines, Taiwan, and Thailand. They found one day of the week which has a significant effect among three of the five studied stock markets. However, they concluded moreover that the risk of market alone can be insufficient to capture the anomalies of calendar. [START_REF] Hui | Day-of-the-week effects in US and Asia-Pacific stock markets during the Asian financial crisis: A non-parametric approach[END_REF], by using the nonparametric test, examine the effect of the day of the week for four markets of the Asia-Pacific and two developed markets. The empirical results show that Hong Kong, Taiwan and Singapore show higher average returns in Fridays and of the weak influence of Monday in the average returns, but for the United States, Japan and South Korea we can show the existence of a mixed model. As a whole, it is only in Singapore that one day ago of the week which has an important effect.

In their studies of the Chinese stock market, Cai et al. (2006) found the presence of the day of the week effect with negative returns on Mondays and Tuesday. Some of the studies in Africa include [START_REF] Aly | An Analysis of the Day-of-the-Week Effects in the Egyptian Stock Market[END_REF], [START_REF] Agathee | Day of the week effect: Evidence from the stock exchange of Mauritius (SEM)[END_REF]), Chukwogur (2006) & Tachiwon (2010). For example, [START_REF] Aly | An Analysis of the Day-of-the-Week Effects in the Egyptian Stock Market[END_REF] examine the day of the week effect on the stock returns in Egypt. On average, its study indicated that Monday has a positive and significant effect on the stock returns. Tachiwon (2010) develops an analysis on the effect of the day of the week on regional stock market in West Africa over the period 1998-2007. Their empirical results show that the returns are lowest in Tuesday and Wednesday and they are higher in Friday.

Al-Mutairi (2010) finds an evidence of the presence of the day of the week effect in the Stock Exchange of Kuwait. Their empirical results show that the outputs of Saturday have a positive and higher impact than other days of the week except Wednesday, which suggests that the Kuwaiti stock exchange market is ineffective. [START_REF] Hussain | Day of the Week Effect and Stock Returns: Evidence from Karachi Stock Exchange-Pakistan[END_REF] analyze the effect of the day of the week on Karachi Stock Exchange. They revealed significant effects for Tuesday. [START_REF] Ulussever | The day-of-the-week effect in the Saudi stock exchange: A non-linear GARCH Analysis[END_REF] study the Stock Exchange of Saudi and they provided evidence of the presence of the day of the week effect on the daily stock returns.

The study of Gonzalez-Perez & Guerro (2013) utilizes data belonging to S&P 500 during the period from 2004 to 2011. Their empirical findings are supportive of U.S. market efficiency with the absence of DoW effect in the daily S&P 500 returns. Therefore, they conclude that designing a trading strategy without taking any risk will not lead to attaining abnormal returns as there is no deterministic seasonal pattern. Confirmative findings that are opposite to the DoW effect are also documented by [START_REF] Carlucci | A Study on the Day of the Week Effect in the Four major Capitals Markets of the Americas[END_REF] for the main stock exchange indices of Canada and U.S. over the period from 2002 to 2012. Furthermore, another research conducted by [START_REF] Puja | Days-of-the-Week-Effect and Stock Return Volatility: Theory and Empirical Evidence[END_REF] shows insignificant results for S&P 500 during the period from January 01, 1990to November 30, 2004[START_REF] Berument Hakan | Stock market return and volatility: Day-of-the-week effect[END_REF] investigate the stock market returns and volatility nexus using US daily returns over the period from May 26, 1952to September 29, 2006. The empirical findings reported did not confirm the proposition that the return-volatility relationship is present and the same for each day of the week.

More recently, [START_REF] Abdalla | Day-of-the-week effect on returns and conditional volatility: Empirical evidence from Sudanese stock market[END_REF] studies the anomalies of calendar in the stock exchange market of Khartoum. The empirical results did not reveal a presence of an effect of the day of the week on the stock returns and volatility. [START_REF] Gharaibeh | Test Of The Day Of The Week Effect: The Case Of Kuwait Stock Exchange[END_REF] investigate empirically the day of the week effect on the available data of daily returns on the weighted index in the Kuwait Stock Exchange (KSE) during the period from January 2002 to September 2011. Their empirical findings show that the KSE exhibits positive returns on the first and the last day of the week with significant negative returns on the Second day of the Trading week.

Methodology

In this section, we define the econometric methodology used in this paper which based in a three General Autoregressive Conditional Heteroscedasticity models, such as GARCH, EGARCH, and TGARCH.

3.1.Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Model

The standard GARCH (p,q) model was introduced by [START_REF] Bollerslev | Generalized Autoregressive Conditional Heteroskedasticity[END_REF] that suggests the conditional variance of returns is not only dependent on the squared residuals of the mean equation but also on its own past values. The standard GARCH model captures the volatility clustering of financial time series. Then, by using an appropriate GARCH model, while controlling for time-varying property of volatility, one can estimate the changes in the information flows, i.e., the impact of recent and old news on volatility. Specifically, Log likelihood ratio tests on the GARCH model for p, q Є {1, 2, …, 5} are employed in order to find the most parsimonious GARCH representation of the conditional variance of returns. A GARCH (p,q) process is represented as follow:

where equations ( 1) and (2) denote the conditional mean equation and the conditional variance equation respectively. R t is the spot returns of the TUNINDEX indexes at time t. R t-1 is a proxy for the mean of R t conditional on past information. h t is the conditional variance of the period t. Only four out of five days in the week are included in the conditional variance equation to avoid the dummy variable trap in the regression model. Thus, D it 's (i = 1, 2, …, 4) are dummy variables for Monday, Tuesday, Thursday and Friday, respectively and Wednesday is excluded. The GARCH (1,1) is weakly stationary if (α i + δ 1 < 1), α i and δ 1 are nonnegative, α i (ARCH parameter) represents the news about volatility from the previous period and δ i (GARCH parameter) represents a persistence coefficient. If the sum of ARCH and GARCH coefficients (α + δ) is very close to one, the volatility shocks are very persistent.

It is an indication of a covariance stationary model with a high degree of persistence and long memory in the conditional variance.

The basic GARCH is symmetric and does not capture the asymmetry effect that is inherent in most stock markets return data also known as the "leverage effect". In the context of financial time series analysis the asymmetry effect refers to the characteristic of times series on asset prices that 'bad news' tends to increase volatility more than 'good news' [START_REF] Black | The pricing of commodity contracts[END_REF][START_REF] Nelson | Conditional Heteroskedasticity in Asset Returns: A New Approach[END_REF]. The Exponential GARCH (EGARCH) model and the Threshold GARCH (TGARCH) model proposed by [START_REF] Nelson | Conditional Heteroskedasticity in Asset Returns: A New Approach[END_REF] and [START_REF] Glosten | On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks[END_REF] respectively are specifically designed to capture the asymmetry shock to the conditional variance.

3.2.Exponential Generalized Autoregressive Conditional Heteroscedasticity

(EGARCH) Model [START_REF] Nelson | Conditional Heteroskedasticity in Asset Returns: A New Approach[END_REF] proposes the Exponential GARCH model which allows the conditional volatility to have asymmetric relation with past data. Statistically, this effect occurs when an unexpected drop in stock price due to bad news increases volatility more than an unexpected increase in price due to good news of similar magnitude. This model expresses the conditional variance of a given variable as a nonlinear function of its own past values of standardized innovations that can react asymmetrically to good and bad news [START_REF] Drimbetas | The effect of derivatives trading on volatility of the underlying asset: evidence from the Greek stock market[END_REF].

Specifically, Log likelihood ratio tests on an EGARCH model for p, q Є {1, 2, …, 5} are employed in order to find the most parsimonious EGARCH representation of the conditional variance of returns. The EGARCH (1,1) model can be specified as follows:

where denotes the estimation of the variance of the previous time period that stands for the linkage between current and past volatility. In other words, it measures the degree of volatility persistence of conditional variance in the previous period. represents information concerning the volatility of the previous time period. It signifies the magnitude impact (size effect) coming from the unexpected shocks. indicates information concerning the leverage (γ 1 >0) and the asymmetry (γ 1 ≠0) effects. δ 1 , α 1 and γ 1 are the constant parameters to be estimated. The parameters, λ i 's are employed to capture the daily effects. ε t represents the innovations distributed as a Generalised error distribution (GED), a special case of which is the normal distribution [START_REF] Nelson | Conditional Heteroskedasticity in Asset Returns: A New Approach[END_REF].

3.3.Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) Model

The Threshold GARCH model (TGARCH) was introduced by [START_REF] Glosten | On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks[END_REF] that captures asymmetric in terms of negative and positive shocks and adds multiplicative dummy variable to check whether there is statistically significant different when shocks are negative.

In TGARCH model, it has been observed that positive and negative shocks of equal magnitude have a different impact on stock market volatility, which may be attributed to a "leverage effect" [START_REF] Black | The pricing of commodity contracts[END_REF]. In the same sense, negative shocks are followed by higher volatility than positive shocks of the same magnitude [START_REF] Engle | Measuring and Testing the Impact of News on Volatility[END_REF]. The conditional variance for the simple TGARCH model is defined by;

where d t takes the value of 1 if u t-1 is negative, and 0 otherwise. So "good news" and "bad news" have a different impact. If γ 1 > 0 the leverage effect exists and news impact is asymmetric if γ 1 ≠0. Notably, the additional parameters, λ i 's are employed to capture the daily effects.

Data

In this study, we use daily closing prices of the principal index in the stock exchange of Tunisia (TUNINDEX). The dataset was considered during the period from December 31, 1997 to April 7, 2014, which including a total of 4043 observations. The dataset was collected from the website of the Stock Exchange of Tunisia. In our paper, the stock exchange returns are defined by ln of the return between two dates (t) and (t-1). The return Rt is calculated, as follows:

(7)
Where, P t and P t-1 are the daily closing prices of index TUNINDEX at the date (t) and date (t-1) respectively. Let us note that t indicates the time (day).

Table 1 summarizes the descriptive statistics for the TUNINDEX daily returns for each day of the week. According to this table, we can remark that on average the highly return is for Wednesday (0.201088), followed by Thursday (0.200346) and Friday (0.200099). The lowest average of TUNINDEX returns is for Monday (0.198615) followed by Tuesday (0.199852) during the period of study.

The highly value of standard deviation is for Wednesday (0.400863), followed by Thursday (0.400309), Friday (0.400124), Monday (0.399938), and Tuesday (0.399007).

According to the two statistics of skewness (asymmetry) and kurtosis (leptokurtic), we can remark that all variables used in this paper are characterized by non-normal distribution. The skewness coefficients reflect that the variable is skewed to the right and it is far from being symmetric for all variables. Also, the Kurtosis coefficient indicates that the leptokurtic for all variables used in this study show the existence of a high peak or a fat-tailed in their volatilities.

Then, the positive sign of estimate coefficients of Jarque-Bera statistics show that we reject the null hypothesis of normal distribution of the variables used in our study. Also, the high value of Jarque-Bera coefficients reflects that the series is not normally distributed at the level of 1%.

Figure 1 reports the distribution of the TUNINDEX returns. So, we can observe that the Tunisian stock market index is very volatile which explain the persistence of volatilities.

Empirical results

The estimation results of three General Autoregressive Conditional Heteroscedasticity models in the case of TUNINDEX returns are presented in table 3.

Based on the estimation results of GARCH (1,1) model, we can show that, in the mean equation, we observe the existence of a significance and positive effect for Thursdays and the returns at date (t-1) with a significance level of 1%. Also, we can remark that Wednesday have a positive impact in the TUNINDEX returns. This impact is significant with a significance level of 5%. Then, Tuesday present a negative impact on the TUNINDEX returns during the period of study from December 31, 1997 to April 7, 2014. However, the results of the variance equation indicate a highly significance level of all GARCH (1,1) parameters specification in the level of 1%. For the daily effect, we can observe a negative impact of Tuesday in a significance level of 1% and a positive impact of Friday in a significance level of 10%.

Additionally, in the mean equation, we can observe that the estimation results from EGARCH

(1,1) and TGARCH (1,1) models are in conformity with the estimation results of GARCH

(1,1) model for the highly impact of the return observed at date (t-1). But, these results are not in conformity with the estimation of GARCH (1,1) model for Thursdays.

From the estimation results of EGARCH (1,1) model, we can find the existence of a significance and positive effect for the TUNINDEX returns at date (t-1) with a significance level of 1%. We can observe that Tuesday present a negative impact on the TUNINDEX returns in a significance level of 1% during the period of study from December 31, 1997 to April 7, 2014. Then, we can show that Wednesday have a positive impact in the TUNINDEX returns. This impact is significant with a significance level of 10%. We can show the existence of a significance and positive effect for Thursdays with a significance level of 1%.

Friday affect positively the TUNINDEX returns at the significance level of 1%. In the results of the variance equation, we can find a highly significance level of all EGARCH(1,1)

parameters specification in the level of 1%. For the daily effect, we can observe a negative impact of Tuesday in a significance level of 1% and a positive impact of Thursday and Friday in a significance level of 5% and 1%, respectively.

By using the estimation results of TGARCH (1,1) model, we can observe the existence of a significance and positive effect for the TUNINDEX returns at date (t-1) with a significance level of 1%. We can remark that Tuesday present a negative impact on the TUNINDEX returns in a significance level of 1% during the period of study from December 31, 1997 to April 7, 2014. Also, we can show that Wednesday have a positive impact in the TUNINDEX returns in a significance level of 5%. We can find the existence of a significance and positive effect for Thursdays and Friday with a significance level of 1%.

From the results of the variance equation, we can show a highly significance level of all TGARCH (1,1) parameters specification in the level of 1%. For the daily effect, we can remark a negative impact of Tuesday in a significance level of 1% and a positive impact of Thursday and Friday in a significance level of 1%.

Finally, the results of ARCH-LM test indicate the absence of an important ARCH effect in the residual series which imply the importance of the conditional variance equations in GARCH models. In this paper, we investigate empirically the day of the week effect on the Tunisian stock exchange returns and volatility. We use a conditional heteroscedasticity specification based on GARCH (1,1), EGARCH (1,1) and TGARCH (1,1) models to examine the presence of the daily anomalies during the period of study from December 31, 1997 to April 07, 2014.

The empirical findings of three GARCH models indicate the presence of the day of the week effect on the Tunisian stock exchange returns and volatility. Then, the estimated results of the GARCH (1,1) model indicate a highly and positive effect for Wednesday, Thursday, Friday and the past return at date (t-1). However, Tuesday have a negative effect on the TUNINDEX returns and volatility.

The estimation results of EGARCH (1,1) and TGARCH (1,1) models show a highly impact of the returns observed at date (t-1). Also, in the case of these two models Thursday have a significance and positive effect on the TUNINDEX returns. We can find that Tuesday have a negative and significant impact with a significance level of 1% on mean and variance equation in the case of EGARCH (1,1) and TGARCH (1,1) models. In consequence of the existence of the effect of the day of the week on the TUNINDEX returns and volatilities, we can suggest that the Tunisian stock market is weak-form inefficient.

Additionally, further research can be directed towards investigating the existence of day of the week anomalies on firm basis rather than focusing on stock market indices.

Figure 2

 2 Figure 2 presents the evolution of the residual series of the TUNINDEX returns during the period of study from December 31, 1997 to April 07, 2014. This figure indicates the presence of highly volatility, impliying the existence of time-varying volatilities in the case of the TUNINDEX returns.

Table 1 : Descriptive Statistics

 1

		D1	D2	D3	D4	D5
		Monday	Tuesday	Wednesday	Thursday	Friday
	Mean	0.199852	0.198615	0.201088	0.200346	0.200099
	Maximum	1.000000	1.000000	1.000000	1.000000	1.000000
	Minimum	0.000000	0.000000	0.000000	0.000000	0.000000
	Std. Dev.	0.399938	0.399007	0.400863	0.400309	0.400124
	Skewness	1.501160	1.510864	1.491524	1.497297	1.499227
	Kurtosis	3.253481	3.282709	3.224643	3.241899	3.247682
	Jarque-Bera	1529.295*	1551.629*	1507.539*	1520.524*	1524.898*
	Probability	0.000000	0.000000	0.000000	0.000000	0.000000
	Observations	4043	4043	4043	4043	4043

Note: This table presents the main statistical features for the Tunindex returns. The data period is from December 31, 1997 through April 07, 2014. * indicate a significance level at 1%. Figure 1:

TUNINDEX returns over the period is from December 31, 1997 to April 07, 2014

	Figure 2:
	2.E+07
	1.E+07
	0.E+00
	-1.E+07
	-2.E+07
	-3.E+07
	1000	2000	3000	4000
		RT

Residuals series of TUNINDEX Return during the period is from December 31, 1997 to April 07, 2014

  The Augmented Dickey-Fuller (ADF) test and the Philips-Perron (PP) test are used to examine the stationary of the time series of the data used in this study. Then, the results of these two tests are presented in table 2. From this table, we can reject the null assumption of non stationary of the TUNINDEX returns. Then, we can conclude that the TUNINDEX returns are stationary during the period of study from December 31, 1997 to April 07, 2014.

Table 2 : Unit Root Test Results Augmented Dickey-Fuller Test

 2 : This table presents the unit root test for the TUNINDEX returns. The data period is from December 31, 1997 through April 07, 2014. * indicate a significance level at 1%.

	Variable	Intercept	With Trend and	Without Trend and
			Intercept	Intercept
	TUNINDEX	-26.27386*	-26.27168*	-26.05671*
		Phillips-Perron Test
	Variable	Intercept	With Trend and	Without Trend and
			Intercept	Intercept
	TUNINDEX	-48.30104*	-48.29572*	-48.24050*

Note

Table 3 : Results of Estimated GARCH Models for TUNINDEX Returns

 3

	Mean Equation
		GARCH(1,1)	EGARCH(1,1)	TGARCH(1,1)
	Rt-1	0.265470	0.260781	0.268641
		(15.86556)*	(15.79673)*	(15.91967)*
	Monday t	69688.57	45686.04
		(1.397639)	(0.967173)