Credit Risk Stress Testing of Commercial Banks in Tunisia

Stress tests of credit risk is greatly affected by data constraints in Tunisian banking system. Aiming to improve the assessment of credit risk in such conditions, we propose a model to conduct a macro stress test of credit risk for a sample of ten Tunisian commercial banks based on scenario analysis. The approach consists first in explaining the credit risk for each bank in terms of macroeconomic and bank-specific variables through a static fixed effects model, second in a stress-testing exercise using the Monte Carlo Simulation for generating credit risk losses distributions in case of different scenarios and for determining unexpected losses for each bank. The panel analysis applied suggests a robust negative relationship between the credit risk of bank loans and real GDP growth, with a lag response of four periods. In addition, return on assets ratio and bank size show significant negative effect on credit quality, while the net loans to total asset ratio is positively associated with it. The credit risk stress testing results indicate that an adverse scenario of economic downturn produces increase of the frequency of the higher credit loss comparatively to the lower ones for all banks of the sample and that the estimated unexpected losses that would take place in a stress situation can be covered by available capital of these banks.

Published by SCHOLINK INC. In Tunisia, the high level of nonperforming loans in the banking sector and the extent of losses supported on their loan portfolios have shown interest to understand the determinants of credit risk for banking institutions in order to manage this risk and maintain macroeconomic and financial stability.
According to the recommendations of the Financial Sector Assessment Program (FSAP) conducted in Tunisia by the World Bank and the IMF in 2012, the prudential supervision in Tunisian Central Bank should be backed up by new techniques based on the "risk model" with rating and stress testing that anticipates banking difficulties (BCT, 2015).
Within the framework, we intend to set up the specific relation between credit risk of Tunisian commercial banks on one side and bank specific factors and macroeconomic variables on another side.
We seek subsequently to explore the impact of macroeconomic shocks on bank's credit risk.
For this aim, our study is based on a bank balance sheet database of ten Tunisian commercial banks for 2002-2016 period. It describes a model to perform credit risk stress testing for main banks in the Tunisian banking sector. The methodology consists first in identifying through panel data technique the bank-specific and macroeconomic determinants of credit risk of Tunisian commercial banks; second, in employing the results to construct macroeconomic stress scenarios and to simulate the impact on credit risk under two given scenarios (baseline and adverse scenarios); third in constructing an indicator to measure resilience of banks to macroeconomic shock. In the study, loan loss provisions ratio is used as a proxy of the bank loss rate for credit risk.
The outcomes of the study indicate that the deterioration of the economy growth and of some bankspecific indicators forces the banks to allocate higher loss provisions, and consequently increase the implied credit risk level. The results suggest also an increase of credit risk under the stress macroeconomic scenarios with an impact under the adverse scenario greater the baseline one. However, banks have resilience to macroeconomic shock.
Motivated by the scarcity of case studies on credit risk stress testing in Tunisian banking system, this paper focuses on ten Tunisian commercial banks that holds 71% of the total assets of the Tunisian banking system, in order to empirically investigate the bank-specific and macroeconomic determinants of credit risk in Tunisian banking system and to measure the risk exposure of banks and to find out their resilience to macroeconomic stress scenarios by using credit stress testing. Another interest of this study is providing recommendations that can be utilized by policymakers and regulators in identifying and dealing with adverse effect of credit risk on the banking sector and also, it may be integrated to allow the strengthening of bank supervision tools in Tunisia.
The remainder of this paper is organized as follows. Section 2 discusses the relevant literature. Section 3 provides a description of the methodology. Section 4 discusses the credit stress testing results. And

Literature Review
Various studies about the credit risk stress testing tool have been carried out with the aim of helping policymakers and monetary authorities assess the consequences of eventual shocks on credit risk and therefore sustaining financial stability. Stress testing is defined in the RiskMetrics technical document (1994) as a part of a risk management process that uses scenarios to estimate risk in crisis conditions. Credit risk stress testing is a recent discipline related to credit risk modeling (Schuermann, 2014); it was mentioned in CreditMetrics (Gupton, Finger, & Bahtia, 1997) and CreditRisk+ (Wilde, 1997) credit portfolio models but was not really essential. In fact, it was only introduced as an essential element to the Basel II framework (Basel Committee on Banking Supervision, 2005). In this field, a review study is made by Foglia (2009) to analyze and discuss the assessment methods of macrofinancial linkages between macroeconomic drivers of stress event and bank-specific measures of credit risk that aim to link prudential supervision to macroeconomy perspectives. He refers to macro stress testing experiences made in different central banks and supervisory authorities.
In the following and in order to adopt the model strategy that could be most applicable to the Tunisian banking system, we observe the different credit risk stress testing approaches applied by different countries to manage their financial stability and that have developed specific modeling expertise in this field. Kalirai and Scheicher (2002) perform a macro stress test for the Austrian banking system to help policymakers in prevailing financial stability. They present a linear regression to analyze the relation between loan loss provisions, which is considered in the study as an indicator of banks credit quality, and macroeconomic factors. Then, they examine if the simulation effect on LLP is beard by the Austrian banks capitalization. For this aim, they choose to define the adverse events by the historical scenarios and compare risks related to these scenarios on the risk bearing capacity of Austrian banks measured by the capital adequacy ratio. Virolainen (2004) employ Wilson's model for the Finnish corporate sector to analyze corporate credit risks conditional on current macroeconomic conditions and also apply the model to macro stress testing which is conducted by comparing the average result of a stressed scenario, where an artificial adverse macroeconomic development is introduced, with that of the average of a base scenario, where no adverse shock takes place. Estimated averages of the default rates for each sector corresponding to the stressed and base scenarios are obtained from simulating a large number of future default rates by applying a Monte Carlo method. Čihák (2004) proposes a number of extensions and modifications to the Czech FSAP (Financial Sector Assessment Program) to improve credit stress tests so as be suitable for the Czech National Bank and pertinent for use on corporate and household borrowers. He proposes to model bank by-bank increases in NPLs based on past data of NPLs and other macroeconomic variables and to improve statistical database on the financial situation in the real sector, both in the corporate sector and, in particular, in the household sector. He suggests also to include in the credit risk stress tests concentration risk in lending and sectoral risk. Sorge and Virolainen (2006) use the Wilson framework to estimate a macroeconomic rate and corporate indebtedness) and corporate sector default rates. For macro stress-testing purposes, they simulate GDP and short term interest rate stress scenarios on credit risk of an aggregated Finnish credit portfolio as prevailing in the Finnish recession of the 90's. They find that the impact of the interest rate shock is temporary, whereas the GDP shock is more persistent. Čihák (2007) design a practical excel file to simplify the stress testing application, including credit stress testing, for new users of different countries within the IMF-FSAP (Financial Sector Assessment Program) and to enable users to see directly the impact of different stress testing scenarios and assumptions on the results. Wong, Choi and Fong (2008) perform Macro stress-testing to assess the Hong Kong retail banks' vulnerability and risk exposures by using an empirical model with a system of equations comprising a multiple regression model explaining the default probability and a set of autoregressive models describing the macroeconomic environment in order to have a joint evolution of economic performance, the associated default rates and their error terms. Then, a Monte Carlo method is applied to estimate the distribution of possible credit losses conditional on an artificially introduced shock. Girault (2008) construct a three-staged approach for performing macro stress testing the Argentine banking system's credit risk. He estimates a dynamic panel data model to explain credit risk proxy with bank-specific and macroeconomic variables. Then, he models the macroeconomic drivers of bank loan loss provisions with a Vector Autoregression (VAR). In the third step, a stress testing model of credit risk loss is performed by a deterministic approach and stochastic approach with Monte Carlo simulation.
The results show that the Argentine financial system is adequately capitalized to absorb the prospective losses in a stress situation. However, Alfaro and Drehmann (2009) highlight the limits of stress testing models of underestimating the risks to the economy and they suggest three methods for sound stress testing practices; one way is to frame the results in confidence intervals; the second is to take account at most of judgments and of views across the organization; the third is a scenario design which requires supposing unusual assumptions and expecting the unexpected. Simons an Rolwes (2009) look for assessing which macroeconomic variables are related to the default behavior of Dutch firms through a macroeconomic-based model and to assess the default behavior by developing on the basis of Virolainen (2004) a framework for stress testing the credit exposure to macroeconomic shocks and precisely the effect in Dutch default behavior given two quarters of zero GDP growth. The default rate corresponding to the stress-test and base scenarios are obtained from simulating a large number of future default rates by applying a Monte Carlo method. They find that Dutch firms default rate has a convincing relationship with GDP growth and oil price and, to a lesser extent, the interest and exchange rate and that the applied stress-test scenario does not significantly influence the default rate. Huang, Zhou and Zhu (2009) propose a framework for measuring and stress testing the systemic risk of the banking sector, using vector auto regression (VAR) system and employing financial market variables to examine the dynamic linkages between the major US banks and the macroeconomy and to assess the resilience of the financial sector. They estimate the probability of default and the asset return correlation of a portfolio and introduce hypothetical shocks to simulate their future dynamic. They www.scholink.org/ojs/index.php/ijafs International Journal of Accounting and Finance Studies Vol. 1, No. 1, 2018 validate their model to measure and stress testing the systemic risk of the banking system and show its lack of resilience in perspective. Moretti, Stolz and Swinburne (2009)  Scenarios to the model to understand how the banking system in Turkey was affected by a baseline and an adverse scenario in two-year horizon.
On the basis of this review of literature, this paper comprises an empirical model that relates credit risk to a number of macroeconomic and microeconomic variables and a Monte Carlo simulation for estimating the impact of adverse macroeconomic conditions.

Panel Data Model
The natural approach to estimate our panel data model is with the static fixed-effects estimator, it constitutes a reasonable assumption since we are working with commercial banks in the financial system. The equation of the panel data model to be estimated is expressed as: Where , are N x 1 vectors, is the dependent variable for bank i in period t and is the bankspecific disturbance in period t, X is N x k matrix that contains bank-specific time varying variables (observed heterogeneity) and a constant, Z has time varying macro variables, common to all the banks.
β is k x 1 vector and represents bank specific and time invariant (fixed) effects (unobserved heterogeneity). In panel data, the observations are indexed through N x T dimension. N is the number of banks (panels) and T is the dimension of a time series, therefore we have t=1, 2…, T of each i=1, 2,…., N cross-section observations in the sample. The common method used to estimate the parameters of this model is applying the OLS (ordinary least squares) to the model in deviation from time means: However, an examination of the time pattern of the loan loss provision ratio leads to apply dynamic specification to model the dependent variable by including the lagged dependent variable as a regressor in the static fixed-effects model in order to account for the time persistence in the LLP structure. This dynamic fixed-effect specification or within estimator is given by: which would be estimated by applying OLS to the model expressed in deviations from time means.
However, this approach as above renders biased estimates: the within estimator is inconsistent for finite T and N→ ∞ (Nickell, 1981). The reason for this bias is the correlation between the transformed lagged dependent variable and the transformed current disturbance.
In order to remedy this latter limit, Anderson and Hsiao (1982) propose an instrumental-variable estimator (AH) which is consistent for T fixed and N→ ∞, this estimator is based on a differenced form of the original dynamic equation: which cancels out the fixed effects, that may be correlated with the exogenous variables. Anderson and Hsiao (1982) , which are expected to be uncorrelated with the differenced error term.
Although N-consistent, the AH estimator is not efficient since it does not use all the available moment conditions. Arellano and Bond (1991) propose a Generalized Method of Moments (GMM) estimator (AB), which is based on the first difference transformation of the static fixed effect model and the subsequent elimination of bank specific effects. This estimator poses the following model : where ∆ is the first difference operator. But, in equation 5 the lagged depended variable, ∆ −1 is by construction correlated with the error term, ∆ , imposing a bias in the estimation of the model.
However, AB which utilizes the estimated residuals in order to construct a consistent variancecovariance matrix of the moment conditions, may impose a downward (upward) bias in standard errors (t-statistics) due to its dependence on the estimated residuals. This may lead to unreliable asymptotic statistical inference (Bond, 2002;Bond & Windmeijer, 2002;Windmeijer, 2005), especially in data samples with relatively small cross section dimension. Therefore, we also compute the system GMM estimator, developed in Blundell and Bond (1998), who exploit further moment conditions. The System GMM estimator is however not free from problems; for example, Hayakawa (2005) shows that when the variances of the individual effects and of the disturbances are unequal the bias of this estimator is fairly large.

Stress Testing
(A) Simulation method In this paper, we stress test the losses for credit risk of the commercial banks. To this purpose, we use the toolkit developed in the previous section, then we suggest macroeconomic scenarios to perform a macroeconomic stress testing on the commercial banks' credit risk in Tunisia. It consists of assuming hypothetical changes of the macroeconomic risk factors in the aim of simulating each bank's credit loss in the extreme scenarios. We suppose the realization of a baseline and harmful macro scenarios. The scenario could be an historical macro occurrence, that is assumed to happen again, or a hypothetical macro realization.
We opt to consider two artificial macroeconomic scenarios, comprised of the following: Scenario 1: baseline scenario: expected trend by the monetary authorities (BCT).
Scenario 2: extreme but plausible adverse scenario with levels similar to those of the year 2011.
In these two scenarios, the perturbations of the selected model were assumed to follow a normal distribution of zero mean and variance estimated by the empirical variance of the residuals.
The idea is to illustrate the model sensitivity to two scenarios considering current conditions and incorporating stressed forward-looking considerations. To anticipate this reaction, a Monte Carlo simulation is used to generate a stochastic scenario based on a random sample from a standard normal distribution. The distribution thus constructed is considered as the baseline scenario. In a similar manner, a Monte Carlo Simulation is used to generate an adverse scenario.
The incorporation of Monte Carlo simulated values of disturbance terms with the assumptions of the evolution of the macroeconomic variables in case of each scenario and the estimates obtained from the model make it possible to have a large number of simulated values of the dependent variable, which allows to estimate its distribution in each scenario. In addition, we assume that all explanatory bankspecific variables in the forecasting horizon of the stress exercise have been fixed.

(B) Unexpected loss
We consider also estimating the banks' capital needs to cover tail credit losses under the distressed scenarios. It's computed as the difference between the estimated LLP in the stressed scenario, and LLP as of the baseline scenario; For this purpose, we use the simulated distributions of LLP for each bank and for each scenario, assuming in one hand the real GDP growth considered according to the scenario and in the other hand that all other bank-specific factors are held fixed since the last observation of the sample.
In this exercise, our main interest lies on the right tails of the simulated distribution in case of the adverse scenario. In fact, we compute the Value-at-Risk corresponding to a 99.9% confidence level of adverse scenario distribution, we subtract the ratio of the expected LLP as of the baseline scenario, in the aim to have the potential downside credit risk that would result from an adverse scenario produced by a harmful worsening of economy growth, with a 99.9% confidence level. Finally, the resulting losses are compared to the available capital because the bank needs to have enough capital to absorb the increase in the ratio of LLP that would result from the stress event Having examined how credit risk proxy for each bank of the sample will behave facing trend-based scenario or distressed scenario. We then use the model to forecast LLP ratio to estimate bank losses for credit risk during the first semester of 2019. Knowing that the bank needs to have enough capital to absorb the increase in the ratio of LLP that would result from the stress event, we quantify the capital needed to cover the unexpected losses for credit risk. For this aim, we compute the Value-at-Risk corresponding to a 99.9% confidence level of the distribution of banks ratio of LLP in the stress scenario, then we subtract expected value of LLP ratio as estimated in the baseline scenario, both forecasted for the first semester of 2019. The result is the unexpected losses that would result from an adverse scenario produced by the risk factor (real GDP growth), with a 99.9% confidence level.

The Data Set
The data is collected from financial statements of 10 Tunisian commercial banks ( complete series of the NPLs variable as the information is not available over the entire period. The loan loss provisions to total loans measure is one of the most commonly used measures in stress testing (Moretti et al., 2009). It should be noted that in the computation of this ratio we include on-balance loans and provisions only. Therefore, loans completely written-off and removed to off-balance accounts have not been included in the computation of the LLP ratio.
The empirical literature identifies two broad sets of drivers that explain NPLs: the macroeconomic and the bank-specific factors. Table 2 presents the bank specific variables and macroeconomic variables used in the econometric analysis and their correspondence to the specific hypothesis.   the tendency of GDP growth and LLP ratio evolution during the estimation period shows in Figure 1 that is evident how the global financial crisis (2008)

Panel Data Estimation
The data is analyzed using Stata 13 software. We start our empirical exercise by examining stationarity properties of loan loss provision ratio per bank applying Dicky Fuller unit root test. In fact, the stationarity status (the order of integration) of the variables helps to choose the appropriate model for estimating the coefficients.  As banks are not chosen randomly, the fixed effect is imposed in the estimations. Moreover, the specifications shown in the estimation methodology was applied after exploring the sensitivity of LLP to a combination of candidate macroeconomic and bank-level variables and after exploring them with various lag structures. The main criterion guiding model selection was the precision of the parameter estimates and the robustness of the results, reflecting the purpose of the exercise to simulate loan quality under alternative macroeconomic scenarios). In particular, the logit-transformed LLP which is expressed as log(LLP/(1−LLP)) ensures that the dependent variable spans over the interval [−∞; +∞] as opposed to between 0 and 1, and is distributed symmetrically. It also allows avoiding non-normality in the error term and accounts for nonlinearities in the sense that larger shocks to the explanatory variables may cause a large, nonlinear response in the transformed dependent variable (Wenzel et al., 2014). The explained variable Y it is computed by taking the first difference to the logit of the loan loss provision ratio in a bank and the explanatory variables that are categorized as macroeconomic and specific variables, described in the previous paragraph, were introduced one by one into the specifications (or models) presented in the estimation methodology, then, they were selected after exploring the relationships between Y it and the larger set of macroeconomic and microeconomic variables restricting the factors to those that were statistically more relevant to the panel specification, also yielding tighter error bands. Only the following variables presented a sufficient level of statistical significance : -GDP growth lagged by 4 periods, defined by difference of order 4 of (log(GDP) t -log(GDP) t-1 ), -the first difference to the ROA, defined by ((ROA) t -(ROA) t-1 ), -the first difference to the bank leverage ratio, defined by ((B_LR) t -(B_LR) t-1 ), -the first difference to the natural log of total assets of the commercial bank, defined by (log(B_S) tlog(B_S) t-1 ), In Table 5, we report the estimated coefficients and their p-values of the static fixed-effects estimator, the dynamic fixed-effect specification Arellano-Bond estimation and the Blundell and Bond estimator.
When treating LLP as endogenous for the panel variables, it appears that it is non-significant, that's why we don't consider a dynamic model (Table 4). ***, ** and * denote significance at 1%, 5% and 10%, respectively.
For estimating the variance of estimated parameters, we have considered robust estimators with respect to the hypothesis of homoscedasticity (robust method).
Consequently, on the basis of a comparison across estimation methods, we select the static fixed effects specification presented in column (1) of Table 5 as the preferred model. In fact, treating as an endogenous lagged dependent variable in columns (2), (3) and (4) indicate that estimates of the coefficients associated with −1 are not significant in each latter specification.  : is the unobserved individual effect. Ɛ i, : is an idiosyncratic error term.
The R 2 in Table 6 for static fixed effect specification is about 25.9% with three bank specific variables and one macroeconomic factor having significant effects on credit risk at the 1% and 5% significance level. As expected, the lagged GDP growth variable is negatively correlated with the first difference of logit transformation of LLP ratio in commercial banks and significant for up to four lags. Hence, the LLP ratio is negatively affected in the short-run by a slowdown in Tunisian economic growth, a result that indicates the relative dependence of the Tunisian banks' ability to repay their loans on the phases of the economic cycle. Our result is in line with the results of other macro-studies on credit risk and with the results of De Bock and Demyanets (2012) and Nkusu (2011) and conforms to our initial hypothesis.
Considering microeconomic determinants, Table 6 shows, in the first specification, that loan loss provision ratio in Tunisian commercial banks is sensitive to bank-specific determinants. As expected, the coefficient on return on assets is significantly negative in relation to the LLP of Tunisian banks.
These findings imply that the higher return on assets in a bank indicates a potentially lower credit risk, which is consistent with the "moral hazard hypothesis". Thus, a more profitable bank is engaged in more prudent lending and carefully originate its loans, implying a reduction in credit loss and hence a decrease in loan loss provisions ratio need to efficiently manage their resources when loans tend to be potentially impaired. This implies in a more profitable banking industry, banks are engaged in more prudent lending and carefully originate their loans, causing a reduction in NPLs. This result is consistent with the findings of Boudriga et al. (2010) and Ghosh (2015).
Proxied by the natural logarithm of total assets, bank size is significant but with unexpected negative sign. This suggests that greater size of commercial banks decreases credit risk. Our empirical evidence is not consistent with Chaibi and Ftiti (2015), which report a significantly positive relation between www.scholink.org/ojs/index.php/ijafs bank size and credit risk, but instead agrees with the findings of Salas and Saurina (2002); this result can be explained by the fact that size allows to benefit from the diversification opportunities.
On the other hand, the leverage ratio positively and significantly influences credit risk in commercial banks. This finding implies that the increase of leverage results in a higher ratio of loan loss provisions.
This result is corroborated by the literature, as similar findings were recorded in the studies of Louzis et al. (2012).
For the unobserved individual effect, the model yields the following results: Since the change of the variables may serve as warning indicators of future credit risk, the results have implications for decision makers at both macroeconomic and bank level. The results lead to recommend for the commercial banks to maintain optimal high credit standards to reduce credit loss while sustaining profits and maintaining them at a safety level, in fact, high profits will lead to more prudent lending. Efficient cost management constitutes a required passageway to reduce credit loss and improve the quality of banks' balance sheet. Moreover, results here provide that hypothesis of bigger size increase credit risk is rejected for the commercial banks in Tunisia.
In terms of regulation and policy implications, the estimation results indicate that structural reforms should be undertaken to improve economic health and to promote financial stability of banks. The significant role of specific bank factors in determining credit risk in commercial banks should incite regulatory authorities in Tunisia to encourage banks to manage less concentrated portfolios, to develop their activities and to gain market share through enhancing their professionalism, service quality and commitment of the teams, to maintain enough liquidity and to improve of effectiveness of their risk management systems, and in that way increasing the efficiency in credit risk analysis and debtors monitoring. On the other hand, analyzing profitability, bank size and indebtedness, supervisors could detect banks with potential for increase in credit risk.

Stress Testing
The exercises to assess stress testing credit risk are based on two macroeconomic scenarios, including a baseline that reflects the expected path of GDP growth by the Tunisian Central Bank and an adverse scenario considering stressed forward-looking.
The macroeconomic scenarios are used to assess the bank's vulnerability to exceptional macroeconomic scenarios. Indeed, the stress test consists of the comparison between the baseline and adverse scenario for the credit loss, which could highlight macroeconomic shocks leverage on the credit risk especially that the revolution of 2011 in Tunisia has shown fragility of the banking system in face of economic crisis.
The evolution of GDP growth under the two scenarios considered was determined as follows: • Baseline scenario. This scenario is taken as reference and considers the expected evolution of economic activity as forecasted by the Tunisian Central Bank. Under this scenario, the GDP growth is projected to be 2.3% (BCT, 2017) in 2017.
• Adverse scenario. An artificial macroeconomic scenario is considered assuming a worsening of the GDP growth as a fall in Tunisia's real GDP by 2% in the first semester of 2017, comparable to the real GDP fall at the dawn of the revolution of 2011.

Scenario Analysis
We use in this section the results found in the estimated results above to stress test each bank's credit risk based on the scenarios. We first evaluate the model developed in methodology section (equation 6) with the bank individual effect.
: is the unobserved individual effect.
Ɛ i, : is the error term.
The simulations were analyzed for each bank of the sample, we estimate a credit loss distribution by performing Monte Carlo from a normal distribution. To that purpose, we take 10,000 random draws from the error terms involved in the model equation and which are supposed following normal distribution with zero mean and variance estimated by the model. These are then used to obtain LLP distribution for each bank and for each scenario, using the model considered above and supposing that bank specific factors remain unchanged relatively to the status in the first semester of 2016. It's www.scholink.org/ojs/index.php/ijafs noteworthy that we consider macro scenarios for the following semester (T=2017:1) and examine their consequences from that semester until two years ahead. The dependent factor in macroeconomic scenario S for bank i is then computed as:  � is the estimated unobserved individual effect for each bank of the sample.
,2019:1 is the siulated error term for each bank. For each bank, histograms derived from the baseline and adverse scenarios were produced. The graphic study of the credit loss distribution for the adverse scenario and for the baseline scenario shows following observations depending on the bank: ATB: Figure 3 shows that introducing a GDP shock shifts the credit loss distribution in this bank to the right, indicating that the mean credit risk under the adverse scenario increases relative to the baseline scenario.

Figure 5. Baseline and Adverse Scenarios under Shock to Tunisian Real GDP Growth in BT
BNA: Figure 6 shows, as in BNA chart, that the distribution of losses after introducing a GDP shock shifts to the right compared to the baseline scenario, suggesting that a GDP shock has resulted in an increase of the expected credit losses proportion.  STB: Under the adverse scenario applied to fundamental macroeconomic variable real GDP growth, the histogram shows a characteristic shift to the right of the stressed distribution (Figure 7) showing an increase in the frequency of the higher credit loss percentages comparatively to the lower ones.

Figure 8. Baseline and Adverse Scenarios under Shock to Tunisian Real GDP Growth in Amen
Bank BH: The results of the two scenarios depicted in Figure 9 show that the adverse scenario generated by GDP shock produces a shift to the right of the loss distribution.  BIAT: The simulated frequency distributions in the two scenarios considered are depicted in Figure 10.

Credit loss distribution under baseline and adverse scenarios in Amen Bank
It indicates that introducing the GDP shock leads to a shift to the right of the frequency distribution.

Figure 10. Baseline and Adverse Scenarios under Shocks to Tunisian Real GDP Growth in BIAT
UBCI: Figure 11 shows that introducing a GDP shock shifts the credit loss distribution in this bank to the right, indicating that the mean credit risk under the adverse scenario increases relative to the baseline scenario.  UIB: Frequency distribution of the baseline and stressed scenarios are simulated in Figure 12. It shows that introducing a GDP shock leads to a shift to the right of the stressed distribution relative to the baseline scenario, showing a small increase in the frequency of the higher credit loss percentages comparatively to the lower ones.

Figure 12. Baseline and Adverse Scenarios under Shock to Tunisian Real GDP Growth in UIB
We could note, for all scenarios, that the histograms exhibit a characteristic shift to the right of the stressed distribution, indicating that the average probability of default under the adverse scenario increases relative to the baseline scenario.
As a summary, the variation intensity of expected default probability is notably recorded in all banks.
So, we conclude that all banks are almost affected similarly, when facing the adverse scenario. It could be explained by the similarity between banks in loan distribution, in risk management.

Unexpected Loss
The bank unexpected loss results for the ten banks in the system are summarized in ones and especially for STB which presents the highest level of unexpected loss and could then be considered a problem bank in the system and may require attention of the prudential supervisor.
Among the remaining seven private banks, there is also difference between them in term of unexpected loss, in fact, for Amen Bank, the unexpected loss is substantially higher, exceeding all other private banks and indicating that it's the most vulnerable among them. While, the most resilient bank is the smallest bank in the sample (UBCI); Under the Stress scenario, the magnitude of the unexpected loss of the latter bank is around 1.7% of its total gross loans.

Conclusion
This paper attempts to conceive a framework for macro stress-testing on credit risk in commercial banks in Tunisia. To this aim, a two-stage approach is used to investigate the impact of a macroeconomic distressed scenario on the credit risk of 10 commercial banks in Tunisia. We proceed by applying a static fixed effect method to examine loan loss provisions ratios of the banks sample, as proxy of credit risk loss, in terms of two types of determinants; specific bank indicators and macroeconomic variables. Return on assets (ROA), return on equity (ROE), net loans to total asset ratio (B_LR), bank revenue (B_R), capital to asset ratio (B_CAR), total loan to total deposit ratio (B_LD) and the bank size are specific indicators depicted in each bank. While, real GDP, oil price, real effective exchange rate (REER), inflation rate (INF), total loans granted to the economy (D) and broad money supply (M2) are macroeconomic variables.
The stress-testing exercises of this paper focus on assessing stress impact of a real GDP growth sharp decrease on credit risk level of a sample of commercial banks in Tunisia and their resilience for that kind of shock. Therefore, we simulate the distribution of each bank loss rate for credit risk by the vulnerability to macroeconomic instability.
The outcomes of the static fixed effect model analysis indicate a significant effect of the changes in bank-specific variables and macroeconomic variables on the credit risk proxy. More precisely, we find that the four-lagged real GDP growth rate has a strong negative effect on the level of LLP, as the only macroeconomic factor. Moreover, return on assets and bank size have an additional negative effect on LLP, while net loans to total assets ratio possesses positive explanatory power in the model. These results confirm our expectations, excepting for the bank size where bigger size doesn't imply credit risk increase in the case of Tunisian commercial banks and hence, a Tunisian policy concern to an eventual excessive risk taking due to bank big size is not necessary. These risk factors should also be monitored by banks' decision makers level in the aim of optimizing credit standards level while sustaining profits at a safety level.
In regards to stress-testing, we note that each bank is affected differently, when facing the adverse scenario. This is due to the difference between banks in their relative specificities. In fact, UBCI which has, on average, better specific indicators (higher return on assets and lower net loans to total assets ratio) is more resistant to GDP shock. Also, BIAT which has the biggest size and a relatively good ROA is resistant to GDP shock. The most vulnerable bank under the GDP shock is STB, it has a relatively low return on assets and a high net loans to total assets ratio.
the results from all the scenario analyses indicate that bank capital is sufficient to cover unexpected losses for credit risk in the stress event applied. The level of LLP ratio increases from a range between 4.51% to 37.99% under baseline conditions to a range from 6.18% to 46.06% under adverse conditions.
Hence, stress test yields unexpected losses that range between 1.67% and 8.07% of loans, below available bank capital, meaning that the credit risk loss would be covered and that commercial banks would be resilient to the macroeconomic shock. But, the Tunisian banking supervisor should carefully consider whether this is enough to weather a prolonged crisis period.
Otherwise, it's noteworthy that the stress impact is dispersed across banks showing, in term of unexpected loss, more harmful effect in two public banks (STB and BNA) and in Amen Bank as a private bank. So, this kind of banks with problems requires special attention from the supervisory authority.
Financial regulatory authorities should consider probable impact of real GDP growth on the stability of the banking sector to deal with likely adverse macroeconomic developments. This would enable assessment of the ability of the commercial banks to resist unexpected macroeconomic risks, in order to introduce monetary policies and financial stability policies. It would also enable assessment of probable impact on these financial institutions when they are faced with macroeconomic instability. The main contribution of this paper to the literature is that the model and the methodology have not been analyzed before for Tunisia and are applied at a bank level. Also, a particular combination of bank balance sheet data and macroeconomic factors are chosen to model the system in function of loan-loss provisions, the credit risk proxy in our model. It would be appropriate to allow each bank, drawing on its own stress indicator, to conduct stress testing on themselves and to have independence to decide on the simulation assumptions, with the aim of preparing banks well to assess their vulnerabilities facing major macroeconomic challenges.
Another interest of this study is the design of a macroprudential tool consisting of stress testing the financial system of an emerging economy such as "Tunisia" in order to guide Tunisian supervisory institutions to timely and efficient supervisory measures and to contribute to the financial sector's stability. This approach has an enormous relevance in banking supervision and monitoring to give useful and well-timed information.
Otherwise, the proposed approach is also useful, in an aggregate form, for monitoring and assessing banking-sector wide credit risk via macroeconomic indicators under the two macroeconomic scenarios that are analyzed. And also, useful, in an individual form, for identifying bank problems and developing individual adjustment programs for the least resilient banks to reduce their credit risk under a suitable supervisory mechanism.
In this direction, a number of recommendations are outlined that would be of benefit to policy makers : -Well-capitalised banking system, some banks are less vulnerable to slowdown in economy that could result in higher credit risk, capital buffers should then be encouraged.
-Encourage diversified asset-bases for banks, authorities should promote and incentivize prudent risktaking in lending to the real economy.
-The estimation is expected to give more insight on the credit risk management of commercial banks.
The banks of the sample differ in terms of profitability, activity, capitalization, leverage, liquidity and size. Therefore, policy makers should encourage banks to focus on their managerial performance.
-The change of the variables may serve as warning indicators of future loan losses, then the decision makers should take account of the nature of estimated variables at both macroeconomic and bank level.
In fact, the key issue is using the estimated results to monitoring credit risk and planning preventive actions before causing a harmful damage to the bank and without delimiting, in the same time, the role of banks as financial intermediaries.
Further studies should extend this approach with the aim of adjusting bank financial soundness indicators to macroeconomic risks within the macroprudential policy and to design a dynamic stress test allowing banking sector and policy makers to assess the response functions of the bank specific indicators to macroeconomic shocks. The direction of future research should also focus on highlighting the bank level granularity in any macroeconomic credit risk model that contains only aggregate factors of the banking system to ensure the practical usefulness of such approach on an individual bank.