Contents


   Indian Journal of Finance and Banking; Vol. 2, No. 1; 2018 

                                                          ISSN 2574-6081  E-ISSN 2574-609X 

 Published by Centre for Research on Islamic Banking & Finance and Business 

 

 

34 
 

Migration Analysis of Credit Risk in Tunisian Banking Sector 
 

Amel Ben Youssef1 

 

1 Faculty of Economic sciencesand Management of Tunisia, FSEGT, El Manar, Tunis, Tunisia 

Correspondence: Amel Ben Youssef, Faculty of Economic Sciences and Management of Tunisia, FSEGT, 

B.P.248 El Manar II 2092 Tunis, Tunisia. Tel: 216-98-544-603. E-mail: amoulaby@yahoo.fr 

 

Received: January 20, 2018          Accepted: January 20, 2018         Online Published: March 9, 2018  

 

 

Abstract 

In this paper, credit migration matrices are built to measuretransition probabilitiesat Tunisian credit institutions, 

allowing a comparison of credit risk quality shiftsfor public banks, private banks and leasing companies. We 

proposeto apply estimating Markov transition matrices using proportions data in order to be adapted to the 

scarcity of individual dataonloan quality transitions. We employ annual classification of assets issued in 

theregistration documents and annual financial reports during 2003-2014 period.It’s found from the analysis that 

the risk grade 2 has the greater tendancy to be downgraded than to be upgraded in public banks and in leasing 

companies.For the other risk grade 3, the upgradation in the category is higher than the downgradation in all 

cases. The resultsindicate that the public banks are the riskiest credit institution in Tunisia and there is a lack of 

rigor in loan classification inpublic and private banks. The findings are useful and critical for supervisory 

purposes and foroptimizing bank credit risk management. 

 

Keywords: Transition Matrices, Credit Risk,Banking Sector 

1. Introduction 

In light of the uncertainty surrounding the credit quality in Tunisian banking sector (IMF, 2012), supervision 

authorities in this country set awork plan on implementing and strengthening of the bank supervision in Tunisia 

to become risk-based in compliance with international best practices (Basel II and III) (BCT, 2014). 

According toBasel II and III guidelines (BCBS, 2004 and BCBS, 2010),banks are appealed to estimate on 

themselves their probability of defaultthrough IRB approach, as long as this system is in compliance with 

minimum quality exigeancesto have validation and approval of supervisors to apply this approach. 

Statistical theory presents different methods for conceiving and estimating internal rating models.  

For example, the transition or migration matrix represents an aspect of theses systems; Credit migration or 

transition matrices characterize past changes in credit quality of obligors (Jafry and Schuermann, 2004) 

The probability of default could be deducted after establishing a transition matrix which is precisely a probability 

table (Nicula, 2013) reflecting the transitions between different profiles of debt arrears observed in a credit 

portfolio between two consecutive periods. 

the added value of the transition matrix is to clearly identify the likelihood of damage and descent to the 

radiation, once we know that the debt is already affected by arrears.  

the transition matrix is useful as a basic observation to justify provisioning in accordance with International 

Accounting Standard 39 (IAS 39), that requires that we reduce the balance sheet value of a debt to the expected 

net present value of likely residual flows as long as there areobjective signs of an emerging risk.  

transitions can also be used to plan and prioritize the management of arrears and recovery activities. by 

identifying the most severe deterioration of points, the institution has interest to focus on these critical phases in 



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the evolution of borrowers' behavior to avoid an ultimate radiation. 

Moreover, Basel accord suggested that probability of default shouldn’t be measured in isolation of the economy 

dynamism, but should be in accordance with its change through time and the variability of economic state. Then, 

estimating the transition matrix between different credit classes in a bank could improve the accuracy of 

probability of default. 

In this paper, we try to assess credit risk at a period from 2003 to 2014 on the basis of transition matrice. 

Our model for estimating transition matrices probabilities is based on proportions data in the sense of Jones 

(2005) 

We apply the methodology to individual banks havingsufficient data, and also on leasing companies with 

appropriate time series data. Then, we compare the behavior of credit quality between public banks, private 

banks and leasing companies. The samples chosen suit the purposes of this study since they represent a wide 

range of loans in the banking sector and since the credit risk classication rules are uniform between them. 

The motivation for comparing these three credit institutions lies in their different performance.The key research 

question explored is whether there are differences in the nature of credit risk quality shifts for transition matrices 

between three credit institutions,public and private banks and leasing companies, through estimatingMarkov 

transition matrices using proportions data.We find that public banks are the riskiest financial institutions studied 

while the leasing companies are the least risky. We also find that the estimated transition matrices for public and 

private banks have an asymmetric and non-monotonic profile, and have little concentration on the diagonals, 

which shows a lack of rigor in loan classification in these two credit institutions. 

The remainder of our paper proceeds as follows. In the next section (2), we review the relevant literature. Section 

3 debate the adopted methodology in order to estimate transition matrices. Section 4 presents the dataset used in 

the study. Section 5 discuss the results obtained. Finally, section 6 concludes the paper 

2. Literature Study  

Migration analysis is one of fundamental techniques of the CreditMetrics methodology. In 1987, J.P.Morgan 

developed transition matrices to study changes in the credit quality through time (J.P. Morgan & Co, 1997). 

Further, analysingand reporting default rates and grade migrationhistories of borrowers is required by Basel II 

(BCBS, 2003). 

Nicula (2013) outlines the relevance of building migration/transition matrix in credit risk modeling to assess 

factors affecting moving of a loan belonging to a credit risk grade to another grade. 

Lando and Skodeberg (2002) show the importance of estimating transition data based on the full story of rating 

transitions. 

Ivičić and Cerovac (2009)estimate credit transition matrice of non-financial businesses entities. They find rating 

stability in the migration matrices estimated, especially for the lowest rated companies, but not for the companies 

belonging to mid-section of the rating structure because they are more exposed to a risk profile change with a 

higher probability of upgrading than downgrading. It appears also from the results that Probability of defaults are 

not sensitive to economic activity and that probabilities of transition between different risks categories depend on 

the economic growth. 

Bajaj (2010) proposes tostudy the credit quality through the migration and default rate conditioned on the ratings 

of debt issuers and on macroeconomic factors. The results provide that the sabilityretention rate in a rating 

gradeand the level of default rate depend on the debt issuer quality, also that default probilityand the rating 

migration are cyclical in nature. 

Jones (2005)emphasizesthe use of proportions data methodology to estimate transition matrices for the cases 

where individual Transitions are not available, just informations about aggregate observation on risk category 



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state. He demonstrates significance of differences in the transition matrices between different states of the 

economic cycle.  

Grzybowska et al.(2012) compare influence of various migration matrices models on risk estimation. they advise 

to adopt statistical longitudinal models (GLMM) because they consider economic factors and thus are more 

appropriate for changing periods as crisis. 

3. The Model 

In order to introduce definition of credit migration matrices and their estimation, let consider S the transition 

space; S=𝑠𝑖 ,…,𝑠𝑘represent credit classes as provided for in circulars related to banks and issued by the Central 

Bank of Tunisia.   

Wherei,j =1,..,k are the indices of all these credit states with i=1 denotes the best credit quality andi = 4 denotes 

default. 

Let this credit state process defined asa Markov chain processover fixed time 

points S𝑡=1 ,  S𝑡=2 ,… ,  S𝑡=𝑚 . LetP(s,t) denote the k × k transition probability matrix that presents this credit state 

process at any time interval; Then, for two states i and j,P(s,t)=𝑝𝑖𝑗  𝑠, 𝑡 = 𝑃(𝑠𝑗  𝑡 \𝑠𝑖 𝑡 − 1 ), that is the 

probability of being in credit state j at time t, conditional on being in credit state i at time t-1. 

So, the migration probability matrix to be estimated is as following: 

 

P= 𝑝𝑖𝑗   

p11 p12 p13 p14

p21 p22 p23 p24

p31 p32 p33 p34

p41 p42 p43 p44

  

 

Where pij≥0 for alli,j, 𝑝𝑖𝑗
𝑘
𝑗=1  =1for alli andk=4  

The default is assumed to be anan absorbing state which means that assets classified 4 are lost.Then, the final 

row of the transition matrix p41 p42 p43 p44 consists of zero for the first three entries and of one for the 

entry on the diagonal. 

The most used method to estimate migration matrices is the cohort method (Perilioglu and Tuysuz, 2015; 

Schechtman, 2013); If𝑛𝑖𝑗  is the number of borrowers started in classification i at t–1 and ended up in 

classification j at t. The estimated transition probability of migrating from i to j isthe migrationfrequency of the 

proportion 𝑛𝑖𝑗 compared to the proportion ofagents 𝑁𝑖that was i in t-1. Then the estimation is as follows: 

𝑝𝑖𝑗  =
𝑛𝑖𝑗

 𝑁𝑖
 

In order toovercome the shortage of data on individual transition matrice of different economic agents in Tunisia 

and in view of hiding the true financial situation by borrowers, we employ a transition matrices estimation from 

proportions data as proposed by Jones (2005). 

Such methodology requiring aggregate data is attractive for a country like Tunisia which is pursuing a policy of 

strengthening banking sector supervision but don’t provide complete database on credit risk classification  of 

debtors. 

Jones (2005) suppose that instead of observing credit quality states sequence for each unit of observation, we 

observe the aggregate data for the proportion in each state ; let consider𝑦𝑗  𝑡 and 𝑦𝑖 𝑡 − 1 the proportions of 

observations with credit quality j and i respectively. We can write a stochastic recursion of the form: 

 

𝑦𝑗  𝑡 =  𝑦𝑖 𝑡 − 1 𝑝𝑖𝑗 + 𝜇𝑗 (𝑡)
𝑖

 

The matrix form of this equation is as following: 

y= 𝑋𝑝 +  𝜇 

where 

𝑦 =  𝑦1 𝑦2 ⋯ 𝑦𝑅−1 ′ 

𝑦 =  𝑦1 1 ,𝑦1 2 ,… , 𝑦1 𝑇 𝑦2 1 ,𝑦2 2 ,… , 𝑦2 𝑇 ⋯ 𝑦𝑅−1 1 , 𝑦𝑅−1 2 , … , 𝑦𝑅−1 𝑇  ′ 

 

𝑋𝑗 =  

𝑦1(0) 𝑦2(0) ⋯ 𝑦𝑅(0)
𝑦1(1) 𝑦2(1) ⋯ 𝑦𝑅(1)

⋮ ⋮ ⋱ ⋮
𝑦1(𝑇 − 1) 𝑦2(𝑇 − 1) ⋯ 𝑦𝑅(𝑇 − 1)

     for j=1,2,…,R-1 

 



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So 

 

𝑋 =  

𝑋1 0 ⋯ 0
0 𝑋2 ⋯ 0
⋮ ⋮ ⋱ ⋮
0 0 ⋯ 𝑋𝑅−1

  

And  

 
𝑝 =  𝑝1 𝑝2 ⋯ 𝑝𝑅−1 ′ 

𝑝 =  𝑝11 ,𝑝21 ,… , 𝑝𝑅1 𝑝12 ,𝑝22 ,… , 𝑝𝑅2 ⋯ 𝑝1,𝑅−1 ,𝑝2,𝑅−1 ,… , 𝑝𝑅,𝑅−1 ′ 

 

𝜇 =  𝜇1 𝜇2 ⋯ 𝜇𝑅−1 ′ 

𝜇 =  𝜇1 1 , 𝜇1 2 ,… ,𝜇1 𝑇 𝜇2 1 ,𝜇2 2 , … , 𝜇2 𝑇 ⋯ 𝜇𝑅−1 1 ,𝜇𝑅−1 2 ,… , 𝜇𝑅−1 𝑇  ′ 

 

Then, we review the constrained least-squares estimator of the transition probability matrix P from proportions 

data, minimized by quadratic forms of the type: 

Minimize𝑝𝑢
′𝑢 = (𝑦 − 𝑋𝑝)′(𝑦 − 𝑋𝑝) 

Subject to 𝑝𝑖𝑗 ≤ 1𝑅−1
𝑗=1  

and  𝑝𝑅𝑗 = 0𝑅−1
𝑗=1  

with𝑝𝑖𝑗 ≥ 0 

 

4. Data 

The database used in this study is based on data drawn from publishdregistration documents and annual financial 

reports, available on the website of the Financial Market Council in Tunisia,the data cover the main commercial 

banks and 7 leasing companies in Tunsia.It consists of time series of credit risk classifications of loans at 

eightmainTunisian banks (BH, STB, BNA, BIAT, BT, Attijari bank, ATB and UIB)and at 7 leasing companies 

(ATL, AIL, El Wifack, Hannibal Lease, Attijari leasing, CIL and TL), the period of 12 years from 2003 until 

2014 has been taken into consideration.  

We test the model under different circumstances: by following both public and private banks and also another 

banking sector activity which is Lease. 

The data exclude banks that didn’t publish the breakdown of their loans per credit risk class such as Amen Bank 

and UBCIand newly created commercial banks because they don’t have sufficiently longtime seriesof 

observations to use Markov Transition Matrices with Proportions Data. 

The Risk classes are defined by Tunisian central bank circular N°91-24 of Decemer 17th, 1991as follows: 

  Class 0: current assets, are considered as current assets, assets whose realization or full recovery in time seems 

assured. 

  Class 1: assets requiring special monitoring, all assets the realization or full recovery in time is still guaranteed 

are included in Class 1. These assets are held on companies that sector is in difficulty or that the financial 

situation is fragile 

  Class 2: uncertain assets, including all assets the realization or full recovery in time is doubtful and loans for 

which payment delays are greater than 90 days and lower than 180 days.It also includes assets unresolved within 

90 days without exceeding 180 days. 

  Class 3: assets source of Concern, it considers all assets whose realization or recovery is threatened and loans t, 

for which payment delays are greater than 180 days and lower than 360 days. It also includes other assets 

unresolved within 180 days without exceeding 360 days. 

  Class 4: impaired assets, it includes in this class loans for which payment delays are greater than 360 days, the 

assets remained outstanding for a period exceeding 360 days and other assets that must be charged-off. 

The class 4 is assumed to be the default or the absorbing state or the non reversible state (it means if a firm reach 

this state can never return to another credit rating (Jafry and Schuermann, 2004)) 

Loans amounnts per credit risk class are converted into proportions in order to be utilized by the model, in such a 



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way that for each year of the study period, four categories of loans or leases quality are expressed as percentage of total loans or leases. 

The credit quality grades we follow in the study consist in four risk grades:  

- Risk grade 1: proportion of performing loans (total of class 0 and class 1) in the total bank claims, 

- Risk grade 2: proportion of non performing loans of the class 2 in the total bank claims, 

- Risk grade 3: proportion of non performing loans of the class 3 in the total bank claims, 

- Risk grade 4: proportion of non performing loans of the class 4 (assimilated to default state) in the total bank 

claims. 

 Descriptive Analysis 

The descriptive statistics for the credit risk classification of the sample of public and private banks and leasing 

companies considered in this paper are reported on table 1 to table 3. 

Table 1. Categories of credit quality in public banks 

  Risk grade 1 Risk grade 2    Risk grade 3 Risk grade 4 

Mean 0,77504845 0,02154105 0,01773665 0,18567385 

Median 0,79710968 0,01623766 0,01372204 0,16949049 

Std. Dev. 0,09077902 0,01729916 0,01180698 0,07510388 

Minimum 0,58889169 0,01155029 0,00795359 0,09471567 

Maximum 0,87865124 0,07202604 0,05150766 0,37204346 

Sum 9,30058136 0,25849265 0,21283983 2,22808616 

observations 12 12 12 12 

 

Table 2. Categories of credit quality in private banks 

 Risk grade 1 Risk grade 2 Risk grade 3 Risk grade 4 

Mean 0,86410871 0,00927953 0,00866097 0,11795079 

Median 0,86783771 0,0087307 0,00784206 0,11621278 

Std. Dev. 0,04458592 0,00442595 0,00391218 0,03862144 

Minimum 0,79258628 0,00261143 0,00322325 0,06616856 

Maximum 0,91796964 0,01708296 0,01548926 0,17859364 

Sum 10,3693046 0,11135434 0,10393162 1,41540949 

observations 12 12 12 12 

 

Table 3. Categories of credit quality in leasing companies 

  Risk grade 1 Risk grade 2 Risk grade 3 Risk grade 4 

Mean 0,86995252 0,01256229 0,01038094 0,10710425 

Median 0,89918248 0,0111145 0,00769068 0,08514725 

Std. Dev. 0,05570782 0,00591622 0,00639617 0,04674944 

Minimum 0,78414331 0,00561773 0,00328578 0,0539073 

Maximum 0,92249812 0,02570038 0,02025412 0,18648104 

Sum 10,4394303 0,15074743 0,12457133 1,28525096 

observations 12 12 12 12 

 

The descriptive statistic of the category 1 of credit quality shows that the mean of performing loans proportion 



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39 

held by the private baks and leasing are at the same level of 86%, while it’s less important in public banks.For 

the second category and the third category, their average is very low in the three samples, but remain higher at 

public banks. The fourth and the riskiest category, the proportion mean reach 18% in public banks versus 11% 

and 10% in private and leasing companies respectively. 

Moreover, the descriptive statistic of the credit risk categories demonstrates that standard deviation is very low in 

all cases and the highest ones are registered in public banks.  

These results show that public banks are riskier than private and leasing companies in spite of the state support.  

The selected time series are plotted in figures 1 to 3.propotion data of four credit quality grades for the period 

2003-2014. If we follow the evolution within time of these four categories for the three chosen groups, we 

remark that: 

- For the public banks,a graphic including the evolutionary curves of the four categories of credit quality 

can be analyzed in a time slicing (figure 1). It seems possible to identify three main phases for category 

4 of credit risk: between 2003 and 2004, propotion of non perfoeming loans in class4 was considerably 

increased. Between 2004 and 2011, there was a decrease of this proportion in the main public banks. 

And finally between 2011 and 2014, the trend was changing another time to a slight increase. While the 

performing loans proportions (category 1) follow the opposite way of the default (category 4) but there 

is in a final way an increase of category 1 in 2014 compared to2003,    

- For the private banks, figure 2 shows a relatively stable evolution of different credit risk categories 

within the period 2003-2014. 

- For the leasing activity, we can note from figure 3 that there was aa slight increase of category 4 of 

credit quality between 2004 and 2005, then, it was decreasing until 2014. While, the plot of category 1 

was having the opposite trend compared to that of category 4 

It should be noted that the proportion of category 2 and 3 were very low and approximately equal in all cases 

studied, also their respective evolution was stable all over the period of study. 

 

Figure 1. Classification of assets for the public banks (2003-2014) 

5. Results 

To evaluate the credit risk and their changes,we apply the proposed methodology to the time series of three 

public banks, 5 private banks and 7 leasing companies from 2003 to 2014. 

The first step in applying the methodology is to standardize the time series into proportions data. 

Second, we use quadratic programming to estimate the transition matrice. Scilabsoftware (version 5.5.2) was 

used to perform the analysis for the current study. It offers two commands to solve such system (qpsolve and qld). 

Only using command qpsolve in conceiving the algorithm of our methodology onscillaballow us to find 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Public banks

risk grade1 risk grade2 risk grade3 risk grade4



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solutions. 

Then, transition matrices are estimated for the credit quality in public banks, private banks and leasing 

companies.Finally, the obtained matrices are compared  

We expect that transition probabilities are more important in the sense of downgrading than upwarding and that 

the migration probability changes with the change of the credit institution activity. Credit and leases in private 

banks and leasing companies are not expected to have high risk to default, contrarily to public banks. 

5.1Transition Matrices 

Table 4 presents the results of the estimated Markov transition matrix using proportions data for the public banks. 

It illustrates the general pattern of transition matrice in this study. Results indicate that: 

• A high graded credit has greater tendency to bedowngraded than to be upgraded. It can be viewed on the 

transition matrix that the proportion of credits classified in category 2 have 95% chance to migrate to a lower 

category and have only 3% chance to migrate to a higher grade. 

• The highest graded credit can only be downgraded with a probability of 0,4% or remain unchanged at the same 

category 1 

• For the category 3, downgrade is 0 and upgrades are 94%. 

• The transition matrix shows less probability on the diagonal and more probability on the extreme columns of 

category 1 and category 2. We can deduce that there is a strong mobility of the transition matrix, especially when 

the credit is classified in category 2 or 3.  

• It’s also interesting to note that in right low corner of table 4, probabilities for transitions between 

classifications are low.  

• we provide evidence on the asymmetry of the migration matrix, in fact probabilities of degradation of credit 

category is higher than probabilities of upgrading. 

• the migration probabilities are not dominant on the diagonal, this pattern can be explained by the fact that there 

is a low probability to remain in the same category for class 2 and 3. 

• Credit classified at category 2 have an important probability to finish with default (50,38%), while category 1 

and category 3 have a zero probability to migrate to default state 

 

  Risk Grade1 Risk Grade2 Risk Grade3 Risk Grade4 

Risk Grade1 0,9963 0,0037 0 0 

Risk Grade2 0,0304 0,0172 0,4486 0,5038 

Risk Grade3 0,4668 0,4788 0,0544 0 

Risk Grade4 0 0 0 1 

 

The estimates of the transition matrix using proportions data for the private banks are shown in table 5. Results 

reveal that: 

• Once a borrower is in the category 3, there is a high probability (68%) that it will migrate to category 2, while 

there is only 32% of chance that it will stay in its same grading. 

• The probability to stay in category 1 is 99,7%, while the creditrisk grading in the other states move around 

more. For credit classified in category 2, there is a zero probability that it remains in the same category, while it’s 

more likelely to be upgraded to category 1 with 77%and to be downgrading with 23% of chance. 

• Transition of credit risk grade to the default state is zero for all the categories 1, 2 and 3 

•The estimated transition matriceusing proportion data exhibit asymmetrical migration shape: the probabilities of 

the upgrades are higher than probabilities of downgrades. 

• In general, credit quality transition matrices show high migration probabilities on the diagonal and then it’s the 

probability next to the diagonal (Banjia 2002). However, this pattern is not noted in our estimated transition 

matrix for the private banks credit quality. It follows that credit in private banks are most likely migrated to 



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another grade and more the time to a higher grade. This can be explained by a phenomenon of not classifying 

someloans in the adequategrade due to a wrong assessment of the companies holding the doubtful receivables. 

 

  Risk Grade1 Risk Grade2 Risk Grade3 Risk Grade4 

Risk Grade1 0,9976      0,001 0,0013 0,0001 

Risk Grade2 0,7737      0 0,2263        0 

Risk Grade3 0      0,6818 0,3182        0 

Risk Grade4 0      0        0        1 

 

Table 6 displays the estimates of the transition matrix for the sample of leasing companies, the results unveil: 

• No credit risk grade migratesto default state in the period of study. 

• Lease credits classified in category 1get 99,7% to keep their score or can migrate into category 2 with a 

transition probability equal to 0,3%. 

• the category 2 of credit risk can fall to category 2 in 50% of cases or stay at the same grade in the other 50% of 

cases. 

• All lease credit of category 3 see their classification upgraded to category 1. 

• Thus, the table 6 indicate that the transition matrix exhibits an asymmetric pattern and the upgradation in the 

grading is higher than the downgradation 

 

  Risk Grade1 Risk Grade2 Risk Grade3 Risk Grade4 

Risk Grade1 0,9973 0,0027 0 0 

Risk Grade2 0 0,4979 0,5021 0 

Risk Grade3 1 0 0 0 

Risk Grade4 0 0 0 1 

 

5.2 Comparison of Migration Matrices 

In order to compare between Tunisian credit institutions at the level of credit risk in which they operate, we 

compare in the rest of this paper estimated transition matrices of three groups of: public banks, private banks and 

leasing companies. 

Among the three groups analysed, the estimated migration matrix for public banks displayhigher transition 

probability fromrisk-grade 2 to the default state than private banks and leasing companies. 

A reason for this may be that these banks have been operating in range of credit risk related to economic sectors 

in difficulty and mainly funded by public banks (agriculture primarily financed by BNA; Tourism sector funded 

in part by STB; Estate sector principally financed by BH)   

Leasing companies migration matrix presents the highest transition probabilities from risk-grade 2 To risk-grade 

3, whereas private banks display the lowest one. 

In the other hand, the three groups of financial institutions experience close transitionbehaviour of credit risk 

when starting from risk-grade 1 (performing loans)and migrating to grades of NPL. While, they present different 

risk profile when it’s about non performing loans starting from grade 2 or 3 and migrating to other classes. 

Besides, leasing companies display a more serious degradation of risk-grade 2 to risk grade 3 than the public and 

the private banks. 



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Furthermore, private banks present the highest improvement of credit quality from category 2 to category 1. 

While, public banks and leasing companies have this migration rate assimilated to zero of chance to improve. 

The three credit institutionsseem similar considering improvement of credit quality of category 3 to risk-grade 1 

or 2; The highest improvement to class 1 appears in leasing companies and the highestimprovement to class 2 is 

registred in private banks. 

In deduction, transition trajectories depict differences with regard to the paths of migration (2 → 4; 2 → 3; 2 → 

1;3 → 2; 3 → 1) between credit institutions. Exploring these trajectories, we note asymmetric pattern of the 

estimated transition matriceswith a majority of upgrading on downgrading for private banks and leasing 

companies, except the case of public banks where downgrading migrations exceed upgrading ones, we observe 

also that there is a low probability of staying at the same risk-grade, except category 1 wich very high. we affirm 

then that public banks are the riskiest creditintitution while the leasing companies are the least risky. 

We identify public banks, among the three types of credit institutions analyzed, as the most risky credit 

institutions. They have a greater migration towards the deterioration of the classification of their bad debts 

compared to private banks and leasing companies, probably related to the nature of the sectors financed by the 

public banks.  

We note also in comparingpublic and private banks that the estimated transition matrices for both have an 

asymmetric and non-monotonic profile, and have little concentration on the diagonals, which show a lack of 

rigorin the loan classificationof these banks. 

6. Conclusion 

In order to alleviate the lack of data on changes of credit quality in Tunisian financial institutions, we propose 

touseproportions data toestimate Markov transition matrices of credit riskin the sense of Jones (2005).The 

proposedcredit risk evaluation method allows to resemble more reality by considering the development of credit 

quality in public banks, private banks and leasing companies. 

Transition matrices estimations are made upon the sequence of temporal data of credit risk classification from3 

forms ofcreditinstitutons in Tunisia (public banks, private banks and leasing companies) along twelve years of 

operations. 

These transition matrices present a high mobility, the majority of time, on the improvement direction. They are 

helpful to explore diverse credit quality migrations, showing characteristics about asymmetry, monotonicity. 

This paper indicates thatpublic banks have more severe downgarde migration of their non performing loans 

comparatively to private banks and leasing companies, which is probably related to the kind of sectors funded by 

the public banks. It appears also that dissimilarities between the the credit institutions studied are more 

pronounced at downgrading transition paths and that estimated transition matrices pattern are asymmetric and 

don’t show monotonicity in the transition probabilities. 

Then, Among the three forms of credit institution analyzed, we identify that the public banks are the riskiest 

financial institutions in the area of credit activity and that the dissimilarities exceed the similarities between the 

groups studied in view of worsening and improvement paths of credit quality transition.  

The asymmetry and non-monotonic profile ofthe estimated transition matrices for public and private banks and 

also the little concentration on their diagonals shows a lack of rigor in the loan classification. It results in a 

grading of credit risk that does not coincide in all cases to the real quality of credit, then, the assessment of bank 

credit risk degree can be distorted. 

Comparison between credit institutions can be useful to supervisory purposes, in fact, the worse transition path 

could constitute an early warning indicator to a forthcoming default or a reverse of migration path to the risky 

direction. Moreover, this sudy has a practical potentiality, because it can constitute a guidance tool to credit risk 

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43 

managementfor progressing toward better credit policies (growth strategy, renegociation). 

References 

Tunisian Central Bank (2014). Rapport sur la Supervision Bancaire. Banque Centrale de Tunisie. 

IMF (2012). Tunisie: Évaluation de la stabilité du système financier. FMI report, 12/241. 

J.P. Morgan & Co (1997). CreditMetrics™ - Technical Document. J.P. Morgan & Co. Incorporated. 

Basel committee on Banking Supervision (2003). The New Basel Capital Accord: consultative document. Bank 

for International Settlements. 

Basel committee on Banking Supervision (2004). International convergence of capital measurement and capital 

standards. Bank for International Settlements. 

Basel committee on Banking Supervision (2010). Basel III: A global regulatory framework for more resilient 

banks and banking systems. Bank for International Settlements. 

Bajaj, R.V.(2010). Migration analysis of Indian corporate: Rating-Based approach. The IUP Journal of 

Financial Risk Management, 7, 24-34. 

BCT (2014). Rapport sur la Supervision Bancaire. Tunisian Central Bank. 

Ivičić, L.,&Cerovac, S.(2009). Credit risk assessment of corporate sector in Croatia.Financial Theory and 

Practice, 33, 373-399. http://hrcak.srce.hr/48606 

Jafry, Y., &Schuermann, T. (2004). Measurement, estimation and comparison of credit migration matrices. 

Journal of Banking & Finance, 28, 2603-2639.doi:10.1016/j.jbankfin.2004.06.004 

Grzybowska, U., Karwańskia, M. &Orłowski, A. (2012). Examples of migration matrices models and their 

performance in Credit Risk Analysis.doi:10.12693/APhysPolA.121.B-40 

Jones, M. (2005). Estimating Markov transition matrices using proportions data : an application to credit risk. 

IMF working paper 05/219 

Nicula, I. (2013). Some aspects concerning the measurement of credit risk.Procedia Economics and Finance, 6, 

668 – 674. doi: 10.1016/S2212-5671(13)00187-1 

Lando,D.&Skødeberg, T. (2002) .Analyzing rating transitions and rating drift with continuous observations. 

Journal of Banking & Finance, 26, 423–444. doi: 10.1016/S0378-4266(01)00228-X 

Perilioglu, A.&Tuysuz, S.(2015). Conditional Sovereign Transition Probability Matrices. Procedia Economics 

and Finance, 30, 643-655. https://doi.org/10.1016/S2212-5671(15)01283-6 

Schechtman, R. (2013).Default matrices : A complete measurement of bank’s consumer credit 

delinquency.Journal of Financial Stability, 9, 460-474. doi:10.1016/j.jfs.2013.07.001 

 

 

 

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