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Regression and decision tree analysis of profitability of Croatian banks.

Abstract: Profitability of banks is influenced by many factors like size, costs structure, income structure, and macroeconomic conditions. Profitability is measured net interest margin. Regression analysis of profitability of Croatian banks is conducted with the goal to investigate to what extents different banks' characteristics and macroeconomic conditions influence profitability of Croatian banks. Unconventional methods like decision trees could also be used in order to estimate the factors of banks' profitability. CR&T decision tree method was applied in order to compare the results of the econometric analysis. Both methods implicated that in short term with stable macroeconomic conditions better profitability is accomplished by well-capitalized banks with bigger market share that are also very efficient in operating costs management. These banks are also very successful in transferring costs of non-income assets to their clients.

Key words: regression analysis, banks' profitability, forecasting, regression analysis, decision trees


Bank is primarily the firm that needs to bring results in profit. However, the profitability of the bank is not important only for directly interested parties (shareholders, management, employees), but also for whole economy. After the transition period, bank sector in Croatia should be competent in efficiency in fulfillment of main resources allocation role in economy.

The aim of the paper is to establish determinants of profitability in Croatian bank sector, with special emphasis on facts--and on specific factors for certain bank. Profitability determinants of banks in Croatia will be analyzed with the regression method and 'decision tree' method. The paper is organized following the next pattern.

After the introduction, some recent research works on profitability in bank sector are described. In third section, we describe measures used to determine bank profitability. In fourth section the analysis of profitability of Croatian banks is conducted by the regression method and 'decision tree' method. The last section of the paper consists of conclusion discussion.


The research papers that analyze bank profitability are mainly focused on American banking system (esc. Berger, 1995. Angbazo, 1997.) Demirguc-Kunt and Levine (2001) measured influence of few independent variables on profitability of banks on large sample of countries and bank institutions.

There are few research papers that analyze profitability of the bank sector, but from different points of view. Kraft and Tirtiroglu (1998) analyze the efficiency of bank institutions in Croatia and in 2004. Kraft with Hofler and Payne conducts similar investigation, but from aspects of privatization and entering of foreign banks on Croatian financial market, where the emphasis rests on cost efficiency of banks.


The Bank Scope database was used as data resource, from which data on Croatian bank business conduct, were extracted in period from 1999. till 2003. The data on banks was not completed for observed period, as only 30 banks had complete data, and those data were used for analysis. In result estimation of this paper it is necessary to consider the fact, that the used data, was only available complete data on banks that had all needed variables for certain year. In following investigation the exchange algorithms for missing variables should be examined and it should be estimated which of those algorithms is the most convenient one for following analysis. In that case the longer time series could be used, what would increase the reliability of research results, and that could be an improvement in credibility and influence of macroeconomic variables on bank profitability.

The efficiency of banks in this paper is measured by net interest margin-NIM, which is calculated as the difference between passive and active interest rate. In table 1 there are values of the net interest margin from the sample banks described, and it is shown that the first net interest margin is starting to decrease in 2000., as it had the lowest value in 2002., and started to increase again in 2003.

The factors of bank profitability can be divided in two basic groups: characteristics of the specific bank and environmental factors. Specific characteristics of the certain bank are following: market share, capital / assets ratio, credit / assets ratio, operative costs /assets ratio, non-profit assets / total assets ratio and short-term credits / assets ratio. Those factors will be used in regression analysis and 'decision tree' analysis.


4.1 Regression analysis

Regression model is simplified picture of relations of observed indications. Regression model is stochastic because it consists deviation variable (accident component). The model of simple linear regression is applied if the movement of dependent variable is observed in dependence of movement of one independent variable and if the form of relation is linear. Multiple regression models are applied if the movement of dependent variable is observed in dependence of movement of two or more independent variables is observed and if the relation between them is linear. The parameters of multiple regression models were estimated through net profit margin as dependent variable, during which the Statistica software was used. Results are shown in table 2. Estimated values of regression parameters were shown in table, along with p-values which resulted from parameter value hypothesis testing.

Model of net profit margin has satisfying adjusted R", what means that connection between independent variables and net profit margin is strong enough. (Brooks, 2002.). The value of Durbin--Watson factor shows that there is no correlation of model residual.

Net profit margin is under the influence of three variables--credit /assets ratio (statistically significant with 1%), operative costs / assets ratio ( 1% significance) and growth rate of GDP (statistically significant with 5%). Estimated values of regression parameters that represent credit /assets ratio and operative costs / assets ratio are positive, which means that between those two variables and net profit margin exists positive connection. However, regression parameter that represents GDP is negative, which means that with the growth of GDP, the spectra of values between active and passive interest rate decreases, what is a well known fact.

By the expectations the connection between net interest margin and credit /assets ratio is positive. Operative costs / assets ratio has positive influence on net interest margin,, which means that operative costs increase due to enlarged mass of business, which results in interest income. GDP growth rate is in negative connection to net interest margin, what shows us that faster the economy grows, the less we can expect net interest margin to increase, from which it can be supposed that fast GDP growth was not financed from bank credit lines but from various other resources. Demirguc-Kunt and Levine (2001) found on enlarged sample from more countries that net profit margin was connected to capital / assets ratio of the bank, non-profit assets / total assets of the bank, to short-term credits / assets ratio and to all macroeconomic conditions.

4.2 'Decision trees'

Decision tree can be used for classification and regression problems, in difference to neuron nets, decision tree generates model that can explain in form of the rules the relation of the incoming and out -coming variables. Decision tree is classification algorithm that has structure of the tree. (McLachlan, 1992). There are two types of knots that are connected with branches: terminal node (leaf node) and the node which is final for certain branch on the tree (decision node), which defines certain condition in the form of certain attribute. It creates itself through algorithm which finds regularities between data, and the most famous algorithms are CHAID, EXHAUSTIVE CHAID, C&RT.

During creation of 'decision tree' using the net profit margin as dependent variable, it was shown that the best method is CHAID method. Again, in decision tree making appeared similar variables that were detected by regression method: operative costs / assets ratio and GDP per capita.



Empirical results of the regression model show that net profit margin of Croatian banks primarily depends on characteristics that are specific for every bank itself, but also on GDP growth rate. Decision tree method as well as regression analysis showed that the operative costs / assets ratio and short-term credits / assets ratio were variables that had the biggest influence on net profit margin.


Allison, P.D., 2001. Missing Data (Quantitative Applications in the Social Sciences). London: SAGE publications.

Angbazo, L. 1997. "Commercial bank net interest margins, default risk, interest-rate risk, and off-balance sheet banking". Journal of Banking and Finance, 21, 55-87.

Berger, A., 1995. "The relationship between capital and earnings in banking". Journal of Money, Credit and Banking, 27, 404-431.

Brooks, C., 2002. Introductory Econometrics for Finance. London: Cambridge University Press.

Demirguc-Kunt, A. and Levine, R., 2001. "Financial Structure and Bank Profitability" in Financial Structure and Economic Growth: A Cross-Country Comparison of Banks, Markets, and Development, Eds. Cambridge, MA: MIT Press.

Kraft, E. and Tirtiroglu, D., 1998. "Bank efficiency in Croatia: A stohastic frontier analysis". Journal of comparative economics, 26, 282-300.

Kraft, E., Hofler, R., and Payne, J., 2004. "Privatizacija, ulazak stranih banaka i efikasnost banaka u Hrvatskoj: analiza stohasticke granice fleksibilne Fourierove funkcije troska". Istrazivanja 1-4.

McLachlan, G. J., 1992. Discriminant Analysis and Statistical Pattern Recognition. New York: Wiley Interscience.
Table 1: Net interest margin 1999-2003, Resource: Bank Scope

1999 2000 2001 2002 2003
6,30 6,23 5,22 4,64 5,43

Table 2. Results of the multiple regression model * 1% ** 5%


Capital / assets ratio 0,23738
Credit / assets ratio 0,401382 *
Short-term credits / assets -0,128683
Non-profit assets / total assets 0,007182
GDP per capita 0,233865
Operative costs /assets ratio 0,603245 *
Market share 0,002746
GDP growth rate -0,494913 **
Average currency -0,115189
Inflation rate 0,144947
F-test 5,819985 *
ADJ R2 0,60046439
Durbin-Watson 1,858,731
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Author:Pejic-Bach, M.; Simicevic, V.; Dabic, M.
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:4EXCR
Date:Jan 1, 2005
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