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[Abstract] This paper adopted the Factor Analysis method to find the most important influential factors for Chinese listed commercial banks， to compute their subitem factor scores and comprehensive scores， on base of which analyzed their economy of scale， management and development ability， safety factors and profitability.
[Keywords] Factor Analysis； competitiveness； listed commercial bank
1 INTRODUCTION
The banking sector is one of the most important parts of China's financial industry. In recent years， China's banking sector has experienced great reform and innovation， and has made remarkable achievements， playing a supporting and facilitating role in China’s economic and social development. However， due to changes in the external environment， economic uncertainty in Europe and the incoming further opening to foreign banks， China’s banking sector will face both more opportunities and more challenges.
2 MAIN IDEA OF THE FACTOR ANALYSI
Factor Analysis is a multivariate statistical analysis method to show relationships among many indicators with several factors. Usually some variables with closer relationships are attributed to a group， which is named factor. All variables are classified into several groups and make several factors. These factors can encapsulate most of the information of the original indicators. This can be shown by model （1）：
are the common factors of ， which are independent of each other and unobservable； is the loading matrix. is the special factor， reflecting the part of information that is not encapsulated in common factors.
The factor analysis is usually conducted by the following procedure：
Data test. The factor analysis aims at extracting information from the original indicators by refining information overlaps. That means that indicators used for factor analysis should highly correlate to each other. If the original indicators independent of each other and have no common factors at all， it is not suitable for factor analysis. The statistical software SPSS provides several test methods， such as correlation coefficient matrix method， KMO， Bartlett’s test of sphericity， and so on.
Common factors extraction. There are many methods for common factors extraction， such as principal factor method， maximum likelihood method， iteration principal factor method. In this paper， we adopted the principal factor method， which means that we pick up several common factors of most variances， and try to encapsulate most of the information of the original indicators with these several factors. Factor rotation. The original loading matrix is usually not clear enough for analysis. To make the factor loading polarize， that is to say， either approach to 0 or approach to 1， researchers should conduct factor rotation. Widely-used rotation methods are varimax orthogonal rotation， oblique crossing rotation， and so on. We adopted the varimax orthogonal rotation in this paper.
Computation of factor scores. On base of the outcome of the factor rotation， subitem scores and comprehensive scores can be computed， on base of which sample units can be ranked.
3 INDEX SYSTEM CONSTRUCTION AND DATA PRETREATMENT
Before conducting the Factor Analysis， there are some basic work to do， such as construction of the index system， data collection， and data pretreatment.
3.1 Construction of Index System and Data Collection
The first step is to set up the index system and collect data about them. The data of this paper came from the annual report of 13 of 16 listed commercial banks of China. Banks under research includes Industrial and Commercial Bank of China （ICBC）， China Construction Bank （CCB）， Bank of China （BOC）， Bank of Communication （BCM）， Shanghai Pudong Development Bank （SPDB）， China Citic Bank （CNCB）， Industrial Bank （IB）， Hua Xia Bank （HXB）， China Minsheng Bank Co. （CMBC）， China Merchants Bank （CMB）， Ping An Bank （PAB）， Ningbo Bank （NBYH）， Bank of Nanjing （BON）. The indicators we selected are total assets （X1）， operation revenue （X2）， total assets growth rate （X3）， operation revenue growth rate （X4）， net margin growth rate （X5）， per-share earnings （X6）， per capita net margin （X7）， average return on total assets （X8）， average return on net assets （X9）， net interest margin （X10）， cost-to-income ratio （X11）， Net fee and commission income to operating income ratio （X12）， capital adequacy ratio （X13）， Shareholders' equity ratio （X14）， NPL ratio （X15）， provision coverage （X16）.
3.2 Data Pretreatment
3.3 Feasibility Test for Factor Analysis
We use factor analysis methods KMO test and Bartlett test of sphericity to make sure whether the scalar data we selected are suitable for factor analysis. The statistical analysis software we used is SPSS. The outcome of the test is shown in table I.
General speaking， so long as the value of KMO is greater than 0.6， the original data can be used for Factor Analysis. Table 2 showed that the KMO for the data of the Listed Commercial Bank is 0.719， which means that it is suit for Factor Analysis. The purpose of the Bartlett test of sphericity is to make sure whether the correlation coefficient matrix is significant. Here the value of is 87.067， the corresponding probability is 0.000， which means that we should reject the null hypothesis that the correlation coefficient matrix of the original indicators is identity matrix. So both the KMO test and the Bartlett test of sphericity show that the data of the Listed Commercial Bank are suit for Factor Analysis. 4 FACTOR ANALYSIS OF LISTED COMMERCIAL BANKS IN CHINA
4.1 Extraction of Eigenvalues
The first step of the Factor Analysis is to find the initial common factors and the loading matrix of them. In this paper， we adopt the principal component analysis as extraction method for common factors， which means to compute the eigenvalues and eigenvectors. By this method， whether a component is extracted is usually determined by cumulative variance and initial eigenvalue. Only those with a cumulative variance more than 85% and initial eigenvalue greater than 1 should be included.
Table 2 shows that the first four eigenvalues are all greater than 1， and their cumulative variance amount to 85%. This means that the first four factors can cover most information reflected by all the original indicators， and are enough to describe the competitiveness of the listed commercial banks.
4.2 Factor Rotation
One of the purposes of the Factor Analysis is comprehensive evaluation of the original index. Some time， the outcome of the factor extraction is not very satisfactory. Though there is no correlation among the factors， the explanatory ability of the factors extracted for original indexes is very weak， and is difficult to explain. If this happen， researchers may carry out some rotation transformation for the factor model， to make the loading coefficients of the common factors either approach to 1 or approach to 0. Usually the outcome after rotation is easier to explain.
To make the information reflected in the factors more dependent to each other， this paper adopted the Variance maximization orthogonal rotation method. After the rotation， the loading coefficients gathered at the either ends， made it easier to explain the economic meaning of the common factors. The loading coefficients after rotation are showed in table III.
The factors model show that F1 is mainly reflected by indicators about the size or scale of the commercial banks， F2 mainly about management and development capacity， F3 about safety， and F4， profitability.
Competitiveness means the ability to create more wealth than one’s competitors. For commercial banks， the most important influential factors of competitiveness are scale factors， Management and development capacity factors， safety factors and profitability factors.
One of the most important influential factors is scale factor， or the size of the commercial banks. Commercial banks scale refers to the ability of the commercial banks to obtain available funding at an appropriate price， so as to meet any customer credit or bank payment needs. It is an important aspect of the measure of the competitiveness of commercial banks. To some extent， it is the determinant of the survival and development for commercial banks. In rivals among banks， those of bigger size usually show better competitiveness than those of small size. A second important influential factor for bank competitiveness is safety factor. Commercial bank security refers to the bank's ability to prevent its assets， income， reputation， and all operating conditions for the survival and development against loss. It is the primary factor to consider for banks. Safety factor of the bank usually means that a commercial bank has good risk-control capability， which is mainly manifested in good risk information feedback mechanism， scientific risk assessment system and a thorough risk correction mechanism.
The third important influential factor for bank competitiveness is management and development ability factor. Management is the core of commercial banks operation. It can affect the core elements of the competitiveness of commercial banks. Cost management and efficiency of commercial banks directly determines their survival， determines the commercial bank's future and destiny. The management and development capabilities have the most direct relationship with the competitiveness of commercial banks.
And another important factor is profitability. Without profit， there will be no survival and development of the commercial banks. The pursuit of profit maximization is the ultimate goal of commercial banks and intrinsic motivation for commercial banks to maintain management and development. Profitability is the foundation of the development of commercial banks as well as the test of the effectiveness of their competition； especially when there is significant size disparity， profitability is a best indicator to reflect the level of commercial banks’ competitiveness.
4.3 Computation of Comprehensive Factor Scores and Rank of the Banks
We may compute the subitem score for each common factor for the listed commercial banks in China and rank them by the scores. The outcome is shown in table IV.
5 ANALYSIS OF THE COMPETITIVENESS OF THE LISTED COMMERCIAL BANK IN CHINA
On base of the Factor Analysis， we can draw some conclusion about the competitiveness of the listed commercial bank in China.
In terms of scale and economies of scale， except for Bank of Communications， the other state-owned commercial banks occupy the top three positions. Especially for Industrial and Commercial Bank of China and China Construction Bank， in addition to the huge advantage in asset size and operating income， low cost to income ratio， the higher the rate of return on total assets enable them to successfully transform scale into advantages. As for non-state-owned ones， assets and operating revenues of Huaxia Bank are far below the Ping An Bank， Bank of Nanjing， Bank of Ningbo， which makes it a disadvantage for Huaxia. As for ability in business management and development， joint-stock commercial banks and city commercial banks get higher scores， among which the highest is Industrial Bank， Ping An Bank the second， both outweighs the state-owned commercial bank. The most important reason that the joint-stock commercial banks have been able to gain an advantage in this regard， fundamentally speaking， is their favorable market development space. Joint-stock commercial banks do not bear too heavy historical burden and huge non-performing loans， coupled with the support of domestic policies， they have great potential for development. The main reason that Huaxia Bank is at the bottom is poor profitability， indicated by lower net interest margin and lower cost-income ratio， both of which hinder the growth of space for Huaxia Bank.
In terms of safety， the city banks performance even better. Without the policy pressure which all state-owned banks have to bear， city banks achieve a good match between risk and return. Nanjing Bank ranks first， with its non-performing loan rate 0.97 percent， the lowest in the sample， and provision coverage ratio 234.71%， showing that Bank of Nanjing has done very well in the robustness of the business.
As for profitability， the various types of commercial banks perform unevenly， with state-owned commercial banks at an intermediate level. CCB scores highest in the state-owned banks， while still have a considerable gap with Minsheng Bank. Due to its higher net interest margins and cost-income ratio， Minsheng Bank occupies the first place in the rankings. Although the cost-income ratio and ROE of Huaxia Bank are high， its capital adequacy ratio is low， more debt， these limit its loan growth， and hence its profitability relatively poor.
REFERENCES：
[1]Ru Duan and Caiqing Zhang， “Design of the Commercial Bank Competitiveness Evaluation Index System”， Statistics and Decision， Jun. 2005， pp 52-53.
[2]Li Zhou and Zhimin Dai， Competitiveness and development of small and medium commercial banks， China Social Sciences Press， 2003.
[3]Jinpu Jiao， Chinese Banking Competitiveness Comparison， China Financial Publishing House， 2002.
[4]Songqi Wang， “Chinese Commercial Bank Competitiveness Report”， Banker， Mar. 2005， pp 13-15.
[Keywords] Factor Analysis； competitiveness； listed commercial bank
1 INTRODUCTION
The banking sector is one of the most important parts of China's financial industry. In recent years， China's banking sector has experienced great reform and innovation， and has made remarkable achievements， playing a supporting and facilitating role in China’s economic and social development. However， due to changes in the external environment， economic uncertainty in Europe and the incoming further opening to foreign banks， China’s banking sector will face both more opportunities and more challenges.
2 MAIN IDEA OF THE FACTOR ANALYSI
Factor Analysis is a multivariate statistical analysis method to show relationships among many indicators with several factors. Usually some variables with closer relationships are attributed to a group， which is named factor. All variables are classified into several groups and make several factors. These factors can encapsulate most of the information of the original indicators. This can be shown by model （1）：
are the common factors of ， which are independent of each other and unobservable； is the loading matrix. is the special factor， reflecting the part of information that is not encapsulated in common factors.
The factor analysis is usually conducted by the following procedure：
Data test. The factor analysis aims at extracting information from the original indicators by refining information overlaps. That means that indicators used for factor analysis should highly correlate to each other. If the original indicators independent of each other and have no common factors at all， it is not suitable for factor analysis. The statistical software SPSS provides several test methods， such as correlation coefficient matrix method， KMO， Bartlett’s test of sphericity， and so on.
Common factors extraction. There are many methods for common factors extraction， such as principal factor method， maximum likelihood method， iteration principal factor method. In this paper， we adopted the principal factor method， which means that we pick up several common factors of most variances， and try to encapsulate most of the information of the original indicators with these several factors. Factor rotation. The original loading matrix is usually not clear enough for analysis. To make the factor loading polarize， that is to say， either approach to 0 or approach to 1， researchers should conduct factor rotation. Widely-used rotation methods are varimax orthogonal rotation， oblique crossing rotation， and so on. We adopted the varimax orthogonal rotation in this paper.
Computation of factor scores. On base of the outcome of the factor rotation， subitem scores and comprehensive scores can be computed， on base of which sample units can be ranked.
3 INDEX SYSTEM CONSTRUCTION AND DATA PRETREATMENT
Before conducting the Factor Analysis， there are some basic work to do， such as construction of the index system， data collection， and data pretreatment.
3.1 Construction of Index System and Data Collection
The first step is to set up the index system and collect data about them. The data of this paper came from the annual report of 13 of 16 listed commercial banks of China. Banks under research includes Industrial and Commercial Bank of China （ICBC）， China Construction Bank （CCB）， Bank of China （BOC）， Bank of Communication （BCM）， Shanghai Pudong Development Bank （SPDB）， China Citic Bank （CNCB）， Industrial Bank （IB）， Hua Xia Bank （HXB）， China Minsheng Bank Co. （CMBC）， China Merchants Bank （CMB）， Ping An Bank （PAB）， Ningbo Bank （NBYH）， Bank of Nanjing （BON）. The indicators we selected are total assets （X1）， operation revenue （X2）， total assets growth rate （X3）， operation revenue growth rate （X4）， net margin growth rate （X5）， per-share earnings （X6）， per capita net margin （X7）， average return on total assets （X8）， average return on net assets （X9）， net interest margin （X10）， cost-to-income ratio （X11）， Net fee and commission income to operating income ratio （X12）， capital adequacy ratio （X13）， Shareholders' equity ratio （X14）， NPL ratio （X15）， provision coverage （X16）.
3.2 Data Pretreatment
3.3 Feasibility Test for Factor Analysis
We use factor analysis methods KMO test and Bartlett test of sphericity to make sure whether the scalar data we selected are suitable for factor analysis. The statistical analysis software we used is SPSS. The outcome of the test is shown in table I.
General speaking， so long as the value of KMO is greater than 0.6， the original data can be used for Factor Analysis. Table 2 showed that the KMO for the data of the Listed Commercial Bank is 0.719， which means that it is suit for Factor Analysis. The purpose of the Bartlett test of sphericity is to make sure whether the correlation coefficient matrix is significant. Here the value of is 87.067， the corresponding probability is 0.000， which means that we should reject the null hypothesis that the correlation coefficient matrix of the original indicators is identity matrix. So both the KMO test and the Bartlett test of sphericity show that the data of the Listed Commercial Bank are suit for Factor Analysis. 4 FACTOR ANALYSIS OF LISTED COMMERCIAL BANKS IN CHINA
4.1 Extraction of Eigenvalues
The first step of the Factor Analysis is to find the initial common factors and the loading matrix of them. In this paper， we adopt the principal component analysis as extraction method for common factors， which means to compute the eigenvalues and eigenvectors. By this method， whether a component is extracted is usually determined by cumulative variance and initial eigenvalue. Only those with a cumulative variance more than 85% and initial eigenvalue greater than 1 should be included.
Table 2 shows that the first four eigenvalues are all greater than 1， and their cumulative variance amount to 85%. This means that the first four factors can cover most information reflected by all the original indicators， and are enough to describe the competitiveness of the listed commercial banks.
4.2 Factor Rotation
One of the purposes of the Factor Analysis is comprehensive evaluation of the original index. Some time， the outcome of the factor extraction is not very satisfactory. Though there is no correlation among the factors， the explanatory ability of the factors extracted for original indexes is very weak， and is difficult to explain. If this happen， researchers may carry out some rotation transformation for the factor model， to make the loading coefficients of the common factors either approach to 1 or approach to 0. Usually the outcome after rotation is easier to explain.
To make the information reflected in the factors more dependent to each other， this paper adopted the Variance maximization orthogonal rotation method. After the rotation， the loading coefficients gathered at the either ends， made it easier to explain the economic meaning of the common factors. The loading coefficients after rotation are showed in table III.
The factors model show that F1 is mainly reflected by indicators about the size or scale of the commercial banks， F2 mainly about management and development capacity， F3 about safety， and F4， profitability.
Competitiveness means the ability to create more wealth than one’s competitors. For commercial banks， the most important influential factors of competitiveness are scale factors， Management and development capacity factors， safety factors and profitability factors.
One of the most important influential factors is scale factor， or the size of the commercial banks. Commercial banks scale refers to the ability of the commercial banks to obtain available funding at an appropriate price， so as to meet any customer credit or bank payment needs. It is an important aspect of the measure of the competitiveness of commercial banks. To some extent， it is the determinant of the survival and development for commercial banks. In rivals among banks， those of bigger size usually show better competitiveness than those of small size. A second important influential factor for bank competitiveness is safety factor. Commercial bank security refers to the bank's ability to prevent its assets， income， reputation， and all operating conditions for the survival and development against loss. It is the primary factor to consider for banks. Safety factor of the bank usually means that a commercial bank has good risk-control capability， which is mainly manifested in good risk information feedback mechanism， scientific risk assessment system and a thorough risk correction mechanism.
The third important influential factor for bank competitiveness is management and development ability factor. Management is the core of commercial banks operation. It can affect the core elements of the competitiveness of commercial banks. Cost management and efficiency of commercial banks directly determines their survival， determines the commercial bank's future and destiny. The management and development capabilities have the most direct relationship with the competitiveness of commercial banks.
And another important factor is profitability. Without profit， there will be no survival and development of the commercial banks. The pursuit of profit maximization is the ultimate goal of commercial banks and intrinsic motivation for commercial banks to maintain management and development. Profitability is the foundation of the development of commercial banks as well as the test of the effectiveness of their competition； especially when there is significant size disparity， profitability is a best indicator to reflect the level of commercial banks’ competitiveness.
4.3 Computation of Comprehensive Factor Scores and Rank of the Banks
We may compute the subitem score for each common factor for the listed commercial banks in China and rank them by the scores. The outcome is shown in table IV.
5 ANALYSIS OF THE COMPETITIVENESS OF THE LISTED COMMERCIAL BANK IN CHINA
On base of the Factor Analysis， we can draw some conclusion about the competitiveness of the listed commercial bank in China.
In terms of scale and economies of scale， except for Bank of Communications， the other state-owned commercial banks occupy the top three positions. Especially for Industrial and Commercial Bank of China and China Construction Bank， in addition to the huge advantage in asset size and operating income， low cost to income ratio， the higher the rate of return on total assets enable them to successfully transform scale into advantages. As for non-state-owned ones， assets and operating revenues of Huaxia Bank are far below the Ping An Bank， Bank of Nanjing， Bank of Ningbo， which makes it a disadvantage for Huaxia. As for ability in business management and development， joint-stock commercial banks and city commercial banks get higher scores， among which the highest is Industrial Bank， Ping An Bank the second， both outweighs the state-owned commercial bank. The most important reason that the joint-stock commercial banks have been able to gain an advantage in this regard， fundamentally speaking， is their favorable market development space. Joint-stock commercial banks do not bear too heavy historical burden and huge non-performing loans， coupled with the support of domestic policies， they have great potential for development. The main reason that Huaxia Bank is at the bottom is poor profitability， indicated by lower net interest margin and lower cost-income ratio， both of which hinder the growth of space for Huaxia Bank.
In terms of safety， the city banks performance even better. Without the policy pressure which all state-owned banks have to bear， city banks achieve a good match between risk and return. Nanjing Bank ranks first， with its non-performing loan rate 0.97 percent， the lowest in the sample， and provision coverage ratio 234.71%， showing that Bank of Nanjing has done very well in the robustness of the business.
As for profitability， the various types of commercial banks perform unevenly， with state-owned commercial banks at an intermediate level. CCB scores highest in the state-owned banks， while still have a considerable gap with Minsheng Bank. Due to its higher net interest margins and cost-income ratio， Minsheng Bank occupies the first place in the rankings. Although the cost-income ratio and ROE of Huaxia Bank are high， its capital adequacy ratio is low， more debt， these limit its loan growth， and hence its profitability relatively poor.
REFERENCES：
[1]Ru Duan and Caiqing Zhang， “Design of the Commercial Bank Competitiveness Evaluation Index System”， Statistics and Decision， Jun. 2005， pp 52-53.
[2]Li Zhou and Zhimin Dai， Competitiveness and development of small and medium commercial banks， China Social Sciences Press， 2003.
[3]Jinpu Jiao， Chinese Banking Competitiveness Comparison， China Financial Publishing House， 2002.
[4]Songqi Wang， “Chinese Commercial Bank Competitiveness Report”， Banker， Mar. 2005， pp 13-15.