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Impact of Credit Risk Management and Capital Adequacy on the Financial Performance of Commercial Banks in Nigeria

OGBOI, Charles

Department of Economics, Accounting and Finance, College of Management Sciences,

Bells University of Technology, Ota Ogun State, Nigeria.

E-mail: ogboii@yahoo.com

UNUAFE, Okaro Kenneth Department of Banking and Finance,

Federal Polytechnic, Ofa, Kwara State, Nigeria.

E-mail: kenokaro@yahoo.com

________________________________________________________________________________________________________________________________________________________________________________________________

Abstract

Nigerian banks have continued to invest huge sums of scarce financial resources on risk management modelling, with a view to maximizing returns and minimizing bank’s risk exposure through provision for loan losses. However, empirical evidence on the magnitude of the relationships between credit risk and bank’s profitability in Nigeria is rather scarce. A few studies that have examined the links failed to consider the role of capital adequacy in accordance with Bassel II accord in a unified framework. Using a time series and cross sectional data from 2004-2009 obtained from selected banks annual reports and accounts in Nigeria, this study examined the impact of credit risk management and capital adequacy on banks financial performance in Nigeria. This is with a view to providing further empirical evidence on how credit risk management strategies and capital requirement variables affect banks’ profitability in Nigeria. Panel data model was used to estimate the relationship that exists among loan loss provisions (LLP), loans and advances (LA), non-performing loans (NPL), capital adequacy (CA) and return on asset (ROA).

Results showed that sound credit risk management and capital adequacy impacted positively on bank’s financial performance with the exception of loans and advances which was found to have a negative impact on banks’ profitability in the period under study. Based on the findings, it is therefore, recommended that Nigerian banks institute appropriate credit risk management strategies by conducting rigorous credit appraisal before loan disbursement and drawdown. It is also recommended that adequate attention be paid to enhance Tier-One capital of Nigerian banks.

______________________________________________________________________________

Key words: credit risk, management, capital adequacy, banks performance

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1. Introduction

Credit risk management has been an integral part of the loan process in banking business.

Credit risk is the current and prospective risk to earnings or capital arising from an obligor’s failure to meet the terms of any contract with the bank or otherwise to perform as agreed. Kargi (2011).

When banks grant loans, they expect the customers to repay the principal and interest on an agreed date.

A credit facility is said to be performing if payment of both principal and interest are up to date in accordance with agreed repayment terms. The non- performing loans (NPL) represent credits which the banks perceive as possible loss of funds due to loan defaults. They are further classified into substandard, doubtful or lost. Bank credit in lost category hinders bank from achieving their set targets. Kolapo et al (2012).

Due to increasing spate of non-performing loans (NPL) and its attendant consequences, the Central Bank authorities entered into agreement in December 1987 known as Basel I and II accord. Both accords emphasized on the importance of capital adequacy for mitigating credit risk.

Capital adequacy in banking business provides protection against sudden financial losses.

Greuning H. (2003)

Considering the importance policy makers and industry practitioners place on risk management and capital adequacy as a distress prevention strategy, it is crucial to know whether this optimism is truly warranted. It is against this backdrop that the present paper set out to empirically ascertain whether credit risk management and capital requirement have enhanced profitability of Nigerian Banks.

1.1 Rationale/Objectives of the Study

As challenges posed by difficult economic development continues to increase, banking and financial institutions are subsequently exposed to increasing risks. The magnitude of non performing credits in the banking system is a cause for concern to different stakeholders including bank management which granted the loans, depositors whose funds has been misappropriated and trapped and regulatory agencies responsible for protecting the banking system.

Nigerian banks have continued to invest huge sums of funds to credit risk management modeling with a view to maximizing returns and minimizing bank’s risk exposure through provision for potential loan losses.

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Meanwhile, empirical studies that examine the actual impact of credit risk management on bank’s financial performance in Nigeria did not capture capital adequacy in a unified framework according to Basel I and II accord. This notwithstanding, the results and findings from these studies produced mixed results thereby leaving the academia and policy makers in quandary.

Some studies on this topic show that credit risk management strategies impact on banks performance, but the impacts are of highly uncertain magnitude and conflicting direction. The implication that emerges from these studies is that the impacts of credit risk management on banks performance are theoretically ambiguous. For example, researchers like Kithinji, (2010), Epure and Lafuente (2012) amongst others found evidence that credit risk management does not impact positively on banks profitability.

In particular, while Kithinji (2010) found that other variables other than credit risk management impact on banks profitability, Epure and Lafuente (2012) found that banks performance improvement follow regulatory changes and not credit risk management.

The overall objective of this study is to investigate the impact of credit risk management and capital adequacy of banks financial performance in Nigeria. The specific objectives are to:

(i) Determine the extent to which non performing loans affect banks profitability in Nigeria.

(ii) Investigate the impact of loan loss provisions on banks profitability in Nigeria.

(iii) Examine the effects of loans and advances on banks performance in Nigeria.

(iv) Establish the nature of relationship between liquidity ratio and banks performance in Nigeria.

(v) Determine whether banks capital adequacy contributes to banks profitability.

1.2 Research Questions

Given the various issues relating to the impact of credit risk management on banks profitability in Nigeria, a number of research questions are raised as follows:

(i) Does non- performing loans affect banks’ profitability?

(ii) What impacts does bank’s loan loss provisions have on profitability?

(iii) What are the effects of bank’s loans and advances on bank’s performance?

(iv) What relationship exists between liquidity ratio and banks performance in Nigeria?

(v) To what extent does enhanced capital base contribute to banks profitability in Nigeria?

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1.3 Statement of Research Hypotheses

The following testable hypotheses are formulated in line with research questions and are therefore subjected to empirical investigation. These hypotheses are stated in null context as follows:

(i) There is no significant relationship between non- performing loans and bank’s profitability.

(ii) Loan loss provisioning has no significant relationship with bank’s performance.

(iii) There is no significant relationship between loans and advances and bank’s performance.

(iv) Liquidity ratio has no significant impact on bank’s profitability.

(v) Capital adequacy does not impact on bank’s performance.

2. Literature Review

There have been debate and controversies on the impact of credit risk management and bank’s financial performance. Some scholars e.g., (Li Yuqi 2007; Naceur and Kandil 2006;

Kinthinji 2010; Kolapo, Ayeni and Ojo 2012; Kargi 2011;) amongst others have carried out extensive studies on this topic and produced mixed results; while some found that credit risk management impact positively on banks financial performance, some found negative relationship and others suggest that other factors apart from credit risk management impacts on bank’s performance. Specifically, Kargi (2011) found in a study of Nigeria banks from 2004 to 2008 that there is a significant relationship between banks performance and credit risk management. He found that loans and advances and non performing loans are major variables that determine asset quality of a bank.

Kolapo, Ayeni and Ojo (2012) using panel data regression for the period 2000 to 2010 found that the effect of credit risk on bank’s performance measured by the Return on Asset (ROA) of banks is cross sectionally invariant. They concluded that the nature and managerial pattern of individual firms do not determine the impact. Also, Hosna, Manzura and Juanjuan (2009) re- emphasized the effect of credit risk management on profitability level of banks. They concluded that higher capital requirement contributes positively to bank’s profitability. Muhammed, Shahid, Munir and Ahad (2012) used descriptive, correlation and regression techniques to study whether credit risk affect banks performance in Nigeria from 2004 to 2008. They also found that credit risk management has a significant impact on profitability of Nigerian banks.

Boahene, Dasah and Agyei (2012) used regression analysis to determine whether there is a significant relationship between credit risk and profitability of Ghanain banks. They followed the line of Hosna, Manzura and Juanjuan (2009) by using Return of Equity as a measure of bank’s

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performance and a ratio of non-performing loans to total asset as proxy for credit risk management. They found empirically that there is an effect of credit risk management on profitability level of Ghaninian banks. The study also suggests that higher capital requirement contributes positively to bank’s profitability. Li yuqi (2007) examined the determinants of bank’s profitability and its implications on risk management practices in the United Kingdom. The study employed regression analysis on a time series data between 1999 and 2006. Six measures of determinants of bank’s profitability were employed. They proxied Liquidity, credit and capital as internal determinants of bank’s performance. GDP growth rate, interest rate and inflation rate were used as external determinants of banks profitability. The six variables were combined into one overall composite index of bank’s profitability. Return on Asset (ROA) was used as an indicator of bank’s performance. It was found that liquidity and credit risk have negative impact on bank’s profitability.

Poudel (2012) appraised the impact of the credit risk management in bank’s financial performance in Nepal using time series data from 2001 to 2011. The result of the study indicates that credit risk management is an important predictor of bank’s financial performance. Fredrick (2010) demonstrated that credit risk management has a strong impact on bank’s financial performance in Kenya. Meanwhile, Jackson (2011) towed the line of Fredrick (2010) by using CAMEL indicators as independent variables and return on Equity as a proxy for banks performance. His findings were also in line with that of Fredrick who also concluded that CAMEL model can be used as proxy for credit risk management. Musyoki and Kadubo (2011), also found that credit risk management is an important predictor of bank’s financial performance;

they concluded that banks success depends on credit risk management.

Onaolapo (2012), while analyzing the credit risk management efficiency in Nigerian commercial banking sector from 2004 through 2009 provides some further insight into credit risk as profit enhancing mechanism. They used regression analysis and found rather an interesting result that there is a minimal causation between deposit exposure and bank’s performance.

Kithinji (2010) analyzed the effect of credit risk management (measured by the ratio of loans and advances on total assets and the ratio of non-performing loans to total loans and advances on return on total asset in Kenyan banks between 2004 to 2008). The study found that the bulk of the profits of commercial banks is not influenced by the amount of credit and non performing loans.

The implication is that other variables apart from credit and non performing loans impact on banks’ profit. Kithinji (2010) result provides the rationale to consider other variables that could

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impact on bank’s performance. Analysis of credit risk along capital requirement on bank’s performance could find solutions to the issue of bank’s performance in Nigeria.

Unfortunately, only few studies have been conducted in developing countries and Nigeria in particular to examine the impact of capital requirement and bank’s performance. Few studies that examined capital requirement and performance in Nigeria and other developing countries concentrated on capital adequacy without considering credit risk in a unified framework.

Meanwhile, Guidara, Lai and Soumare (2010) investigated bank’s performance, risk and capital buffer under business cycles and banking regulation in Canada. They concluded that Canadian banks were well capitalized and that explains why Canadian banks were insulated for global financial crisis. Naceur and Kandil (2006) examined the impact of capital requirement on bank’s performance in Egypt using generalized method of moment (GMM). Their findings re- emphasized the importance of capital regulation to bank’s performance. The result of the study also suggests that the state of the economy is a major determinant of bank’s performance.

Again, Naceur and Kandil (2008) appraised the impact of capital requirement on banks cost of intermediation and performance using Generalized Method of Moment (GMM) on time series data between 1989 through 2004. They used ratio of capital to total asset and ratio of net loans to deposit as independent variables while return on asset (ROA) and return on equity (ROE) was used as dependent variables. The result of the study is in agreement with their earlier result that capital adequacy is a predictor of banks performance. Ravindra, Vyasi and Manmeet (2008) examined the impact of capital adequacy requirement on performance of selected commercial banks in India using panel data models. The results of the study indicate that capital adequacy ratio increases the profitability of commercial banks in India.

Gurdmundssoa, Ngok-Kisingula and Odongo (2013) examined the role of capital requirement on bank competition and stability in Kenya using panel data estimation on time series data between 2000 and 2011. The result of the study indicates that regulatory efficiency improves competition in the banking sector. Oladejo and Oladipupo (2011), examined whether there is a link between capital regulation and performance of Nigeria banks. They found that consolidation has increased the potential of banks to compete effectively at national, regional and global level.

In general, studies that examined the impact of capital adequacy on bank’s performance tend to conclude that capital adequacy enhance performance (Ravindra, Vyasi and Manmeet 2008;

Gurdmundssoa, Ngok-Kisingula and Odongo 2013;). While the evidence on contemporaneous impact of capital adequacy on banks performance may be mixed it is likely that capital adequacy can impact on bank profits by cushioning the effect of loan loses.

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3. Research Methodology

This section deals with the methods of data collection and the methodology employed in the research analysis.

Secondary data were collected for the purpose of empirical analysis.

The six banks selected by purposive sampling technique are First Bank of Nigeria, Access bank, Diamond bank, First city monument bank, Fidelity bank and Union bank of Nigeria. Panel data regression analysis was used to investigate the extent to which credit risk management and capital adequacy affect bank’s financial performance in Nigeria in the period between 2000-2009.

Panel data estimation technique is adopted because “it takes care of heterogeneity associated with individual banks by allowing for individual specific variables. Also, by combining time series of cross sectional observations, panel data give more informative data, more variability, less colinearity among variables, more degrees of freedom and more efficiency”. Besides, panel data will minimize the bias that can result if individual banks are aggregated. It also enriches empirical analysis in such a way that may not be possible if either only time series data or cross sectional data is used.

3.1 Sample Selection

Data for the study were obtained from the published financial statement of six out of twenty one banks operating in Nigeria as at December 2009. In order to ensure uniformity in presentation, some banks were excluded because of the following factors. Banks that merged or acquired during the period covered in the study were excluded. Also excluded are banks that had course to change their financial accounting year- end from those selected. In all, six banks with complete data for the period 2005-2009 were used for the study.

3.2 Model Specification

This study is modelled according to the work of Kolapo, Ayeni and Oke (2012),Hosna, Manzura and Juanjuan (2009), Kithinji (2010), Poundel (2012), which studied the effect of credit risk and commercial bank performance. Specifically, the authors adopted the model of Poundel (2012), and specifies that commercial bank’s performance (Return on Asset) is influenced by credit risk management (ratio of non-performing loan to loans and advances, ratio of loan loss provision to classified loans and ratio of loans and advances to total deposit) and capital requirement by ratio of equity capital to total asset.

The functional form of the model is expanded thus:

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=

=

=

=

=

=

= ℎ ℎ

= =

= + + + + +µ ………. ( )

,

The equation (2) can be written as follows;

= + + + + +µ…………. ( )

==

1 < 0 implies that the independent variables (ratio of non- performing loans to loans and advances), is expected to have an inverse relationship with banks performance.β2, β3, β4 and β5>0

3.3 Description of variables

Variable Description

Return on Asset(ROA) The is the ratio of net operating profit that a company earns from its business operations in a given period of time to the amount of the company’s total asset

Non- performing Loans (NPL) These are credits which the banks perceive as possible losses of

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funds due to loan default.

Loan loss provisions (LLP) This is an amount of money that a bank set aside fromits annual earnings as a precaution against possible loss of a non performing loan, or to off-set a lost credit facility.

Loans and Advances (LA)

This is a facility granted to a bank customer that allows the customer make use of banks funds which must be repaid with interest at an agreed period

Liquidity (LR) This is the ability of a bank to meet its short term obligation as and when due.

Capital Adequacy Ratio (CAR)

This is the index regulatory authorities use to determine the optimum amount of money (i.e equity, retained earnings, and other

reserves)that a bank must have to be able to take certain levels of risk endangering deposits funds, or its existence

4. The result of the fixed effect Model

One way to take into account the individuality of each bank is to let the intercept vary for each bank but still assume that the slope coefficients are constant across firms. The term “Fixed Effect” is due to the fact that although the intercept may differ across individual banks, each individual bank intercept does not vary over time. This implies that, it is time invariant. This is the major assumption under this model. That is, while the intercept are cross sectionally variant, they are also time invariant.

The Result Of The Pooled Ols With Fixed Effect Model Dependent Variable: ROA

Coefficient Std. Error t-ratio p-value

const 2.45774 2.47147 0.9944 0.33250

NPL -0.0474918 0.0575748 -0.8249 0.41968

LLP 0.0111815 0.0143267 0.7805 0.44473

LA -0.0639616 0.0247243 -2.5870 0.01808 **

LR 0.00941314 0.0135445 0.6950 0.49548

CAR 0.141024 0.0651587 2.1643 0.04338 **

Mean dependent var 2.714667 S.D. dependent var 2.320607

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R-squared 0.649437 Adjusted R-squared 0.464931

F(10, 19) 3.519860 P-value(F) 0.008847

Log-likelihood -51.59126 Akaike criterion 125.1825

Schwarz criterion 140.5957 Hannan-Quinn 130.1133

Rho 0.159531 Durbin-Watson 1.935050

Source: Authors Computation 2013

The result of the pooled OLS show that 0.64 (64%) of the systematic variation in the dependent variable (ROA) is explained by the five independent variables, computed as the ratio of non-performing loans to loans and advances, loan loss provisioning to classified loans; Loan and advances to Total deposit, Total deposit to loans and advances and ratio of equity to loans and advances. The F-statistic value is significant at 5% level, which also indicates that there is a linear relationship between Return on Asset and the Five independent variables. This also indicates the goodness of fit of the estimated model.

Durbin Watson of 1.9 indicates the absence of serial auto correlation. The intercept values of the banks are statistically significant. The attributes of the intercept may be due to the unique features of the banking environment in Nigeria. From the result, all the coefficients except loans and advances are consistent with the a priori expectations.

For non performing Loans (NPL), the coefficient is negatively signed, though not statistically significant at 5% level.

For loan loss provisions (LLP), the coefficient shows a positive relationship on Return on Asset (ROA). This implies that holding other variables constant, 100% increase in (LLP) increased banks profitability by 4.7%.

For loans and advances, a 100% increase in loans and advances, banks profits declined by 6.3% and statistically significant at 5% level. For liquidity ratio, a 100% increase in the liquidity of banks increased banks profit ability by 0.9% while a 100% increase in capital adequacy of Nigerian banks enhance profitability by 14.1% and significant at 5% level.

4.1 Discussion of the Result

The result of this study is consistent with the findings of Felix and Clandine (2008), Naceur and Kandil (2006)(, (2008), Oladejo and Oladipupo (2011) Kinthinji (2010), Kargi (2011), Hosna et al (2009) Kudubo (2011), Pondel (2012) amongst others who found that effective credit risk management and capital adequacy is a good promoter of banks performance.

For instance Kargi (2011) found that credit risk management is an important predictor of banks financial performance. He however stated that the degree of impact strongly depends on regulatory environment in which banks operate. The most interesting aspect of the result is the

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positive and significant relationship between capital adequacy and banks financial performance.

Expectedly, the enhancement of capital base of Nigerian banks in the period under study from N2billion to N25 billion significantly improved the profitability of banks. The lesson one draws from this is that enhanced capital base, especially Tier one capital protected Nigerian banks against financial losses from default loans, and also afforded banks opportunity to compete internationally especially in the area of downstream oil sector.

It was also discovered that loans and advances decreased the profitability of Nigerian banks.

This is at variance with the findings of Kolapo et al (2012) who found positive relationship. The inverse relationship is true of Nigerian banking system during the period under study when most loans and advances were concentrated in the stock market to create what is known as margin loans. (This is the art of granting loans to stock brokers to purchase share using the share as security for the loan). Unfortunately, most of these loans were lost as a result of global financial crisis when foreign portfolio investors had to divest their funds. One can conclusively say that the enhanced capital base of Nigerian banks reduced the effect of Global Financial crisis on Nigerian financial sector.

The result of liquidity on banks profitability is also at variance with the findings of Liyugi (2007) who found negative relationship between credit risk and liquidity on banks performance.

The result of this finding could be attributed to the high liquidity ratio requirement of Central Bank of Nigeria to prevent liquidity risk.

5. Conclusion

The evidence provided in this study based on the empirical findings, showed that sound credit risk management strategies and enhanced capital requirement can promote banks profitability.

It is also imperative to state that the strategy of making provision for loan loss or reducing non performing loan has never been misleading. Rather, some other factors can be attributed to have rendered these policies lesspotent.

5.1 Policy Recommendation

From the findings of the study, the following recommendations are made:

For Nigerian banks to achieve enhanced and sustained profitability through interest income, from loans and advances, appropriate credit risk strategies to be instituted. Banks therefore need adequate and accurate information from both internal and external sources in order to access the multiplicity of credit risks they face when presented with a loan proposal.

Banks are also advised to patronize credit bureaus. Credit information bureaus would bridge the information gap that exists whenever there loan request, in commercial and consumer finance, by tracking the financial behaviour of individuals over a period of time. Bank staff that are

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Performance measures should include the ratio of Non-performing assets to total risk asset or ratio of Loan Loss Provisions to Non performing assets.

The result of the study clearly shows that capital adequacy is a great predictor of banks profitability. This becomes necessary where banking regulation specifies that a bank should not land above a specified amount of its shareholders funds (unimpaired by losses) to a single obligator. Small banks which are poorly capitalized, cannot offer certain categories of credit facilities. In the final analysis, the worth of capital for a bank serves as a buffer against loss of depositors’ funds. Nigerian banks should be well capitalized even without the promptings of the regulatory authority.

References

BGL Banking Report (2010) ‘Getting Banks to Lend Again The Banker’s Magazine of July 2012, publication of the Financial Times Ltd. London.

Basel Committee on Banking Supervision (2001). Risk Management Practices and Regulatory Capital: Cross Sectional Comparison (available at www.bis.org).

Boahene, S. H. Dasah, J and Agyei S. K. (2012), “Credit risk and profitability of selected banks in Ghana” Research Journal of finance and accounting.

Epure, M. and Lafuente,I (2013). Monitoring Bank Performance in the Presence of Risk, Barcelona GSE Working Paper Series No. 61.

Felix, A.T and Claudine, T.N (2008). Bank Performance and Credit Risk Management, Unpublished Masters Dissertation in Finance, University of Skovde.

Fredrick O. (2010), “The impact of credit risk management on financial performance of commercial banks in Kenya”. DBA African Management Review.

Greuning H AND Sonja B (2003) “Analyzing and Managing Banking Risk” The World Bank Washington.

Gudara, A. Lai, V. S. and Soumare (2010), “Performance risk and capital buffer Under Business Cycles and Banking Regulation: Evidence from Canadian Banking Sector”. Centre for research on Financial Markets Policy.

Gudmundssoa, R. Ngoka-Kisingul, K. and Odongo M. T. (2013), “The role of capital requirement on bank competition and stability: The Case of Kenyan Banking Industry” Centre for Research on Financial Markets and Policy.

Gujarati, D. N. (2004), “Basic Econometrics” 4th Edition, Tata McGraw-Hill Publishing Company Limited.

Hosna, A. Manzura, B and Juanjuan S. (2009), “Credit risk management and profitability in

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commercial banks in Sweden” School of Business Economics and Law.

Jackson O. (2011), “The impact of credit risk management on financial performance of commercial banks in Kenya”. University of Nairobi.

Kargi, H. S. (2011), “Credit risk and the Performance of Nigeria banks” Ahmadu Bello University Zaria.

Kinthinji, A. M. (2010), “Credit risk management and profitability of commercial banks in Kenya”.

kolapo, T. F, Ayeni R. K. and Oke, O. (2012), “Credit Risk Management and Banks Performance” Australian Journal of Business and Management Research.

Liyuqi (2007), “Determinants of Banks profitability and its implication on Risk management practices: Panel Evidence from the Uk”. University of Nothingham.

Muhammed et al (2012), “Credit risk and the performance of Nigerian banks” interdisciplinary Journal of contemporary research in business.

Musyoki, D and Kadubo, A. S. (2011), “The impact of credit risk management on the financial performance in Kenya”. International Journal of Business and Public Management.

Naceur, S. B. and Kandil, M. (2006), “The impact of capital requirement on- banks performance:

The case of Egypt” Social Science Research Network.

Naceur, S. B. and Kandil, M., (2008), “The impact of capital requirement on banks costs of intermediation and performance” IMF working paper.

Oladejo, M. O. and Oladipupo, A. U. (2011), “Capital regulation and performance of Nigerian banks: Need for review” Journal of emerging trents in Economics and Management Sciences.

Olusemore, G.A. (2009) “Lending Principles and Practice. 2ndedition Nesbet Nigeria Limited Onaolapo, A. R. (2012), “Analysis of credit risk management efficiency in Nigerian commercial banking sector” Far East Journal of Marketing and Management.

Poudel, R. P. S. (2012), “The impact of credit risk management in financial performance of commercial banks in Nepal”. International Journal of arts and commerce.

Ravindra Y, Vyasi R. K. and Manmeet S. (2008), “The impact of capital adequacy requirements on performance of scheduled commercial banks” Asian-pacific Business review.

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Appendix

Model 1: Fixed-effects, using 30 observations Included 6 cross-sectional units, Time-series length = 5

Dependent variable: ROA

Coefficient Std. Error t-ratio p-value

const 2.45774 2.47147 0.9944 0.33250

NPL -0.0474918 0.0575748 -0.8249 0.41968

LLP 0.0111815 0.0143267 0.7805 0.44473

LA -0.0639616 0.0247243 -2.5870 0.01808 **

LR 0.00941314 0.0135445 0.6950 0.49548

CAR 0.141024 0.0651587 2.1643 0.04338 **

Mean dependent var 2.714667 S.D. dependent var 2.320607

Sum squared resid 54.74782 S.E. of regression 1.697488

R-squared 0.649437 Adjusted R-squared 0.464931

F(10, 19) 3.519860 P-value(F) 0.008847

Log-likelihood -51.59126 Akaike criterion 125.1825

Schwarz criterion 140.5957 Hannan-Quinn 130.1133

rho 0.159531 Durbin-Watson 1.193505

Test for differing group intercepts - Null hypothesis: The groups have a common intercept Test statistic: F(5, 19) = 0.912978 with p-value = P(F(5, 19) > 0.912978) = 0.493503

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

-4 -2 0 2 4

Density

uhat1

uhat1 N(-2.7386e-016,1.5104) Test statistic for normality:

Chi-square(2) = 8.254 [0.0161]

References

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