INTRODUCTION
In an effort to promote efficiency in the banking industry and after a period of worldwide liberalization and deregulation, the Basel Capital Accord of 1988 (Basel I) which led to the endorsement of a new capital adequacy framework (Basel II) in 2004 (operational from 2007) marked the beginning of a new phase of reregulation with an attempt to bring about an international harmonization of banking regulations (Bichsel and Blum, 2005). Kenyan banks are by and large yet to adopt model based approaches to assessing their capital adequacy needs (Central Bank of Kenya, 2008a). In assessing bank’s efficiency, the level, nature and composition of capital and the cost income ratio are some of the key measures used (Bourke, 1989; Berger, 1995; Thompson et al., 2002; Navapan and Tripe, 2003; Hess and Francis, 2004; Welch, 2006; Giokas, 2007). Kwan and Eisenbeis (1995) and Hughes and Moon (1995) argued that it is necessary to recognize explicitly the concept of efficiency in the empirical models linking bank capital to risk and to distinguish between efficient and inefficient risk undertaking.
Capital adequacy has been the focus of many studies and regulator as it is considered to be one of the main drivers of any financial institution’s profitability (Bourke, 1989; Berger, 1995; Thompson et al.., 2002; Navapan and Tripe, 2003; White and Morrison, 2001). In contrast, other studies argue that in a world of perfect financial markets, capital structure and hence capital regulation is irrelevant (Modigliani and Miller, 1958). However, White and Morrison (2001) posited that the regulator ensures that banks have enough of their own capital at stake. Bichsel and Blum (2005) supported this proposition arguing that these regulations help in reducing negative externalities (e.g., disruptions to the payments system and a general loss of confidence in the banking system) in addition to boosting the slow economic growth hence the Gross Domestic Product (GDP). These propositions leads to the question: what then do prudential capital requirements accomplish in the banking sector? This study suggests that these requirements have something to do with a bank’s performance. In Kenya, the government, through the Central Bank of Kenya has put requirements that all commercial banks should gradually increase their capital base to one billion Kenya shillings from the current 250 million Kenya shillings by 2012 (currently, 1US$ = 77.20 Kenya shillings) (Central Bank of Kenya, 2008b). This represents a 300% increase. This means that the level of capital has some implication on the performance and bankruptcy of a bank, a subject which is being investigated by this study.
The Cost Income Ratio (CIR), with its limitations (Welch, 2006), is another emerging measure of bank’s efficiency and a benchmarking metric (Tripe, 1998; Hess and Francis, 2004). Being a standard benchmark of bank’s efficiency, the CIR measures a bank’s operating costs as a proportion of its total (i.e., net interest and noninterest) income (Welch, 2006). This study also seeks to establish whether the CIR affects bank’s profitability.
In measuring the profitability of a bank, bank regulators and analysts have used Return On Assets (ROA) and return on equity (ROE) to assess industry performance and forecast trends in market structure as inputs in statistical models to predict bank failures and mergers and for a variety of other purposes where a measure of profitability is desired (Gilbert and Wheelock, 2007; Mostafa, 2007; Christian et al., 2008).
Navapan and Tripe (2003) explained that comparing banks’ Returns On Equity (ROE) is one way of measuring their performance relative to each other. The return on equity looks at the return on the shareholder’s investment and thus from the shareholder’s perspective, allows a comparison of investment in a bank’s shares with other investment opportunities, while it can also provide a measure of the bank’s riskiness (Gilbert and Wheelock, 2007).
Cotter (1966) noted that where shareholder interests are controlling, capital is an important managerial decision variable and the capital position of the wealthmaximizing bank theoretically will affect its capital structure and the loan policy. To the extent that capital does affect lending, it has implications for the performance of banks as financial intermediaries and hence for the allocation of real resources within the economy. Cotter (1966) concluded by pointing out that from this standpoint, market determined capital positions seem preferable.
Capital (equity and longterm debt) represents a source of funds to the bank along with deposits and borrowings. Pringle (1971) observed that an undercapitalized bank will find itself subjected to high levels of shortterm borrowing at potentially high excess costs during periods of tight money. Flamini et al. (2009) postulated that bank returns are affected by macroeconomic variables, suggesting that macroeconomic policies that promote low inflation and stable output growth does boost credit expansion.
According to Christian et al. (2008), capital adequacy measures provide significant information regarding a firm's returns, while a few of the individual variables representing asset quality and earnings are informative. Size and growth and loan exposure measures do not appear to have any significant explanatory power when examining returns. The study establishes that the change in total assets is also significant. Thus the present study has included these variables in its model to examine the relationship between capital adequacy, cost income ratio and profitability.
Navapan and Tripe (2003) asserted that the proposition that there should be a negative relationship between a bank’s ratio of capital to assets and its return on equity may seem to be selfevident as to not need empirical verification. It is therefore important to note that Berger (1995) found evidence for a positive relationship that is, the ratios of capital to assets and returns on equity were positively related. He argued that a higher capital ratio (with reduced risk of bankruptcy) should reduce a bank’s cost of funds, both by reducing the price of funds and the quantity of funds required, thus improving a bank’s net interest income and hence profitability.
However, Navapan and Tripe (2003) found the contrary  that is, negative relationship
between capital and profitability exists. Ghosh et al. (2003) explained
that banks are required to hold capital equal to a certain percentage of the
total riskweighted assets. Under the riskbased standards, capital consists
of two parts: tierI capital (comprising equity capital and published reserves
from posttax retained earnings) and tierII capital (comprising perpetual preferred
stock, loan loss reserves, subordinated debt, etc.). Using the expected bankruptcy
theory, Lewis (2008) explained that the expected bankruptcy costs hypothesis
can be used to explain part of the observed positive relationship between capital
asset ratios (CARs) and return on assets (ROA) under certain circumstances.
This reasoning forms the basis for the first set of testable hypotheses as follows:
H_{1} 
: 
Capital adequacy is positively related to bank profitability.
This leads to individual tests of the following subhypotheses: 
H_{1A} 
: 
The core capital (leverage) ratio is positively related to bank profitability 
H_{1B} 
: 
The equity capital to assets ratio is positively related to bank profitability 
H_{1C} 
: 
Tier 1 riskbased capital ratio is positively related to bank profitability 
H_{1D} 
: 
The ratio of total capital to assets is positively related to bank profitability 
The other factor affecting bank’s profitability is its efficiency as measured by the costincome ratio. The cost income ratio, defined by operating expenses divided by operating income, can be used for benchmarking by the bank when reviewing its operational efficiency. Hess and Francis (2004) observed that there is an inverse relationship between the cost income ratio and the bank’s profitability. Ghosh et al. (2003) also found that the expected negative relation between efficiency and the costincome ratio seems to exist.
The study shows that the costincome ratio is negative and strongly significant
in all estimated equations, indicating that more efficient banks generate higher
profits. This analysis means that the cost income ratio also affects the profitability
of the bank. It is from this reasoning that this study develops the second hypothesis:
H_{2} 
: 
Costincome ratio is negatively related to bank profitability 
This study focuses on the relationship between two determinants (i.e., capital adequacy and costincome ratio) and the profitability of commercial banks in Kenya with a view to drawing conclusions as to what extent they do account for the performance of banks in Kenya. The purpose of this research is to examine closely the capitalearnings relationship so as to determine which among the potential explanations of the relationship appear to be important.
This study, examine the direction with which efficiency measures (as measured by capital adequacy ratios (CARs) and the CIR)) affect bank’s profitability (as measured by ROA and ROE) so as to provide some insight as to why bank regulation and efficiency should be upheld. Previous research shows that a positive relation exists between capital adequacy and profitability (Berger et al., 1995; Ghosh et al., 2003) while a negative relationship exists between cost income ratio and profitability (Francis, 2004; Ghosh et al., 2003).
MATERIALS AND METHODS
The data used in this study was acquired from the Kenyan Capital Market’s Authority Library, the Kenyan Banking Survey (Think Business, 2009), internet and web sites of the licensed commercial banks operating in Kenya. Data was obtained from the annual financial statements for a selected sample of 41 out of the 44 licenced commercial banks in Kenya (Centrel Bank of Kenya, 2008a) for a period of ten years (1998 to 2007). This represents 93% of all registered commercial banks in Kenya. The three banks omitted from the sample had missing financial data for most years. This is because they were established in later years hence omitted from the sample.
The collected data was analyzed and interpreted with the help of different financial ratios and statistical tools including percentages, averages, trend analysis, regression, correlation and the significance test using Minitab Software. The five hypotheses were tested statistically to arrive at the conclusions and policy implications. The approached used in this studies is used by Lazaridis and Tryfonidis (2006) to analyze the different variables.
Using Gilbert and Wheelock’s (2007) approach, I measured profitability using the two ratios, ROA and ROE. The sources and formulae of the variables used in this study are summarized in Table 1.
Table 1: 
Variable definitions 

RESULTS AND DISCUSSION
Table 2 shows the summary statistics of the collected variables. The total observations are n = 410 with the exception of the debt to equity ratio with 407 observations. The banks included in the sample had an average (median) of 1.75 (1.92) per cent return on assets and a higher mean (median) of 9.71 (10.57) percent return on equity. The core capital to assets ratio averaged 16.87% (median = 10.62%). On average, the equity capital to assets ratio was 17.54% (median = 14.73%). The average (median) core capital to risk weighted assets averages 25.59 (20.66%)while the total capital to total assets ratio was 16.82 (10.81%). All the CARs indicate that Kenyan banks operate above the minimum statutory levels. A typical bank in the sample had a cost income ratio of 67.66% (median = 62.49%). This ratio implies that Kenyan banks are keen on managing their efficiency levels in relation to costcutting innovations. On average, the typical bank had the size of 8.66 (as measured by the natural logarithm of total assets). The mean (median) asset growth was 20.38 (9.75%). The total assets to total liabilities averaged 126.66% (median = 117.25). On average, a typical bank in the sample had a 17.30% debt to equity ratio (median = 7.62%). These descriptive statistics imply that most banks are keen on ensuring that their capital levels are above the minimum required statutory limits.
This Table reports summary statistics for the full sample of 410 firmyear observations for the periods 19982007. Except for debt to equity ratio with 407 firm years, all the other variables share a common sample size of 410 firm years.
In Table 3, we have the Pearson correlation Table for the variables that were included in the regression models. The results indicate that the Return On Assets (ROA) is negatively correlated with the CIR, the debt to equity ratio (DE) and the auditor dummy (Aud). The results also indicate that the Return On Equity (ROE) is negatively correlated with the core capital ratio, the risk weighted capital ratio, the total capital ratio, the CIR, the total assets to liabilities ratio, the debt to equity ratio and the auditor dummy.
The consistency of the two profitability negative correlation with CIR is consistent with the view that the higher the CIR, the lower the profitability. Most banks strive to minimize the CIR as much as possible. The other CARs are positively correlated with the two profitability measures, demonstrating a consistent view that there exists a positive relationship between capital adequacy and profitability. The higher the capital levels, the higher the profitability (Bourke, 1989; Berger, 1995). These findings are in support of the current proposed directive by the Central Bank of Kenya (2008) that the bank capital levels need to be raised from 250 million Kenya shillings to 1 billion Kenya shillings.
Table 2: 
Summary statistics 

Source: 19982007 survey data, author’s computation 
Table 3: 
Pearson Table for the variable correlations 

The pvalues are in parentheses with ^{*} , ^{**}
and ^{*** }denoting significance at the 10, 5 and 1% levels, respectively 
In order to adhere to this directive which becomes effective in 2012, most
banks will be forced to merge or even seek additional capital. Some banks will
be forced to seek additional capital by being listed on the Nairobi Stock Exchange
(NSE), an action this study seems not to advise banks to do. Other banks will
consider floating corporate bond inorder to raise their capital levels.
Table 3 shows the Pearson product moment coefficient of correlation (also called the correlation coefficient or correlation) for pairs of variables. The correlation coefficient is a measure of the degree of linear relationship between two or more variables. The dependent variables for the study are bank profitability as measured by the Return On Assets (ROA) (defined as net income after taxes and extraordinary items as a percentage of total assets) and the Return On Equity (ROE) (defined by net income scaled by total equity) (Gilbert and Wheelock, 2007). The independent variable are: the core capital (leverage) (CCR) ratio (given by tier 1 (core) capital to total assets), the equity capital to assets ratio (ECA) (given by total equity capital scaled by total assets), tier 1 riskbased capital ratio (TRC) (given by tier 1 (core) capital to riskweighted assets), the ratio of total riskbased capital to assets (TCA) (defined as the ratio of total riskbased capital to riskweighted assets), the costincome ratio (CIR)(expressed as operating expenses scaled by operating income), bank size (given by the natural logarithm of total assets of the bank) and the asset growth(AG) (arrived at as follows ([this year’s total assetsprevious year’s total assets]/previous year’s total assets)). Consistent with Bichsel and Blum (2004), the debt to equity ratio will be used as a control for the bank’s leverage and the ratio of total assets to total liabilities will also be used as a control variable. The auditor (Aud) for a particular company is shown as a dummy variable given as 1 for the big 4 and 0 for any other auditor. Other controls (although not indicated) include firm year controls (D_{t}).
Inorder to assess the relationship between profitability and capital adequacy ratios, the profitability is modeled as a function of the core capital ratio, the equity capital ratio, the total risk based capital and the total capital ratio. Consistent with Gilbert and Wheelock (2007), I use ROA and ROE as the proxies for bank profitability. Table 1 shows that the mean ROA and ROE in the sample is 1.75 and 9.71, respectively. These means are close to the median ROA and ROE of 1.92 and 10.57, respectively. This means that there is minimal skewness in the results and hence, no need to adjust for skewness. Panels A and B show the regression results in five different models.
Table 4: 
Regression estimates of the various capital adequacy determinants
and cost to income ratio for the banks under study. The dependent variable
is return on assets 

The pvalues are in parentheses with ^{*} , ^{**}
and ^{***} denoting significance at the 10, 5 and 1% levels respectively.
Source: 19982007 survey data, author’s computation 
The total number of observations is 410, which represents stacked data for
the period 19982007 for the 41 commercial banks operating in Kenya. Five regression
models were developed to test the five hypotheses developed earlier. Panels
A and B present the results from the data.
Panel A: Regression of return on assets, core capital, equity capital, risk weighted capital, total capital and cost income ratio.
The OLS Regression equation used:
Table 4 presents regression estimates of the various capital adequacy determinants and cost to income ratio for the banks under study. The dependent variable is return on assets. Each of the regression models represents a regression of one of the independent variables against the dependent variable. For all regression models, the control and dummy variables have been incorporated. Firm year controls and variance inflation indicators (VIFs) have also been estimated but not reported.
Panel B: Regression of return on equity, core capital, equity capital, risk weighted capital, total capital and cost income ratio.
The OLS Regression equation used:
Table 5 presents regression estimates of the various capital adequacy determinants and cost to income ratio for all banks under study. The dependent variable is return on equity. Each of the regression models represents a regression of one of the independent variables against the dependent variable. For all regression models, the control variables and dummy variables have been incorporated. Firm year controls and Variance Inflation Indicators (VIFs) have also been estimated but not reported.
Table 5: 
Regression estimates of the various capital adequacy determinants
and cost to income ratio for all banks under study. The dependent variable
is return on equity 

The pvalues are in parentheses with ^{*} , ^{**}
and ^{***} denoting significance at the 10, 5 and 1% levels, respectively Source: 19982007 survey data,
author’s computation 
In the first model in both panels, I regress the core capital ratio (CCR) with
bank profitability as measured by both ROA and ROE. The regression equation
used is as follows:
The results indicate the core capital is positively related both profitability measures at significance level, α = 10% for ROA. These results are consistent with prior research that there exists a positive relationship between capital adequacy and profitability (Bourke, 1989; Berger, 1995).
In the second model, I regress the equity capital ratio (ECA) with profitability as measured by both ROA and ROE. The regression equation used to establish this is formulated as follows:
The results reveal that a negative relationship exists at for both measures of profitability and equity capital ratio. Although these findings are not significant, they are consistent with previous studies which find that a negative relationship between bank capital and profitability exists (e.g., Navapan and Tripe, 2003). The negative relationship can be explained by the fact that the more the equity providers to a bank, the higher the claim from the bank’s retained earnings in the form of dividends. This leads to less retained funds available to the bank for growth purposes, hence less funds available to boost profits.
Next, I regress the risk based capital ratio (defined as core capital scaled by risk weighted assets) to profitability as measured by ROA and ROE. The results are shown under model 3 in both Panels A and B. The regression equation used is:
Consistent with Bourke (1989) and Berger (1995), the results indicate that a significant positive relationship exists between bank profitability and risk weighted capital at α = 5%.
In the fourth regression model, the total capital (both core capital and supplementary capital) has been regressed against ROA and ROE. The regression equation used is as follows:
This produces mixed results. The results indicate that a positive relationship exists between this total capital and bank profitability as measure by ROA, while a negative relation exists between the total capital ratio and profitability as measure by ROE. None of these results are significant.
In the fifth model, I regress the cost income ratio with bank profitability using the following regression equation:
Consistent with previous studies, there exists a negative relationship between the CIR and bank profitability at significance level, α = 1% for all regression models.
Finally, the significant negative constant coefficient in all regression models implies that if all the other variables were set to zero, then the bank would report a loss. This makes economic sense because if there was no capital, it is expected that the bank would not report any activity nor profits.
All models reveal that the larger the bank, the more profitable it is. This finding is highly significant at α = 1% for all regression models. This means that larger banks are more profitable compared to smaller banks. Consistent with this finding, all regression models also show that the bank asset growth has a significant positive relation to its profitability. This means that as the bank grows in its asset base (depicting an increase in its size), it reports higher profits since the assets are being used to generate more profits.
Table 6 shows the summary results of the expected signs from the study and the actual sign developed from the study data analysis.
All regression models were tested for multicollinearity. The Variance Inflation Factor (VIF) (not disclosed in the findings) is used to detect whether one predictor has a strong linear association with the remaining predictors (the presence of multicollinearity among the predictors) (Lazaridis and Tryfonidis, 2006). The VIF measures how much the variance of an estimated regression coefficient increases if your predictors are correlated (multicollinear).
Table 6: 
Summary findings on key variables 

Source: 19982007 survey data, author’s computation 
The largest VIF among all predictors is often used as an indicator of severe
multicollinearity. Montgomery et al. (2007) suggest that when VIF is
greater than 510, then the regression coefficients are poorly estimated. In
all the regression equations discussed above, all the predictors had a VIF ranging
between 1 and 3 implying that there is absence of multicollinearity between
the predictors in the regression models.
Figure 1 shows the time series plot of the CIR over the ten year period for all the 41 banks in the sample. The Figures have been calculated from the Banking Survey data (Think Business, 2009). The trend line shows that the CIR increased sharply in the periods 1999 to 2002, then fell in 2003, rose again in 2004 and it has been falling since then to 2007 where a 59.75% CIR was reported. This is due to the move by banks to improve their efficiency by employing robust information systems in banking which can handle large numbers of clients.
The trend can also be explained by the stiff competition in the banking sector in Kenya whereby even though there is extensive expansion, banks are keen on cutting their costs to either improve or maintain their profitability positions. Even though not captured completely in the figure, the effects of the global financial crisis of 2007/2008 seem not to have affected Kenyan banks as of 2007 because the CIR ratio was still low at 59.75% at this particular time of the study.
From the selected countries in Table 7, Kenya ranks 9th with an average CIR of 69.3% which, compared globally, is quite high. This means Kenyan banks need to strive hard to reduce their CIRs to global levels (5060%) as indicated in Table 7. This will make them globally competitive. Being globally competitive will expose the banks to a wide range of global opportunities including global service offering and the possibility of being cross listed in global stock exchange markets. This has an added advantage such as the exposure to larger capital sources and a large clientele.
This study adds to the existing literature such as Navapan and Tripe (2003)
who found out that the expected negative relationship between capital and profitability
exists. The study also adds to previous findings that there is a positive relationship
between capital adequacy and profitability (Bourke, 1989; Berger, 1995). This
makes economic sense from the point of view that an increase in capital may
raise expected earnings by reducing the expected costs of financial distress,
including bankruptcy. This means that a bank can acquire more capital to improve
its more profits.

Fig. 1: 
The time series plot of the CIR over the ten year period for
all the 41 banks in the sample. Source: 19982007 survey data, author’s
computation 
Table 7: 
Comparison of CIR in some selected countries 

*Represents the CIR for the years 19982002. The data has
been derived from OECD (2005) augmented by author’s calculations. Source:
19982002 survey data, author’s computation and secondary data (OECD,
2005) 
A bank that acquires more capital is able to realize more returns by either
investing this additional capital or even using it to generate a return on loans
(in form of interest income). The differential relationships between bank profitability
and capital can be explained by the fact that there are differential effects
of the various measures of capital adequacy (due to risk measurement) on the
profitability of the bank.
The study also reveals that the CIR is inversely related to both bank profitability measures. This finding adds to existing literature such as that of Ghosh et al. (2003) and Hess and Francis (2004) that there exists a negative relationship between the costincome ratio and profitability.
CONCLUSIONS
This study examines the relationship between bank profitability, CARs and the CIR. While prior research documents that a positive or negative relation exists between CARs and bank profits and that a negative relation exists between the CIR and bank profitability, no study has addressed the more fundamental question of whether the two bank profitability measures are related to the CARs and CIR simultaneously.
Using ROA and ROE as proxies for bank profitability, the study finds that bank profitability is positively related with the core capital ratio and the riskbased capital. The study also shows that bank profitability is negatively related to the equity capital ratio and the CIR.
The most significant finding in this study which other similar studies have not pointed out is the fact that there are differential effects of the various measures of capital adequacy on the profitability of the bank. This study finds out that the nonrisk weighted capital adequacy measure (i.e., the equity capital ratio) is negatively related with the profitability of a bank (as measured by both ROA and ROE) while there is a positive relationship between the riskadjusted capital adequacy measure (i.e., tier 1 riskbased capital ratio and core capital ratio) and bank profitability (as measured by both ROA and ROE). The total capital ratio also reveals the same. These findings are significant in the sense that the risk adjustment helps to account for the uncertainty associated with bank’s capital levels. This acts a reliable measure of the nature and the composition of capital inherent in a bank’s capital structure.
Another major finding in the study is that the CIR is negatively related to both bank profitability measures. The study also reveals that the Kenyan banks CIRs are quite high compared to CIRs of developed countries. This means that Kenyan banks should strive to keep the CIR to its minimum, if possible, below the 50% threshold for them to be more efficient hence be globally competitive.
Future research could incorporate more variables such as taxation and other regulation indicators, exchange rates as well as indicators of the quality of the services offered by banks in the models used in this study. Another possible extension could be the use of dual regression models where the ROA and ROE variables are regressed at the same time with the various independent, control and dummy variables.
ACKNOWLEDGMENTS
This study was initially submitted to Professor Jacquelyn Sue Moffit (E.J. Ourso College of Business, Louisiana State University) for reviewing. The author expresses sincere thanks to her for her review comments. The author thanks Mr. Stephen Mucheri, a research assistant at Strathmore University for his comments. The author also thanks Dr. Jim Boyd Mcfie (Strathmore University) for providing data sources for this study. The author wishes to thank two anonymous reviewers who have contributed in their comments on this paper. Finally, special thanks go to Strathmore University for providing research publication funds for the study.