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  • 标题:An analysis of alternative profit efficiency scores and financial ratios: does bank size matter?
  • 作者:Lacewell, Stephen K. ; White, Larry R. ; Rogers, Kevin E.
  • 期刊名称:Academy of Banking Studies Journal
  • 印刷版ISSN:1939-2230
  • 出版年度:2002
  • 期号:January
  • 语种:English
  • 出版社:The DreamCatchers Group, LLC
  • 摘要:Although there is probably no one correct measure of performance, the area of performance measurement can be divided into two rather large streams of research: bank efficiency measures and accounting-based financial ratios. Thus, determining the correct performance measure of a bank operating in the United States today is a diverse and complicated issue. The two performance measures mentioned above may seem varied and appear to utilize different information, which is why most previous studies investigate these areas in isolation. This paper merges the topics of bank efficiency and accounting-based financial ratio performance and examines the relationship between these seemingly separate areas to determine when and if they should be used in combination.
  • 关键词:Bank management

An analysis of alternative profit efficiency scores and financial ratios: does bank size matter?


Lacewell, Stephen K. ; White, Larry R. ; Rogers, Kevin E. 等


INTRODUCTION

Although there is probably no one correct measure of performance, the area of performance measurement can be divided into two rather large streams of research: bank efficiency measures and accounting-based financial ratios. Thus, determining the correct performance measure of a bank operating in the United States today is a diverse and complicated issue. The two performance measures mentioned above may seem varied and appear to utilize different information, which is why most previous studies investigate these areas in isolation. This paper merges the topics of bank efficiency and accounting-based financial ratio performance and examines the relationship between these seemingly separate areas to determine when and if they should be used in combination.

This study involves a multi-stage process. Stage one is the calculation of alternative profit efficiency scores, using the stochastic frontier approach (SFA), for all banks operating in the United States during the years 1996 and 1999. This model is termed the national model per Mester (1997) due to the fact that all banks, for which sufficient data are available, are used to estimate the efficient alternative profit frontier. Stage two involves gathering and/or calculating financial ratios that are, according to previous research, highly correlated with each of the CAMELS rating components used by financial regulators. Stage three involves the use of multiple regression to determine 1) if a relationship exists between the chosen financial ratios, which serve as a proxy for the publicly unavailable CAMELS ratings, and the alternative profit efficiency scores and 2) the strength and direction of the aforementioned possible relationship.

It is hypothesized that accounting-based financial ratios utilized by various financial institution examination agencies in the formulation of CAMELS ratings provide significant information regarding the efficiency measure of a bank. It is further hypothesized that different types of relationships will exist among banks of varying asset size. If different relationships do exist, this will shed new light on the issue proposed by many researchers regarding the use of efficiency measures as complements to CAMELS ratings in the financial institution examination process. The results of this paper will be of interest to many parties due to the fact that determining a correct measure of bank performance must take into account the high degree of competitiveness, technological change, customer-base diversity, and other areas of the firm's operating environment found in the U.S. banking industry.

LITERATURE REVIEW

While the area of production frontiers was introduced by Farrell (1957), the stochastic frontier, also called the composed error, is relatively new having been introduced by Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977). Many of the first papers on this topic were applied to manufacturing data, as were other efficiency methods. Much study has taken place regarding the early problems associated with this method. (See also Battese and Corra (1977), Lee and Tyler (1978), Stevenson (1980), Pitt and Lee (1981), Kalirajan (1982), Bagi and Huang (1983), Schmidt and Sickles (1984), Waldman (1984), and Battese and Coelli (1988) for early examples of SF estimation.) Stochastic frontier analysis (SFA) is today, however, one of the most popular efficiency estimation techniques due in part to its robustness and relative ease of use.

Among the first to examine the relationship between financial performance, measured by accounting-based ratios, and production performance proxied by efficiency indices, are Elyasiani, Mehdian, and Rezvanian (1994). They find a significant association between financial ratios and bank efficiency and suggest that efficiency analysis should be considered as a supplement to financial ratio analysis by regulatory agencies and bank managers. The article focuses, however, on large banks and utilizes a rather small sample. Thus, the true nature of the relationship is not explored across a wide variety of banks operating in the U.S. One study which provides a very brief although interesting attempt to integrate the information provided by efficiency measures with that found in CAMELS ratings is by Simeone and Li (1997). Their study, which focuses on a limited sample of 35 closed Rhode Island credit unions ranging in asset size from $131 thousand to $338 million, seeks to determine if stochastic frontier analysis (SFA) measures of efficiency would have been useful in identifying and preventing the failure of the aforementioned credit unions. The authors determine that SFA can be considered a good substitute for, or a valid supplement to, the CAMELS rating due to the fact that SFA avoids the subjective and difficult management rating utilized by CAMELS.

Studies concerning bank size and efficiency are readily available. However, as there are many types of efficiency measures, the ability to make direct comparisons with this study are inherently difficult. An early survey article by Clark (1988) reveals just how far the area of efficiency measurement has progressed in a relatively short time period. His review covers only 13 studies from the early- and mid-80s and finds that large diversified depository institutions have not enjoyed a large cost advantage over smaller, more specialized institutions. This, compared to the 130 articles covered by Berger and Humphrey (1997) shows how popular and important this area is with researchers. Studies regarding productive efficiency by bank size include Evanoff (1998) and Elyasiani and Mehdian (1995). They find that under the hypothesis of identical frontiers for large and small banks that the efficiency measures for each are similar in 1979 but separate in favor of large banks in 1986. This finding is consistent with Shaffer (1989) but inconsistent with Rhodes and Savage (1981) and Zimmerman (1990). It is also found that large and small banks possess separate and dissimilar best practice frontiers. Thus, the efficiency patterns of the two groups may be said to be correlated with distinct characteristics of the markets and environments in which the two groups operate. Rogers (1998) assess the viability of small banks by examining their X-efficiency relative to larger institutions. He uses a balanced panel of 8,386 banks over the years 1991 to 1996 to estimate both cost and alternative profit frontiers using the translog specification of the distribution free approach. Results suggest that after adjusting the frontier for size, small banks are found to be less profit efficient than larger institutions but more cost efficient. It is posited that this will allow small banks to compete with large banks in terms of costs but may hamper their profitability as industry consolidation continues. Other studies of interest include DeYoung, Hasan and Kirchhoff (1997), Park and Simar (1995) and Park, Sickles and Simar (1998).

As evidenced by the above array of literature, the area of bank efficiency measurement is vast. Many studies have been performed regarding cost, revenue, and profit efficiency. Although studies have been performed which touch on the relationship between efficiency measures, financial ratio performance, and CAMELS ratings, none have been conducted as yet which combine all of these factors in the way of the examination undertaken here.

DATA AND METHODOLOGY

The data used in this study are obtained from the Sheshunoff BankSearch Commercial and Savings Banks database for the years 1996 and 1999, respectively. A sample of all banks for which there is available data is obtained for the two years with 7,514 banks for 1999 and 8,179 banks for 1996. The sample is then decomposed, by asset size, into sub-samples representing banks that fit into small, medium, and large categories. The definition of a small bank, for purposes of this study, is a bank with less than $100 million in total assets. A medium bank is an institution with $100 million to $1 billion in assets and large bank is one with greater than $1 billion in total assets. The size categories include 319 large, 2,577 medium, and 4,618 small banks in 1999 and 338 large, 2,533 medium, and 5,308 small banks in 1996.

Efficiency Estimation

A relatively new model concerning the measurement of profit efficiency is used in this study. The alternative, or nonstandard, profit efficiency model, as given by Berger and Mester (1997) and Humphrey and Pulley (1997), differs from the standard profit efficiency model in that it measures how efficient a bank is at earning its maximum available profit given its output levels. Alternative profit efficiency is especially useful when there is a violation of at least one of the underlying assumptions of cost and standard profit efficiency. These assumptions include:

1. the quality of banking services has no substantial unmeasured variations;

2. a bank can achieve its optimum volume and mix of output, meaning outputs are completely variable;

3. a bank cannot affect output price due to perfectly competitive output markets; and

4. output prices are accurately measured allowing for unbiased standard profit efficiency estimation.

It is apparent from the above assumptions that the data used for this study would violate at least assumptions i and ii. Thus, alternative profit estimation is chosen as the profit efficiency measure of choice over standard profit efficiency.

The alternative profit frontier function is:

[pi] = [pi] (y, w, [u.sub.[pi]] [v.sub.[pi]]), (1)

where [pi] represents the variable profits of the bank, y is a vector of variable output quantities, w is a vector of prices for variable inputs, [u.sub.[pi]] represents profit inefficiency and [v.sub.[pi]] is random error.

The alternative profit efficiency score for any bank can be calculated once the alternative profit frontier has been constructed. The alternative profit efficiency of bank i is calculated as the predicted actual observed profit of bank i divided by the predicted maximum profit of the best practice bank, i.e., the predicted maximum profit across all banks, adjusted for random error. This calculation is given by the following:

Alt[pi][Eff.sub.i] = [[??].sup.i]/[[??].sup.max], (2)

where [[??].sup.max] represents the predicted maximum profit, associated with the best practice bank, across N banks in the sample and [[??].sup.i] denotes the predicted actual profit for the ith bank, with i = 1, ..., N. The calculated raw profit efficiency scores are then truncated at the top 5 and 10 percent levels, per Berger (1993), so as to eliminate any distortion which may be caused by outliers when the maximum profit is used. The truncated profit efficiency scores can range from 0 to 1 with 1 representing the most efficient bank or the best practice bank. The profit efficiency score represents the percentage of profits or resources that are used efficiently. Thus, a bank that receives a profit efficiency score of 0.75 is 75% efficient or consequently loses 25% of its potential profits relative to the best practice bank facing similar operating conditions.

A modified intermediation approach is used for the analysis, which views a bank's primary goal as that of intermediating funds between savers and borrowers and uses the dollar volume of various deposit accounts and loan categories as output variables. Input variables include the cost of funds utilized in the process of transferring funds between savers and borrowers. The modification to this approach occurs due to the inclusion of nontraditional activities. Due to increased competition banks are placing increased emphasis on nontraditional activities. Rogers (1998b) finds that bank efficiency measures which do not account for these nontraditional activities as an output tend to understate the true bank efficiency measure. Considering the aforementioned information, the variables included for analysis include the following:
Input Variables (Cost) Output Variables (Quantity)

1. Labor 1) Demand Deposits
2. Physical Capital 2) Time and Savings Deposits
3. Time and Savings Deposits 3) Real Estate Loans
4. Purchased Funds 4) Other Loans
 5) Net Non-interest Income


Given the above inputs and outputs, and based on Berger's (1993) similar model specification, the empirical profit frontier model is given as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where: j = 1, ..., 5 outputs,

k = 1, ..., 4 inputs,

[pi] = total profit

[y.sub.j] = the amount of output j,

[w.sub.k] = the input price of k, and

[[epsilon].sub.[pi]] = the natural residual or total error

If the two components of the disturbance term, [u.sub.[pi]] and [v.sub.[pi]], meet the following assumptions:

[u.sub.[pi]] ~ [absolute value of N(0, [[sigma].sup.2.sub.u[pi]]), [v.sub.[pi]] ~ [absolute value of N(0, [[sigma].sup.2.sub.v[pi]]), (4)

then per Jondrow, et.al. (1982) the natural residual, [[epsilon].sub.[pi]], will be decomposed into an inefficiency measure, [u.sub.[pi]], and random noise, [v.sub.[pi]].

Estimation of the Association Model

After the efficiency estimates have been calculated the next step of the analysis involves the selection of variables which theoretically correlate to each of the CAMELS rating categories used by examiners. The efficiency estimates obtained in stage one are then regressed on the group of financial variables obtained in stage two to determine the direction and strength of the association and to allow for comparisons of such relationships considering bank size. A control variable representing a bank's regulatory affiliation is also included in the regression.

Due to the non-availability of data needed to calculate all of the financial ratios chosen for the analysis, the sample size of banks included in stage two of the study is reduced. (All of the banks used in frontier estimation did not have the appropriate financial information available to construct the financial ratios needed for the second stage of the analysis. However, all of the banks are included for frontier estimation, since this allows for more accurate individual efficiency estimates. These individual efficiency scores are used in stage two as the dependent variable with various financial ratios serving as independent variables.) The final sample consists of 4,376 banks in 1999 and 5,158 banks in 1996. The sample by size category includes 282 large, 1,916 medium, and 2,178 small banks for 1999 and 318 large, 2,003 medium, and 2,837 small banks for 1996.

Several regression models are estimated for this study utilizing identical independent variables with only the dependent variables changing. The appropriate method of estimation in this situation is the seemingly unrelated regression (SUR), since it would be unrealistic to believe that the disturbance terms of the equations are unrelated. However, in some instances ordinary least squares (OLS) is as efficient as SUR. One of these situations is when the equations contain identical explanatory variables (Greene, 1997). Since the regressors used for analysis are the same across all models the OLS method is chosen and is as efficient as SUR per a previous study by Elyasiani et. al., (1994).

The model used for estimation is specified as follows:

[EFF.sub.ijt] = [[alpha].sub.it] + [k.summation over (k=1) [[beta].sub.kt] [R.sub.kjt] + [e.sub.ijt] (5)

where [EFF.sub.ijt] is the ith type of efficiency index estimated (i = Alt[pi]EFF]) of bank j (j = 1, ... n) in year t(t = 1996 or 1999). It should be noted that the efficiency score utilized as the dependent variable is the raw efficiency index before normalization on the 0,1 interval. Hence, the dependent variable is not bounded by a 0,1 scale. [[alpha].sub.it] represents the intercept term, [[beta].sub.kt] (k = 1, ..., k) are coefficients to be estimated, [R.sub.kjt] is the kth financial performance ratio and [e.sub.ijt] represents the error term.

Association Model Variable Selection

The selection of accounting-based financial ratios which accurately represent a bank's CAMELS rating is the most difficult yet meaningful undertaking of the empirical portion of this study for a number reasons. First, CAMELS ratings are proprietary information, which means that only regulatory personnel and researchers with regulatory associations have access to this data. Second, CAMELS ratings are based on a combination of objective and subjective information. Although a large portion of a bank's rating is derived from the analysis of various financial ratios corresponding to a specific CAMELS component, an important aspect of the rating results from examiner subjectivity. Thus, items such as differences among regulatory agencies, examiner experience, and inconsistencies among examination districts arguably have an effect on the ratings received by banks. Finally, empirical literature on this topic is scarce due to the aforementioned proprietary nature of the data. Literature on the financial performance of banks is found in great supply but few researchers have tackled the more elusive CAMELS modeling issue unless they have access to private CAMELS data (see Cole et.al., 1995 and DeYoung, 1998). The problems of a study of this type not withstanding, it is very realistic to conclude that most of the CAMELS categories can be proxied by financial ratios corresponding to the component in question per previous studies by Cole, et al. (1995) and Cole and Gunther (1998).

The one area that meets with a greater degree of subjectivity is the management component (M). A study by DeYoung (1998) suggests that there is a high degree of correlation between the M rating and the overall financial performance of a bank. Other variables such as unit costs and insider loans are shown to be good predictors of the M rating as well. As various financial ratios are used in this study as proxies of the C, A, E L, and S components, the M component will be proxied by the amount of insider loans, overhead expense, and the number of full-time equivalent employees to average assets, which mirrors Gilbert, et. al. (1999). Although in no way a perfect measure of management quality, these variables should provide useful insight into an otherwise unmeasurable rating component.

Financial theory regarding the operation of banking firms provides some insight into the use of certain financial ratios to proxy the six categories of a CAMELS rating. These ratios and their definitions are given in Exhibit 1. The aforementioned theory also allows for the formulation of hypotheses as to the expected signs of these proxies when efficiency scores are regressed upon them. Risk-based capital is chosen to represent the capital component. Although there are many other capital measures, the level of risk-based capital is chosen because of the importance regulators have placed on this measure in recent years. One would expect a positive relationship between the level of risk-based capital and profit efficiency due to the fact that a more well-capitalized bank results in a lower exposure to financial risk, which leads to a lower cost of both purchased funds and deposit insurance (Elyasiani, et. al. 1994).

The ratios of past due loans, nonaccrual loans, and the allowance for loan and lease loss are chosen to represent asset quality. A negative relationship is expected between the amount of nonaccrual loans and charged-off loans and profit efficiency, while a positive relationship between the allowance for loan and lease loss (ALLL) and profit efficiency is predicted. This stems from the fact that nonaccrual loans and charged-off loans are a drain on profits, while a healthy ALLL will provide an adequate cushion against further profit decreases. However, since money is transferred to the ALLL as an expense on the income statement there is an increased cost to the bank. The predicted relationship is, however, based only on the current balance of the allowance for loan and lease loss account and doesn't include any predictions regarding future transfers to the account due to the non-performance of loans and leases.

The three management quality ratios--insider loans, overhead expense, and the number of full-time employees--are discussed previously. They are expected to exhibit negative relations with profit efficiency. This is fairly self-explanatory in terms of overhead expense and the number of employees. Banks with lower overhead and fewer employees per million dollars of assets should be more efficient in the profit area. The amount of insider loans would also be expected to display a negative coefficient because a higher proportion of insider loans may indicate closely held or family owned institutions which tend to be smaller and more conservative than other banks.

Operating income, return on equity, and noninterest income are chosen to represent the earnings component. All of these are expected to show a positive relation with profit efficiency since all are directly related to the profits of a bank.

Liquidity is represented by liquid assets, jumbo CDs, and core deposits. Theory dictates that the more money a bank has in liquid assets the less it has invested in profitable loans and other products, thus a negative relation is forecast for profit efficiency. Jumbo CDs are time deposits in excess of $100,000 and are not FDIC insured above the $100,000 level. Thus these types of deposits tend to be purchased by banks needing funding for more profitable investments. This would lead to a positive relation between profit efficiency. Core deposits, on the other hand, tend to be very stable and low cost. Thus, a positive relation is predicted for core deposits. The final CAMELS category, interest rate sensitivity, is represented by the one year gap. There is no explicit assumption made regarding the relationship of this variable with the efficiency estimate.

A dummy variable is also included in the regression to determine if a bank's regulatory authority is a significant determinant of its level of profit efficiency. The bank is coded a 1 if it has a federal charter and a 0 if it has a state charter. This will allow for a comparison of charter authority among the total sample of banks as well as by asset size.

EMPIRICAL RESULTS

The results of the efficiency estimation as well as the association regressions prove interesting. Given in Exhibit 2 is an analysis of total assets for all banks utilized in the formulation of the efficient profit frontier for the years 1999 and 1996. The numbers, as expected, show the effects of frenzied merger activity in the mid and late 1990s. The average asset size, when considering all banks, increased by $108,489 while there was a decrease of 665 banks from 1996 to 1999. When considering large banks--banks with assets greater than $1 billion--the average asset size increased by over $2 billion from $9.6 billion to $11.67 billion. The number of large banks declined from 338 to 319. Banks that fall in the medium-size category for purposes of this study increased their average asset size by $5.4 million to slightly over $248 million and their numbers, the only category to show an increase, grew by 44 institutions. As for small banks, those with assets under $100 million, their average asset size increased from $45.2 million to $47.8 million. The number of small or community banks, easily the largest category, decreased by 690 from 5,308 in 1996 to 4,618 in 1999. This shows that while large banks are becoming larger, small and medium banks' asset growth is fairly stagnant.

Exhibit 3 shows the descriptive statistics for all variables utilized in the estimation of profit efficiency for the years 1999 and 1996, respectively, when using the national model. Specifically the mean and standard deviation for total profit, as well as the four input variables and five output variables, are reported. The mean of each category for its respective year of observation remains relatively stable. Additionally, the cost of inputs appear to make sound intuitive sense when examined by size classification. The number of observations do vary slightly for each year. However, as discussed previously, this is due to the many mergers and acquisitions occurring at this time as well as a very few bank failures. Since this study uses the population of all banks for which data were available this should not induce bias into the study and should not affect the comparability of efficiency and its relationship with selected financial ratios over the chosen years.

Exhibit 4 provides the mean profit efficiency scores as well as the standard deviation and minimum and maximum scores at the 5% and 10% truncation levels for the years 1999 and 1996. The efficiency scores by size category are also reported. While the degree of truncation used in a particular study is largely a matter of subjectivity, the 5% and 10% levels are most common. It is shown by Berger (1993) that profit efficiency scores rise very fast up to the 5% level and tend to taper-off after that. Thus, to be consistent with other studies in this area both the 5% and 10% truncation scores are reported but, for consistency purposes, the discussion will focus on the 10% truncation scores. Exhibit 4 shows that the mean profit efficiency for all banks in 1996 was 46.22% and increased to 48.84% in 1999 at the 10% truncation level. These numbers indicate that banks have considerable room for improvement in the area of profit efficiency. For example, the 1999 estimate of 48.84% means that the average bank generates only 48.84% of the profit of the "best-practice" bank operating in the United States. The relatively large standard deviation of 26.78% additionally indicates a wide dispersion in profit efficiency among banks. The profit efficiency estimates as a whole are consistent with previous studies (e.g., Bauer et al., 1993; Berger and Mester, 1997; and Berger and Humphrey, 1997) which is the key factor for purposes of the second-stage regression to be discussed later. Also, when compared to Huang (1999), a study using the same input and output variables, the estimates are consistent. Finally, to add additional credibility to the current investigation, the results are in line with previous studies (e.g., Hermalin and Wallace, 1994; Berger and Mester, 1997; and Rogers, 1998) when the profit efficiencies are examined by size classification. Large banks are shown to be less profit efficient than medium banks and medium banks less efficient than small banks in both 1999 and 1996.

The summary statistics of the financial ratios used as explanatory variables in the second stage regressions are contained in Tables 5 and 6 by size category for 1999 and 1996, respectively, and in Table 7 for all banks. Due to the unavailability of data in all of the financial ratio categories the number of banks used in the deterministic regression is decreased to 4,376 for 1999 and 5,158 for 1996. The ratios tend to be consistent with the operation of banks by size category. For example, in 1999 large banks had a mean risk-based capital ratio (RBC) of 11.04%, which is lower than that of both medium and small banks. This is consistent with the fact that smaller banks tend to be better capitalized than their larger counterparts. Large banks also have a lower full-time equivalent employee ratio (FTE) than either medium or small banks. Thus, large banks on average can manage more dollars of assets with fewer employees than can smaller institutions.

Medium banks tend to outperform large and small institutions when asset quality ratios are considered. They exhibit a lower level of nonaccrual loans (NONACCRL), a lower allowance for loan and lease loss reserve (ALLL), and a lower instance of charged-off loans (COFF) for both years. There is, however, a direct relationship shown between bank size and the profitability ratios.

Large banks have higher ratios in the areas of operating income (OI), return on equity (ROE), and net noninterest income (NII) than do their smaller counterparts for 1999 and 1996. However, as typically is the case, small banks are shown to be more liquid than medium and large banks with a higher proportion of liquid assets (LA) and core deposits (COREDEP) for each year.

Exhibit 8 provides evidence regarding the direction and strength of the relationship between the financial variables selected to represent a bank's CAMELS rating and its measure of profit efficiency. Reported are the coefficients for each variable, the standard error, and the adjusted [R.sup.2] of the model. Raw profit efficiency scores estimated from the national model are used as dependent variables as opposed to the scores normalized to lie between 0 and 1. Thus, to allow for more accuracy regarding a bank's true efficiency score the raw scores are regressed on the 14 financial variables and the signs of the coefficients as well as their significance levels are examined for all banks as well as by asset size. As shown in Exhibit 8 the regression using all banks displays an adjusted [R.sup.2] of .2058 for 1999 and .2128 for 1996. This gives a starting point for comparison when the same regression is used to analyze the association between variables. It is very interesting to note that when large banks are analyzed the [R.sup.2] increases to .3839 in 1996 and .3014 in 1999. The model using large banks displays the best fit of any size category, as medium banks have [R.sup.2]s of .2904 and .2935 while small banks display a rather low .1800 and .1688 for 1996 and 1999, respectively.

The signs of the coefficients are mostly as hypothesized earlier. The capital category proxy of risk-based capital (RBC) is found to be positive and significant for each size bank, lending to the theory that a more well-capitalized bank is more profit efficient. The proxies for asset quality provide a mixed output as to that predicted. For all banks , large banks, and small banks the nonaccrual loans coefficient (NONACCRL) is negative and significant as predicted. This is strangely enough not the case for medium-sized banks as the coefficient is found to be positive and insignificant. The coefficient for charged-off loans (COFF) is also found to have the expected negative sign and is significant for every category except 1999 large banks. Both of these findings make intuitive sense in that a bank with a lower percentage of nonaccrual and charged-off loans should display a higher degree of profit efficiency. The allowance for loan and lease loss variable (ALLL) displays the predicted positive sign and significance for all categories except 1999 small banks. The ratios selected to represent management quality are all predicted to display a negative relationship with profit efficiency. This is indeed the case for insider loans (IL) and overhead expense (OE). Both are also significant except for the large bank category.

The number of full-time equivalent employees (FTE) shows mixed results with both positive and negative coefficients for varying years in different categories. Variables representing the earnings component are all expected to be positively related to profit efficiency. The return on equity (ROE) is indeed positive and significant except for medium banks in 1999, for which no significance is noted. Net noninterest income (NII) is positive for all categories except large banks in 1999. This variable also displays a high degree of significance across all categories excluding large 1999 banks. The variable representing operating income (OI), however, shows a completely opposite outcome as to what is predicted. It is found to be negative and significant across all bank sizes and years of operation, for which there is no readily available explanation. This finding does, however, compare to that of Taylor, et al. (1997). The variables which serve as a proxy for the liquidity category display a mixture of outcomes compared to that expected. Liquid assets (LA) are hypothesized to have a negative relationship with profit efficiency, but all categories are shown to be positive and significant. Jumbo CDs (JMBOCD), which often are purchased by banks to fund profitable investments, are expected to display a positive relation with profit efficiency. This is indeed the case, with all categories displaying significance, except for large banks in 1996. Core deposits (COREDEP) are a low cost of funds for banks and result in positive and significant coefficients for all categories with the exception of large banks. A bank's one year gap (ONEGAP) proxies the difficult to measure interest rate sensitivity category. It is found to be negative and significant for all categories. The dummy variable, CHARTER, is included to determine if the chartering authority of a bank is a significant determinant of its level of profit efficiency. A nationally chartered bank is coded 1 and a state chartered bank is 0. The results show CHARTER to be positive and significant in 1999 and 1996 for the all banks category, implying nationally chartered banks are more efficient than state chartered banks. However, when decomposed by size classification the results show positive and significant coefficients for medium and small banks in 1996 and medium banks in 1999, with large banks having negative coefficients for both years and significance for 1996 only.

The results of the regression as a whole seem to support a priori expectations and are mostly consistent with Elyasiani et al. (1994), with the exception being the operating income variable. The output shows that many of the relationships that exist using the results of the national model and financial ratios in the all banks category disappear when the banks are segmented by asset size. Additionally, these differences indicate that large and small banks are fundamentally not the same in terms of input and output mix, which is consistent with previous studies. Thus, as evidenced by the inconsistency of the relationships between financial ratios and profit efficiency estimates by asset size, if an efficiency indicator is to be used as an addition to the CAMELS rating, one should be chosen that takes these differences into account so as not to penalize either large or small institutions.

CONCLUSIONS

There is no refuting the fact that banks today are more complicated entities than ever before. The added duties and services, permitted by the passage of laws such as the Gramm-Leach-Bliley Act, place a greater importance on the reliability of regulators to adequately assess a bank's efficiency and financial performance due to the allowance of increased risk-taking scenarios. In turn, the methods regulators utilize to assess the viability and productivity of banks must increase in sophistication to handle the added complexity of today's banking environment.

Furthermore, the areas of accounting-based financial ratios and efficiency are much debated in terms of the best measure of bank performance. While most studies tend to examine the two areas in isolation, this study chooses to merge the areas of bank efficiency and financial ratio performance. It examines the relationship between financial ratios deemed highly correlated with a bank's CAMELS rating and measures of profit efficiency to determine when and if the two should be used in combination, as suggested by previous studies. This examination, unlike others, is not solely dependent on data derived from large institutions. The data consists of banks of all sizes and is segmented by asset size to determine if the aforementioned relationship is the same for all banks. As shown in the previous section, the relationship between financial ratios and profit efficiency estimates is indeed different for banks of varying size. The relationship also differs when analyzing all banks together versus segmenting them by asset size. It is found that large banks achieve, on average, a better fit between financial ratios and profit efficiency scores. This supports the hypothesis that an efficiency measure added to the financial ratio analysis currently used by regulators would be more beneficial to large banks than small banks, thus penalizing smaller institutions. Furthermore, the findings indicate that, as widely hypothesized, large and small banks are fundamentally not the same in terms of input and output mix, which is consistent with previous studies. Thus, as evidenced by the inconsistency of the relationships between financial ratios and profit efficiency estimates by asset size, if an efficiency indicator is to be used as an addition to the CAMELS rating, one should be chosen that takes these differences into account so as not to penalize either large or small institutions.

This study expands on the claim by previous researchers that an efficiency indicator should be added to the current bank rating system used by regulators. The findings are promising that an equitable model can be developed to rate fairly an institution regardless of size. However, this study uses only the parametric stochastic frontier efficiency approach. A similar analysis using other parametric and nonparametric techniques would provide more insight into this area. Furthermore, while a strong introduction to the problem, the research presented in this paper contains only two years of data. The use of a more comprehensive time frame would serve to better justify the results. Finally, the choice of the financial ratios used to simulate a CAMELS rating is arbitrary. As long as the CAMELS system remains proprietary information it is a researcher's best guess as to the accuracy of the ratios chosen to represent a bank's rating. Thus, making the CAMELS rating available to researchers not affiliated with a regulatory agency would greatly enhance study in this area. This in turn would provide beneficial results to bankers, regulators, and academicians alike.

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Exhibit 1
Financial Ratios Representing Each CAMELS Category

 VARIABLE DESCRIPTION

Capital Adequacy (C)

Risk-Based Capital (RBC) Total capital divided by
 risk-weighted assets

Asset Quality (A)

Nonaccrual Loans (NONACCRL) Nonaccrual loans divided by
 average assets

Allowance for Loan and Lease Allowance for loan and lease
Loss (ALLL) loss divided by average loans
 and leases

Charge-Offs (COFF) Charged-off loans and leases
 divided by average loans and
 leases

Management Quality (M)

Insider Loans (IL) Loans to insiders divided by
 average assets

Overhead Expense (OE) Overhead expense divided by
 average assets

FTE Employees (FTE) Number of full-time equivalent
 employees divided by millions of
 dollars of average assets

Earnings (E)

Operating Income (OI) Total operating income divided
 by average assets

Return on Equity (ROE) Total income divided by total
 stockholder's equity

Noninterest Income (NII) Total noninterest income divided
 by average assets

Liquidity (L)

Liquid Assets (LA) Liquid assets divided total assets

Jumbo CDs (JMBOCD) $100,000+ time deposits divided by
 total assets

Core Deposits (COREDEP) Core deposits plus equity divided
 total assets

Sensitivity (S)

1 Year Gap (ONEGAP) Rate sensitive assets repricing
 within 1 year minus rate sensitive
 liabilities repricing within one
 year divided by total assets

Exhibit 2
Summary Statistics of Total Assets for All Banks
Analyzed for 1999 and 1996

 1999 1996 Difference

All Banks Mean 610,219 501,730 108,489
 Std. Dev 8,762,162 5,346,773 3,415,389
 Minimum 2,306 2,374 -68
 Maximum 571,732,000 272,429,000 299,303,000
 No. of Obs. 7,514 8,179 -665

Large Mean 11,671,792 9,605,605 2,066,187
Banks Std. Dev 41,069,115 24,629,191 16,439,924
($1 Minimum 1,002,227 1,015,159 -12,932
Billion +) Maximum 571,732,000 272,429,000 299,303,000
 No. of Obs. 319 338 -19

Medium Mean 248,913 243,415 5,498
Banks Std. Dev 177,163 175,059 2,104
($100 MM Minimum 100,031 100,151 -120
to $1B) Maximum 999,137 994,385 4,752
 No. of Obs. 2,577 2,533 44

Small Banks Mean 47,835 45,287 2,548
(< $100 MM) Std. Dev 24,413 24,453 -40
 Minimum 2,306 2,374 -68
 Maximum 99,822 99,971 -149
 No. of Obs. 4,618 5,308 -690

Note: Mean, Std. Dev., Minimum and Maximum values are in thousands
of dollars.

Exhibit 3
Descriptive Statistics of Variables Used in the 1996 and
1999 SFA Profit and Cost Frontier National Models

Variables: Mean Std. Dev.

Total Profit (a) 19,758 341,355
Input Price:
Price of Labor (a) 39.50 9.09
Price of Capital (b) .3472 .3535
Cost of Deposits 3.90 .65
Cost of Purch. Funds 4.63 1.12
Output Quantity:
Transaction Deposits (c) 80,382 916,932
Time & Savings Dep (c) 233,290 2,853,011
Real Estate Loans (c) 179,734 2,315,876
Other Loans (c) 215,566 3,491,460
Net Nonint. Income (c) 13,591 214,203
No. of Observations 7,514

Variables: Mean Std. Dev.

Total Profit (a) 14,741 221,818
Input Price:
Price of Labor (a) 35.14 8.58
Price of Capital (b) .3747 .3802
Cost of Deposits 4.15 .63
Cost of Purch. Funds 4.92 1.30
Output Quantity:
Transaction Deposits (c) 92,243 759,512
Time & Savings Dep (c) 185,332 1,295,194
Real Estate Loans (c) 133,856 1,065,328
Other Loans (c) 182,113 2,237,613
Net Nonint. Income (c) 9,687 128,553
No. of Observations 8,179

Variables: Mean Std. Dev.

Total Profit (a) 5,017 119,537
Input Price:
Price of Labor (a) 4.36 0.51
Price of Capital (b) -.0275 -.0267
Cost of Deposits -.25 .02
Cost of Purch. Funds -.29 -.18
Output Quantity:
Transaction Deposits (c) -11,861 157,420
Time & Savings Dep (c) 47,958 1,557,817
Real Estate Loans (c) 45,878 1,250,548
Other Loans (c) 33,453 1,253,847
Net Nonint. Income (c) 5,904 85,650
No. of Observations -659

Note: (a) Values are in thousands of dollars per full-time
equivalent employee

(b) Values are in dollars per dollar of fixed assets

(c) Values are in thousands of dollars

Exhibit 4
Summary Statistics of Profit Efficiency Estimates Obtained
from the National Model

 1999 1996
 5% 10% 5% 10%
 Trun- Trun- Trun- Trun-
 cation cation cation cation

All Mean .39722 .48845 .37692 .46220
Banks Std. Dev .24424 .26787 .24928 .27488
 Minimum .00911 .01169 .02568 .03286
 Maximum 1.0000 1.0000 1.0000 1.0000
 No. of 7,514 7,514 8,179 8,179
 Observations

Large Mean .28376 .35581 .25743 .32661
Banks Std. Dev .19275 .22015 .17243 .21040
 Minimum .00915 .01174 .02568 .03286
 Maximum 1.0000 1.0000 1.0000 1.0000
 No. of 319 319 338 338
 Observations

Medium Mean .37542 .46154 .35737 .44052
Banks Std. Dev .23765 .25803 .23707 .26349
 Minimum .00912 .01169 .03201 .04095
 Maximum 1.0000 1.0000 1.0000 1.0000
 No. of 2,577 2,577 2,533 2,533
 Observations

Small Mean .41725 .51267 .39387 .48120
Banks Std. Dev .24790 .27218 .25627 .28061
 Minimum .01403 .01800 .02830 .03620
 Maximum 1.0000 1.0000 1.0000 1.0000
 No. of 4,618 4,618 5,308 5,308
 Observations

Exhibit 5
Summary Statistics for Financial Ratios Used as Independent
Variables for 1999

 Variable Mean Std. Dev. No. of Obs.

Large RBC 11.04 3.60
Banks NONACCRL .39 .35
($1 ALLL 1.66 .70
Billion +) COFF .54 .57
 IL 1.01 1.46
 OE 3.45 1.61
 FTE .35 .16 282
 OI 2.08 .95
 ROE 17.48 8.60
 NII 1.76 1.70
 LA 10.34 6.56
 JMBOCD 11.09 9.19
 COREDEP 68.89 13.91
 ONEGAP -21.31 15.42

Medium RBC 13.28 4.71
Banks NONACCRL .37 .49
($100 MM ALLL 1.42 .60
to $1B) COFF .36 .64
 IL 1.56 1.58
 OE 3.26 1.44
 FTE .44 .15 1,916
 OI 1.77 1.28
 ROE 14.21 7.12
 NII 1.05 1.80
 LA 10.26 5.84
 JMBOCD 12.12 6.75
 COREDEP 80.85 8.73
 ONEGAP -21.28 14.20

Small RBC 15.65 6.24
Banks NONACCRL .52 .72
(< $100 ALLL 1.56 .72
MM) COFF .48 .76
 IL 1.44 1.52
 OE 3.28 1.12
 FTE .47 .16 2,178
 OI 1.37 .87
 ROE 10.80 8.35
 NII .77 .78
 LA 13.85 7.96
 JMBOCD 11.97 6.62
 COREDEP 84.42 7.68
 ONEGAP -18.48 15.15

Note: Definitions given in Exhibit 1.

Exhibit 6
Statistics for Financial Ratios Used as Independent
Variables for 1996

 Variable Mean Std. Dev. No. of Obs.

Large Banks RBC 11.54 4.97
($1 Billion +) NONACCRL .46 .43
 ALLL 1.97 1.01
 COFF .76 1.00
 IL 1.48 2.33
 OE 3.84 2.03
 FTE .40 .20 318
 OI 2.14 1.19
 ROE 17.68 9.69
 NII 1.95 2.17
 LA 15.41 8.02
 JMBOCD 9.09 7.44
 COREDEP 72.75 14.87
 ONEGAP -5.75 14.86

Medium Banks RBC 14.44 4.60
($100 MM to $1B) NONACCRL .46 .60
 ALLL 1.55 .67
 COFF .47 2.04
 IL 1.55 1.46
 OE 3.31 1.51
 FTE .49 .16 2,003
 OI 1.94 .83
 ROE 14.65 6.54
 NII 1.02 1.45
 LA 14.76 7.12
 JMBOCD 10.26 6.04
 COREDEP 85.23 7.53
 ONEGAP -10.72 13.49

Small Banks RBC 16.13 6.07
(< $100 MM) NONACCRL .51 .66
 ALLL 1.63 .79
 COFF 0.49 .72
 IL 1.41 1.41
 OE 3.38 1.35
 FTE .54 .18 2,837
 OI 1.67 .83
 ROE 12.02 6.82
 NII .86 1.04
 LA 17.57 8.41
 JMBOCD 10.50 6.29
 COREDEP 87.50 6.53
 ONEGAP -9.08 14.09

Note: Definitions given in Exhibit 1.

Exhibit 7
Summary Statistics for Financial Ratios Used as Independent
Variables for All Banks (1999 and 1996)

 Variable Mean Std. Dev. No. of Obs.
 1999 1996 1999 1996 1999 1996

 RBC 14.31 15.19 5.66 5.62
 NONACCRL .45 .49 .62 .63
 ALLL 1.51 1.62 .68 .77
 COFF .43 .50 .70 1.40
 IL 1.46 1.47 1.55 1.51
 OE 3.28 3.38 1.30 1.47
All FTE .45 .51 .15 .18 4,376 5,158
Banks OI 1.59 1.80 1.10 .87
 ROE 12.72 13.39 8.12 7.12
 NII .95 .99 1.40 1.33
 LA 12.05 16.35 7.24 8.03
 JMBOCD 11.98 10.32 6.87 6.28
 COREDEP 81.86 85.71 9.48 8.44
 ONEGAP -19.89 -9.51 14.82 13.96

Note: Definitions given in Exhibit 1.

Exhibit 8: Regression Results Using Raw Profit Efficiency
Scores Estimated from the National Model

Variable All Banks
 1999 1996

INTERCEPT -.3590 ** -.1657
 (.1496) (.1547)

RBC .0215 *** .0343 ***
 (.0024) (.0023)

NONACCRL -.0388 * -.0467 ***
 -.0206 -.0171

ALLL .0455 ** .0510 ***
 (.0181) (.0141)

COFF -.1124 *** -
 .0419 ***

IL (.0206) (.0095)
 -.0292 *** -

OE .0207 ***
 (.0073) (.0067)

FTE -.2477 *** -
 .0785 ***

OI (.0212) (.0181)
 -.2617 ** .1760 **

ROE -.1045 -.0857
 -.3311 *** -

NII .4016 ***
 (.0257) (.0257)

LA .0059 ** .0200 ***
 (.0026) (.0030)

JMBOCD .2306 *** .1052 ***
 (.0209) (.0177)

COREDEP .0086 *** .0187 ***
 (.0018) (.0014)

ONEGAP .0107 *** .0080 ***
 (.0021) (.0021)

CHARTER .0238 *** .0079 ***
 (.0017) (.0017)

Adjusted [R.sup.2] -.0101 *** -
N .0122 ***
 (.0008) (.0008)
 .0602 ** .0585 ***
 (.0246) (.0218)
 .2058 .2128
 4,376 5,158

Variable Large Banks
 1999 1996

INTERCEPT -.2721 .1307
 (.2624) (.1691)

RBC .0284 ** .0384 ***
 (.0119) (.0060)

NONACCRL -.4463 *** -.2335***
 -.1163 -.0640

ALLL .1406 ** .1003 ***
 (.0638) (.0311)

COFF .0910 -.1746 ***
 (.0965) (.0357)

IL -.0135 -.0197 *
 (.0249) (.0112)

OE -.0093 -.0334
 (.0611) (.0338)

FTE .5439 .4765 **
 (.3361) (.2053)

OI -.3189 *** -.3036 ***
 (.1005) (-.0650)

ROE .0221 ** .0282 ***
 (.0107) (.0078)

NII -.0506 .0516 **
 (.0610) (.0258)

LA .0177 *** .0186 ***
 (.0062) (.0033)

JMBOCD .0112 ** .0012
 (.0049) (.0035)

COREDEP .0054 -.0016
 (.0033) (.0020)

ONEGAP -.0121 *** -.0107 ***
 (.0027) (.0019)

CHARTER -.0103 -.1027 **
 (.0675) (.0468)

Adjusted [R.sup.2] .3014 .3839
N 282 318

Variable Medium Banks
 1999 1996

INTERCEPT -.6054 *** -.5318 **
 (.2286) (.2564)

RBC .0405 *** .0549 ***
 (.0040) (.0043)

NONACCRL .0121 .0060
 -.0343 -.0264

ALLL .0601 ** .1018 ***
 (.0273) (.0240)

COFF -.1534 *** -.0281 **
 (.0335) (.0124)

IL -.0377 *** -.0248 **
 (.0099) (.0101)

OE -.3493 *** -.0977 ***
 (.0299) (.0271)

FTE -.3406 ** .4975 ***
 (.1481) (.1389)

OI -.4597 *** -.4446 ***
 -(.0356) (.0388)

ROE .0053 .0206 ***
 (.0039) (.0047)

NII .3608 *** .1185 ***
 (.0292) (.0266)

LA .0152 *** .0243 ***
 (.0030) (.0024)

JMBOCD .0172 *** .1004 ***
 (.0030) (.0033)

COREDEP .0274 *** .0057 **
 (.0025) (.0028)

ONEGAP -.0112 *** -.0140 ***
 (.0012) (.0012)

CHARTER .0638 * .0700 **
 (.0332) (.0304)

Adjusted [R.sup.2] .2935 .2904
N 1,916 2,003

Variable Small Banks
 1999 1996

INTERCEPT -.3891 .1066
 (.3492) (.4511)

RBC .0121 *** .0277 ***
 (.0033) (.0030)

NONACCRL -.0588 ** -.0738 ***
 -.0270 -.0238

ALLL .0092 .0356 *
 (.0258) (.0200)

COFF -.1069 *** -.1166 ***
 (.0273) (.0246)

IL -.0243 ** -.0262 **
 (.0111) (.0104)

OE -.2410 *** -.1085 ***
 (.0362) (.0286)

FTE -.2764 * -.0030
 (.1644) (.1243)

OI -.3561 *** -.4958 ***
 (.0434) (.0377)

ROE .0073 * .0218 ***
 (.0043) (.0043)

NII .1333 *** .1338 ***
 (.0404) (.0291)

LA .0060 ** .0155 ***
 (.0026) (.0020)

JMBOCD .0073 * .0083 *
 (.0042) (.0048)

COREDEP .0287 *** .0111 **
 (.0037) (.0047)

ONEGAP -.0086 *** -
 .0102 ***

CHARTER -.0012 -.0012
 .0384 .0754 **

Adjusted [R.sup.2] -.0393 -.0334
N .1688 .1800
 2,178 2,837

***, **, and * indicates significance at the .01, .05
and .10 levels, respectively
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