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