- 标题：A parsimonious and predictive model of the recent bank failures.
- 作者：Trussel, John ; Johnson, Larry
- 期刊名称：Academy of Banking Studies Journal
- 印刷版ISSN：1939-2230
- 出版年度：2012
- 期号：January
- 语种：English
- 出版社：The DreamCatchers Group, LLC
- 摘要：The collapse of the housing and equity markets and the ensuing recession has led to the largest number of bank failures since the Savings and Loan crisis of the late 1980s and early 1990s. Since the start of the financial crisis in 2008 through 2009, there have been 167 bank failures in the United States (FDIC Bank Failures, 2010). The purpose of this analysis is to examine the financial condition of banks during this recent financial crisis and determine whether there are key financial indicators that could signal potential failure. The seriousness of the financial crisis is described by the Federal Deposit Insurance Corporation (FDIC) in the 2008 Quarterly Report.
- 关键词：Artificial neural networks;Bank failures;Bank loans;Bank reserves;Banks (Finance);Econometric models;Economic policy;Foreign exchange;Neural networks;Risk assessment;Television production companies;Valuation

**A parsimonious and predictive model of the recent bank failures.**

Trussel, John ; Johnson, Larry

INTRODUCTION

The collapse of the housing and equity markets and the ensuing recession has led to the largest number of bank failures since the Savings and Loan crisis of the late 1980s and early 1990s. Since the start of the financial crisis in 2008 through 2009, there have been 167 bank failures in the United States (FDIC Bank Failures, 2010). The purpose of this analysis is to examine the financial condition of banks during this recent financial crisis and determine whether there are key financial indicators that could signal potential failure. The seriousness of the financial crisis is described by the Federal Deposit Insurance Corporation (FDIC) in the 2008 Quarterly Report.

FDIC-insured institutions reported a net loss of $32.1 billion in the fourth quarter of 2008, a decline of $32.7 billion from the $575 million that the industry earned in the fourth quarter of 2007 and the first quarterly loss since 1990. Rising loan-loss provisions, large write-downs of goodwill and other assets, and sizable losses in trading accounts all contributed to the industry's net loss. More than two-thirds of all insured institutions were profitable in the fourth quarter, but their earnings were outweighed by large losses at a number of big banks (p. 1).

The increase in bank failures that began in 2008 was largely precipitated by the collapse of the U.S. housing market. Falling home prices led to declines in securities tied to home loans forcing banks to take write-downs on their balance sheets. Falling home prices combined with losses in the stock and bond markets resulted in historic declines in household wealth. The U.S. officially entered into recession in December 2007.

The financial crisis that began in early 2008 worsened the recession, making this not only one of the longest but also one of the most severe U.S. recessions since World War II. Real gross domestic product (GDP) declined at an annualized rate of 5.4% in the fourth quarter of 2008, 6.4% in the first quarter of 2009, and 0.7% quarter of 2009. Real GNP returned to positive growth of 2.2% on an annualized basis for the third quarter of 2009 and 5.7% in the fourth quarter of 2009. (Bureau of Economic Analysis, 2010). Because of the recession, bank failures continued with 130 failed banks in 2009 (FDIC Bank Failures, 2010).

The current banking crisis is broad based and linked closely to defaults on residential real estate and small business loans. Smaller banks that were linked to construction, real estate development, and small businesses loans were most at risk. This current bank crisis is different from the bank crisis of the late 1980s and 1990s, which was largely linked to defaults in the commercial real estate, agricultural, and petroleum industries, and particularly in oil and agricultural producing regions.

This paper investigates the financial indicators associated with recent bank failures. The number of predictor variables is limited to six for reasons of parsimony. Previous literature has addressed the topic of predicting bank failure; however, our model differs from previous studies in four important ways. First, our model is parsimonious, using only six financial indicators to predict bank failure. Second, our model uses logistic regression to weight the six financial indicators into a composite measure of failure. Third, we use data from the recent bank failures to develop our model. Fourth, we incorporate various costs of misclassifying banks as failed or not failed. The regression model results in a prediction of the likelihood of failure, which correctly classifies up to 98% of the sample as failed or not.

The remainder of the paper is organized as follows: Section 1 describes the extant literature on failure in banks. Section 2 discusses the indicators associated with failure and the related hypotheses testing. The results of testing the failure model are analyzed in Section 3, and the Section 4 concludes the paper.

BANK FAILURE MODELS IN THE LITERATURE

The Uniform Financial Institutions Rating System

The Uniform Financial Institutions Rating System (UFIRS) was adopted by the Federal Financial Institutions Examination Council (FFIEC) on November 13, 1979, with revisions made since then. Federal supervisory agencies use this system to evaluate the soundness of financial institutions and to identify those institutions requiring special attention. Under the UFIRS, each financial institution is rated based on six components: the adequacy of capital, the quality of assets, the capability of management, the quality and level of earnings, the adequacy of liquidity, and the sensitivity to market risk. This rating approach is called the CAMELS system, which is an acronym for these six components--Capital adequacy, Asset quality, Management risk, Earnings strength, Liquidity, and Sensitivity to market risk. In previous iterations of the rating system there was no measure of market risk, and the acronym was CAMEL.

Each of the CAMELS components is evaluated and assigned a score from one-to-five with one being the best relative to the institution's size, complexity, and risk profile. The scores from each of the six categories are summed and the institution is placed into one of five composite groups based on this total score. Institutions in the bottom group will cause the highest level of supervisory concern.

Bank regulators evaluate the financial condition of banks using on-site examinations and off-site statistical analysis. On-site exams use the CAMELS system and result in a rating of one-to-five with one being the highest rating and five the lowest rating for financial condition. While on-site examinations are the most extensive reviews, the rating can decline between on-site examinations. (Cole and Gunthner, 1998)

Existing Early Warning Systems

Besides the UFIRS, the FDIC also uses a bank's capital adequacy as an early warning for further action. The FDIC has minimum capital requirements, below which a bank must (with certain exceptions) file a written capitalization plan with the FDIC regional director (FDIC Bank Examinations, 2010, Section 325.3). The minimum ratio of tier one (or core) capital to total capital is four percent (and in some cases three percent). Tier one capital is common equity plus noncumulative perpetual preferred stock plus minority interests in consolidated subsidiaries less goodwill and other ineligible intangible assets. The amount of eligible intangibles (including mortgage servicing rights) included in core capital is limited in accordance with supervisory capital regulations. If a bank's tier one capital falls below two percent of total assets, then the FDIC considers the bank to operating in an "unsafe or unsound condition" (FDIC Bank Examinations, 2010, Section 325.4). However, only one of the 167 banks that failed in 2008 and 2009 had tier one capital less than two-percent, and only two had tier one capital less than four-percent at the end of 2007. Thus, this system is not a good predictor of failure.

Numerous studies have focused on early warning systems as a supplement to on-site bank examinations with the purpose of determining troubled banks between bank examinations. Such systems typically utilize indicators from the CAMELS system as inputs into a prediction model. For example, Jagtiani, et al. (2003) evaluated early warning systems using a simple logit analysis, a more complete stepwise logit analysis, and a non-parametric trait recognition (TRA) model. They concluded that the simple logit was better in predicting capital inadequate banks.

Kumar and Arora (1995) also used a logit model to predict bank failures during 1991. They used a risk rating rather than the CAMELS system as their predictors and compared both linear and quadratic models. They concluded that both models give similar and satisfactory results. Likewise, Gunsel (2007) used the CAMEL rating system and logit analysis to measure the probability of bank failure for banks in North Cyprus. He concluded that the CAMEL modeling approach is appropriate for predicting bank failures in emerging economies.

Kolari, et.al. (2002) compared logit analysis as an early warning system to a nonparametric trait recognition model for large bank failures during the late 1980's and early 1990's. They found that both approaches for an early warning system are appropriate but the trait recognition model worked best for minimizing Type I (misclassifying failures as not failures) and Type II errors (misclassifying not failures as failures). Kasa and Spiegel (2008) also used logit regression to compare bank failures using an "absolute closure rule" (when asset-liability ratios fall below a threshold) versus a "relative closure rule" (when asset-liability ratios fall below an industry average) which implies forbearance during economic downturns. They conclude that bank closures are based more on relative performance than an absolute closure rule.

Thomson (1991), in his article on predicting bank failures in the 1980's, also used logit analysis to predict default using a combination of accounting and economic variables as the explanatory variables. His results indicate that solvency and liquidity are the most important variables and showed hints of distress up to thirty months before default. His final model included solvency, capital adequacy, asset quality, management quality, earnings performance, and relative liquidity variables.

Cole and Gunther (1998) in their comparison of on-and off-site monitoring systems used a probit model as the early warning system. They suggested the econometric model was useful for monitoring banks six months past their on-site examination date. Other studies of early warning systems using advanced analytical techniques include Swicegood and Clark (2001), who compared neural networks and discriminant analysis to professional human judgment, and Salchenberger, et al. (1992), who also used neural networks in an analysis of thrift failures. Both concluded that neural networks could perform as good as or better than other early warning systems for bank failure. Ozkan-Gunay and Ozhan (2007) recommend neural networks for monitoring banks in emerging economies. Curry, et al. (2007) take a different approach and analyze bank failures based on equity market data and conclude that market data could improve the early warning system based solely on accounting data. Jesswein (2009) tests the so-called "Texas ratio" (non-performing assets divided by the sum of tangible equity capital and loan loss reserves). He finds that the ratio provides important insights, but it is probably not a good tool for an overall analysis of bank failure.

Various financial, accounting, and economic variables are used across the different studies. For example, Jagtiani, et. al (2003) incorporated forty-two explanatory variables in their analysis as compared to Cole and Gunther (1998) who used only eight. A review of different analytical techniques and variables used in the different analysis was completed by Demirguc-Kunt (1989), who summarized significant independent variables from seven previous studies. Table 1 includes a representative sample of variables used in previous studies by CAMELS category. In this study, we utilize one variable per category, similar to the ones used in these previous studies.

MODEL DEVELOPMENT AND FINANCIAL INDICATORS

Previous models of bank failure are deficient for several reasons. Our model incorporates methods to compensate for the shortcomings of previous studies.

First, the UFIRS/CAMELS system used by bank regulators and previous researchers is problematic. Several items are considered and measured to evaluate each category, making the system quite complex. Including too many variables to proxy for each category could over-specify the model and cause multicollinearity. For example, in the capital adequacy category, evaluators consider these items at a minimum (FDIC, 2009):

* The level and quality of capital and the overall financial condition of the institution.

* The ability of management to address emerging needs for additional capital.

* The nature, trend, and volume of problem assets, and the adequacy of allowances for loan and lease losses and other valuation reserves.

* Balance sheet composition, including the nature and amount of intangible assets, market risk, concentration risk, and risks associated with nontraditional activities.

* Risk exposure represented by off-balance sheet activities.

* The quality and strength of earnings, and the reasonableness of dividends.

* Prospects and plans for growth, as well as past experience in managing growth.

* Access to capital markets and other sources of capital, including support provided by a parent holding company.

Our model is parsimonious, with one variable per CAMELS category, chosen based on popularity in the literature.

Second, there is no conceptually sound system for weighting each of these items to determine the score for each category and the composite score. We use logistic regression analysis to develop our model of bank failure. The multivariate model weights each of the variables using the sample data and results in a composite likelihood of failure. Unlike the composite score from the UFIRS system, our composite score will weight each variable according to results of the regression analysis.

Third, the recent failures arise from differing reasons than previous failures. The recent failures occurred during a unique economic period. Banks tied to home mortgages were faced with unprecedented foreclosures especially in areas that had experienced rapid increases in home prices. Defaults on sub-prime loans and subsequent foreclosures depressed home prices in many regions of the country. Defaults then moved to prime borrowers as many owed more on their mortgages that the homes were worth. Many community banks also became vulnerable due to exposure from real estate and construction loans and commercial loans linked to the residential sector. Thus, the relationship among the predictor variables is likely different than previous periods.

Fourth, we take into account various costs of misclassification errors. Previous studies do not take into account the likelihood that costs of Type I errors (misclassifying failures as non-failures) are higher that the costs of Type II errors (misclassifying non-failures as failures)..

Indicators of Failure

We incorporate the same six categories from the UFRIS to develop our failure model; however, we use one variable to proxy each category. The variables were chosen based upon their usage in the literature on bank failure to best reflect each category. Obviously, one variable cannot capture the complexities of each category; however, our goal is to have a parsimonious model that will result in a reliable model of failure prediction.

Capital Adequacy (CAP). A financial institution is expected to maintain capital corresponding with the risks to the institution. The nature and extent of inherent risk will drive the levels of capital needed by the institution to meet these risks. There are also regulatory minimums that are required of financial institutions. We proxy capital adequacy as the ratio of tier one capital to total assets and expect a negative correlation with the likelihood of failure. Tier one (or core) capital includes common equity, noncumulative perpetual preferred stock, minority interests in consolidated subsidiaries and excludes goodwill and other ineligible intangible assets. The amount of eligible intangibles (such as mortgage servicing rights) is limited in accordance with supervisory capital regulations.

Asset Quality (QUAL). Asset quality reflects "the quantity of existing and potential credit risk associated with the loan and investment portfolios, other real estate owned, and other assets, as well as off-balance sheet transactions" (FDIC 2009). One of the most risky assets is the institution's loan portfolio. We measure asset quality as the ratio of total loans and leases to total assets and anticipate a positive correlation with the likelihood of failure. Higher amounts of loans and leases in the asset portfolio imply more risk of failure.

Management Risk (MGT). This category represents a measure of "the capability of the board of directors and management, in their respective roles, to identify, measure, monitor, and control the risks of an institution's activities and to ensure a financial institution's safe, sound, and efficient operation in compliance with applicable laws and regulations" (FDIC 2009). Management must address all risks, maintain appropriate controls, and monitor the information systems. We proxy management risk as the ratio of insider loans to total loans and expect a positive correlation with the likelihood of failure. Insider loans are a measure of potential management fraud.

Earnings Strength (EARN). Financial institutions, as well as any proprietary organization, need to be profitable in order to continue to operate. We measure earnings strength as the return on assets, which is the ratio of net income to total assets. We anticipate a negative association with failure.

Liquidity Position (LIQ). Liquidity is the ability of an entity to pay its short-term obligations in a timely manner. Also, financial institutions must consider the funds necessary to meet the banking needs of their communities. We proxy the liquidity position as the ratio of cash plus securities to total deposits and expect a negative relationship with failure.

Sensitivity to Market Risk (RISK). This component reflects the degree to which changes in market conditions, such as interest rates, foreign exchange rates, commodity prices, or equity prices, can adversely affect earnings and capital. For many institutions, the primary source of market risk arises from loans and deposits and their sensitivity to changes in interest rates. We measure the sensitivity to market risk as the ratio of loan loss reserves to total loans and anticipate a positive correlation with the probability of failure. The six indicators of bank failure are summarized in Table 2.

RESULTS OF TESTING THE FAILURE PREDICTION MODEL

This study focuses on a limited set of financial indicators and the prediction of recent bank failures. Certain financial indicators are hypothesized to be related to failure and are described in the previous section. This section presents the empirical tests of the failure prediction model.

Sample Selection and Descriptive Statistics

According to the FDIC, there have been 193 bank failures since 2000, of which 167 were in 2008 and 2009. Thus, we focus on the huge number of failures in recent years. We define a failed bank as one that fell under the receivership of the FDIC during 2008 or 2009. In order to develop a predictive model, we obtained data from the FDIC for all banks as of 2007. There are 8,548 banks on the FDIC database as of December 31, 2007. Of these, 86 do not have complete data to compute the indicators from Table 1 and are not included in the sample. This leaves 8,462 banks in the sample, of which 165 (2%) failed in 2007 or 2008.

Summary statistics are included in Table 3. As predicted, statistically speaking, failed banks have less tier one capital (as a percent of total assets), less net income (as a percent of total assets), and less cash and securities (as a percent of total deposits) than banks that did not fail. Also as expected, failed banks have more loans and leases (as a percent of total assets) and a higher allowance for loan losses (as a percent of total loans) than their counterparts that did not fail. However, we did not expect that failed banks have fewer insider loans (as a percent of total loans).

The Multivariate Model

We use cross-sectional data from 2007 to test our model of failure. Since the dependent variable is categorical, the significance of the multivariate model is addressed using logistic regression analysis. Carlson (2010) suggests using both logit analysis and survival analysis in a similar situation of bank failures. We only use logit analysis, due to the short time period of the study. Using this method, the underlying latent dependent variable is the probability of failure for bank i, which is related to the observed variable, [Status.sub.i], through the relation:

[Status.sub.i] = 0 if the organization has not failed,

[Status.sub.i] = 1 if the organization has failed.

The model includes all of the independent variables from Table 2. The predicted probability of the kth status for bank i, P([Status.sub.ik]) is calculated as:

P([Status.sub.ik]) = 1/1 + [e.sup.-z] (1)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

We use a random sample of approximately one-half of the banks to develop the model (the estimation sample) and the other half to test the model (the holdout sample). The results of the logistic regression model are included in Table 4. Overall, the model is statistically significant at less than the 0.01 level according to the chi-square statistic. Also, all of the indicators, except LIQ, are significantly related to the probability of failure (at less than the 0.05 level). LIQ is not statistically significant in the multivariate model. All of the variables have the predicted signs, except for MGT. As with the univariate results, the multivariate results find that failed banks actually have fewer insider loans that do banks that did not fail. A review of literature shows Thomson (1991) finds a positive and significant relationship between insider loans and bank failure but it is not identified as a significant variable in the seven studies summarized by Demirguc-Kunt (1989). Perhaps more insider loans in a bank that did not fail reflect management's confidence in the bank to continue operating.

The results of the regression analysis also allow one to address the impact of a change in a financial indicator on the likelihood of failure. In Table 5, Exp(B) is the odds ratio, which is the change in the odds of the event (failure) occurring for a one-unit change in the financial indicator. The last column in Table 3 represents the impact on the predicted likelihood of failure due to a 0.01 increase in the value of the financial indicator. The impact for the 0.01 increase is computed as [Exp(b).sup.0010]--1. The financial indicators CAP, EARN and RISK have the biggest influences on the likelihood of failure. An increase in CAP (EARN) by 0.01 will decrease the likelihood by 0.290 (0.289). A decrease in RISK of 0.01 will increase the predicted likelihood of failure by 0.219. Based on the financial indicators in this model, banks attempting to reduce the likelihood of failure will have the biggest impact by increasing the amount of tier one capital (relative to total assets), by increasing the return on assets or by decreasing loan loss reserves (relative to total loans). Also, an increase in MGT (insider loans as a percent of total loans) of 0.01 will decrease the risk of failure by 0.194. Changes in QUAL or LIQ do not have nearly the impact on the likelihood of failure.

Predicting Failure

We use the results of the logistic regression analysis to test the predictive ability of the failure model. The observed logistic regression equation (from Table 4) for bank i at time t is:

P(i,t) = 1/(1+[e.sup.-Zi])

where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The predicted dependent variable, P(i,t) the probability of failure for bank i, is computed using the actual financial indicators for each bank in the estimation sample. The resulting probabilities are used to classify banks as failed or not. Jones (1987) suggests adjusting the cutoff probability for classifying as failed or not failed in two ways. Following the suggestion of Jones, we first incorporate the prior probability of failure and then include the expected cost of misclassification.

Using logit, the proportion of failed banks in the sample must be the same as the proportion in the population to account for the prior probability of failure. If the proportion is not the same, then the constant must be adjusted (Maddala 1991). This is more of a problem when a paired sample method is used, which is not the case here. Since two percent of the banks in the sample are failed, we assume that the prior probability of failure is 0.02. We evaluated the sensitivity of the model to other assumptions of the prior probability of failure by using prior probabilities of 0.005, 0.01 and 0.03. These assumptions did not alter the results (not shown) significantly. The tenor of the results is similar; however, the cutoff probabilities for classification differ.

The ratios of the cost of type I errors (incorrectly classifying failed banks as not failed--a false negative) to type II errors (incorrectly classifying banks that are not failed as failed--a false positive) also must be determined. The particular cost function is difficult to ascertain and will depend on the user of the information. For example, a creditor may want to minimize loan losses (and thus type I errors); however, he or she will suffer an opportunity cost (type II error) if credit is granted to another borrower at a lower rate. In most cases, the cost of a type II error is likely to be much smaller than a type I error. Thus, we incorporate several relative cost ratios (and cutoff probabilities) into our analysis. Specifically, we include the relative costs of type I to type II errors of 1:1, 10:1, 20:1, 30:1, 40:1, 60:1, and 100:1 (Beneish 1999; Trussel 2002).

The results of using the logit model to classify banks as failed or not are included in Table 5, Panel A, for the estimation sample. The cutoff probabilities presented are those that minimize the expected costs of misclassification. Following Beneish (1999), the expected costs of misclassification (ECM) are computed as:

ECM = P(FAIL)[P.sub.I][C.sub.I] + [1 - P(FAIL)][P.sub.II][C.sub.II],

where P(FAIL) is the prior probability of failure, [P.sub.I] and [P.sub.II] are the conditional probabilities of type I and type II errors, respectively, and [C.sub.I] and [C.sub.II] are the costs of type I and type II errors, respectively.

The validity of the model is tested on the holdout sample using the same cutoff probabilities from the estimation sample. Table 5, Panel B, includes the results for the holdout sample. The results indicate that the model can identify failed banks with 46% (at a cost ratio of 100:1) to 98% (at a cost ratio of 1:1) of the banks in the estimation sample correctly classified. Although the overall classification results are strong at the lower cost ratios, the type I error rates are very high. A more balanced result is obtained at the middle cost ratios of 40:1 and 60:1. Similar results are obtained using the holdout sample.

To test the usefulness of the model, we compare these results to a naive strategy. This strategy classifies all banks as failed (not failed) when the ratio of relative costs is greater than (less than or equal to) the prior probability of failure. This switch in strategy between classifying all organizations as not failed to classifying all of them as failed occurs at relative cost ratios of 50:1 [i.e., 1/P(Fail) or 1 / 0.02]. If all banks are classified as failed (not failed), then the naive strategy makes no type I (type II) errors. In this case, [P.sub.I] ([P.sub.II]) is zero, and [P.sub.II] ([P.sub.I]) is one. The expected cost of misclassification for the naive strategy of classifying all banks as not failed (failed) reduces to 0.98 [C.sub.II] (0.02 [C.sub.I]), since the prior probability of failure is 0.02.

We also report the relative costs or the ratio of the ECM for our model to the ECM for the naive strategy in both panels of Table 5. Relative costs below 1.0 indicate a cost-effective model. For both the estimation and holdout samples, our model has a much lower ECM than the naive strategy, except for the 1:1 cost ratio. In fact, the relative costs are below 84% for all levels of type I to type II errors except 1:1. These results provide evidence to suggest that our failure model is extremely cost-effective in relation to a naive strategy for almost all the ranges of the costs of type I and type II errors. Applying the prediction model

We use one of the banks from the sample to illustrate the model. The model allows one to predict the status of the bank as failed or not failed. From the results of the logistic regression, the probability of the failure for bank i at time t, P(i,t) is:

P(i, t) = 1 / 1 + [e.sup.-zi] (1)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Substituting the actual variables from the example entity (in parentheses), we obtain:

[Z.sub.i] = -3.416 - 34.217(0.052) + 3.940(0.118) - 21.560(0) - 34.143(0.009) - 0.021(0.861) + 19.801(0.001) [Z.sub.i] = -5.036

Substituting the value into equation (1) obtains:

P = 1 / (1 + [e.sup.-5.036])

P = 0.006.

Table 5, Panel A, shows that the selected bank is predicted not to be failed, since the actual probability of failure at the end of 2007 (0.006) is less than the cutoff at all levels of the ratio of type I to type II errors. The entity's actual status is not failed as of the end of 2009. Thus, the model correctly predicted the financial status of this bank.

CONCLUSION

The collapse of the housing and equity markets and the ensuing recession has led to the largest number of bank failures since the Saving and Loan crisis of the late 1980s and early 1990s. The recent failures arise from a unique economic period compared with the previous failures. The purpose of this analysis is to examine the financial condition of banks during this recent financial crisis and determine whether there are key financial indicators that could signal potential failure. Our model uses logistic regression to weight the six financial indicators into a composite measure of failure from recent bank failures. In addition, the study incorporates various costs of misclassifying banks as failed or not.

The regression model results in a prediction of the likelihood of failure, which correctly classified up to 98% of the sample as failed or not. The model also allowed for an analysis of the impact of a change in a financial indicator on the likelihood of failure. As predicted, statistically speaking, failed banks have less tier one capital (as a percent of total assets), less net income (as a percent of total assets), and less cash and securities (as a percent of total deposits) than banks that did not fail. Also as expected, failed banks have more loans and leases (as a percent of total assets) and a higher allowance for loan losses (as a percent of total loans) than their counterparts that did not fail. However, we did not expect that failed banks have fewer insider loans (as a percent of total loans).

We also report the relative costs or the ratio of the ECM for our model to the ECM for a naive strategy. For both the estimation and holdout samples, our model has a much lower ECM than the naive strategy, except for the 1:1 cost ratio. In fact, the relative costs are below 84% for all levels of type I to type II errors except 1:1. These results provide evidence to suggest that our failure model is extremely cost-effective in relation to a naive strategy for almost all the ranges of the costs of type I and type II errors.

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John Trussel, Dalton State College

Larry Johnson, Dalton State College

TABLE 1 REPRESENTATIVE INDICATORS OF FAILURE FROM SELECTED PREVIOUS STUDIES VARIABLES BY CATEGORY REFERENCE Capital Adequacy Total Equity / Total Assets Swicegood and Clark (2001) Earned Surplus / Total Assets Salchenberger, Cinar and Lash (1992) Regulator Recognized Capital / Gajewski (1988) Total Assets Asset Quality (Loans + Leases) / Total Assets Thompson (1991) Real Estate Loans / Total Loans Hirtle and Lopez (1999) Non-accrual Loans / Total Loans Gajewski (1988) Real Estate Owned / Total Assets Salchenberger, Cinar and Lash (1992) Management Competence Insider Loans / Total Assets Thompson (1991) Operating Expense / Gross Salchenberger, Cinar and Lash Operating Income (1992) Compensation / Gross Operating Pantalone and Platt (1987) Income Sensitive Deposits / Total Gajewski (1988) Deposits Earnings Net Income / Total Assets Thompson (1991) Non-interest Income / Total Swicegood and Clark (2001) Assets Net Interest Margin Salchenberger, Cinar and Lash (1992) Retained Earnings / Total Assets Pantalone and Platt (1987) Liquidity Non-deposit Liabilities / (Cash Thompson (1991) + Securities) Total Securities / Total Assets Swicegood and Clark (2001) Cash / Total Assets Hirtle and Lopez (1999) (Cash + Securities) / Savings + Swicegood and Clark (2001) Borrowings Cash / Total Deposits Carlson (2010) Sensitivity to Risk Loan Loss Allowance / Total Loans Swicegood and Clark (2001) Off Balance Sheet Commitments / Swicegood and Clark (2001) Total Assets Non-performing Assets / Total Swicegood and Clark (2001) Assets Asset Growth Swicegood and Clark (2001) TABLE 2 INDICATORS OF FAILURE USED IN THIS STUDY CAMELS CATEGORY MEASURE EXPECTED RELATIONSHIP WITH FAILURE Capital Adequacy (CAP) Tier one Capital(a) - Total Assets Asset Quality (QUAL) Total Loans + Leases + Total Assets Management Risk (MGT) Insider Loans + Total Loans Earnings (EARN) Net Income - Total Assets Liquidity (LIQ) Cash + Securities - Total Deposits Sensitivity to Risk (RISK) Loan Loss Allowance + Total Loans (a) Tier one (core or regulatory) capital includes: common equity plus noncumulative perpetual preferred stock plus minority interests in consolidated subsidiaries less goodwill and other ineligible intangible assets. The amount of eligible intangibles (including mortgage servicing rights) included in core capital is limited in accordance with supervisory capital regulations. TABLE 3 DESCRIPTIVE STATISTICS AND TESTS OF SIGNIFICANCE OF DIFFERENCES BETWEEN FAILED AND NOT FAILED BANKS Panel A: Descriptive Statistics CATEGORY STATUS MEAN STANDARD T-STATISTIC DEVIATION (SIGNIFICANCE) CATEGORY Not Failed 0.1206 0.09443 4.762 CAP Failed 0.0870 0.03243 (<0.001) QUAL Not Failed 0.6525 0.17459 -6.920 Failed 0.7473 0.12225 (<0.001) MGT Not Failed 0.0143 0.01881 2.399 Failed 0.0116 0.01527 (0.018) EARN Not Failed 0.0084 0.05032 4.198 Failed -0.0018 0.01956 (<0.001) LIQ Not Failed 1.0060 21.46679 2.327 Failed 0.2163 0.27656 (0.020) RISK Not Failed 0.0131 0.01562 -4.880 Failed 0.0191 0.01459 (<0.001) Panel B: Correlations CAP QUAL MGT EARN QUAL -0.377 ** MGT 0.074 ** 0.145 ** EARN 0.034 ** -0.059 ** -0.056 ** RISK 0.098 ** -0.142 ** -0.016 -0.028 ** LIQ 0.060 ** -0.063 ** -0.026 * 0.098 ** TABLE 4 THE LOGISTIC REGRESSION RESULTS OF THE RELATION AMONG THE FINANCIAL INDICATORS AND FAILURE VARIABLE COEFFICIENT STD. ERROR P-VALUE IMPACT (0.01) Constant -3.416 .878 .000 CAP -34.217 6.503 .000 -.290 QUAL 3.940 1.025 .000 .040 MGT -21.560 9.805 .028 -.194 EARN -34.143 7.591 .000 -.289 LIQ -.021 .082 .798 .000 RISK 19.801 4.586 .000 .219 Model Summary: -2 Log Likelihood = 1,422.427; Nagelkerke [R.sup.2] = 0.136; [chi square] (Significance) = 203.675 (<0.001) NOTE: See Table 2 for a description of the independent variables. The latent dependent variable equals 0 if the bank is not failed and 1 if the bank is failed. The last column represents the impact on the predicted likelihood of failure due to a 0.01 increase in the value of the covariate. The impact is the change in the probability of failure due to a 0.01 increase in the variable and is computed as [Exp(B).sup.010]-1. TABLE 5 THE PREDICTIVE ABILITY OF THE FAILURE MODEL INCLUDING THE EXPECTED COSTS OF MISCLASSIFICATION AND THE RELATIVE COSTS OF TYPE I ERROR TO TYPE II ERROR Panel A: Estimation Sample Ratio of the Cost of Type I to Type II Errors 1:1 10:1 20:1 30:1 40:1 60:1 100:1 Cutoff 0.120 0.060 0.040 0.040 0.020 0.020 0.010 Type I Error 0.885 0.718 0.564 0.564 0.231 0.231 0.064 Type II Error 0.004 0.025 0.080 0.080 0.309 0.309 0.550 Overall Error 0.020 0.038 0.089 0.089 0.307 0.307 0.541 ECM Model 0.021 0.165 0.299 0.409 0.483 0.573 0.665 ECM Naive 0.020 0.195 0.390 0.585 0.780 0.981 0.981 Relative Costs 1.065 0.844 0.766 0.699 0.619 0.584 0.678 Overall Correct 0.980 0.962 0.911 0.911 0.693 0.693 0.459 Panel B: Holdout Sample Ratio of the Cost of Type I to Type II Errors 1:1 10:1 20:1 30:1 40:1 60:1 100:1 Cutoff 0.120 0.060 0.040 0.040 0.020 0.020 0.010 Type I Error 0.885 0.705 0.551 0.551 0.231 0.231 0.064 Type II Error 0.005 0.028 0.089 0.089 0.316 0.316 0.554 Overall Error 0.021 0.040 0.097 0.097 0.314 0.314 0.545 ECM Model 0.022 0.165 0.302 0.409 0.490 0.580 0.668 ECM Naive 0.020 0.195 0.390 0.585 0.780 0.981 0.981 Relative Costs 1.149 0.844 0.774 0.700 0.628 0.591 0.681 Overall Correct 0.979 0.960 0.903 0.903 0.686 0.686 0.455 NOTE: The cutoff is the probability of failure that minimizes the expected cost of reclassification, ECM. ECM is computed as P(FAIL)[P.sub.I][C.sub.I] + [1-P(FAIL)][P.sub.II][C.sub.II], where P(FAIL) is the prior probability of failure (0.02), [P.sub.I] and [P.sub.II] are the conditional probabilities of Type I and Type II errors, respectively. [C.sub.I] and [C.sub.II] are the costs of Type I and type II errors, respectively. The relative costs are the ECM Model divided by the ECM Naive.