Financial distress in Brazilian banks: an early warning model*,**

is study aims to propose an early warning model for predicting nancial distress events in Brazilian banking institutions. Initially, a set of economicnancial indicators is evaluated, suggested by the risk management literature for identifying situations of bank insolvency and exclusively taking public information into account. For this, multivariate logistic regressions are performed, using as independent variables nancial indicators involving capital adequacy, asset quality, management quality, earnings, and liquidity. e empirical analysis was based on a sample of 142 nancial institutions, including privately and publicly held and state-owned companies, using monthly data from 2006 to 2014, which resulted in panel data with 12,136 observations. In the sample window there were nine cases of Brazilian Central Bank intervention or mergers and acquisitions motivated by nancial distress. e results were evaluated based on the estimation of the in-sample parameters, out-of-sample tests, and the early warning model signs for a 12-month forecast horizon. ese obtained true positive rates of 81%, 94%, and 89%, respectively. We conclude that typical balance-sheet indicators are relevant for the early warning signs of nancial distress in Brazilian banks, which contributes to the literature on nancial intermediary credit risk, especially from the perspective of bank supervisory agencies acting towards nancial stability.


INTRODUCTION
Particularly in periods following nancial crises -such as the 2007-2008 subprimes crisis, in which the fall of Lehman Brothers showed the systemic risk of a series of bankruptcies and the high cost for society resulting from government interventions (bail-outs) in the nancial sector, such as in the United States and other European countries -the relevance of the issue of nancial stability comes under focus, with the leadership of important multilateral organizations, such as the Basel Committee for Banking Supervision, of which Brazil has been a member since 2009, and the Financial Stability Board, linked to the Group of 20 biggest economies in the world.
e Basel recommendations involve three pillars: minimum levels of capital requirement (Basel ratio), in which financial institutions must have adequate levels of own capital in relation to the risks of their assets; supervision processes, which concern banking supervision practices for nancial institutions; and market discipline. For this last pillar, nancial institutions should maintain e ective processes for disclosing information and displaying transparency to the market. e studies found in the literature on predicting financial distress are based on samples of financial institutions from the European Union (Betz, Oprica, Peltonen, & Sarlin, 2014), Russia (Peresetsky, Karminsky, & Golovan, 2011), North America (Cleary & Hebb, 2016;Lane, Looney, & Wansley, 1986), Iran (Valahzaghard & Bahrami, 2013), and Malaysia (Wanke, Azad, & Barros, 2016), as well as cross-country samples (Liu, 2015).
However, a lack of studies was found involving the modeling of early warnings for Brazilian banking institutions, possibly due to the particularities of banking industry business models and the relatively small number of publicly-held nancial institutions. As a result of this nding, which is consistent with Brito, Assaf Neto, and Corrar (2009) with regards to the potential to explore this area of knowledge -of interest to both supervisory bodies and market investors -, this study's main aim is to propose an early warning model for predicting nancial distress events in Brazilian banking institutions.
Despite the rarity of the occurrence of the events of interest in this study -the sample related to the period between 2006 and 2014 contains nine cases in the treatment group -, it is understood that assessing the risks of a nancial system is based on identifying vulnerabilities at its micro level, which can trigger systemic risk events via contagion processes due to the interconnectivity of the nancial relationships between the agents participating in the market, independent of their relative size.
Moreover, early warning systems constitute important tools from the banking supervision framework (Pillar 2). In the search to maintain nancial stability, which is typically attributed to central banks, anticipating potential sources of nancial distress can contribute to streamlining the use of resources when executing public policies for regulation and supervision, as well as providing information for monitoring systemic risk.
On the other hand, by using data from banks' balance sheets, the study contributes to evaluating disclosure practices in the country (Pillar 3), which are also relevant for savers. e study sets out the following research proposal: the information set in the public domain involving nancial statements constitutes a su cient element for modeling an early warning system for nancial distress events in Brazil.
Using monthly data to compose an unbalanced panel of pooled data, it is concluded that the categories of the CAMELS system (capitalization, asset quality, management, earnings, and liquidity) constitute important measures for analyzing situations of nancial distress in banks in the National Financial System and contribute to modeling an early warning system on a 12-month timescale.
The literature review and research methodology sections are presented next, followed by the results analysis and conclusion sections.

INFERENTIAL FINANCIAL DISTRESS MODELS
Ever since the study from Altman (1968), with the classic model known as Z-score for discriminate analysis among groups, the literature accumulated on models for predicting corporate bankruptcies is diversi ed in terms of variables used, as well as the methodology for estimating the probability of default. ere are models that extract their inputs from nancial statements, add macroeconomic indicators, and also those that use market information, such as nancial asset prices. Many studies compare the main approaches developed for identifying the nancial situation of companies, such as discriminant analysis, factor analysis, logit and probit models, arti cial Extension of the traditional analysis of indicators, with scienti c analysis. Z-score = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 + 0.999X5, with X 1 = working capital/assets; X 2 = retained earnings/assets; X 3 = EBIT/ assets; X 4 = market value of equity/book value of liabilities; X 5 = sales/assets. Insolvency: Z < 2.675. Altman (1977) 212 savings and loans associations (USA) Quadratic discriminant analysis One of the pioneers in the application to nancial institutions. Use of computer program for the study. Use of results for the roles of banking supervision. Martin (1977) 5,700 commercial banks (USA) Linear and quadratic discriminant analysis; logit Discussion on conceptual approaches for the default probabilty models. Introduction of logistic regression analysis. Kanitz (1978) 5,000 nancial statements of Brazilian companies (Brazil)

Multiple discriminant analysis
Numerical scale based on composite liquidity indexes, denominated Kanitz Thermometer, to measure the company's nancial health and its approach to bankruptcy situation. Collins and Green (1982) 323 credit cooperatives (USA) Logit Examination of assumptions and properties of linear probability, discriminant analysis, and logistic regression models, with the latter having more consistent results with the theory on nancial distress. West (1985) 1,900 banks (USA) Factor analysis and logit Context of early warning systems and CAMELS approach, with 16 independent variables derived from balance sheets and 3 variables extracted from banking supervisor reports. Frydman, Altman, and Kao (1985) 200 companies (USA) Recursive partitioning algorythm Non-parametric method, using binary classi cation tree. Performed better than discriminant analysis. Lane, Looney, and Wansley (1986) 130 banks (USA) Survival analysis (Cox) Introduction of the Cox model in the nancial literature. Prediction of time to fail. Similar accuracy to discriminant analysis, with a lower rate of type I errors. Context of early warning systems and CAMELS. Whalen (1991) 1,200 banks (USA) Survival analysis (Cox) Context of early warning systems, with bankruptcies occurring between 1988 and 1990 in the treatment group and another 1,000 banks in the control group.
intelligence, and hazard models. In the main Brazilian journals there are studies on solvency, generally related to publicly-traded Brazilian companies; however none covering Brazilian banks in their sample. ese studies include those from Brito and Assaf Neto (2008), Brito, Assaf Neto, and Corrar (2009), Guimarães andAlves (2009), Minardi (2008), Minussi, Damacena, and Ness Jr. (2002), Onusic, Nova, and Almeida (2007), and Bressan, Braga, and Bressan (2004), with the latter analyzing insolvency risk in credit cooperatives from the state of Minas Gerais. e study from Liu (2015), also published in a Brazilian journal, addresses factors determining nancial di culties in banks from various countries, but in its sample it does not explain which observations were used, as well as obtaining a low predictive power in the models.  Boyd and Runkle (1993) 122 banks (USA) Panel regression Test of theories of information asymmetry and moral risk resulting from deposit insurance systems.
Restricts the sample to big banks. Use of Tobin's q indicator to attribute performance and de nes Z-score (homonymous of the Altman model) as a risk indicator: Z-score = (ROA + Equity/Asset)/σ ROA. Altman, Marco, and Varetto (1994)  Distance-to-default and Z-score Compares model based on market data (options theory) and model based on accounting data (Z-score).
0.67% of the companies in the treatment group, which captured different aspects of bankruptcy risk.

Financial Institutions and the CAMELS System
In the area of integrated nancial systems, studies aim to show indicators for measuring systemic risks or the importance of systemically important institutions (too big to fail), such as in Canedo and Jaramillo (2009), Capelletto and Corrar (2008), Fazio, Tabak, and Cajueiro (2014), and Tabak, Fazio, and Cajueiro (2013). Along these same lines, Souza (2014) simulates the e ects of credit risk, changes in capital requirements, and price shocks in the Brazilian banking system, showing that the contribution of medium-sized banks can also be signi cant for systemic risk.
According to Chan-Lau (2006), estimating the probabilities of default for individual agents is the rst step in evaluating credit exposure and potential losses. e probabilities of default are, therefore, the basic inputs for analyzing systemic risk and nancial system distress tests. It is important for the proactive analysis of systemic risk measures to take into account the individual evaluation of bank failure risks for each institution in the system, whether small, medium or large-sized.
Speci cally for the case of banks, the introduction of the CAMEL classi cation system by American regulators in 1979 resulted in a major boost to the development of the literature on bank failures. e CAMEL acronym stands for capital adequacy, asset quality, management quality, earnings, and liquidity, and represents a banking supervision tool for evaluating the strength of nancial institutions. In 1996, the sensitivity to market risk item was added to the abbreviation currently known as CAMELS.
A pioneer in the use of logistic regression to predict bank failures, Martin (1977) analyzes the importance of early warning models, both from the theoretical and practical points of view, for measuring the strength of the commercial banking sector and implications for supervisors, regulators, and system users. e author evaluates the different approaches for defining the dependent variable, that is, what constitutes a bank failure: the recording of negative net equity, the impossibility of continuing operations without incurring losses that would result in negative equity, and intervention by the banking supervisor to coordinate mergers and acquisitions.
For the empirical analysis, Martin (1977) uses 5,700 banks from the Federal Reserve of the United States of America system, in which there were 58 cases of failures in the period between 1970 and 1976. Using logit and discriminant analyses, combinations of eight independent variables in year t are generated for analyzing the model with the greatest explanatory power in year t + 1. e results do not present stability, with some variables having explanatory power in some periods and even an opposite sign to that expected in subsequent periods. e author ponders whether the banking solidity criteria can vary over the business cycle. In periods in which bankruptcies are extremely rare, the relationship between capital adequacy, for example, and the occurrence of failures will be weak. In periods of nancial distress, earnings measures and asset composition can be indicators of risk. West (1985) explores combining the analysis of factors and logistic regression to measure the individual conditions of commercial banks and attribution of probabilities of problems, taking commonly used nancial indicators and information extracted from bank inspections as explanatory variables. e factors produced to use in the logit estimation are similar to the CAMEL classi cation system used in the eld work of banking supervisors. 19 variables are used that characterize dependency in relation to particular categories of loans, source of fund raising, liquidity, capital adequacy, fund raising costs, bank size, earnings measures, quality, and portfolio risk.
Concerned about the performance measures of early warnings models -such as those of Martin (1977) and of West (1985) - Korobow and Stuhr (1985) propose a new weighted measure of e ciency analysis to correct the problem related to the small percentage of the sample involving problematic banks: weighted efficiency = percentage of correct classi cations * TP/(TP+FP) * TP/ (TP+FN), in which TP, FP, and FN are true-positive, falsepositive, and false-negative, respectively, and correspond to the classi cations in the contingency matrix. Besides observing the existence of di erent levels of separation (cut-o threshold) of healthy and critical banks in the models evaluated, the authors apply a new measure proposed, showing the low performance of early warning models.
In situations in which the sample is composed of a low number of events in the treatment (insolvent) group in relation to the control (solvent) group, Lane, Looney, and Wansley (1986) make an important consideration with relation to the prior probabilities of belonging to a group for use in the analysis. ese probabilities should be de ned via a reasonable estimation of the probability of a member belonging to a group of the population, assuming that the sample is random.
One of the models most widely used as a banking risk indicator is the Z-score (homonymous of the indicator produced by Altman, in 1968), presented by Boyd and Runkle (1993), who test two important theories applied to banks -information asymmetry among agents and moral risk resulting from deposit insurance systems -which indicate a correlation between a company's size and its performance. e Z-score indicator is generated as a risk measure for large banks, using the rate of returns on assets and the ratio between equity and assets as variables. e authors observe that the estimates with accounting data for the Z-score may not generate good results. Chiaramonte, Croci, and Poli (2015) use the Z-score and evaluate that its popularity derives from the simplicity of computing it, requiring few data: Z-score = (ROA + Equity/Assets) /σ ROA . Chiaramonte, Croci, and Poli (2015) apply the Z-score indicator and the CAMELS system for a sample of European banks, concluding that the ability of that indicator is as good as the covariates of this system for identifying nancial distress events and more e ective when sophisticated business models are involved, as in the case of big banks. e authors argue that other measures such as the distance-to-default from Merton (1974) and credit default swaps prices are unviable for use in the presence of banks that are not listed on stock exchanges.
The CAMELS indicators are also used by Betz, Oprica, Peltonen, and Sarlin (2014) to analyze situations of nancial distress in European banking institutions, with quarterly observations in the period from 2000 to 2013. e authors de ne three categories of nancial distress: (i) bankruptcies; (ii) state assistance for banks in distress, both via direct capital injections and participation in protection or guarantee programs; and (iii) private sector solutions for mergers and acquisitions of entities in nancial distress.
As a methodology for studying nancial distress, Betz, Oprica, Peltonen, and Sarlin (2014) indicate that there is a preference for the pooled logit type model in relation to panel data analysis, due to the relatively small number of crisis cases. Instead of using lagged explanatory variables, Betz, Oprica, Peltonen, and Sarlin (2014) de ne the dependent variable as "1" in the eight quarters before the nancial distress event and "0" otherwise and use a recursive logit model with quarterly estimations via increasing data windows.

Data Sources, Sample Selection, and
Computational Support e database for the study is composed of information from the Accounting Plan for Institutions of the National Financial System (Cosif), available from the Brazilian Central Bank website (http://www.bcb.gov.br); from historical data on economic indicators, obtained from the website of the Applied Economic Research Institute (http://www.ipea.gov.br); from real estate market price ratios, available from the São Paulo Stock, Commodities, and Futures Exchange (BM&FBOVESPA) website (http://www.bm ovespa.com.br); from publications on special regimes decreed by the Central Bank (Temporary Special Administration Regime, Decree-Law 2,321/1987; Intervention or Receivership, Law 6,024/1974) (Brazilian Central Bank, 1974, 1987; from merger and acquisition events with the assumption of nancial distress for the acquired institution, reported by the country's media. e analysis window covers the period from January 2006 to June 2014, which enables the period of the last nancial crisis to be incorporated and a series of nancial distress events needed for the study. All in all, the sample contains 142 nancial institutions, already taking into account the exclusion of 17 for which it was not possible to calculate the independent variables, and also the Caixa Econômica Federal and the National Bank for Economic and Social Development (BNDES), due to their speci cities. e sample description can be found in Table 2. e treatment group (Table 3) has nine nancial institutions, which underwent intervention and/or receivership processes or were considered by the authors, for the purposes of this study, as merger and acquisition events with the assumption of nancial distress.  The balance sheet data were obtained monthly, totaling approximately 2.7 million records (lines). As a form of computational support for the research, a database generating system, automization of structured consultations, and procedural programming language were used to compile the panel and implement the signs of the early warning model. e Stata statistical package was used for the econometric procedures.

Study Variables
e explanatory variables were selected based on the studies from Betz, Oprica, Peltonen, and Sarlin (2014), Lane, Looney, and Wansley (1986), and West (1985), which used the CAMELS system for evaluating nancial institutions, and on the availability of accounting information in Cosif (Table 4).   e following control variables were added: market share continuous variable (PART_SIS); credit portfolio percentage continuous variable (PERC_CRED); and securities portfolio percentage continuous variable (PERC_SEC).
Market share was calculated in accordance with the total assets of each institution in relation to the other institutions in the sample. e credit and securities portfolio percentages were calculated in relation to all of the portfolios generated by the institution. e six-month cumulative returns for the Bovespa Index (IBOV6M) were also used, as well as the securities nancial segment index (IFNC6M), the annual variation in gross domestic product (GROWTH_GDP), and the annual rate of unemployment (UNEMP).
In order to de ne the two dependent variables related to the predictive model time horizons, the Y12 and Y24 variables were generated, in accordance with Betz, Oprica, Peltonen, and Sarlin (2014): us, as in equation 1, sequences of 12 values equal to "1" were attributed for Y12 in situations in which the institution belongs to the treatment group and the date of reference of the observation is equal to or less than 12 months from the nancial distress event. Similarly, a 24-month temporal window was used to de ne Y24.

Modeling
Binomial logistic regression is used in the estimation of the model parameters for predicting the probabilities of distress. In the logistic regression, the z variable is formed by the vector of the covariates and respective parameters, with a transformation function being used to generate a value between 0 and 1, representing the probability of occurrence of the event of interest for each observation in the sample: For a set of n observations, the joint probability and its resolution via the maximum vraisemblance function are given by equations 5 and 6, respectively: � � e logistic regression with pooled data has been used in studies of this type, as analyzed by Betz, Oprica, Peltonen, and Sarlin (2014) and Sarlin (2013). us, the pooled logit model was used for the regression of the independent variables over the selected dependent variable. e data were grouped in a panel, with the crosssectional units being monitored over the course of the sampling period (spatial and temporal dimensions). e panel is of the unbalanced type, since because of a lack of data in the monthly balance sheets, some economicnancial indicators were not calculated. Of the total of 12,136 observations in the panel, 10,994 are complete observations, containing values for all of the independent variables.

Early warning signs.
Taking into account that the observations collected are monthly, it would not be e cient to generate signs of nancial distress if a high probability was identi ed in isolation; that is, P (Y it = 1), for a particular nancial institution. is would tend to generate high costs of classification errors for possible false alarms (falsepositives).
us, for the purposes of early warning signs, in this study it is de ned that the signs of nancial distress or of return to normality will be a ected when there are sequences of six observations with P (Y it = 1) or P (Y it = 0), respectively. erefore, based on the initial states without signs (S i,t=0 = Ø), for each nancial institution at t = 0, signs are generated indicating normality (0) and distress (1)

Preliminary Tests
First, comparison tests were carried out between the sampling averages of the nancial indicators for the two groups of institutions (Table 6), determining the discrimination potential of the selected variables.
Univariate tests were also carried out (Table 7). e variables have predictive power for a 1% level of signi cance and are more indicated for the 12-month time horizon, as denoted by the AUC (area under the curve) indicator, with the exception of the liquidity variable, which shows slight superiority for regressions over Y24.
us, the subsequent tests of the econometric models were carried out with the dependent variable Y12.   Using the complete sample, three econometric models were tested, successively adding independent variables, starting with the simplest model with only nancial indicators and control variables. In the second model, the market indices were included and in the third the macroeconomic indicators were added. Table 8 shows that the initial model presents good predictive power, with a greater area under the ROC (receiving operating characteristics) curve than those obtained by the univariate analyses (Table 7), but it is exceeded by model 2, which considers market indicators in the estimation of the parameters. e performance increases when the macroeconomic covariables are incorporated (AUC = 89%), corroborating with Betz, Oprica, Peltonen, and Sarlin (2014) and Peresetsky, Karminsky, and Golovan (2011), with the e ect of adding variables being bene cial, which is con rmed by the adjustment measures, such as the Akaike information criteria (AIC) and Schwarz's Bayesian information criteria (BIC).  (1985)  It is also observed that the rate of true-positives increases to around 89%, while the Korobow and Stuhr index (1985) also shows this improvement. e type I errors (erroneous classi cation of nancial distress as normal situations) fall to 10%. In light of these results, the following tests are conducted in accordance with the speci cation of model 3.

Adjustment, Adequacy, and Validation of the Model
Tserng, Chen, Huang, Lei, and Tran (2014) highlight that the construction of a predictive model requires validation in a di erent sample (cross-validation) from the estimation to avoid the problem of over-tting, which would result in models that only perform well in the sample used.
For this, the total sample of 10,994 observations was divided into two subsets: the rst, with 70% of the observations and ve ninths of the cases of nancial distress, was used in the estimation of the parameters and the second, with 30% of the observations and four ninths of the cases of the event of interest, was assigned to the validation tests (out-of-sample). e model estimation can be found in Table 9. e classi cation of the estimation sample observations can be found in Table 10.  Considering the estimators with residuals calculated using the least squares method, fourth fifths of the nancial indicators were obtained with 1% signi cance (capitalization, provisioning, liquidity, and return on assets), with the funding expenses variable being 5% signi cant. When the White correction is applied for the presence of heteroskedasticity in the error terms, all of the coe cients present 1% signi cance. e estimation of the residuals with the clusterization criterion is consistent with the previous ndings. e signs of the variables were as expected: increases in the levels of capital, in the ROA, and in liquidity reduce the probability of nancial distress, while an increase in funding expenses and provisioning for credit operations increases this probability.
It is worth observing that a one percentage point increase in return on assets, all else remaining constant, reduces the risk of nancial di culties by around 37% (odds ratio). is impact is greater with relation to the liquidity indicator, whose inference is of a reduction of around 64% in the probability of distress for a one percentage point increase.
On the other hand, each percentage point increase in the funding expenses indicator (EXP) generates an increase in the expected probability of nancial distress in the order of 5%. For the provisioning variable, the increase is almost in the same order (6%), suggesting that an increase in portfolio provisions does not necessarily represent poorer quality credit assets. e analysis of residuals from the generalized linear model estimation (Figure 1) indicates the presence of outliers in the observations, which mainly refer to capitalization and liquidity variables. However, the use of the distributions of these variables with winsorization in the 95% percentile did not alter the general results of the tests.    Korobow and Stuhr (1985)   e ROC curves for the in-sample and out-of-sample tests ( Figure 2) show that the classi cations indicated by the model studied di er from a random classi cation, which has equal probabilities for failure and non-failure (reference line, whose AUC is 0.50). In Figure 2, it is perceived that while the true-positive (sensitivity) classi cations reach almost 75%, the false-positive (1 -speci city) classi cations reach only around 12% for a particular cut-o .
As shown in Table 11, the estimation with the out-ofsample data supports the predictive power of the model, both in relation to the total accuracy percentage and the speci c type I (false-negative) and type II (false-positive) error classi cations.

Signs
Finally, the algorithm for the early warning model signs (equation 7) and the respective evaluations (equation 8) were applied. Of the nine nancial institutions that experienced nancial distress in the sampling period, eight received a sign of distress (Table 12). Of the institutions that were correctly classi ed, there is one case of fraud, which shows that the multivariate analysis enables a combination of various factors to identify the events of interest.  Korobow and Stuhr (1985) 13 presents a summary of the performance of the estimation and validation model and of the early warning model's signs. With a higher performance indicator (4.95), the warning sign model, based on the need for a sequence of monthly probabilities of distress to characterize a warning, was shown to constitute an e ective and timely approach for microprudential monitoring, at a nancial institution level, as well as producing inputs that contribute to monitoring systemic risk, as observed by Chan-Lau (2006).
It is important to observe that, given the treatment group, the only institution that did not obtain a sign of nancial distress (Unibanco) had three consecutive monthly signs with ( ) � = 1 , but the warning sign criterion required a sequence of six months with ( ) � = 1 . It bears mentioning that sensitivity to market risk was the only dimension of the CAMELS system that was not included in the research model, due to the inviability of computing it with the data used. On the other hand, the PERC_SEC covariable aims to incorporate this aspect into the model as a measure of the securities portfolio percentage, without considering other market risk factors, such as exposures to o -balance derivatives, which at times of crisis, such as in 2007/2008, can generate raised margin calls and e ective losses in the contracts. It also bears mentioning that, in reality, this institution may not have su ered from nancial distress as is supposed in the study.
Ninety undue signs were generated with type II errors, whose cost of classi cation tends to be lower from the point of view of banking supervision, which routinely monitors all nancial institutions. As 16% of this total refers to state-owned banks, the performance of the early warning model could increase if these institutions did not participate in the research sample. However, the decision was made to maintain the complete sample, with the exception of the exclusions mentioned in the methodology section. Figure 3 presents the average probabilities of default by control type. Robustness tests were carried out with the probit regression instead of the logistic regression, following the same estimation procedures of the models and veri cation procedures of the classi cation statistics, which was consistent with the observation of Porath (2004) regarding the similar predictive performance of these transformation functions, since there was no qualitative alteration in the results.
Complementarily, the performance of the Z-score model was evaluated, in accordance with Chiaramonte, Croci, and Poli (2015), but with di erent results. A lower level of accuracy was obtained in relation to the model developed in this study, which confirms the observation by Boyd and Runkle (1993) regarding the critical performance of the Z-score for accounting data.
Another factor that may have in uenced this nding relates to the sample containing di erent sized and not exclusively large banks. e Z-score tests resulted in 57% TP, 28% FP, 70% correct classi cations, and an AUC of 75%. e regression coe cient obtained 1% signi cance.
With relation to the size of the institutions ( Figure  4), it is observed that the average probability of default calculated by the model is, in general, more accentuated for the medium-sized banks, which con rms the ndings of Souze (2014) regarding the relevance of this type of bank for systemic analysis. Similarly, the small banks also have signi cant average probabilities in the system. It is also observed that peaks occur in the probabilities of distress close to the ending of nancial periods, such as in 2011, 2012, and 2014.

CONCLUSION
A matter of key importance for macroprudential decision making -such as systemic risk analysis focused on financial stability and interfinancial contagion among market participants -, company solvency studies have been present in the financial literature since Altman (1968), with the Z-score model. However, few studies have addressed the specificities of financial institutions and even fewer involve Brazilian empirical investigations.
This study aims to fill this gap by analyzing the viability of applying financial indicators to identify financial distress events in Brazil in advance, including interventions by supervisors and mergers motivated by financial difficulties, and using the monthly balance sheets of banks and financial conglomerates as a main source of data. Early warning systems are useful for the actions of regulatory and supervisory bodies of the financial system and also for market participants when evaluating the credit risk of investments. They can also be applied in other areas, such as in civil engineering, as in the study presented by Tserng, Chen, Huang, Lei, and Tran (2014).
In the logistic regression analysis, the capitalization, credit portfolio provisioning, return on assets, funding costs, and liquidity variables were shown to be signi cant, showing the importance of the CAMELS dimensions for analyzing the nancial situation of banks, which is in line with other papers that have used this categorization (Betz, Oprica, Peltonen, & Sarlin, 2014;Lane, Looney, & Wansley 1986;Wanke, Azad, & Barros, 2016;West, 1985).
Using logit regressions with pooled data and a 12-month time horizon for predicting distress, the predictive power of the estimation, validation, and early warning signs models was shown to perform well, even considering the inclusion of state-owned and investment banks in the sample. e true-positive rates for the models were 81%, 94%, and 89%, respectively. Of the nine institutions belonging to the treatment group, eight received truepositive signs.
Considering the weighted analysis of the efficiency of the signs of financial distress, it was verified that the use of monthly data -together with criteria to avoid excessive type II errors (false-positives), due to the occurrence of sporadic probabilities of distress related to the monthly observations -results in timeliness in identifying the events of interest, in terms of an early warning model. In this study, six consecutive monthly observations with ( ) � = 1 were defined as the warning sign criterion.
Regarding the structural pillars of the Basel recommendations, the study con rmed the importance of the capitalization (Pillar 1) of the institutions as one of the modeling variables, as well as ratifying the proposition of this research: the publicly available information set involving nancial statements constitutes a su cient element for modeling an early warning system for nancial distress events in Brazil.
Thus, the empirical analysis contributes to studies on banking supervision processes (Pillar 2), which by anticipating possible cases of financial distress benefit from the effectiveness and efficiency of conducting public policies to maintain financial stability. By using data from the balance sheets of financial institutions, the study contributes to disclosure analysis (Pillar 3) in Brazil, and is in line with Brito and Assaf Neto (2008) and Brito, Assaf Neto, and Corrar (2009), who use accounting statement information to model credit risk in Brazilian companies.
Future research could incorporate the usefulness of the model for policy makers and the classi cation costs of the early warning model, in a similar way to Betz, Oprica, Peltonen, and Sarlin (2014) in their study on European banks in the post-2008 crisis period. e use of recursive models and moving windows to estimate parameters and predict out-of-sample probabilities tends to improve the comparison between the predictive power of models of this type.
The main limitations of this study were: (i) the relatively small number of observations for the treatment group, taking into account the limited amount of financial distress events identified; (ii) the subjective portion in the selection of merger and acquisition events with assumptions of financial distress; and (iii) the model's lack of an independent variable related to the sensitivity to market risk of the CAMELS categorization.