Should we trust the Z-score? Evidence from the European Banking Industry

Global Finance Journal 28 (2015) 111–131

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Should we trust the Z-score? Evidence from the European Banking Industry Laura Chiaramonte, Ettore Croci, Federica Poli ⁎ Department of Economics and Business Administration, Faculty of Economics, Università Cattolica del Sacro Cuore, Largo Gemelli 1, 20123 Milan, Italy

a r t i c l e

i n f o

Article history: Received 8 October 2014 Received in revised form 27 January 2015 Accepted 5 February 2015 Available online 18 April 2015 JEL classification: G01 G21 Keywords: Bank distress Z-score CAMELS Financial crisis

a b s t r a c t We investigate the accuracy of the Z-score, a widely used proxy of bank soundness, on a sample of European banks from 12 countries over the period 2001–2011. Specifically, we run a horse race analysis between the Z-score and the CAMELS related covariates. Using probit and complementary log–log models, we find that the Z-score's ability to identify distress events, both in the whole period and during the crisis years (2008–2011), is at least as good as the CAMELS variables, but with the advantage of being less data demanding. Finally, the Z-score proves to be more effective when bank business models may be more sophisticated as it is the case for large and commercial banks. © 2015 Elsevier Inc. All rights reserved.

1. Introduction Bank distress has been at the center of the political and economic debate during the recent financial crises. Both the credit crisis and the sovereign debt crisis have emphasized the need to properly assess the measures of bank soundness. As a matter of fact, the existence of informational asymmetries and the limitations of bank publicly disclosed information pose severe restrictions on the ability of external stakeholders (i.e., depositors, borrowers, investors, financial analysts, to name just a few) to identify in a timely way which banks are in jeopardy of failing. Unlike supervisors, who have often access to confidential information on bank conditions, other external parties must rely on regulated, disclosed information, such as financial statements, which turn out to be the main source of available data, especially for unlisted banks. Indeed, some of the most sophisticated

⁎ Corresponding author. Tel.: +39 02 72342942; fax: +39 02 72342670. E-mail addresses: [email protected] (L. Chiaramonte), [email protected] (E. Croci), [email protected] (F. Poli)

http://dx.doi.org/10.1016/j.gfj.2015.02.002 1044-0283/© 2015 Elsevier Inc. All rights reserved.

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approaches to quantify the risk of bank distress, like the Merton distance-to-default (DD), bond spreads and credit default swaps (CDS), cannot be used to ascertain the financial health of several banks, especially in Europe where a large number of banking firms are not listed on Stock Exchanges and they have neither traded bonds nor CDS quotes.1 When market-based measures of risk are not available or the quality of the market data is poor, depositors, investors, analysts, and the public in general, have to rely on accounting data to determine the likelihood of financial distress. In the empirical literature, there is a general agreement on the ability of accounting-based CAMELS variables (which stand for Capital, Asset quality, Management, Earnings, Liquidity and Sensitivity to market risk) to capture banks' financial vulnerability and to predict their distress (Poghosyan & Čihák, 2011). Few recent studies complement CAMELS indicators with the Z-score (Poghosyan & Čihák, 2011; Vazquez & Federico, 2012), which is a widespread accounting measure of bank financial soundness. The popularity of the Z-score stems from its simplicity and the fact that it can be readily calculated using few accounting data. In this paper, we examine whether the Z-score is a valuable tool to predict distress relative to the CAMELS-related covariates, and if its ability of signaling differs through time, bank size, business model (shareholders vs. stakeholders oriented banks), and geographic area. Using probit and survival analysis models on a European sample banks from 12 countries over the period 2001–2011, we find that the Z-score is overall a valuable and parsimonious measure to predict bank distress. Indeed, the ability of the Z-score to predict distress, both over the whole period (2001–2011) and in the crisis years (2008–2011), is at least as good as more data demanding models, like the one that employs CAMELS variables. We also observe similar results when we compare the Z-score to its components: return on assets (ROA); volatility of returns; and equity over total assets. When we add the Z-score to the CAMELS variables, the model ability to predict bank distress slightly improves, but only in the whole period. During the financial and economic slowdown, as bank performances weaken the predictive accuracy of both the Z-score and the set of CAMELS variables increases. Again, both models achieve substantially similar results. Finally, we show that our results on the predictive ability of the Z-score are robust to changes in the computation of the Z-score. We also find that the Z-score is a more effective predictor for large banks and for commercial banks. This suggests that the Z-score is a superior measure when bank business models are more complex of the financial institutions increases and their accounting practices are more scrutinized. Finally, the Z-score has relatively more success in predicting distress and non-distress events in those European countries less affected by the financial crises. This latter result is consistent with the view that when a systematic crisis hits, firm-level variables lose some of their ability to predict distress. This study offers several contributions to the literature. Our horse race analysis between the sole Z-score and CAMELS variables provides evidence that the former is a reliable leading indicator of bank distress. This finding could be relevant to external bank stakeholders (for example, investors, borrowers, depositors, suppliers) as well as, even if to a lesser extent, to supervisors when market-based measures of distress are not available. Second, we improve the limited and controversial empirical literature that complements CAMELS explanatory variables with the Z-score in order to predict bank distress. Finally, we compare a pooled probit model and a survival model, specifically a complementary log–log model (cloglog), and find that the results are remarkably similar. We organize the remainder of this article as follows: in Section 2, we present a brief review of the literature. Section 3 describes the sample and how we identify distress events. Section 4 discusses the methodology as well as the variables used in our paper and their descriptive statistics. Sections 5 and 6 present empirical results and robustness tests. Section 7 concludes and offers some policy implications.

2. Literature review The early detection of bank distress enables supervisory authorities to undertake prompt corrective actions designed to minimize the negative externalities and bailout's costs due to bank distress. To this aim, bank supervisors of developed countries have developed their own early warning statistical models for the last two decades, which are based on diversely heavy sets of economic and financial variables. In the empirical literature, the prediction of bank distress has been primarily focused on the identification of leading indicators 1

In our sample, only 160 banks out of 3125 are publicly listed on a stock exchange.

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that contribute to generate reliable early-warning systems. Such signals may be grouped into two broad categories: market-based measures and accounting-based measures. The first group of indicators relies mostly on market prices of bank equity, to estimate bank's distance to default (Hagendorff & Kato, 2010; Hagendorff & Vallascas, 2011; Vassalou & Xing, 2004); bond spreads (Bharath & Shumway, 2008; Flannery, 1998, 2000; Flannery & Sorescu, 1996; Jagtiani & Lemieux, 2001; Morgan & Stiroh, 2001; Sironi, 2000); and more recently CDS spreads (Chiaramonte & Casu, 2013; Constantinos, 2010; Flannery, 2010; Norden & Weber, 2010; Volz & Wedow, 2011). The adoption of market-based indicators is generally motivated by their forward-looking nature, which should lead to a superior ability to anticipate a material weakening in banks' financial conditions as also confirmed by evidence for the US and Europe (Gropp, Vesala, & Vulpes, 2002). Market-based indicators of bank distress have several advantages: firstly, they are generally available at high frequency, providing more observations and shorter lags than financial statements data. Secondly, they are forward-looking since they incorporate market participants' expectations. Finally, they are not subject to confidentiality biases as may be the case for some accounting data, i.e., those reported solely to supervisory authorities (Čihák, 2007).2 Nevertheless, the quality of market prices is conditional to the degree of liquidity and transparency of financial markets where bank stocks, debentures and CDS are traded. As a matter of fact, the usefulness of market-based indicators is severely affected in case of illiquid and opaque markets. Moreover since market-based indicators are usually available only for large and listed banks, they can be used just for a relatively small fraction of banks, especially in Europe. The second group of indicators of bank distress probability is dependent on financial and accounting values. In this approach, accounting data are proxies for fundamental bank attributes aimed to measure bank's financial vulnerability (Sinkey, 1979). The so-called CAMELS methodology is a well-known tool for supervisory risk assessment.3 In the empirical literature, there is a general agreement on the ability of CAMELS variables to assess banks in terms of their financial vulnerability and to predict bank distress (Poghosyan & Čihák, 2011). Low capital and risky assets are major causes of banks distress (Oshinsky & Olin, 2006). Larger capital cushions allow banks to write-off bad loans in the future (Berger, Herring, & Szegö, 1995; Estrella, Park, & Peristiani, 2000; Kick & Koetter, 2007) and make them less prone to distress during the global financial crisis (Beltratti & Stulz, 2012; Berger & Bouwman, 2013; Demirgüç-Kunt & Huizinga, 2010). Vazquez and Federico (2012) analyze the evolution of bank funding structures in the run up to the global financial crisis and show that banks with weaker structural liquidity, higher leverage, and risk-taking in the pre-crisis period were more likely to fail afterward. The significant episodes of systemic banking crises experienced by many emerging countries over the past two decades stimulated several studies that use bank-level data focusing on a particular country or region or at cross-country level (Arena, 2008; Bongini, Claessens, & Ferri, 2001; Gonzalez-Hermosillo, 1999). According to Arena (2008), bank-level fundamentals, proxied by CAMELS related variables, explain why banks are likely to fail in East Asia and Latin America. Among the recent studies, mostly focused on the prediction of failures of commercial banks in the US, traditional CAMELS indicators are found to be successful in anticipating distress phenomena. However, the explanatory power of the models increases with the addition of information on the banks' internal controls on risk taking (Jin, Kanagaretnam, Lobo, & Mathieu, 2013), audit quality (Jin, Kanagaretnam, & Lobo, 2011), income from non-traditional banking activities (De Young & Torna, 2013), market and macroeconomic data (Cole & Wu, 2009), and commercial real-estate investments (Cole & White, 2012). In recent studies, some efforts have been devoted to complement the CAMELS variables with book-based indicators, such as a proxy of bank's distance-to-default, like the Z-score (Rojas-Suarez, 2001). The empirical attractiveness of Z-score banks on the fact that it does not require strong assumptions about the distribution of returns on assets (Boyd & Graham, 1986; Roy, 1952; Strobel, 2011). The latter represents an interesting advantage of Z-score, especially from the practitioners' point of view (Ivičić, Kunovac, & Ljubaj, 2008). Contrary to market-based risk measures, which are quantifiable only for listed financial institutions, the Z-score can be computed for an extensive number of unlisted as well as listed banks. Despite its advantages, the Z-score is not 2 Indeed, if some relevant information is not publicly disclosed since it is collected and held by supervisors, prudential data can be superior to market-based indicators in measuring banks' financial soundness. 3 For example, the Federal Deposit Insurance Corporation (FDIC) in the US uses a composite CAMELS rating to determine whether a bank must be included in its “Problem list”.

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immune from some caveats. Firstly, as for the other accounting-based measures, its reliability depends on the quality of underlying accounting and auditing framework, which is a serious concern in less-developed countries. Additionally, as banks may smooth accounting data over time, the Z-score may offer an excessively positive assessment of the risk of bank distress (Leaven & Majnoni, 2003). Secondly, as pointed out by Čihák (2007), the Z-score, as well as other market-based measures like the distance-to-default look at each bank separately, potentially overlooking the risk that a distress in one financial institution may cause loss to other financial institutions in the system. The few available results on the predictive power of Z-score are mixed. Poghosyan and Čihák (2011) find that when the Z-score is added to the baseline predicting model, the coefficient in front of the Z-score variable is insignificant, suggesting that the Z-score scarcely contributes to predict bank distress. On the contrary, Vazquez and Federico (2012) find that bank risk profiles play a significant role. Finally, Lepetit and Strobel (2013) compare different existing approaches to the construction of Z-score measures, using a panel of banks for the G20 group of countries covering the period 1992–2009. Their results are supportive of a time-varying Z-score measure which uses mean and standard deviation estimates of the return on assets calculated over full samples combined with current values of the capital–asset ratio. 3. Sample selection and identifying distressed banks 3.1. Sample description The study focuses on active and non-active banks operating in two main business models: commercial banks (shareholders oriented banks), and cooperative, savings and real estate and mortgage banks (stakeholders oriented bank), belonging to the following 12 European countries: Austria, Belgium, Denmark, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, and the United Kingdom. The sample period covers the years from 2001 to 2011, which also allows us to investigate the predictive power of the Zscore over the crisis years (2008–2011).4 We obtain accounting data from the Bureau Van Dijk's BankScope database. We carry out our analysis using data from annual consolidated financial statements and, when not available, unconsolidated statements.5 Overall 4298 banks survive the screens described above. Unfortunately, data necessary to compute our target variable (the natural logarithm of Z-score) are not available for all banks. We remove banks for which we are not able to compute the Z-score from the sample. The final sample consists of 3242 banks, with 23,312 bank-year observations in total. 3.2. Identifying distressed banks Our identification process starts from Bureau Van Dijk's BankScope database. BankScope assigns a status to a bank that can take the following forms: active; under receivership; bankruptcy; dissolved; dissolved by merger; in liquidation.6 We classify distressed banks as those banks that satisfy at least one of the following three conditions during our sample period (2001–2011). The first condition is that a formerly active bank changes its status to under receivership,7 bankruptcy, dissolved, or in liquidation. The second condition regards banks that change 4 Considering our European sample banks, we identify the onset of the financial crisis in 2008 rather than in 2007. Our results are remarkably similar if we set the beginning of the financial crisis in 2007. 5 We also attempted to run the analysis using quarterly data. Unfortunately, we are unable to perform the analysis due to the limited availability of quarterly data for the majority of banks in our sample. 6 BankScope database defines: ‘under receivership’ those banks that remain active, though they are in administration or receivership; ‘bankruptcy’ those banks that no longer exist because they have ceased their activities since they are in the process of bankruptcy; ‘dissolved’ those banks that no longer exist as a legal entity; ‘dissolved by merger’ those banks that no longer exist as a legal entity because they have been included in a merger; ‘in liquidation’ those banks that no longer exist because they have ceased their activities, since they are in the process of liquidation. In BankScope database there are also the three following type of bank status: ‘active, no longer with accounts on BankScope’ that are banks still active, though their accounts are no longer updated on BankScope following an acquisition by another bank with accounts on BankScope integrating the accounts of its subsidiary in its consolidated accounts; ‘dissolved by demerger’, that are banks no longer exist as a legal entity. The reason for this is a demerger, the bank has been split; and ‘inactive’, that are banks no longer active and the precise reason for inactivity is unknown. In our analysis we don't consider them given that they show no information for our sample banks. 7 In light of the numerous data missing in BankScope database on banks ‘under receivership’, this kind of bank distress event is thus not included in our analysis.

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their status to dissolved by merger in BankScope. Unlike the majority of related studies (Poghosyan & Čihák, 2011; Vazquez & Federico, 2012), we do not include banks dissolved by merger in the distressed banks' definition. Merger and acquisitions (M&As) might have been carried out for strategic reasons rather than for rescuing troubled banks (Arena, 2008). For this reason, following Betz, Peltonen, and Sarlin (2014), banks with status dissolved by merger are classified as distressed banks only if they have a negative coverage ratio (defined as the ratio of total equity and loan loss reserve minus non-performing loans all divided to total assets, CR) during the twelve months prior to the M&A. Finally, a bank is distressed when it receives state aids during the period considered. State aids can take different forms such as: nationalization, recapitalization, guarantee lines, loans, etc. Data on government bail-outs are collected from the database provided by Mediobanca (2012).8 Panel A of Table 1 presents the sample distribution by bank status (healthy banks versus distressed banks) for each of the 12 European countries during the period 2001–2011. We identified 261 distress events for 214 banks,9 which are not distributed evenly across countries and years. In particular, Panel A of Table 1 shows that highest number of cases of distress occurred in Greece, followed by Ireland, Denmark, Netherlands and Portugal. This result is to some extent expected because Greece, Ireland and Portugal were the most vulnerable European countries during the sovereign debt crisis. The Danish banking system was also severely affected by the crisis due to a strong presence of subsidiaries in Ireland (for example, Danske Bank10). Concerning the Netherlands, two large banks like ABN AMRO and ING went bankrupt. Other countries that experienced a relatively high number of distress events are France, Spain, United Kingdom and Belgium. The banking systems of Italy, Austria and Germany show the lowest ratio of troubled banks on total banks (see panel A of Table 1). The low percentage of distressed banks in Germany is consistent with the evidence provided by Dam and Kotter (2012). Regarding the temporal distribution of distress events, Panel B of Table 1 displays that the majority of bank distress events in Europe took place mainly during the financial crises (73% of all cases of bank distress). This pattern is analogous to what happened in the US, where more than 500 commercial banks under FDIC supervision went bankrupt between 2008 and 2013 compared to less than 50 between 2001 and 2007.11 4. Methodology, variables and descriptive statistics 4.1. Empirical methodology Our analysis focuses on the near-term vulnerability of banks, and not on medium-to-long-term vulnerabilities, which require the identification and evaluation of potential structural weaknesses that can affect incentives to screen and monitor risks. We use two different econometric models to investigate the signaling properties of the Z-score based indicator of bank fragility. The first is a standard probit model: 

  Pr DBi;t ¼ 1 X i;t−1 Þ ¼ ∅ X i;t−1 ; β

ð1Þ

where Pr is the probability; ∅ is the standard cumulative normal probability distribution; and β parameter is estimated by maximum likelihood. DBi,t is the binary variable that identifies bank distress at time t.12 The vector Xi,t − 1 contains the independent variables (see paragraph 4.2 and Table A.1 in Appendix A) for bank i at time t − 1. As a second model, we use a discrete time representation of a continuous time proportional hazards model, the so-called complementary log–log model (cloglog) where, as for the probit model, the binary 8 Mediobanca is an Italian investment bank whose research department actively collects and publishes data on the banking industry. For each European country considered, Mediobanca database includes all operations put in place to save the banks. Mediobanca database is based only on official sources: the budgets of individual institutions, the official documents of the European Commission or the central banks. 9 The number of banks is smaller than the number of distress events, since some banks experienced multiple distress events over time. 10 See for example, Sandstrom, G., “Danske Bank Names New CEO”, The Wall Street Journal, 19 December 2011. 11 See http://www.fdic.gov/bank/individual/failed/banklist.html. 12 In order to take into account the time varying nature of the bank status, we assigned to DB dummy variable the value of 0 in the years before the distress and the value of 1 in the year of distress. In addition, distressed banks are eliminated from our dataset if the bank ceases to operate.

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Table 1 Database overview. This table shows in Panel A the sample distribution by bank status (non-distressed banks versus distressed banks) and in Panel B the distressed banks distribution for each European country in each year. The numbers reported in the table refers only to those banks with data available to compute our target variable (the natural logarithm of the Z-score). The sample period is from 2001 to 2011. The ‘non-distressed banks’ includes banks that satisfy one of these following two conditions during 2001–2011: (1) banks directly classified by BankScope database as ‘active’ entities; (2) banks defined by BankScope database as ‘dissolved by merge’ but with a coverage ratio equals or higher than 0 within 12 months before the operation. Instead, the ‘distressed banks’ includes banks that satisfy one of these following three conditions during 2001–2011: (1) banks that, as defined by BankScope database, changed their status from ‘active’ to either: ‘under receivership’, ‘bankruptcy’, ‘dissolved’, or ‘in liquidation’; (2) banks defined by BankScope database ‘dissolved by merger’ but with a coverage ratio (CR) smaller than 0 within 12 months before the M&A; (3) banks that received state aids. Data on government bail-outs are collected by Mediobanca (2012). The coverage ratio is defined as the ratio of total equity and loan loss reserve minus nonperforming loans all divided to total assets. In light of the numerous data missing in BankScope database on banks ‘under receivership’, this kind of bank distress event is thus not included in our analysis. % is computed as the ratio of distressed banks on total banks. Panel A: distressed banks by country Country

Austria Belgium Denmark France Germany Greece Ireland Italy Netherlands Portugal Spain United Kingdom Total

Bank-year observation

Banks

Distressed

Non-distressed

Total

Distressed

Non-distressed

Total

%

8 3 35 37 37 16 15 33 16 7 26 28 261

1753 249 574 1493 14,253 68 109 2595 178 96 590 1093 23,051

1761 252 609 1530 14,290 84 124 2628 194 103 616 1121 23,312

7 3 34 35 23 9 10 33 12 7 19 22 214

210 34 85 216 1538 16 22 547 38 27 129 167 3029

217 37 119 251 1561 25 32 580 50 34 148 189 3243

3.22 8.10 28.57 13.94 1.47 36 31.25 5.68 24 20.58 12.83 11.64 6.59

Panel B: distressed banks by country and year (bank-year observation) Distress by year Country Austria Belgium Denmark France Germany Greece Ireland Italy Netherlands Portugal Spain United Kingdom Total

2001

6 5

2002

2003

2 5

2 2

3

2 6 1 2

1 12

1 11

15

2004

2005

2

1

3 1

4 2

2006

2007

1 2 2 3

1 2

2 1 1 1 1 8

1 8

2008

1 8

1 4 10

7 5 1 4 1 7 4 1 8 41

2009 4 1 4 7 7 9 3 4 5 2 2 7 55

2010

2011

28 3 4 4

3 3 2 2 2 17 2

13 3 55

6 1 38

variable to identify bank distress is the dependent variable. Complementary log–log models are frequently used when the probability of an event is very small or very large. In fact, cloglog belongs to the discrete time functional specifications applied when survival occurs in continuous time, but spell length is observed only in interval as it is the case for bank distress recorded on annual basis in our sample.13 Guo (1993) observes that time-varying covariates offer an opportunity to examine the relation between the distress

13 Complementary log–log model specification for the hazard regression is also consistent with a continuous time model and interval censored survival time data (Jenkins, 2005).

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probability and the changing conditions under which the distress happens. Following Männasoo and Mayes (2009), the cloglog hazard with time-varying covariates has the form:
h i ′ log − log 1−hj ðXÞ ¼ γjþ β X

ð2Þ

where X contains time-varying covariates and intercept. The hazard rate is derived from Eq. (2) as follows: h
i ′ pðtÞ ¼ 1− exp − exp γjþ β X :

ð3Þ

Prentice and Gloeckler (1978) show the equivalence among interval censored discrete-time model and continuous time model with the proportional hazards assumption. As a consequence, it is possible to transform the coefficients of this analysis into hazard ratios, which facilitate interpretations of the regression results.14 Traditional probit and cloglog models assume duration independence, i.e., the probability of surviving or failing at any point in time is always the same. In order to deal with time dependency problems arising when using these models, we use robust standard errors clustered on the unit of analysis and include in the vector X temporal dummy variables for each period or ‘spell’. In addition, the cloglog model yields estimates of the impact of the indicators on the conditional probability of distress, which means that we obtain distress probabilities, conditional on surviving to a certain point in time. In order to examine whether the models are able to correctly identify the banks in distress, we compute two types of errors: Type 1 and Type 2. Type 1 error occurs when the model fails to identify distressed banks (i.e., a missed distress). It is computed as the ratio of false negative (FN) events to the sum of false negative and true positive (TP) events. Type 2 error occurs when a healthy bank is falsely identified as distressed (i.e., a false alarm). It is computed as the ratio of false positive (FP) events to the sum of false positive and true negative (TN) events. To assign a particular bank into one of the two categories (distressed versus healthy), we set up a cut-off point in terms of the probability of bank distress. All banks above (below) that cut-off point are considered as distressed (healthy) banks. A higher cut-off point results in a lower number of banks on the blacklist of distressed banks, which tends to increase the Type 1 errors. In our analysis we report the two types of errors (Type 1 and Type 2) and their sum computed using two different cut-off points: 1 and 10%.15 However, as already mentioned, policy-makers are more concerned of missing bank distress than issuing false alarms, and early-warning signals trigger an in-depth review of fundamentals, business model and peers of the bank predicted to be in distress (Betz et al., 2014).16 For these reasons, we primarily focus on the Type 1 error results obtained using the cut-off point equal to 1%. The analysis based on errors is based on the arbitrary decision of the cut-off point. To overcome this problem, we also assess the accuracy of distress forecasts using the empirical distribution of the predicted probabilities of distress generated by probit and cloglog models. We assign each observation to a decile of this empirical distribution, and we count how many distress events fall into each decile. The accuracy of the model increases when a high fraction of distress events fall in the deciles associated to high predicted probabilities of distress. 14 In a cloglog model, the regression coefficients can be interpreted as in a Cox proportional hazard rate model. Having the underlying variables in percentage form means that the coefficient captures a proportional percentage change in the hazard given a one percentage point change in the covariate (Männasoo & Mayes, 2009). 15 Setting a lower cut-off point can reduce the Type 1 errors, but at the expense of generating more Type 2 errors. The optimal cut-off point depends on the relative weights that an analyst puts on Type 1 and Type 2 errors. Some of the available literature simply adds Type 1 and Type 2 errors; however, from a prudential perspective, there is a case for putting a larger weight on Type 1 errors (Persons, 1999), because supervisors are primarily concerned about missing a distressed bank (Poghosyan & Čihák, 2011). This implies a preference for relatively low cut-off points, which limit the Type 1 errors at the expense of relatively long blacklists (and potentially more Type 2 errors). 16 Betz et al. (2014) also argue that if the analysis reveals that the signal is false, there is no loss of credibility on behalf of the policy authority.

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4.2. Variables and descriptive statistics Our variable of interest is the Z-score (Beck, De Jonghe, & Schepens, 2011; Beck & Laeven, 2006; Boyd & Graham, 1986; Boyd & Runkle, 1993; Garcia-Marco & Roblez-Fernandez, 2008; Hannan & Hanweck, 1988; Hesse & Cihák, 2007; Laeven & Levine, 2006; Maechler, Srobona, & Worrell, 2005), which is calculated as: Z‐score ¼

ROAA þ ETA : σROAA

ð4Þ

ROAA is the bank's return on average assets, ETA represents the equity to total assets ratio and σROAA is the standard deviation of return on average assets. In order to capture the changing pattern of the bank's return volatility, we use a three-year rolling time window to calculate σROAA.17 The Z-score reflects the number of standard deviations by which returns would have to fall from the mean in order to wipe out the bank equity. Higher values of Z-score are indicative of lower probability of insolvency risk and greater bank stability. Hence, we expect a negative sign for the relation between Z-score and our dependent variable, the probability of bank distress. Since the Z-score is highly skewed, we use the natural logarithm of the Z-score, which is normally distributed (Ivičić et al., 2008; Laeven & Levine, 2009; Liu, Molyneux, & Wilson, 2013). We label the natural logarithm of Z-score as ln_Z. As alternative to the Z-score, we use the CAMELS variables, which are related to bank characteristics like Capital, Asset quality, Managerial skills, Earnings, Liquidity and Sensitivity to market risk. The first CAMELS variable is a proxy for the bank's capital, which is measured as the ratio of total equity to total assets (ETA). We expect a negative sign for the relation between ETA and our dependent variable. A low ETA means high leverage, which makes the bank less resilient to shocks, other thing being equal. Asset quality, is computed as the ratio of impaired loans to gross loans (CRED). The higher the ratio, the lower the quality of the loan portfolio. Hence, an increase in CRED should lead to an increase in probability of bank distress. The managerial quality of the bank, the third covariate, is approximated by the cost to income ratio (CIR).18 Since low values of CIR indicate better managerial quality, the relationship between CIR and probability of distress is expected to be positive. To measure bank earnings, the fourth covariate, we use the return on average assets (ROAA).19 We expect a negative sign for the relation between ROAA and distress, since an increase in profitability reduces the likelihood of a distress event. Liquidity, the fifth covariate, is measured by the ratio of net loans to deposits and short term funding (LIQ). The relationship between LIQ and the probability of bank distress is expected to be positive: banks that finance large portions of their loan portfolios with short term liabilities (i.e., they engage in maturity transformation) are more exposed to refinancing problems in adverse macroeconomic scenarios. In such circumstances, banks may find difficult to raise wholesale short-term funds and customer deposits and eventually incur into deposits drainages. An increase in LIQ should therefore correspond to a higher probability of bank distress. The last CAMELS variable is a proxy for the sensitivity to market risk, which is measured as the ratio of noninterest income to net operating revenue, INC_OPREV (Stiroh, 2004). Due to data availability constraints, we use such a proxy because the magnitude of non-interest income greatly reflects bank participation to financial markets such as securities trading, asset management services, to name a few. The expected sign is uncertain. On the one hand, we expect a negative sign because diversification leads to risk reduction and therefore lower probability of insolvency risk and greater bank stability. On the other hand, the sign may be positive since a high dependence from market related income may threaten banks stability in times of financial market downturns. This 17 Z-score may be estimated both for cross-sectional and time-varying analyses. Additionally, a number of approaches have been developed for its construction. For instance, Boyd, De Nicoló, and Jalal (2006) employ in a cross-sectional study three years mean capital-toasset ratio (CAR), current values of return on average assets (ROAA) and standard deviations of returns computed over the recent three years. In the same work, they use for an international sample the Z-score calculated at each date as the sum of the current ROAA, the current CAR and an instantaneous estimation of standard deviation of returns. Beck and Laeven (2006) calculated the Z-score as the sum of current values of ROAA and CAR, divided by the standard deviation of ROAA over the full period of investigation. In longitudinal crosscountry studies, Maechler, Srobona, and DeLisle (2007) use a three year rolling Z-score which is computed by using the three-year moving ROAA plus the three-year moving average of CAR over the three-year standard deviation of return on average assets. Hesse and Cihák (2007) use for a cross-country, time series research current values of CAR, average return as a percentage of banks' assets and standard deviations of ROAA computed over the period. Yeyati and Micco (2007) computed Z-scores for each bank and year, using the sample mean and variance of ROAA over a three-year period and current values of CAR. 18 All values for the CIR variable are positive in our sample. 19 We also computed the Return on Average Equity (ROAE) rather than ROAA and we obtained very similar results in the regressions.

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Table 2 Summary statistics of Z-score and CAMELS variables by bank status. This table reports summary statistics on our target variable, the natural logarithm of the Z-score (ln_Z), and on the CAMELS variables for the full sample and for the distressed and non-distressed banks. Each descriptive statistic is tested on the whole period (2001–2011) and on the crisis period (2008–2011). It also summarized their hypothesized relationships (irrespective of the time horizon) with the dependent variable. The natural logarithm of the Z-score (ln_Z) is defined in Section 4. Equity to total assets (ETA), impaired loans to gross loans (CRED), cost to income ratio (CIR), return on average assets (ROAA), net loans to deposits and short term funding (LIQ), and non-interest income to net operating revenue (INC_OPREV) are the CAMELS variables. The numbers reported in the table refers only to those banks with data available to compute our target variable. To mitigate the effect of outliers, we winsorize observations in the outside 1% of each tail of each variable. The ‘full sample’ includes the distressed and non-distressed banks. The ‘non-distressed banks’ includes banks that satisfy one of these following two conditions during 2001–2011: (1) banks directly classified by BankScope database as ‘active’ entities; (2) banks defined by BankScope database as ‘dissolved by merge’ but with a coverage ratio equals or higher than 0 within 12 months before the operation. Instead, the ‘distressed banks’ includes banks that satisfy one of these following three conditions during 2001–2011: (1) banks that, as defined by BankScope database, changed their status from ‘active’ to either: ‘under receivership’, ‘bankruptcy’, ‘dissolved’, or ‘in liquidation’; (2) banks defined by BankScope database ‘dissolved by merger’ but with a coverage ratio (CR) smaller than 0 within 12 months before the M&A; (3) banks that received state aids. Data on government bail-outs are collected by Mediobanca (2012). The coverage ratio is defined as the ratio of total equity and loan loss reserve minus non-performing loans all divided to total assets. In light of the numerous data missing in BankScope database on banks ‘under receivership’, this kind of bank distress event is thus not included in our analysis. The values in the table are the averages. The medians are reported in parentheses. ***, **, and * denote statistical significance at 1%, 5%, and 10% levels, respectively. Variables

ln_Z ETA CRED CIR ROAA LIQ INC_OPREV

Non-distressed banks (1)

Distressed banks (2)

Difference (1)–(2)

Full sample

Whole period

Crisis period

Whole period

Crisis period

Whole period

Whole period

Crisis period

4.551 (4.430) 0.080 (0.062) 0.006 (0) 0.685 (0.690) 0.003 (0.002) 0.770 (0.714) 0.271 (0.250)

4.461 (4.292) 0.086 (0.070) 0.008 (0) 0.681 (0.685) 0.003 (0.002) 0.820 (0.725) 0.275 (0.260)

3.030 (2.970) 0.104 (0.060) 0.021 (0.010) 0.635 (0.630) 0.001 (0.002) 0.991 (0.908) 0.322 (0.280)

2.987 (2.922) 0.079 (0.053) 0.024 (0.018) 0.650 (0.621) 0.0006 (0.002) 1.085 (0.981) 0.315 (0.280)

4.533 (4.418) 0.080 (0.062) 0.006 (0) 0.685 (0.689) 0.003 (0.002) 0.773 (0.715) 0.272 (0.251)

4.436 (4.272) 0.086 (0.070) 0.008 (0) 0.681 (0.684) 0.003 (0.002) 0.825 (0.728) 0.276 (0.260)

1.521***

Crisis period 1.474***

−0.024***

−0.007*

−0.015***

−0.016***

0.05*

0.031*

0.002***

0.002***

−0.221***

−0.265***

−0.051**

−0.04**

Expected sign

NEGATIVE NEGATIVE POSITIVE POSITIVE NEGATIVE POSITIVE NEGATIVE/ POSITIVE

conjecture is supported by the US evidence provided by De Young and Torna (2013), who find that the failure probability increases with income from nontraditional banking activities. Table 2 reports descriptive statistics relating to Z-score and the CAMELS variables for the full sample and for the distressed and non-distressed banks. Each descriptive statistic is tested on the whole period (2001– 2011) and on the crisis period (2008–2011).20 The average value of ln_Z is 4.553 in the whole period and 4.436 during the crisis years. As expected, nondistressed banks show higher values for the average ln_Z than distressed banks both in the full period (4.551 vs. 3.030) and in the crisis period (4.461 vs. 2.987). This result can be largely explained both by a lower volatility of returns (proxied by the standard deviation of ROAA)21 of non-distressed banks compared to distressed banks and by higher average ROAA values (0.003 vs. 0.001 in the whole period and 0.003 vs. 0.0006 in the crisis years). Not surprisingly, the average value of ROAA decreases during the crisis period only for the distressed banks. The reduction is due principally to the decline in operating profit. During the financial crisis distressed banks show higher level of capitalization (ETA) compared to the non-distressed banks (0.079 vs. 0.086). In particular, ETA remains substantially unchanged for the non-distressed banks in the two time periods considered (0.080 in the whole period and 0.086 in the crisis years), while show a strong decrease for the distressed-banks (0.104 in the full period vs. 0.079 during the financial crisis). The difference in 20 As a robustness check, we also define the crisis period as the period from 2007 to 2011. Starting the crisis period from 2007 does not produce any remarkable change in our findings. Results are omitted for brevity and available from the authors. 21 Active banks show lower values for the average standard deviation of ROAA than distressed banks both in the full period (0.002 vs. 0.007) and in the crisis period (0.002 vs. 0.006).

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Table 3 Correlations. This table shows the correlation matrix for the variables used in the empirical analysis: the natural logarithm of the Z-score (ln_Z), our target variable, and the CAMELS variables. Variables are defined in Section 4. Data in the table are referred to the whole period: 2001–2011.

ln_Z ETA CRED CIR ROAA LIQ INC_OPREV

ln_Z

ETA

CRED

CIR

ROAA

LIQ

INC_OPREV

1.0000 −0.0904 −0.2610 −0.0957 0.0432 −0.0918 −0.1496

1.0000 0.1755 −0.0265 0.2526 0.1832 0.2068

1.0000 0.0072 −0.0275 0.1791 0.0678

1.0000 −0.4579 −0.1322 0.1597

1.0000 0.0694 0.1549

1.0000 −0.1579

1.0000

terms of the mean test between active and distressed banks for the Z-score and its components is statistically significant at the 1% level during the whole period. This is true also for the crisis period, with the sole exception of ETA that is statistically significant at the 10% level. Due to the deterioration of the credit quality in the last years, the average value of CRED grows for both types of banks, but showing higher values for distressed banks (0.024 vs. 0.008 during the crisis period). The average CIR values remains substantially unchanged between the whole period and the crisis period for both the non-distressed banks and the distressed banks. The average value of LIQ shows a significant growth in the recent years for both distressed and non-distressed banks, mostly because of the drainage of bank deposits and short term funding experienced by banks during the financial turmoil than to the increase in net loans. The average value of INC_OPREV remains stable across sub-periods in both groups, with distressed banks showing a larger incidence of non-interest income. During the sample period, the test for difference in means between active and distressed banks is statistically significant at 1% level for LIQ and CRED; at 5% level for INC_OPREV; and at 10% level for CIR. When we restrict the sample period to the crisis years, LIQ and INC_OPREV are statistically significant at 1 and 5%, respectively, while CRED and CIR are significant at 10%. Finally, Table 3 presents the correlation matrix for the variables used in our estimations.22

5. Main results We present the results of the regressions for bank distress in Table 4, which shows both the probit estimations results and the hazard ratios of the complementary log–log models. All these regressions are carried out on the full sample period (2001–2011). Following Männasoo and Mayes (2009), we assume that the fragility of each bank is closely related to the overall propensity to banking crisis in which the bank-specific factors play an important role in systemic stability. We include in the vector Xi,t − 1 year and country dummy variables in all regressions. Given that our sample includes banks from 12 different European countries, we include a country dummy to control for the different institutional and economic settings. To mitigate the effect of outliers data of each variable are winsorized at the 1% percentile of the distribution. The first three columns report a comparison between our target variable, the natural logarithm of the Z-score (ln_Z),23 its components, and the CAMELS variables as alternative to ln_Z variable, see regressions (I), (II), and (III), respectively. Finally, in regression (IV) we include both ln_Z and the CAMELS variables. The log of the Z-score (ln_Z) is strongly significant, showing the expected negative effect in both models (see regression (I) of Table 4).24 The negative relation between the probability of bank distress and ln_Z 22 Table 3 shows that between Z-score and its components ETA and ROAA, used as CAMELS variables, there isn't any problem of multicollinearity. 23 We obtain similar results if instead of a three-year rolling time window to calculate σROAA we use a five-year rolling time window. 24 The Z-score's hazard ratio in column (I) means that banks with one unit higher of ln_Z have around 63% lower hazard rates or in other words are less likely to fail. Generally speaking, the hazard ratios represent the complement to one of the probability of failure. For instance, if the estimated hazard ratio for a bank characteristic j is 0.7, then the banks with that characteristic have a 30% lower probability of exiting from the banking system than the referring group; instead, if the hazard ratio is 1.3 the banks have a 30% higher probability of exiting from system.

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Table 4 Predicting distress. This table shows the probit estimations results and the hazard ratios of the complementary log–log model estimations obtained regressing bank distress on: (I) our target variable, the natural logarithm of the Z-score (ln_Z); (II) the components of the Z-score: equity to total assets (ETA), return on average assets (ROAA), and three-years standard deviation of ROAA (σROAA); (III) the CAMELS variables: equity to total assets (ETA), impaired loans to gross loans (CRED), cost to income ratio (CIR), return on average assets (ROAA), net loans to customer deposits and short term funding (LIQ), and non-interest income to net operating revenue (INC_OPREV); and (IV) the natural logarithm of the Z-score plus the CAMELS variables. The sample period is 2001–2011. The dependent variable is the Distressed Bank dummy variable (DBi,t) that takes the value of 1 if bank i becomes distressed (that is: under receivership, bankruptcy, dissolved, in liquidation, dissolved by merger with a coverage ratio smaller than 0 within 12 months before the M&A, or government bail-out) at time t (the year in progress) and 0 otherwise. The dependent variable and independent variables are defined in Section 4. All explanatory variables are lagged by one year. All variables are winsorized at the 1% of each tail. Year and country dummy variables are also included in the model. Robust standard errors are reported in parentheses. The superscripts ***, **, and * denote coefficients statistically different from zero at the 1%, 5%, and 10% levels, respectively, in two-tailed tests. This table also displays the relationship between model predictions and actual distress events on the full sample for the whole period using a cut-off point equals to 0.01. TP stands for ‘True Positive’; FN stands for ‘False Negative’; FP stands for ‘False Positive’; TN stands for ‘True Negative’. Type 1 error occurs when the model fails to identify the distressed bank. It is computed as: FN/(FN + TP). Type 2 error occurs when a healthy bank is falsely identified as distressed (i.e., a false alarm). It is computed as: FP/(FP + TN). Variables

ln_Z (−1)

Probit model

Complementary log–log model

(I)

(II)

(III)

(IV)

(I)

(II)

(III)

(IV)

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

−0.179*** (0.031)

0.629*** (0.050)

−0.199*** (0.027)

σROAA (−1)

29.177*** (4.807) −0.363 (0.450)

ETA (−1)

Year FE Country FE N. of obs. Pseudo R2

Yes Yes 20,122 0.2107

Yes Yes 20,122 0.2075

0.321 (0.378) 2.986** (1.354) −0.212 (0.217) −16.526*** (4.387) 0.248*** (0.065) 0.570*** (0.171) Yes Yes 20,122 0.2042

Type errors: TP FN FP TN Type 1 Type 2

199 41 5296 14,586 0.170 0.266

197 43 5434 14,448 0.179 0.273

197 43 5123 14,759 0.179 0.257

CRED (−1) CIR (−1) −7.283** (3.101)

ROAA (−1) LIQ (−1) INC_OPREV (−1)

0.494 (0.363) 1.790 (1.354) −0.296 (0.190) −9.769** (3.815) 0.249*** (0.060) 0.335** (0.161) Yes Yes 20,122 0.2257

203 37 5003 14,879 0.154 0.251

0.639*** (0.061) 7.63em22*** (7.40em23) 0.347 (0.348)

Yes Yes 20,122

Yes Yes 20,122

0.908 (0.903) 101.128 (290.925) 0.549 (0.280) 1.40e-15*** (1.12e-14) 1.645*** (0.281) 3.386*** (1.390) Yes Yes 20,122

196 44 5117 14,765 0.183 0.257

196 44 5508 14,374 0.183 0.277

194 46 5159 14,723 0.191 0.259

7.04e-06 (0.000)

1.935 (1.703) 4.146 (11.588) 0.453 (0.201) 1.71e-07** (1.30e-06) 1.672*** (0.270) 1.978* (0.728) Yes Yes 20,122

199 41 4876 15,006 0.170 0.245

means that high values of Z-score are associated with low probability of insolvency risk and greater bank stability. This result is in line with Vazquez and Federico (2012), who find that the probability of failure is influenced by the bank risk profile. We also regress the binary variable for bank distress on the three components of the Z-score: ROA; volatility of returns, and the equity to total assets ratio. The results are presented in regressions (II) of Table 4, which show that, regardless of the model used, the bank probability of distress is largely explained by the volatility of returns (proxied by the standard deviation of ROAA, σROAA). As expected, higher values for the average σROAA imply an increase of the probability

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Table 5 Distress forecasts. This table reports the frequencies of distress events by deciles of the distribution of the predicted probabilities for the probit and the complementary log–log models on the whole period (2001–2011) presented in Table 4. Decile 10 (1) is the decile with the highest (lowest) predicted probabilities of distress events. Both probit the probit and the complementary log–log model include the following regressors: (I) on our target variable, the natural logarithm of the Z-score (ln_Z); (II) on its components; (III) on the CAMELS variables and (IV) on the natural logarithm of the Z-score plus the CAMELS variables. Deciles

10 9 8 7 6 1–5

Probit model

Complementary log–log model

(I)

(II)

(III)

ln_Z

Components of ln_Z

CAMELS

0.629 0.108 0.120 0.045 0.025 0.070

0.625 0.104 0.133 0.058 0.016 0.062

0.604 0.129 0.137 0.033 0.016 0.079

(IV)

(I)

(II)

(III)

(IV)

ln_Z and CAMELS

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

0.620 0.166 0.083 0.058 0.004 0.066

0.612 0.116 0.129 0.054 0.016 0.062

0.612 0.108 0.137 0.062 0.012 0.066

0.591 0.120 0.133 0.054 0.012 0.087

0.612 0.158 0.087 0.058 0.025 0.058

of bank distress. The capitalization (proxied by the ratio of equity to total assets, ETA) is never significant, while the ROAA variable is significant only in the probit model, but with a lower degree compared to σROAA. Concerning the CAMELS indicators, Table 4 shows that the asset quality measure (CRED), the earnings variable (ROAA), the liquidity bank indicator (LIQ) and the sensitivity to market risk variable (INC_OPREV) are significant in the probit model. All these indicators show the expected sign. CRED is positive, confirming that if the quality of the bank's loans decreases, the bank is more likely to fail. As expected, the positive relation between liquidity and the probability of bank distress seems to be related to tough conditions in the interbank market and the loss of deposits (bank runs) experienced by several banks during the crisis years. The result on ROAA is in line with those of Poghosyan and Čihák (2011) and Betz et al. (2014), who obtain a negative and significant relationship between bank profitability and financial distress. Consistent with De Young and Torna (2013), INC_OPREV has a positive coefficient. The positive sign supports the view that a high dependence from market related income may increase a bank's vulnerability in times of financial crisis. Overall, we find that, in the 2001–2011 period, characteristics like poor quality loan portfolio, low profitability, and diversification increase the likelihood that a bank will face distress. The CAMELS results of the complementary log–log model are qualitatively similar to those of the probit regressions, with the surprising exception of ROAA that shows a hazard ratio larger than 1, which corresponds to a positive coefficient rather than negative. Finally, in columns IV and VIII, we include both the Z-score and the CAMELS variables in the model. Unlike the Z-score, which always remains highly significant, most of CAMELS indicators become less statistically significant. This latter holds for both the probit and the complementary log–log specification.25 The pseudo R2 slightly improves considering together Z-score and CAMELS covariates. Table 4 also displays the relationship between model predictions and actual distress events for both models on the full sample for the whole period using a cut-off point equals to 1%.26 As already stated, we mainly focus on the Type 1 error and we find that in the two models considered the performance using the ln_Z alone in the full period is similar to that of both its components and the CAMELS variables. Specifically, column (I) of Table 4 shows that during 2001–2011 the probit and the complementary logistic models using only the ln_Z fail to correctly classify 41 distress events out of 199 and 44 distress events out of 196, respectively. Thus, in the full period the probit model with only our target variable correctly classifies 199 out of 240 distress events (83%), while the cloglog model correctly classifies 196 out of 240 distress events (82%).

25 To mitigate the concern that the number of distress events is extremely low compared to the total number of observations, we also estimate a logistic regression in rare events data (King & Zeng, 2001) on the period from 2001 to 2011. The findings of the logistic regression are remarkably similar to those in Table 4. 26 We obtain similar results if instead of 1% cut-of point we use 10% cut-off point.

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The probit (complementary logistic) model using the components of the Z-score (see column II (VI) of Table 4) fails to correctly classify 43 (44) distress events out of 197 (194). Hence, the probit (complementary logistic) model with the Z-score's components correctly classifies 197 (196) out of 240 distress events (82%). We obtain similar results using the CAMELS variables. Column (III) of Table 4 shows that during the whole period the CAMELS variables fail to correctly classify 43 (46) distress events out of 197 (194) using the probit (cloglog) model. Consequently, probit model with only the CAMELS variables correctly classifies 197 out of 240 distress events (82%), while the cloglog model correctly classifies 194 out of 240 distress events (81%).

Table 6 Predicting distress in the financial crisis period. This table shows the probit estimations results and the hazard ratios of the complementary log–log model estimations obtained regressing bank distress on: (I) our target variable, the natural logarithm of the Z-score (ln_Z); (II) the components of the Z-score: equity to total assets (ETA), return on average assets (ROAA), and three-years standard deviation of ROAA (σROAA); (III) the CAMELS variables: equity to total assets (ETA), impaired loans to gross loans (CRED), cost to income ratio (CIR), return on average assets (ROAA), net loans to customer deposits and short term funding (LIQ), and non-interest income to net operating revenue (INC_OPREV); and (IV) the natural logarithm of the Z-score plus the CAMELS variables. The sample period is the crisis period 2008–2011. The dependent variable is the Distressed Bank dummy variable (DBi,t) that takes the value of 1 if bank i becomes distressed (that is: under receivership, bankruptcy, dissolved, in liquidation, dissolved by merger with a coverage ratio smaller than 0 within 12 months before the M&A, or government bailout) at time t (the year in progress) and 0 otherwise. The dependent variable and independent variables are defined in Section 4. All explanatory variables are lagged by one year. All variables are winsorized at the 1% of each tail. Year and country dummy variables are also included in the model. Robust standard errors are reported in parentheses. The superscripts ***, **, and * denote coefficients statistically different from zero at the 1%, 5%, and 10% levels, respectively, in two-tailed tests. This table also displays the relationship between model predictions and actual distress events on the full sample for the whole period using a cut-off point equals to 0.01. TP stands for ‘True Positive’; FN stands for ‘False Negative’; FP stands for ‘False Positive’; TN stands for ‘True Negative’. Type 1 error occurs when the model fails to identify the distressed bank. It is computed as: FN/(FN + TP). Type 2 error occurs when a healthy bank is falsely identified as distressed (i.e., a false alarm). It is computed as: FP/(FP + TN). Variables

ln_Z (−1)

Probit model

Complementary log–log model

(I)

(II)

(III)

(IV)

(I)

(II)

(III)

(IV)

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

−0.154** (0.044)

0.651*** (0.060)

−0.190*** (0.037)

σROAA (−1)

27.473*** (8.090) −2.393 (1.319)

Yes Yes 10,849 0.2358

Yes Yes 10,849 0.2329

−2.168** (0.980) 6.749*** (1.882) −0.097 (0.288) −10.220 (6.651) 0.523*** (0.077) 0.783*** (0.213) Yes Yes 10,849 0.2630

158 25 3275 7391 0.136 0.306

154 29 3034 7632 0.158 0.284

161 22 2820 7846 0.120 0.264

ETA (−1) CRED (−1) CIR (−1)

−5.140 (5.443)

ROAA (−1) LIQ (−1) INC_OPREV (−1) Year FE Country FE N. of obs. Pseudo R2 Type errors: TP FN FP TN Type 1 Type 2

−1.815** (0.922) 5.346*** (1.887) −0.187 (0.258) −4.274 (6.081) 0.524*** (0.074) 0.645*** (0.205) Yes Yes 10,849 0.2757 159 24 2845 7821 0.131 0.266

0.676*** (0.084) 3.16em23*** (4.81em23) 0.0004* (0.002)

Yes Yes 10,849

Yes Yes 10,849

0.004 (0.012) 59,248.53*** (21,994.2) 0.833 (0.509) 1.12e-08 (1.58e-07) 2.397*** (0.435) 4.395*** (1.938) Yes Yes 10,849

154 29 3182 7484 0.158 0.298

151 32 3113 7553 0.174 0.291

161 22 2997 7669 0.120 0.280

0.184 (2.271)

0.013 (0.038) 1616.063** (6075.855) 0.617 (0.360) 0.393 (4.836) 2.448*** (0.430) 3.235*** (1.319) Yes Yes 10,849

160 23 2912 7754 0.125 0.273

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Table 7 Distress forecasts in the financial crisis period. This table reports the frequencies of distress events by deciles of the distribution of the predicted probabilities for the probit and the complementary log–log models on the crisis period (2008–2011) presented in Table 6. Decile 10 (1) is the decile with the highest (lowest) predicted probabilities of distress events. Both probit the probit and the complementary log–log model include the following regressors: (I) on our target variable, the natural logarithm of the Z-score (ln_Z); (II) on its components; (III) on the CAMELS variables and (IV) on the natural logarithm of the Z-score plus the CAMELS variables. Deciles

10 9 8 7 6 1–5

Probit model

Complementary log–log model

(I)

(II)

(III)

(IV)

(I)

(II)

ln_Z

Components of ln_Z

0.672 0.109 0.109 0.038 0.016 0.054

0.677 0.120 0.114 0.043 0.016 0.027

(III)

(IV)

CAMELS

ln_Z and CAMELS

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

0.710 0.142 0.092 0.016 0.000 0.038

0.721 0.136 0.076 0.027 0.005 0.032

0.666 0.120 0.098 0.043 0.021 0.049

0.661 0.114 0.114 0.071 0.016 0.021

0.688 0.147 0.098 0.016 0.010 0.038

0.699 0.147 0.065 0.049 0.005 0.032

Adding the Z-score to CAMELS variables improves the predictive power of both the models. In particular, the probit model correctly classifies 203 out of 240 distress events (84%), while the cloglog model correctly classifies 199 out of 240 distress events (83%). The distress forecasts presented in Table 5 confirm the predictive accuracy of the Z-score alone compared to both its components and the CAMELS variables. Following Bharath and Shumway (2008), we assess the accuracy of our models by sorting banks in deciles based on the predicted probabilities and calculating the percentage of defaults by decile of Z-score, its components, the set of CAMELS variables, and the combination of the latter with the Z-score. Focusing on the probit model, we observe that 63% of the bank distress events are in the top decile (i.e., banks with the largest probability of distress) of the estimated probabilities when we consider the natural logarithm of the Z-score alone. This percentage is about 62% for the Z-score's components, 60% for the CAMELS variables, and 62% for the model with the Z-score plus CAMELS covariates. Results on deciles for the cloglog model are qualitatively similar. Overall, we find that the highest percentage of distress is in the tenth decile, which confirms that Z-score and CAMELS are good predictor of bank distress. In light of the numerous distress events that characterized many European banks during the recent years, we investigate the suitability of the Z-score as a measure of bank distress relative to both its components and the CAMELS variables also on the only crisis period 2008–2011 (see Table 6). As in Table 4, we run the probit and the complementary log–log model on the Z-score alone, its components, the CAMELS variables, and all the covariates considered together. Our variable of interest, ln_Z, remains highly significant with the correct sign (negative) also during 2008–2011 in both models. As for the Z-score's components and the CAMELS variables, results are remarkably similar to those of the whole period. Among the Z-score's components, the bank probability of distress is mostly explained by the volatility of returns. The ROAA variable is no longer significant. Moreover, with reference to the CAMELS variables, ETA becomes significant with the hypothesized sign, but only in the probit model (see column (III) of Table 6). The managerial quality variable (CIR), both in Tables 4 and 6, is not significant factor for determining bank vulnerability. This finding is in line with those of Poghosyan and Čihák (2011), who show that low costs do not indicate a better ability to prevent bank distress. In addition, we determine the relationship between model predictions and actual distress events during the financial turmoil using a cut-off point equals to 1%.27 Focusing on the type 1 error, Table 6 shows that

27

We obtain similar results if instead of 1% cut-of point we use 10% cut-off point.

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the predictive power of the Z-score, its components, the CAMELS variables improves compared to Table 4, although the Z-score performs slightly worse than the CAMELS variables. The slightly improved predictive power of the two models in the crisis period is also confirmed by the results of Table 7, which reports annual distress forecast accuracy by deciles. Finally, we evaluate the effectiveness of the Z-score as a bank distress predictor compared to the CAMELS variables across bank size. Large banks may be deemed too-big-too-fail, and therefore they may be prevented from entering financial distress. For this reason, in Table 8 we run the probit and the complementary logistic models on the smallest banks (bottom quartile by total assets on the country's gross

Table 8 Predicting distress by bank size. This table reports the probit estimations results and the hazard ratios of the complementary log–log model estimations for the smallest banks (bottom quartile by total assets on the country's gross domestic product, TA_GDP) and for the biggest banks (top quartile by TA_GDP) over the whole period, 2001–2011. Bank distress is: (I) the natural logarithm of the Z-score (ln_Z); and (II) the natural logarithm of the Z-score plus the CAMELS variables. The dependent variable is the Distressed Bank dummy variable (DBi,t) that takes the value of 1 if bank i becomes distressed (that is: under receivership, bankruptcy, dissolved, in liquidation, dissolved by merger with a coverage ratio smaller than 0 within 12 months before the M&A, or government bail-out) at time t (the year in progress) and 0 otherwise. The dependent variable and independent variables are defined in Section 4. All explanatory variables are lagged by one year. All variables are winsorized at the 1% of each tail. Year and country dummy variables are also included in the model. Robust standard errors are reported in parentheses. The superscripts ***, **, and * denote coefficients statistically different from zero at the 1%, 5%, and 10% levels, respectively, in two-tailed tests. This table also displays the relationship between model predictions and actual distress events on the full sample for the whole period using a cut-off point equals to 0.01. TP stands for ‘True Positive’; FN stands for ‘False Negative’; FP stands for ‘False Positive’; TN stands for ‘True Negative’. Type 1 error occurs when the model fails to identify the distressed bank. It is computed as: FN/(FN + TP). Type 2 error occurs when a healthy bank is falsely identified as distressed (i.e., a false alarm). It is computed as: FP/(FP + TN). Variables

Small banks

Large banks

Probit model

ln_Z (−1)

(I)

(II)

ln_Z

CAMELS

−0.357*** (0.104)

ETA (−1)

Year FE Country FE N. of obs. Pseudo R2

Yes Yes 5139 0.3927

Type errors: TP FN FP TN Type 1 Type 2

15 4 287 4833 0.210 0.056

14 5 186 4934 0.263 0.036

CIR (−1) ROAA (−1) LIQ (−1) INC_OPREV (−1)

Probit model

(I)

(II)

(I)

(II)

ln_Z

CAMELS

Complementary log–log model

ln_Z

CAMELS

−0.203*** (0.033)

0.466*** (0.119) 1.027 (0.7709) 7.685** (3.644) −0.704 (0.764) −9.841 (12.217) −0.390 (0.330) 0.739 (0.482) Yes Yes 5139 0.3715

CRED (−1)

Complementary log–log model

Yes Yes 5139

8.688 (20.273) 8.27em07*** (5.67em08) 0.239 (0.459) 0.084 (2.690) 0.546 (0.513) 3.888 (3.611) Yes Yes 5139

15 4 232 4888 0.210 0.045

14 5 155 4965 0.263 0.030

(I)

(II)

ln_Z

CAMELS

0.676*** (0.052)

Yes Yes 4860 0.1871

−0.672 (0.830) 0.966 (1.751) −0.091 (0.251) −18.088*** (5.806) 0.264*** (0.071) 0.480*** (0.184) Yes Yes 4860 0.1858

164 11 2726 1959 0.062 0.581

164 11 2733 1952 0.062 0.583

Yes Yes 4860

0.047 (0.109) 3.936 (14.752) 0.842 (0.452) 3.131*** (3.721) 1.697*** (0.294) 2.527** (0.922) Yes Yes 4860

165 10 2700 1985 0.057 0.576

163 12 2669 2016 0.068 0.569

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Table 9 Distress forecasts by bank size. This table reports the frequencies of distress events by deciles of the distribution of the predicted probabilities for the probit and the complementary log–log models on the whole period (2001–2011) presented in Table 8. Decile 10 (1) is the decile with the highest (lowest) predicted probabilities of distress events. Both probit the probit and the complementary log–log model include the following regressors (I) the natural logarithm of the Z-score (ln_Z), and (II) on the natural logarithm of the Z-score plus the CAMELS variables. Deciles

Small banks

Large banks

Probit model

10 9 8 7 6 1–5

Complementary log–log model

Probit model

Complementary log–log model

(I)

(II)

(I)

(II)

(I)

(II)

(I)

(II)

ln_Z

CAMELS

ln_Z

CAMELS

ln_Z

CAMELS

ln_Z

CAMELS

0.473 0.210 0.105 0.000 0.105 0.105

0.736 0.000 0.000 0.000 0.052 0.210

0.473 0.157 0.105 0.052 0.105 0.105

0.684 0.052 0 0 0 0.263

0.617 0.091 0.074 0.028 0.068 0.120

0.685 0.017 0.017 0.051 0.097 0.131

0.600 0.080 0.085 0.028 0.057 0.148

0.657 0.028 0.011 0.074 0.097 0.131

domestic product, TA_GDP28) and the biggest banks (top quartile by TA_GDP). In the table, we report the results of the two regressions for the whole period on: (I) the natural logarithm of the Z-score; and (II) the CAMELS variables. Results for type 1 errors using the probit model show that the model including CAMEL variables does not offer any advantage in terms of predictive power when we compare them to a simple model based on ln_Z.29 Moreover, the predictive power of the natural logarithm of the Z-score is higher for banks having a large size. These results indicate that the natural logarithm of the Z-score is more effective when the size of the financial institution increases. An explanation for these results is that smaller banks may result more financially opaque since less subject to accounting and reporting scrutiny than larger banks. Finally, the predictive power of the Z-score for the largest banks is also confirmed by the distress forecasts of Table 9.

6. Robustness tests To assess whether the predictive ability of the Z-score shown in previous tables relies on the way it is computed, we compute our target variable using an alternative measure. We follow Yeyati and Micco (2007) and compute the Z-score using the sample mean and variance of ROAA over a three-year period (A_ROAA) and current values of ETA. Table 10 shows the probit estimations results and the hazard ratios of the complementary log–log models over the whole period (2001–2011). Comparing the results of Table 10 (see Panels A and B) with those of Tables 4 and 5, we find that the ability of the alternative Z-score measure to predict bank distress improves in both models,30 but the number of observations drastically decreases (8711 vs. 20,122 of Table 4).

28 As measure of bank size we use the ratio of total assets to the country's GDP in order to take into account the importance of banks compared to the size of the economy. We obtain very similar results using only total assets rather than TA_GDP. 29 We obtain similar results estimating the probit and the complementary log–log models on the Z-score's components. 30 Panel A of Table 10 shows that, during 2001–2011, the probit model on the alternative Z-score measure correctly classifies 86 out of 100 distress events (86% vs. 82% of the Z-score of Table 4). This finding is also confirmed by the distress forecasts of Panel B (see Table 10). Results for the cloglog model are qualitatively similar.

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Finally, in Table 11 we perform further additional tests to assess the validity of our results in the following subsamples: commercial bank versus cooperative, savings, and real estate and mortgage banks, (which we call ‘other banks’); and banks from a PIIGS countries (Portugal, Ireland, Italy, Greece, Spain) versus nonTable 10 Predictions and forecasts of bank distress using an alternative Z-score measure. This table shows in Panel A the probit estimations results and the hazard ratios of the complementary log–log model estimations using an alternative measure of our target variable, the Z-score (ln_Z). Following Yeyati and Micco (2007), we compute the Z-score using the three-year moving return of average assets (A_ROAA) in the numerator. The other components of the Z-score are: equity to total assets (ETA) and three-year moving return of average assets (A_ROAA). We regress the distress bank binary variable on: (I) the natural logarithm of the Z-score (ln_Z); (II) the components of the Z-score (ETA, A_ROAA, and σA_ROAA); (III) the CAMELS variables: equity to total assets (ETA), impaired loans to gross loans (CRED), cost to income ratio (CIR), three-year moving return of average assets (A_ROAA), net loans to customer deposits and short term funding (LIQ), and non-interest income to net operating revenue (INC_OPREV); and (IV) the natural logarithm of the Z-score plus the CAMELS variables. The sample period is 2001–2011. The dependent variable is the Distressed Bank dummy variable (DBi,t) that takes the value of 1 if bank i becomes distressed (that is: under receivership, bankruptcy, dissolved, in liquidation, dissolved by merger with a coverage ratio smaller than 0 within 12 months before the M&A, or government bailout) at time t (the year in progress) and 0 otherwise. The dependent variable and independent variables are defined in Section 4. All explanatory variables are lagged by one year. All variables are winsorized at the 1% of each tail. Year and country dummy variables are also included in the model. Robust standard errors are reported in parentheses. The superscripts ***, **, and * denote coefficients statistically different from zero at the 1%, 5%, and 10% levels, respectively, in two-tailed tests. The table of Panel A also displays the relationship between model predictions and actual distress events on the full sample for the whole period using a cut-off point equals to 0.01. TP stands for ‘True Positive’; FN stands for ‘False Negative’; FP stands for ‘False Positive’; TN stands for ‘True Negative’. Type 1 error occurs when the model fails to identify the distressed bank. It is computed as: FN/(FN + TP). Type 2 error occurs when a healthy bank is falsely identified as distressed (i.e., a false alarm). It is computed as: FP/(FP + TN). In addition, Panel B reports the frequencies of distress events by deciles of the distribution of the predicted probabilities for the probit and the complementary log–log models in Panel A. Decile 10 (1) is the decile with the highest (lowest) predicted probabilities of distress events. Panel A: estimations results and type errors (whole period) Variables

ln_Z (−1)

Probit model

Complementary log–log model

(I)

(II)

(III)

(IV)

(I)

(II)

(III)

(IV)

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

−0.250*** (0.051)

0.552*** (0.068)

−0.260*** (0.047)

σA_ROAA (−1)

74.614*** (14.252) −0.614 (0.755)

Year FE Country FE N. of obs. Pseudo R2

Yes Yes 8711 0.2845

Yes Yes 8711 0.2804

−0.111 (80.625) 3.964* (2.133) 0.025 (0.332) −20.049*** (9.629) 0.415*** (0.115) 0.456 (0.280) Yes Yes 8711 0.2677

Type errors: TP FN FP TN Type 1 Type 2

86 14 1458 7153 0.140 0.169

77 23 1217 7394 0.230 0.141

81 19 1237 7374 0.190 0.143

ETA (−1) CRED (−1) CIR (−1)

−8.674 (6.770)

A_ROAA (−1) LIQ (−1) INC_OPREV (−1)

0.402 (0.556) 1.244 (2.129) −0.135 (0.286) −10.889 (8.428) 0.388*** (0.103) 0.095 (0.265) Yes Yes 8711 0.3044

88 12 1367 7244 0.120 0.158

0.539*** (0.086) 8.77em57*** (2.28em59) 0.230 (0.258)

Yes Yes 8711

Yes Yes 8711

0.616 (0.894) 195.884 (794.636) 0.864 (0.629) 2.631* (4.851) 1.858* (0.532) 2.690 (1.754) Yes Yes 8711

83 17 1351 7260 0.170 0.156

76 24 1190 7421 0.240 0.138

77 23 1189 7422 0.230 0.138

0.0003 (0.004)

2.210 (2.578) 1.069 (4.457) 0.554 (0.364) 7.860 (0.00001) 1.883** (0.497) 1.158 (0.658) Yes Yes 8711

85 15 1310 7301 0.150 0.152

(continued on next page)

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Table 10 (continued) Panel B: Forecasts Probit model

10 9 8 7 6 1–5

Complementary log–log model

(I)

(II)

(III)

(IV)

(I)

(II)

(III)

(IV)

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

ln_Z

Components of ln_Z

CAMELS

ln_Z and CAMELS

0.680 0.200 0.020 0 0.030 0.070

0.730 0.120 0.040 0.010 0.030 0.070

0.380 0.360 0.130 0.030 0.030 0.070

0.780 0.110 0.020 0.010 0.020 0.060

0.670 0.210 0.020 0 0.020 0.080

0.690 0.130 0.030 0.060 0.010 0.080

0.420 0.290 0.160 0.010 0.040 0.080

0.720 0.160 0.030 0.010 0.010 0.070

PIIGS banks. In the table, we report the results of probit regressions on: (I) the natural logarithm of the Z-score; and (II) the CAMELS variables.31 Focusing on the probit and the type 1 errors results obtained using a cut-off point equal to 1% (see Panel A),32 we observe that the model based on CAMEL variables does not offer any advantage in terms of predictive power when we compare it to a simple model based on ln_Z. Moreover, the predictive power of the natural logarithm of the Z-score is higher for commercial banks. This result combined with those of Table 8, which show a higher predictive power for the Z-score in banks having a large size, indicate that the natural logarithm of the Z-score is more effective as bank business models may become more sophisticated. An explanation for these results is that smaller banks may result more financially opaque as less subject to accounting and reporting scrutiny than larger and listed banks. Concerning PIIGS, the models tend to overidentify events of distress because of the severity of the crises in these countries. In fact, while the type 1 error is low in the PIIGS sample, the type 2 error is extremely high. Finally, the predictive power of the Z-score in each subsample considered during 2001–2011 is also confirmed by the distress forecasts of Panel B, with the exception of PIIGS/no PIIGS countries. In fact, for these two subsamples Panel B shows that the models perform better (i.e., more distress events in the top deciles) for countries that were less affected by the financial crises. 7. Conclusions We examine whether the Z-score, a well-known accounting-based proxy for bank stability, is an accurate tool to predict bank distress on a sample of banks from 12 European countries. Estimating probit and complementary log–log models, we find that specifications that use the natural logarithm of the Z-score show a good predictive power to identify banks in distress. In particular, the key results indicate that the Z-score performs as well as the CAMELS variables, but it has the advantage to be more parsimonious than CAMELS models, because it demands less accounting and questionable data (i.e., the covariates to be used in CAMELS related analyses). Such a result is extremely valuable for those stakeholders (i.e., investors, depositors, financial analysts, etc.) who rely solely on public available information and look for simple and trustable measures of bank soundness. Finally, we find that the predictive ability of the Z-score holds even using a different computational approach which takes into account the average of returns on assets over a three year period. We also assess the predictive power of the Z-score according to different bank characteristics and find that the Z-score is slightly more effective when the organizational and productive complexity of banks increase along with the public incentives to scrutinize bank riskiness, as it is the case for large banks. Finally, we show that during the financial crisis the accuracy of the Z-score (and also of the

31 32

Similar results were achieved carrying out the complementary log–log model. We obtain similar results if instead of 1% cut-of point we use 10% cut-off point.

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Table 11 Predictions and forecasts of bank distress in different subsamples. This table reports in Panel A the probit and the type errors results (see Panel A) for different subsamples: commercial bank versus ‘other banks’ (i.e.,: cooperative, savings and real estate and mortgage banks); and PIIGS banks versus banks non-PIIGS banks. The sample period is 2001–2011. The dependent variable is the Distressed Bank dummy variable (DBi,t) that takes the value of 1 if bank i becomes distressed (that is: under receivership, bankruptcy, dissolved, in liquidation, dissolved by merger with a coverage ratio smaller than 0 within 12 months before the M&A, or government bail-out) at time t (the year in progress) and 0 otherwise. The dependent variable and independent variables are defined in Section 4. All explanatory variables are lagged by one year. All variables are winsorized at the 1% of each tail. Year and country dummy variables are also included in the model. Robust standard errors are reported in parentheses. The superscripts ***, **, and * denote coefficients statistically different from zero at the 1%, 5%, and 10% levels, respectively, in two-tailed tests. In addition, Panel B reports the frequencies of distress events by deciles of the distribution of the predicted probabilities for the probit models in Panel A. Decile 10 (1) is the decile with the highest (lowest) predicted probabilities of distress events. Panel A: probit estimations results and type errors (whole period) Variables

ln_Z (−1)

Commercial banks

Other banks

(I)

(I)

(II)

−0.172*** (0.034)

ETA (−1)

−0.184*** (0.048)

Year FE Country FE N. of obs. Pseudo R2

Yes Yes 3644 0.1281

0.498 (0.349) −0.693 (1.684) −0.006 (0.221) −10.942** (4.721) 0.216*** (0.071) 0.094 (1.684) Yes Yes 3644 0.1209

Type errors: TP FN FP TN Type 1 Type 2

137 5 2797 705 0.035 0.798

134 8 2980 522 0.056 0.850

CRED (−1) CIR (−1) ROAA (−1) LIQ (−1) INC_OPREV (−1)

PIIGS (II)

(I)

Non-PIIGS (II)

−0.173*** (0.057)

Yes Yes 16,478 0.2090

−1.251 (1.208) 8.719*** (2.571) −0.351 (0.367) −28.104*** (7.745) 0.391*** (0.103) 0.763** (0.343) Yes Yes 16,478 0.2436

73 25 2429 13,951 0.255 0.148

(I)

(II)

−0.210*** (0.032)

Yes Yes 2788 0.1936

−3.343** (1.629) 7.297*** (2.750) −0.667 (0.369) −17.956** (8.597) 0.206 (0.127) 1.310*** (0.331) Yes Yes 2788 0.2460

Yes Yes 17,313 0.2101

0.863** (0.373) 1.768 (81.654) 0.107 (247) −11.579*** (5.256) 0.329*** (0.074) 0.338* (0.199) Yes Yes 17,313 0.2007

76 22 2055 14,325 0.224 0.125

91 4 1784 909 0.042 0.662

93 2 1520 1173 0.021 0.564

116 29 2971 14,197 0.200 0.173

108 37 2598 14,570 0.255 0.151

Panel B: forecasts Commercial banks

Other banks

Deciles

(I)

(II)

(I)

(II)

(I)

PIIGS (II)

(I)

No PIIGS (II)

10 9 8 7 6 1–5

0.690 0.091 0.049 0.035 0.042 0.091

0.605 0.105 0.028 0.063 0.070 0.126

0.530 0.204 0.102 0.030 0.020 0.112

0.612 0.193 0.051 0.020 0.000 0.122

0.526 0.221 0.052 0.073 0.042 0.084

0.578 0.221 0.115 0.021 0.031 0.031

0.634 0.179 0.034 0.048 0.013 0.075

0.627 0.186 0.034 0.027 0.041 0.082

CAMELS variables) marginally improves with respect to the whole period. The latter finding may result from the mounting efforts of European supervisors and regulators to make bank balance sheet less opaque and subject to accounting manipulations (i.e., see the several changes in the EU regulations on IAS and IFRS occurred in 2008 and 2009 aimed to strengthen transparency and minimize accounting discretion). Overall such evidence calls for further analyses on the effects of earnings management and accounting rules on bank riskiness.

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Appendix A Table A.1 Variable definitions. This table reports variable definitions. Data used to compute the variables are from BankScope. Variable

Definition

Defined as the natural logarithm of the sum of ROAA and ETA all divided by σROAA (the standard deviation of return on average assets computed using a three-year rolling time window). ETA Computed as the ratio of equity (i.e., book value of common equity) to total assets. CRED Defined as the ratio of impaired loans (obtained as the sum of impaired loans & advances to customers and impaired loans and advances to banks) to gross loans (computed as net loans plus reserves for impaired loans). CIR Computed as the ratio of the overheads (or costs of running the bank) to the sum of net interest income (defined as the difference between gross interest & dividend income and total interest expense) and other operating income. ROAA Defined as the ratio of net income to average total assets. LIQ Computed as the ratio of net loans to customer deposits and short term funding. INC_OPREV Defined as the ratio of non-interest income to net operating revenue. Non-interest income is equal to the sum of net gains (losses) on trading and derivatives, net gains (losses) on other securities, net gains (losses) on assets at fair value through income statement, net insurance income, net fee and commissions and other operating income. Net operating revenue is equal to the sum of total non-interest income and net interest income. ln_Z

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