Altman (1968) |
66 commercial companies (USA) |
Multiple discriminant analysis |
Extension of the traditional analysis of indicators, with scientific analysis. Z-score = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 + 0.999X5, with X1 = working capital/assets; X2 = retained earnings/assets; X3 = EBIT/assets; X4 = market value of equity/book value of liabilities; X5 = 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 financial 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 financial statements of Brazilian companies (Brazil) |
Multiple discriminant analysis |
Numerical scale based on composite liquidity indexes, denominated Kanitz Thermometer, to measure the company’s financial 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 financial 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 classification tree. Performed better than discriminant analysis. |
Lane, Looney, and Wansley (1986) |
130 banks (USA) |
Survival analysis (Cox) |
Introduction of the Cox model in the financial 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. |
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 defines Z-score (homonymous of the Altman model) as a risk indicator: Z-score = (ROA + Equity/Asset)/σROA.
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Altman, Marco, and Varetto (1994) |
1,000 industrial companies (Italy) |
Neural networks |
Neural networks can generate very close scores to parametric discriminant functions. Long processing time for training the network and large number of tests needed to identify its structure. The resulting weights are not transparent and are sensitive to structural changes. |
Altman (2000) |
5 samples of companies (USA) |
Multiple discriminant analysis |
Reassessment of the Z-score model (Altman, 1968), using current indicators combined with advances in the application of discriminant analysis, including privately held companies in the sample, with adjustments for emerging markets. Comparison with the zeta-analysis model, in 1 to 5 year prediction horizons. |
Shumway (2001) |
300 non-financial companies (USA) |
Hazard model |
Analyzes aspects of bias and consistency of the estimators used in the bankruptcy studies. Similar model to logit, but with a greater amount of multiperiod data. Analytical tests comparing maximum vraisemblance estimators. |
Minussi, Damacena, and Ness Jr. (2002) |
323 banking clients from the industrial sector (Brazil) |
Logit |
49 indicators selected. Working capital analysis quotients dynamic. |
Bressan, Braga, and Bressan (2004) |
107 rural credit cooperatives (Brazil) |
Cox proportional risk model |
15 insolvent and 92 solvent cooperatives. Significant variables: growth in total fund raising, general liquidity, cashflow, personnel expenses, growth in operating revenue, and leverage. |
Porath (2004) |
15,456 credit cooperatives and 4,537 deposit banks (Germany) |
Hazard model |
Univariate preliminary analysis. Uses ROC and IV analysis to analyze the variables. |
Onusic, Nova, and Almeida (2007) |
10 companies in the process of bankruptcy and 50 healthy companies (Brazil) |
DEA |
Input variables: general and long term debt, composition of debt. Result variables: growth in sales, ROA, asset turnover. |
Brito and Assaf Neto (2008) |
60 publicly-traded non-financial companies (Brazil) |
Logit |
25 economic-financial indicators tested, with the inclusion of 4 in the final model. Validation with Jackknife method and ROC. |
Minardi (2008) |
25 publicly-traded companies (Brazil) |
Black Model and Scholes/Merton (1974) |
Classifications of the model converge, in general, for the ratings (S&P and Moody’s) |
Campbell, Hilscher, and Szilagyi (2008)Campbell, J. Y., Hilscher, J., & Szilagyi, J. (2008). In search of distress risk. The Journal of Finance, 63(6), 2899-2939.
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Publicly-traded companies (USA) |
Logit (dynamic panel) |
Monthly, accounting, and market data. Comparison with the Merton model (1974) (distance-to-default measure). |
Agarwal and Taffler (2008) |
2,006 non-financial companies (United Kingdom) |
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. |
Brito, Assaf Neto, and Corrar (2009) |
66 publicly-traded non-financial companies (Brazil) |
Logit and cluster analysis |
8 classes of risk (1 being insolvent) reflect the growth of mortality rates in the respective classes. ROC curve for the model evaluation. |
Guimarães and Alves (2009) |
600 health plan operators (Brasil) |
Logit |
17 financial indicators in the categories of leverage, liquidity, earnings, activity, and debt and coverage. |
Peresetsky, Karminsky, and Golovan (2011) |
1,569 banks (Russia) |
Logit |
Preliminary clusterization and evaluation of separate models for each cluster. Use of macroeconomic variables. Use of heuristics for utility of model for investor. |
Valahzaghard and Bahrami (2013) |
20 banks (Iran) |
Logit |
Significance for the dimensions of management quality, earnings, and liquidity (CAMELS). |
Tserng, Chen, Huang, Lei, and Tran (2014) |
87 civil engineering companies (USA) |
Logit |
Analyzes 21 financial indicators divided into 5 groups (liquidity, leverage, market activity, and earnings), with the market factor making a large contribution to the model. Use of the ROC curve. Validation via the leave-one-out process. |
Betz, Oprica, Peltonen, and Sarlin (2014) |
546 banks (Europe) |
Recursive logit |
Early warning model. Considers the utility of the model for decision makers. The performance is better for small banks and for a 24-month timeframe. |
Liu (2015) |
772 banks (OECD, NAFTA, ASEAN, EU, G20, and G8) |
Logit |
Analysis in the pre and post 2008 crisis periods. Comparison of the predictive power between the regions addressed. |
Gartner (2015)Gartner, I. R. (2015). Multi-attribute utility model based on the maximum entropy principle applied in the evaluation of the financial performance of Brazilian banks. In: Guarnieri, P. Decision models in engineering and management (pp. 29-55). Cham: Springer.
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99 banks (Brazil) |
Optimization by maximum entropy |
Attribution of performance and classification of the banks into 10 risk groups. Application of the beta distribution for risk analysis. |
Chiaramonte, Croci, and Poli (2015) |
3,242 banks (Europe) |
Z-score, probit, and complementary log-log |
Ability of the Z-score indicator is as good as the CAMELS covariates for identifying financial distress and more effective for sophisticated business models, such as those of big banks. |
Cleary and Hebb (2016) |
132 banks (USA) |
Discriminant analysis |
Main variables: capital and asset quality, as well as returns. Out-of-model validation, with 192 cases in the treatment group and 90-95% accuracy. |
Wanke, Azad, and Barros (2016) |
43 banks (Malaysia) |
DEA and GLMM |
Simulates CAMELS risk assessment for analyzing banking efficiency and financial distress. |