Article

Financial and Non-Financial Variables as Long-Horizon Predictors of Bankruptcy

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Abstract

Reviews on financial distress prediction models indicate that these techniques give highly reliable estimates of probabilities of default (PDs) and loss given default (LGD) only for relatively short horizons, rarely beyond two years. Major stakeholders, e.g. investors and bank risk and capital analysts, therefore, have such models sanctioned by portfolio managers and regulators for the same short horizons; for example, the Basel Committee on Banking Supervision recommends PD and LGD estimates for one year. This is especially the case when financial variables make up the sole or primary estimates, and only a bit longer reliable estimators when these models include non-financial variables as additional early warning signals. Beyond three years, such models, regardless of their structure, rarely give reliable estimates, perhaps not much better than flipping a coin. The objective of this study is to assess the predictive ability of both financial and non-financial variable constructs for longer term horizons of up to ten years based on rigorous post-development distress and non-distress financial events in the Finnish environment. Our model, built with cross-section data from 2003, analyses results for 2004-2013. Results show that measures of solvency, turnover, industry risk, payment behaviour, and board member characteristics can be significant predictors of bankruptcies for as long as ten years. The most accurate long-range prediction results combine financial and non-financial variables. Subsequent tests should attempt to extend such models in a multi-country setting, whether or not bankruptcy regimes are similar across national borders.

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... Shakila et al / Developing a Credit Scoring of the SMEs Manufacturing based on Mutli Criteria Decision Making (MCDM) Algorithm. 13 The key rational of this paper is to examine the financial position of the SMEs company (manufacturing sector) applying loans from banks. ...
... The inclusion of non-financial criteria are necessary since the financial ratio of small companies do not contain enough and reliable annual income information. Study by [13] showed that the model with both financial and non-financial criteria is more efficient as compared to purely financial model and purely non-financial model. [14] in his study proved that the non-financial criteria are more important than the financial criteria. ...
... Applied Mathematics and Computational Intelligence Volume 14, No. 1, 2025 22 Once the value of r is obtained, the score for each financial sub-criterion is calculated. Equations (4) to (13) The total sub-criteria (financial) score is obtained by using (3) and to measure f, formula (2) For non-financial score, the performance scale sca  is evaluated by the credit officer at the first time the customers applied for credit facility. The sample of credit rating is provided in Appendix 3. ...
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Credit risk is a very important risk to banks since failure of borrowers to make required payment will lead to high non-performing loans. Hence, it is necessary for banks to develop a mechanism to gauge the credit risk of its borrowers. One of the methods is credit scoring. Small and Medium Enterprises (SMEs) are the backbone of the Malaysian economy comprising 98.5% of the total business established in Malaysia. Despite their importance, access to finance is relatively limited. According to banks, lending money to SMEs are risky compared to large companies due to few factors such as less of publicly available information, young and lack of collateral. Hence, this study tried to predict the credit risk of SMEs in Malaysia by developing a credit scoring that combined financial and non-financial criteria. This study proposes a credit scoring method based on MCDM algorithm that will be able to forecast the score of the potential borrowers at a certain time by using the historic information. Result obtained is verified via the comparison with the given credit risk level provided by banks and by measuring the correlation. The correlation value is 0.88640526 indicates the high positive linear relationship.
... Some aspects, such as, among others, the selection and/or treatment of explanatory variables, the fact of not contemplating among them some relevant parameters of the macroeconomic environment, highly changing economic environments, and/or the incidence of non-economic variables on the dependent variable, are pointed out as possible causes of the aforementioned relationship (between the dependent variable and the independent variables) not being stable over time (Altman et al. 2015(Altman et al. , 2020Altman and Sabato 2007;Cybinski 2001;Dakovic et al. 2010;du Jardin 2009;Séverin 2011, 2012). This will result in models whose predictive power deteriorates after the learning period. ...
... From the earliest works, the usual practice in academic work on business failure has been to limit the population under study, generally by making explicit the sectors covered without expressing specific exclusions (e.g. manufacturing firms) (Altman 1968) and, on occasions, also explicitly limiting the size of companies (Altman et al. 2015). On the other hand, different studies have specifically analysed sectors such as banking or energy, etc. due to their peculiarities Climent et al. 2019;Doumpos et al. 2017;Manthoulis et al. 2020). ...
... However, there are many authors who propose the use (either alone or together with financial ratios) of other types of explanatory variables. These proposed explanatory variables range from payment behaviour, tax-related, macroeconomic, company-specific, etc. (Altman et al. 2015(Altman et al. , 2020Ciampi et al. 2020;Cybinski 2001;Dakovic et al. 2010;Noga and Schnader 2013). On the other hand, some authors maintain the sufficiency of financial ratios for the construction of BMPs (Beaver et al. 2005;Das et al. 2009;Tian et al. 2015). ...
Article
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This study focuses on the deterioration of the predictive power and the analysis of the predictive stability of business failure prediction models, an aspect not sufficiently analysed in previous research. Insolvency prediction is considered with three temporal horizons (1 year, 3 years and 5 years prior to failure). The Genetic Programming (GP) tool has been used to achieve prediction models with high performance and stability over time, considering a long post-learning period in the stability analysis. In addition, novel scenarios representative of actual model use are proposed and considered, as well as metrics to assess the deterioration of the models’ predictive power. The optimised GP prediction models (in the three temporal horizons) present a higher performance with respect to external references and, more importantly in relation to the objective of our study, the selected GP models substantially improve on the stability reported in previous studies, meeting the pursued requirements of degree of deterioration (less than 5%) and stability (Pearson’s coefficient of variation less than 5%). Thus, the predictions of the GP models after the learning are very stable (period 2008–2019), to a certain extent immune, with respect to their environment, responding adequately in both procyclical and countercyclical modes, all of which is particularly relevant as this period includes a strong recession and a strong recovery. This should help to increase the reliability of business failure prediction models. Moreover, the relevance of including variables other than the usual financial ratios as predictors of failure is confirmed.
... • Variables related to payment behaviour (Altman et al., 2015;Ciampi et al., 2020). • Variables related to taxes (specifically the difference between accounting income and disposable income) (Noga & Schnader, 2013). ...
... • Variables related to taxes (specifically the difference between accounting income and disposable income) (Noga & Schnader, 2013). • Variables related to the company not related to financial ratios (e.g., age and audit reports) (Altman et al., 2015(Altman et al., , 2020Dakovic et al., 2010). • Macroeconomic variables (Altman et al., 2015(Altman et al., , 2020Cybinski, 2001). ...
... • Variables related to the company not related to financial ratios (e.g., age and audit reports) (Altman et al., 2015(Altman et al., , 2020Dakovic et al., 2010). • Macroeconomic variables (Altman et al., 2015(Altman et al., , 2020Cybinski, 2001). ...
Article
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This study considers multiperiod bankruptcy prediction models, an aspect scarcely considered in research despite its importance, since creditors must assess the risk of loans over the entire life of the debt and not at a specific point in the future. Two possibilities for the implementation of multiperiod prediction models are considered: Multi-Model multiperiod Bankruptcy Prediction Models (MMBPM) and Single-Model multiperiod Bankruptcy Prediction Models (SMBPM). The former considers the conditional probabilities obtained by individual models predicting bankruptcy at specific times in the future, while the latter is a single model predicting bankruptcy at a specific time interval in the future. The results show that there are no significant differences between the two approaches when compared using data after the learning period. However, SMBPMs have the important advantage of interpretability for decision-making, which is discussed with examples. Moreover, a comparison of SMBPM performance with external references is performed.
... In line with the above study, Altman et al. (2015) constructed a prediction model for a longer period, i.e. up to a 10-year horizon period. Using a sample of Finnish SMEs, three logistic models were constructed, i.e. financial model, non-financial model and a combined model (financial and non-financial). ...
... The classification rates of the model for the one year, two years, three years and four years prior to distress was 90 percent, 87.5 percent, 75 percent and 66.5 percent, respectively in the holdout sample. Similar to Yazdanfar and Nilsson (2008), Altman et al. (2015), and Klepac and Hampel (2018), findings of their study revealed that the model prediction accuracy decreased as the period prior to the distress situation increased. Furthermore, they concluded that the sign of a firm in financial distress could be detected as early as four years before the actual event occurred. ...
... (5) Size refers to the company size and is measured by the natural logarithm of total assets Altman et al., 2010Altman et al., , 2015Back, 2005;Ma'aji et al., 2019). As for non-financial variables, age is the company age and is measured by the natural logarithm of company age in years (Altman et al., 2010(Altman et al., , 2015Ma'aji et al., 2019). ...
Article
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The objectives of this study are to predict bankruptcy risk among SMEs in the hospitality industry for a three-year horizon period and to investigate the factors that are significant in determining bankruptcy. The contribution of SMEs in the hospitality industry is essential as businesses in the hospitality industry are dominated by SME operators. However, the failure rate among SMEs is relatively high and almost 50 percent of hospitality establishments do not survive beyond five years of operation. The Stepwise logistic model was employed to determine significant predictors that could predict bankruptcy for the period of one year, two years and three years before bankruptcy. Return on assets and firm age were found to be significant in all periods while other variables were identified to be important at a specific period prior to bankruptcy. In addition to return on assets and firm age, debt ratio and total assets turnover were found to be significant predictors of bankruptcy one-year prior to bankruptcy. However, in the two years prior to bankruptcy, debt ratio and total assets turnover were no longer important but current ratio, ownership concentration and gender diversity were found to be significant. As for the three years prior to bankruptcy, additional variables namely debt-to-equity ratio and board size were found to be significant, but ownership concentration and gender diversity ceased to be important. The findings of this study contribute to the limited literature in predicting the bankruptcy risk of small firms for a three-year horizon period by providing empirical evidence from SMEs in the hospitality industry of Malaysia.
... Many different approaches have been adopted to improve the accuracy of distress assessments, such as the application of different methodologies, the use of longer term processes in the prediction, and the selection of other types of variables like market data or non-financial variables (Altman et al., 2015). The majority of empirical papers focus on listed companies because the development of risk models for private companies is obviously limited by data availability as market data is not available (Altman et al., 2010). ...
... Also, in the case of private companies, Balcaen and Ooghe (2006) point out the importance of supplementing accounting ratios by non-financial information, as annual financial statements might not be very reliable and stable over time. Similarly, Altman et al. (2015) suggest that the reliability of financial variables, especially for small and medium enterprises, is low because of instability and window dressing due to earnings management. In this setting, the financial statements of private firms might be combined with other data sources to complement their deficiencies and obtain a more accurate prediction. ...
... Testing 15 non-financial variables, Lussier (1995) indicates that the company's internal information related to its planning, counseling, education, and staff characteristics represent accurate predictors of failure for small companies. For credit risk estimation of Finnish companies, Laitinen (1999) uses a total of 35 variables, and 16 of them are non-financial variables related to characteristics of the firm: age, industry, payment behavior, management, and legal structure, as well as inquiries about the firm in credit information bureaus (Altman et al., 2015). Back (2005) uses a reduced number of factors such as those related to age, size, and group membership, and the results suggest that the number of payment delays is the variable with the highest predictive ability. ...
Article
We analyze empirically the usefulness of combining accounting and auditing data in order to predict corporate financial distress. Concretely, we examine whether audit report information incrementally predicts distress over a traditional accounting model: the Altman's Z‐Score model. Although the audit report seems to play a critical part in financial distress prediction because auditors should warn investors about any default risks, this is the first study that uses audit report disclosures for predicting purposes. From a dataset of 1,821 Spanish distressed private firms, we analyze a sample of distressed and non‐distressed firms and develop logit prediction models. Our results show that while the only accounting model registers a classification accuracy of 77%, combined models of accounting and auditing data exhibit considerably higher accuracy (about 87%). Specifically, our findings indicate that the number of disclosures included in the audit report, as well as disclosures related to a firm's going concern status, firms’ assets, and firms’ recognition of revenues and expenses contribute the most to the prediction. Our empirical evidence has implications for financial distress practice. For managers, our study highlights the importance of audit report disclosures for anticipating a financial distress situation. For regulators and auditors, our study underscores the importance of recent changes in regulation worldwide intended to increase auditor's transparency through a more informative audit report.
... We supplement Ohlson's (1980) logit model for bankruptcy prediction with auditors characteristics. The model includes the most common financial ratios, which were applied in prior bankruptcy literature (Bellovary et al. 2007;Altman et al. 2015). We complement the model with the following auditor attributes: fees, size, tenure and industry expertise. ...
... We also contribute to prior accounting-based bankruptcy studies. Prior literature encourages the use of non-financial variables to improve bankruptcy prediction (Cassar 2011;Altman et al. 2015). Non-financial variables include significant information about the firm and cover non-financial aspects such as external audits, governance mechanisms and management changes. ...
... Non-financial variables include significant information about the firm and cover non-financial aspects such as external audits, governance mechanisms and management changes. Such variables can be relevant in determining the probability of a firm defaulting in future (Back 2005;Altman et al. 2015). Our study answers this call for research about non-financial variables by showing how auditor characteristics affect a firm's default risk. ...
Article
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In this paper, we investigate the relationship between external auditor characteristics and the likelihood of bankruptcy. We use a sample of US public companies to analyse whether auditor attributes are associated with default. We also test whether the inclusion of such attributes in bankruptcy prediction models improves their predictive ability. We find that firms audited by industry-expert auditors, large audit firms and long-tenured auditors are less likely to default. Firms with higher audit fees are more likely to default. Our results also show that the inclusion of auditor attributes significantly increases the predictive ability of bankruptcy prediction models. This paper contributes to the literature about auditing and bankruptcy prediction. Our results suggest that the auditor attributes can provide predictive signals concerning a default risk and that an external audit can play a relevant role in early warnings of financial distress. Our study also suggests that bankruptcy prediction models can become more effective if they are complemented with audit data. Our results are of interest to market participants, auditors, regulating authorities, banks and other financial institutions that are interested in credit risk assessment.
... Desde los modelos pioneros de Beaver y Altman en los años 60, que utilizan ratios financieros en su pronóstico (Altman, 1968;Beaver, 1966), la mayoría de los estudios hacen uso de la información contable para la predicción (Altman, Iwanicz-Drozdowska, Laitinen, & Suvas, 2016;Baldwin & Glezen, 1992). Al objeto de mejorar su diagnóstico, algunos autores añaden otras variables a la información financiera: información macroeconómica (Hernández-Tinoco & Wilson, 2013), datos de mercado (Hillegeist, Keating, Cram, & Lundstedt, 2004;Shumway, 2001), así como otras variables no financieras (Altman, Iwanicz-Drozdowska, Laitinen, & Suvas, 2015;Laitinen, 2013;Lussier, 1995). Por ejemplo, destaca un estudio actual sobre predicción de quiebra analizando el uso del lenguaje y la opinión de los gestores en el informe de gestión de empresas americanas (Formulario 10-K) 2 (Mayew, Sethuraman, & Venkatachalam, 2015). ...
... Nos planteamos analizar si existe alguna relación entre los comentarios en los informes de auditoría y cuatro factores estructurales: el tamaño de la firma de auditoría, el cambio de auditor, el sector de la compañía auditada y la situación financiera de ésta. Todos estos factores han sido considerados como relevantes a la hora de tratar conflictos de viabilidad empresarial, tanto en estudios previos sobre emisión de salvedades sobre GC como en trabajos relacionados con la utilidad de la información de auditoría en la predicción del fracaso empresarial (Altman et al., 2010(Altman et al., , 2015Carson et al., 2013;Lennox, 1999b). Aunque estos factores han sido analizados por separado, este estudio examina por primera vez los cuatro factores en su conjunto, y lo hace para una muestra de empresas en situación concursal que entraron en el procedimiento legal de insolvencia a lo largo de la crisis económica que comenzó a mediados de 2007. ...
... Existen estudios que revelan que la fecha de formulación de las cuentas anuales es un factor a tener en cuenta a la hora de predecir la quiebra empresarial (Altman et al., 2015;Piñeiro-Sánchez et al., 2013). Asimismo, la fecha de entrada en el procedimiento concursal puede afectar a la información financiera y de auditoría de las compañías en el año anterior a la declaración del concurso (Van Hemmen Almazor, 2015). ...
Article
Este trabajo analiza empíricamente el contenido del informe de auditoría de empresas concursadas correspondiente al año anterior al concurso de acreedores, con un doble objetivo: proponer una clasificación de dicho contenido y estudiar la existencia de diferencias en los informes en función de características del auditor y de la firma auditada. Utilizando una muestra de deudores españoles concursados en el período 2004–2014, los resultados revelan que el 13% de los informes son limpios o no incluyen ningún comentario del auditor, y que son más frecuentes las salvedades que los párrafos de énfasis. Un 23% de las advertencias emitidas informan sobre la declaración concursal y un 45% alertan sobre dudas a la gestión continuada. Asimismo, existen diferencias en función del tamaño del auditor, del sector y la situación financiera de la concursada, del trimestre en que se dicte el auto de declaración y de la resolución, mientras que el contenido es independiente del cambio de auditor. Nuestros resultados avalan la utilidad del informe en el pronóstico del riesgo empresarial, utilidad que se verá incrementada con la nueva Ley de Auditoría de Cuentas y su requerimiento de hacer mención expresa del riesgo financiero en caso de dudas a la gestión continuada.
... However, if the total value of a company's debts exceeds the fair value of its total assets, meaning the company's net worth is negative, the company is considered bankrupt (Danilov, 2014). Thus, examining the indicators affecting financial health plays a crucial and increasing role in the economy, as it imposes significant costs on the company, shareholders, creditors, and, on a larger scale, the entire economy (Altman et al., 2015). Among the costs of declining The potential costs of missed sales, decreased profitability, and losses from losing market position, which deteriorates the company's capacity to pay back loans, are what make financial health. ...
... (Chiaramonte & Casu, 2017). In identifying signs of financial health or failure of companies, following pioneering studies in this field (Altman et al., 2015), this issue can be summarized into five categories or general terms: ...
Article
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Organizational stability, insolvency, financial hardship, and accounting data quality are all connected to a company's financial health. Examining the financial health of companies is important from various aspects, especially in light of globalization and the expansion of communications. There are multiple methods to assess the financial health of companies and predict financial bankruptcy, among which statistical techniques are prominent. This study investigates the financial ratios impacting the Logit model-based financial stability of businesses listed on stock exchanges. The members of the statistical sample include 152 businesses that are listed on the Tehran Stock Exchange since 2011 to 2021. To test the hypotheses, regression analysis and Logit and Probit models were employed using EViews software. The results indicated that profitability and agency costs have a significant impact on the financial health of companies. However, financial leverage, current ratio, cash holding level, and working capital to total assets did not significantly affect the financial health of the companies.
... For analysts and investors, default risk is the primary risk factor and the key determinant of bond rating and valuation (Collin-Dufresne & Goldstein, 2001;Duffee, 1999). Whereas the literature documents extensive evidence of the roles of financial ratios (Bellovary et al., 2007), non-financial factors (Altman et al., 2016) and market factors (Hernandez-Tinoco & Wilson, 2013) in explaining default risk, there is limited research on how a firm's life stage impacts its default risk. The primary objective of our study is to fill the void in the literature by examining the likelihood of default faced by a firm across its life stages. ...
... Wilson et al. (2013) show that management quality and reliability and payment behavior are additional effective nonfinancial variables. Altman et al. (2016) document that industry risk, payment behavior, and board member characteristics can be significant predictors in combination with financial variables. As the accountingbased default risk measures are mainly based on financial statements that are designed to measure past performance and may not be very informative about the future status of a firm, and also the measures fail to incorporate asset volatility that is a crucial variable in default prediction, Hillegeist et al. (2004), and Bharath and Shumway (2008) develop market-based default risk measures based on structural models of default risk (e.g. ...
Article
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We find a nonlinear relation between corporate lifecycle and default risk. Default risk is significantly higher for growth and decline firms when compared to mature firms, after controlling for firm specific and macroeconomic factors on default risk. The shorter distance to default for introduction firms vis-a-vis mature firms are, however, mostly explained by known determinants of default risk. Whereas the 2008 financial crisis adversely impacted all firms, the elevation in default risk was intensified among mature firms. Further results show greater default risk is associated with firms that are lifecycle leaders among their industry peers but is lower for laggards.
... Many different approaches have been adopted to improve the accuracy of distress assessments, such as using different methodologies (i.e. multi-discriminate analysis, neural network, logistic regression), the use of longer-term processes in the prediction (Altman et al., 2015). Researchers, additionally, tried to find an alternative way to overcome many of the limitations of accounting-based models. ...
... Researchers, additionally, tried to find an alternative way to overcome many of the limitations of accounting-based models. The literature incorporates particularly information such as firm age, type of business and industry, auditor size and rotation, and audit report (Muñoz-Izquierdo et al., 2019;Altman et al., 2010Altman et al., , 2015Back, 2005). ...
Article
Purpose This study examines the effect of non-financial variables related to governance on the accuracy of financial distress prediction among Egyptian listed small and medium-sized enterprises (SMEs), by using the logistic regression technique. Design/methodology/approach This study used a sample of 24 Egyptian-listed SMEs in each year, totaling 120 firm observations, of which 25 were classified distressed and 95 of them non-distressed between 2014 and 2018. The variables for the study included five financial variables and thirteen non-financial variables related to governance. The models were developed using financial variables alone as well as combining financial and non-financial variables related to governance. Findings The results showed that the model with financial variables had a prediction accuracy of 91.7% , whereas models with a combination of financial and non-financial variables related to governance predict with comparatively better accuracy of 92.7 and 93.6% . Research limitations/implications Although the results seem to be conclusive, it could be noted that the non-distressed sample was not paired with the distressed sample. Other studies showed that paired samples increase the financial distress prediction rate. Furthermore, due to the small sample size, this study was unable to create a hold-out sub-sample for the accuracy test. Practical implications The proposed distress prediction model for SMEs is effective for stakeholders, including banks and other financial institutions, in the assessment of the credit risk of SMEs. Using such a model, they could better identify SMEs with a higher risk of failure in their lending decisions. Moreover, SME managers' could be interested in using such models as a tool for planning corrective action, in addition to planning and controlling current operations to avoid financial failure in the future. Originality/value This study contributes to financial distress prediction literature in different ways. First, few studies were conducted in the area of financial distress among SMEs. Second, neither of these studies was conducted within the Egyptian context, nor any of them had used non-financial variables related to governance in the prediction of financial distress among SMEs.
... We define this category to add all other types of, typically descriptive, data, as in [38]. Based on the surveyed papers, the majority of instrumentalized datasets are private data sources, however, more studies instrumentalize annual reports of publicly listed companies. ...
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Bankruptcy prediction is an important research area that heavily relies on data science. It aims to help investors, managers, and regulators better understand the operational status of corporations and predict potential financial risks in advance. To improve prediction, researchers and practitioners have begun to utilize a variety of different types of data, ranging from traditional financial indicators to unstructured data, to aid in the construction and optimization of bankruptcy forecasting models. Over time, not only instrumentalized data improved, but also instrumentalized methodology for data structuring, cleaning, and analysis. With the aid of advanced analytical techniques that deploy machine learning and deep learning algorithms, bankruptcy assessment became more accurate over time. However, due to the sensitivity of financial data, the scarcity of valid public datasets remains a key bottleneck for the rapid modeling and evaluation of machine learning algorithms for targeted tasks. This study therefore introduces a taxonomy of datasets for bankruptcy research, and summarizes their characteristics. This paper also proposes a set of metrics to measure the quality and the informativeness of public datasets The taxonomy, coupled with the informativeness measure, thus aims at providing valuable insights to better assist researchers and practitioners in developing potential applications for various aspects of credit assessment and decision making by pointing at appropriate datasets for their studies.
... Precisely, these models are reliable only for time horizons up to 2 years. Motivated by this shortcoming, in their work Altman et al. (2015) combine non-financial predictors with the financial variables to provide a modelling framework that can predict possibility of default up to 10 years. Their findings indicate that the solvency, payment behavior and characteristics of board members can significantly improve the predictive power of the model. ...
Article
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We examine the default risk spillover for two groups of global energy firms, including top energy firms from seven different sectors as well as energy firms scoring highest in terms of environment disclosure. We first perform a bibliometric review to uncover the trends in existing literature related to our research objectives. We then utilize novel, daily frequency data of ‘distance to default’ measure to perform two important co-movement techniques namely wavelet and TVP-VAR. The sample period is from 29 June 2009 to 30 June 2021. Our wavelet results reveal that both the groups exhibit spillover of default risk. However, there is higher interdependence of default risk in environment conscious energy firms during normal as well as crisis periods. The TVP-VAR results portray the interaction across both groups of firms and show heightened connectedness between the sampled firms for the sample period. We also identify net transmitters and receivers of shocks. The results carry important implications for investors and policymakers.
... Said et al. (2003) stated that customer satisfaction, employee satisfaction, quality, market share, productivity, and innovation are factors that affect performance. Altman et al. (2015) indicated that the ability to pay, turnover, industrial risk, and Board member characteristics are important non-financial predictors. Blanco-Oliver et al. (2015) obtained a higher prediction accuracy of insolvency than when using only financial information by using the age of the company, creditor legal action, and company governance structure. ...
Article
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This study proposes a harmonic average of support and confidence method (HSC), which is a new way to select important rules from the many rules in the decision tree and thereby build a core rule-based decision tree (CorDT) that more easily explains the insolvency factors related to small and medium-sized enterprises (SMEs) using the HSC. To this end, an insolvency prediction model for SMEs was developed using a decision tree algorithm and technological feasibility assessment data as non-financial datasets. We divided these datasets into three types, a general type, a technology development type and a toll processing type applying characteristics of SMEs. We also applied a cost-sensitive approach and several data balancing techniques to construct the same proportion of healthy and insolvent company samples in the datasets. As a result, the insolvency prediction model applied using the synthetic minority over-sampling technique (SMOTE), an over-sampling technique, showed the highest performance with an average hit ratio of 77.6%. Next, we selected important rules by applying HSC to the decision trees with the highest performance and built CorDTs for three types of SMEs using the selected rules. Finally, using the developed CorDTs, we explained the causes of insolvency by type of SME and presented insolvency prevention strategies customized to the three types of SMEs.
... They use a static methodology to study this phenomenon. In fact, they focus on examining which variables best identify failure and distinguish between healthy and failed companies, involving an analytical vision in the short term (Altman, E., Iwanicz-Drozdowska, M., Laitinen, E., & Suvas, 2015), looking for specific points in time in the data to identify when the frustration in the entity actually occurred. ...
Article
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NPOs (Non-Profit Organisations) are entities created to respond to the social needs of the economy, many of which fall into financial difficulties and are forced to close. Given the importance that these entities have both socially and economically, the study of their financial vulnerability is an area of special interest. It is important to highlight the factors that characterize this type of entity in a situation of vulnerability and also to anticipate future undesirable situations which could result in closure without timely supervision. In this way, the entity could redirect its management and make the necessary changes in its structure to ensure its continuity. Our study analyses the academic literature, from a theoretical perspective, in relation to this vulnerability allowing us to construct a pentagram of five dimensions, some interrelated, which we propose to be taken into consideration in the study of an entity’s vulnerability. These five dimensions are performance, operational dimension, leverage, liquidity and most importantly reputation. This research offers a proposal to evaluate financial vulnerability in NPOs in a more comprehensive way and facilitate its management.
... Logistic regression, also known as logit, has been used in several business failure forecasting studies (Ohlson, 1980;Huang et al., 2013;Altman et al., 2016). The rationale for the use of this technique includes the high degree of predictive power it has demonstrated in previous studies and its potential for bias reduction, as compared to discriminant analysis, for example. ...
Article
Purpose The aim of this paper is to provide an overview of the impact of the implementation of Colombian Corporate Insolvency Act 1116 of 2006 in the period 2008–2018 and to assess the relevance of a broad set of financial predictors, as well as variables related to the economic context or the characteristics of the process itself, in explaining the failure of reorganization processes. Design/methodology/approach Both logit and probit models are estimated, starting from a large number of variables proposed in the literature which are then narrowed down to a final selection based on their individual significance and machine learning. Findings The results show the prevalence of a limited number of financial variables related to equity, indebtedness, profits and liquidity as predictors of the failure of reorganization processes. The use of financial information from the year prior to the completion of the reorganization improves predictive accuracy and reliability. The debt-to-equity indicator provides no significant explanatory power, while voluntary entry into a reorganization process favors its success. Originality/value While financial and accounting information is used across the literature to predict insolvency events, it is used here to predict success or failure in reorganization processes under the conditions imposed by a specific legislative act in a Latin American context.
... This variable is measured as the age of the company in years at the beginning of the reorganization agreement, and both the natural logarithm (LN_Age) and the square of the natural logarithm (SLN_Age) are used in the estimations, to control for quadratic effects. The analysis of firm age is motivated by the use of age as a non-financial predictor in previous works (Back, 2005;Altman et al., 2015;Steff and Bissieux, 2022 Dummy variables for the industry and the region in which the company is located are also considered, since the impact of financial crises on firm solvency and performance varies across sectors of activity. In particular, the Covid-19 crisis has had significant effects on the travel & leisure sectors (Salisu and Tchankam, 2022). ...
Article
Purpose Using data from business reorganization processes under Act 1116 of 2006 in Colombia during the period 2008 to 2018, a model for predicting the success of these processes is proposed. The paper aims to validate the model in two different periods. The first one, in 2019, characterized by stability, and the second one, in 2020, characterized by the uncertainty generated by the COVID-19 pandemic. Design/methodology/approach A set of five financial variables comprising indebtedness, profitability and solvency proxies, firm age, macroeconomic conditions, and industry and regional dummies are used as independent variables in a logit model to predict the failure of reorganization processes. In addition, an out-of-sample analysis is carried out for the 2019 and 2020 periods. Findings The results show a high predictive power of the estimated model. Even the results of the out-of-sample analysis are satisfactory during the unstable pandemic period. However, industry and regional effects add no predictive power for 2020, probably due to subsidies for economic activity and the relaxation of insolvency legislation in Colombia during that year. Originality/value In a context of global reform in insolvency laws, the consistent predictive ability shown by the model, even during periods of uncertainty, can guide regulatory changes to ensure the survival of companies entering into reorganization processes, and reduce the observed high failure rate.
... Al hacerlo de esta manera, utilizan una metodología estática para estudiar este fenómeno. De hecho, se centran en examinar qué variables son las que mejor identifican y clasifican a las empresas sanas de las fracasadas involucrando una visión analítica en el corto plazo (Altman, E., Iwanicz-Drozdowska, M., Laitinen, E., & Suvas, 2015), al buscar puntos concretos en el tiempo y en los datos para estudiar la frustración de la entidad. ...
Conference Paper
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Modelo teórico que construye la forma de analizar la vulnerabilidad de las entidades sin ánimo de lucro
... 11 The objective is to see if the sample, and therefore the characteristics of the companies that comprise it, influences the predictability of the different measures in order to observe how each measure will behave against the rest, considering all 10 See Hambrick and D'Aveni (1988), Laitinen (1991Laitinen ( , 1999, Ooghe and de Prijcker (2008), among others. Thus, Altman et al. (2016) study the predictive ability of both financial and non-financial variables over a long horizon of up to ten years for small and medium-sized private enterprises (SMEs), finding several variables that can help analysts to identify early bankruptcy symptoms even five years and longer prior to failure. 11 The results of the mean difference test between pairs of subsamples confirm significant differences of the characteristics of the companies that belong to the different subsamples, especially with respect to size and intangibility. ...
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This paper examines the predictive power of the main default-risk measures used by both academics and practitioners, including accounting measures, market-price-based measures and the credit rating. Given that some measures are unavailable for some firm types, pair wise comparisons are made between the various measures, using same-size samples in every case. The results show the superiority of market-based measures, although their accuracy depends on the prediction horizon and the type of default events considered. Furthermore, examination shows that the effect of within-sample firm characteristics varies across measures. The overall finding is of poorer goodness of fit for accurate default prediction in samples characterised by high book-to-market ratios and/or high asset intangibility, both of which suggest pricing difficulty. In the case of large-firm samples, goodness of fit is in general negatively related to size, possibly because of the “too-big-to-fail” effect.
... There is an opinion that management is not well remunerated, but managementís salary is not the main cause of bankruptcy. In turn, Altman et al. (2015) indicate, that frequent change in management is one of the causes of bankruptcy, according to a study conducted by Keasey and Watson (1991). ...
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The research aims at clarifying the opinion of experts to identify factors indicating possible intentional nature of bankruptcy and its assessment. In the article, the authors analysed such concepts as fraudulent bankruptcy, criminal bankruptcy, etc., distinguish division of bankruptcy and defined its distinctive characteristics. On the basis of literature review and expert estimation, the authors searched indicators of fraudulent bankruptcy. The study is based on opinions of the experts related to fraudulent bankruptcy (insolvency administrators, investigators, academics of accountancy and forensic accountants), using the analytic hierarchy process (AHP method). Experts identified the 10 most popular indicators related to fraud bankruptcy cases and evaluated them. The authors tested the possibility of the appearance of these indicators in non-criminal insolvency cases in various conditions of three internal characteristics of the company (quality of management, organisation of accounting and internal control of the company) using the simulation approach. The results of the empirical research can be applied to the construction of models for fraudulent bankruptcy evaluation. The authors summarized also the terminology of fraudulent bankruptcy in different countriesí law and identified a common concept ñ deliberate illegal activity or fraud. At least three forms of fraudulent bankruptcy were identified: fictitious, intentional and hidden. The authors proposed also their own definition ñ fraudulent bankruptcy is a white-collar crime, which contains any type of offences and detrimental transactions, which result in companyís bankruptcy.
... Terdapat beberapa penelitian yang telah dilakukan di luar Indonesia terkait metode Altman Z-Score. Pada penelitian di Italia ditemukan bahwa metode Altman Z-Score adalah metode yang memiliki keakuratan dalam menggambarkan kondisi keuangan suatu negara dimana zona financial distress dalam metode Altman Z-Score Modifikasi sesuai dengan konteks di Italia (Altman et al., 2015). Berdasarkan penelitian yang telah dilakukan di Malaysia, tingkat ketepatan metode Altman Z-Score dalam memprediksi financial distress cukup besar yaitu sebesar 76,7% (Thai et al., 2014). ...
... Globally studies are now focusing on designing models which use specific factors from the relevant industry for which the model is being developed. This approach has been found to give a prediction accuracy which is much higher than industry generic models (Avenhuis, 2013;Tinoco and Wilson, 2013;Nanayakkara and Azeez, 2015;Altman et al., 2016;Sayari and Mugan, 2017;Bandyopadhya, 2006). The factors which are incorporated into these models are taken from the internal operating conditions and also from the external environment in which the company operates. ...
... Globally studies are now focusing on designing models which use specific factors from the relevant industry for which the model is being developed. This approach has been found to give a prediction accuracy which is much higher than industry generic models (Avenhuis, 2013;Tinoco and Wilson, 2013;Nanayakkara and Azeez, 2015;Altman et al., 2016;Sayari and Mugan, 2017;Bandyopadhya, 2006). The factors which are incorporated into these models are taken from the internal operating conditions and also from the external environment in which the company operates. ...
... The studies as precursors of business failure prediction are by Beaver (1966) and Altman (1968 The short-term accuracy of failure prediction models has directed the focus of research towards short-term analyses (Altman et al., 2015). ...
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This work is framed in the research of business failure. We examine a method of analyzing the dynamics of financial failure. The authors examine a method of analyzing the dynamics of financial failure, because our goal is to analyze how the economic and financial indicators show the risk of failure in a group of companies. Using a sample of 163 companies declared bankrupt or dissolved, the authors show how to depict company trajectories of behavior and movement to terminal failure. They analyze these trajectories to find and describe empirical evidence of the different dynamics of bankruptcy. The authors also show that the estimation of failure risk is more accurate when these different failure trajectories are defined. In conclusion, the authors can see that there are different failure trajectories. One can use these different trajectories to identify more efficiently the indicators warning of the failure risk of the companies analyzed.
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SYNOPSIS We contend that tax-related information, which has not yet been considered by extant research, can significantly improve bankruptcy prediction. We investigate the association between abnormal changes in book-tax differences (BTDs) and bankruptcy using a hazard model and out-of-sample testing as in Shumway (2001). We find that information regarding abnormal changes in BTDs significantly increases our ability to ex ante identify firms that have an increased likelihood of going bankrupt in the coming five-year period. The information provided by BTDs significantly adds information to traditional models for predicting bankruptcy, such as that proposed by Ohlson (1980), and also expands the prediction window beyond the traditional two-year time frame.
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We estimate probabilities of bankruptcy for 5784 industrial firms in the period 1988–2002 in a model where common equity is viewed as a down-and-out barrier option on the firm's assets. Asset values and volatilities as well as firm-specific bankruptcy barriers are simultaneously backed out from the prices of traded equity. Implied barriers are significantly positive and monotonic in the firm's leverage and asset volatility. Our default probabilities display better calibration and discriminatory power than the ones inferred in a standard Black and Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. J. Pol. Econ. 81, 637–659]/Merton [Merton, R.C., 1974. On the pricing of corporate debt: the risk structure of interest rates. J. Finance 29, 449–470] and KMV frameworks. However, accounting-based measures such as Altman Z- and Z″-scores outperform structural models in 1-year-ahead bankruptcy predictions, but lose relevance as the forecast horizon is extended.
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Purpose - The purpose of this paper is to show that previous research about financial and non-financial causes of bankruptcy has neglected the time dimension of failure. The paper seeks to gain deeper insight into the failure process of a company, giving it a more grounded understanding of the relationship between the characteristics of a company, the underlying causes of failure and the financial effects. Design/methodollogy/approach - The findings are based on a literature overview and in-depth case study research. Findings - Four types of failure processes were observed: the failure process of unsuccessful startups, the failure process of ambitious growth companies, the failure process of dazzled growth companies, and the failure process of apathetic established companies. Between these four failure processes, there exist major distinctions in terms of the presence and the importance of specific causes of bankruptcy, i.e. errors made by management, errors in the corporate policy and the importance of external factors. Research limitations/implications - The results of the study are based on qualitative, case study research. No attempt is made to quantify the existence and the importance of the findings. The major constructs that emerged as important in the research are well-known concepts in the management literature. As a consequence, they should be further developed in order to quantify their effect in large-scale studies. Practical implications - Based on the findings, stakeholders of a company can have a clearer view of both the time dimension inherent in corporate failure and the impact of their own actions on bankruptcy. Originality/value - The paper lays the ground for understanding the process of company failure. Company failure does not happen overnight and therefore a longitudinal and holistic perspective is needed.
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This exploratory study of 57 large bankruptcies and 57 matched survivors examined the dynamics of major corporate failure. Prior research was used to guide selection of the four major constructs studied: domain initiative, environmental carrying capacity, slack, and performance. What emerges is a clear portrayal of a protracted process of decline, aptly portrayed by prior theorists, and modeled here, as a downward spiral. In the firms studied, significant features of the downward spiral included early weaknesses in slack and performance, extreme and vacillating strategic actions, and abrupt environmental decline. An elaboration of the last two stages of decline is also presented, based on the findings from this study. The down-ward-spiral model is then illustrated with a case example. The study sheds light on major debates and dilemmas in the fields of organization theory and strategy regarding why major firms fail.
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This paper investigates the forecasting accuracy of bankruptcy hazard rate models for U.S. companies over the time period 1962–1999 using both yearly and monthly observation intervals. The contribution of this paper is multiple-fold. One, using an expanded bankruptcy database we validate the superior forecasting performance of Shumway’s (2001) model as opposed to Altman (1968) and Zmijewski (1984). Two, we demonstrate the importance of including industry effects in hazard rate estimation. Industry groupings are shown to significantly affect both the intercept and slope coefficients in the forecasting equations. Three, we extend the hazard rate model to apply to financial firms and monthly observation intervals. Due to data limitations, most of the existing literature employs only yearly observations. We show that bankruptcy prediction is markedly improved using monthly observation intervals. Fourth, consistent with the notion of market efficiency with respect to publicly available information, we demonstrate that accounting variables add little predictive power when market variables are already included in the bankruptcy model.
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A common feature of previous work on failure prediction models of UK companies is that the non-failed samples are restricted to include only sound or healthy companies. This may be considered a major weakness since, as a consequence, the models are biased in statistical design and have unclear relevance to a potential user.The major purpose of this paper is to develop models which explicitly allow for loss-making companies in the non-failed sample. We novelly experiment with rnultilogit analysis; we also report, as joint products of our analysis, some empirical results on the determinants of the going concern qualification, the time lag in reporting annual accounts and the formal type of legal failure.
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Standard bankruptcy prediction methods lead to models weighted by the types of failure firms included in the estimation sample. These kinds of weighted models may lead to severe classification errors when they are applied to such types of failing (and non-failing) firms which are in the minority in the estimation sample (frequency effect). The purpose of this study is to present a bankruptcy prediction method based on identifying two different failure types, i.e. the solidity and liquidity bankruptcy firms, to avoid the frequency effect. Both of the types are depicted by a theoretical gambler's ruin model of its own to yield an approximation of failure probability separately for both types. These models are applied to the data of randomly selected Finnish bankrupt and non-bankrupt firms. A logistic regression model based on a set of financial variables is used as a benchmark model. Empirical results show that the resulting heavily solidity-weighted logistic model may lead to severe errors in classifying non-bankrupt firms. The present approach will avoid these kinds of error by separately evaluating the probability of the solidity and liquidity bankruptcy; the firm is not classified bankrupt as long as neither of the probabilities exceeds the critical value. This leads the present prediction method slightly to outperform the logistic model in the overall classification accuracy.
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This paper shows evidence that it is possible to explain financial difficulties in small and medium sized firms based on non-financial variables. The results indicate that the estimated model based on non-financial variables classified firms even better than the financial ratio model, especially when classifying bankrupt firms and firms with payment delays. The best overall classification was achieved using the model combining financial ratios and non-financial variables. The non-financial variables measuring the number of payment delays were statistically the most important. The main implication of the results is that non-financial variables embrace important information in attempts to explain financial difficulties, and this should be of interest given that payment behavior variables (payment delays and payment disturbances) may occur more frequently than the publication of intermittent financial statements.
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In this article we develop statistical models for bankruptcy prediction of Norwegian firms in the limited liability sector using annual balance sheet information. We fit generalized linear, generalized linear mixed and Generalized Additive Models (GAM) in a discrete hazard setting. It is demonstrated that careful examination of the functional relationship between the explanatory variables and the probability of bankruptcy enhances the models' forecasting performance. Using information on the industry sector we model the unobserved heterogeneity between different sectors through an industry-specific random factor in the generalized linear mixed model. The models developed are shown to outperform the model with Altman's variables.
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The purpose is to predict corporate credit analyst's risk estimate by the weighted logistic (binary response) and linear regression (20-class risk estimate) analyses. The data comprise filed register information from Finska (Suomen Asiakastieto Oy) including 35 variables from 3200 companies. The coefficient of concordance was 95% and the rate of multiple determination 75% for the logistic and linear models, respectively. In a binary classification the differences in performance between the models were insignificant provided that the linear model is rotated. Both of the models give a classification accuracy of 90% in the estimation sample and 96% in the test sample.
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The considerable interest in the prediction of business failures is reflected in the large number of studies presented in the literature. Various methods have been used to construct prediction models. This paper provides a review of the literature and a framework for the presentation of this information. Articles can be classified according to the country, industrial sector and period of data, as well as the financial ratios and models or methods employed. Relationships and research trends in the prediction of business failure are discussed.
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This paper investigates the value added by private information exchanges that share information on business payment performance. We discuss how this information is collected and disseminated by the world’s largest private information broker, Dun & Bradstreet. We provide the first empirical examination of the importance of this information at the lending decision level. Our findings indicate that exchange-generated information provides significant explanatory power in failure prediction models controlling for other credit information that is easily available to lenders. Our study complements the work of Jappelli and Pagano [Information sharing, lending and defaults; Cross country evidence, Centre for Economic Policy Research, Discussion Paper 2184, 1999] who find in cross-country macro level tests that information exchanges add value.
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Over the last 35 years, business failure prediction has become a major research domain within corporate finance. Numerous corporate failure prediction models have been developed, based on various modelling techniques. The most popular are the classic cross-sectional statistical methods, which have resulted in various ‘single-period’ or static models, especially multivariate discriminant models and logit models. To date, there has been no clear overview and discussion of the application of classic statistical methods to business failure prediction. Therefore, this paper extensively elaborates on the application of (1) univariate analysis, (2) risk index models, (3) multivariate discriminant analysis, and (4) conditional probability models in corporate failure prediction. In addition, because there is no clear and comprehensive analysis in the existing literature of the diverse problems related to the application of these methods to the topic of corporate failure prediction, this paper brings together all problem issues and enlarges upon each of them. It discusses all problems related to: (1) the classical paradigm (i.e. the arbitrary definition of failure, non-stationarity and data instability, sampling selectivity, and the choice of the optimisation criteria); (2) the neglect of the time dimension of failure; and (3) the application focus in failure prediction modelling. Further, the paper elaborates on a number of other problems related to the use of a linear classification rule, the use of annual account information, and neglect of the multidimensional nature of failure. This paper contributes towards a thorough understanding of the features of the classic statistical business failure prediction models and their related problems.
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The last decade has witnessed the development of many empirical models to predict corporate bankruptcy and of several bankruptcy theories. This paper reviews and integrates these two strands of research and finds a substantial amount of overlap. However, the overlap is not perfect. The paper presents a new theory of bankruptcy that appears to fit the data better. The paper also suggests directions for future empirical and theoretical research.
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Assistant Professor of Finance, New York University. The author acknowledges the helpful suggestions and comments of Keith V. Smith, Edward F. Renshaw, Lawrence S. Ritter and the Journal' reviewer. The research was conducted while under a Regents Fellowship at the University of California, Los Angeles.
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One of the most well-known bankruptcy prediction models was developed by Altman [1968] using multivariate discriminant analysis. Since Altman's model, a multitude of bankruptcy prediction models have flooded the literature. The primary goal of this paper is to summarize and analyze existing research on bankruptcy prediction studies in order to facilitate more productive future research in this area. This paper traces the literature on bankruptcy prediction from the 1930's, when studies focused on the use of simple ratio analysis to predict future bankruptcy, to present. The authors discuss how bankruptcy prediction studies have evolved, highlighting the different methods, number and variety of factors, and specific uses of models.Analysis of 165 bankruptcy prediction studies published from 1965 to present reveals trends in model development. For example, discriminant analysis was the primary method used to develop models in the 1960's and 1970's. Investigation of model type by decade shows that the primary method began to shift to logit analysis and neural networks in the 1980's and 1990's. The number of factors utilized in models is also analyzed by decade, showing that the average has varied over time but remains around 10 overall.Analysis of accuracy of the models suggests that multivariate discriminant analysis and neural networks are the most promising methods for bankruptcy prediction models. The findings also suggest that higher model accuracy is not guaranteed with a greater number of factors. Some models with two factors are just as capable of accurate prediction as models with 21 factors.
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This paper first briefly discusses six alternative methods that have been applied to financial failure prediction: linear discriminant analysis, logit analysis, recursive partitioning, survival analysis, neural networks and the human information processing approach. The main objective was to study empirically whether the results stemming from the use of alternative methods differ from each other. This was conducted using the Finnish data one, two and three years prior to failure in empirical analysis. The results indicated that there was a statistically significant difference in prediction accuracy only between logistic analysis and survival analysis one year prior to failure. Two and three years prior to failure statistically significant differences were not found. The results indicate, with the three variables employed in this study, that no superior method has been found. Even one of the latest applications, neural networks, is in its present form only as effective as discriminant analysis was as early as thirty years ago.
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This is the first study that uses Merton's (1974) option pricing model to compute default measures for individual firms and assess the effect of default risk on equity returns. The size effect is a default effect, and this is also largely true for the book-to-market (BM) effect. Both exist only in segments of the market with high default risk. Default risk is systematic risk. The Fama-French (FF) factors SMB and HML contain some default-related information, but this is not the main reason that the FF model can explain the cross section of equity returns. Copyright 2004 by The American Finance Association.
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Considering the fundamental role played by small and medium sized enterprises (SMEs) in the economy of many countries and the considerable attention placed on SMEs in the new Basel Capital Accord, we develop a distress prediction model specifically for the SME sector and to analyse its effectiveness compared to a generic corporate model. The behaviour of financial measures for SMEs is analysed and the most significant variables in predicting the entities' credit worthiness are selected in order to construct a default prediction model. Using a logit regression technique on panel data of over 2,000 U.S. firms (with sales less than $65 million) over the period 1994-2002, we develop a one-year default prediction model. This model has an out-of-sample prediction power which is almost 30 per cent higher than a generic corporate model. An associated objective is to observe our model's ability to lower bank capital requirements considering the new Basel Capital Accord's rules for SMEs.
Wald Chi-Square statistics and the signs of parameter estimates. Non-financial variable models by year
  • Watson Keasey
Table 9. Wald Chi-Square statistics and the signs of parameter estimates. Non-financial variable models by year. 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 1. Firm type BOARD_SIZE Number of board members (No deputy members) Keasey and Watson (1987);
change within 3 years
  • Watson Keasey
Keasey and Watson (1987) change within 3 years; Laitinen (1999);
LNBOARD_OWN_PDEFS Number of board member's own payment defaults Laitinen
  • Wilson
Wilson et al. (2013) LNBOARD_OWN_PDEFS Number of board member's own payment defaults Laitinen (1999);
1. Firm type BOARD_SIZE Number of board members (No deputy members
  • Watson Keasey
Wald Chi-Square statistics and the signs of parameter estimates. Non-financial variable models by year. 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 1. Firm type BOARD_SIZE Number of board members (No deputy members) Keasey and Watson (1987);