Predicting Corporate Bankruptcy: An Evaluation of Alternative Statistical Frameworks

Corporate bankruptcy prediction has attracted significant research attention from business academics, regulators and financial economists over the past five decades. However, much of this literature has relied on quite simplistic classifiers such as logistic regression and linear discriminant analysis (LDA). Based on a large sample of US corporate bankruptcies, we examine the predictive performance of 16 classifiers, ranging from the most restrictive classifiers (such as logit, probit and linear discriminant analysis) to more advanced techniques such as neural networks, support vector machines (SVMs) and “new age” statistical learning models including generalised boosting, AdaBoost and random forests. Consistent with the findings of Jones et al. ( 2015 ), we show that quite simple classifiers such as logit and LDA perform reasonably well in bankruptcy prediction. However, we recommend the use of “new age” classifiers in corporate bankruptcy modelling because: (1) they predict significantly better than all other classifiers on both the cross‐sectional and longitudinal test samples; (2) the models may have considerable practical appeal because they are relatively easy to estimate and implement (for instance, they require minimal researcher intervention for data preparation, variable selection and model architecture specification); and (3) while the underlying model structures can be very complex, we demonstrate that “new age” classifiers have a reasonably good level of interpretability through such metrics as relative variable importances (RVIs).     

35 years of studies on business failure: an overview of the classic statistical methodologies and their related problems

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.     

DEA as a business failure prediction tool Application to the case of galician SMEs

In the research group we are working to provide further empirical evidence on the business failure forecast. Complex fitting modelling; the study of variables such as the audit impact on business failure; the treatment of traditional variables and ratios have led us to determine a starting point based on a reference mathematical model. In this regard, we have restricted the field of study to non-financial galician SMEs in order to develop a model¹ to diagnose and forecast business failure. We have developed models based on relevant financial variables from the perspective of the financial logic, voltage and financial failure, applying three methods of analysis: discriminant, logit and multivariate linear. Finally, we have closed the first cycle using mathematical programming –DEA or Data Envelopment Analysis– to support the failure forecast. The simultaneous use of models was intended to compare their respective conclusions and to look for inter-relations. We can say that the resulting models are satisfactory on the basis of their capacity for prediction. Nevertheless, DEA contains significant points of criticism regarding its applicability to business failure.     

DECOMPOSITION MEASURES AND THE PREDICTION OF FINANCIAL FAILURE

Lev has indicated that the decomposition measures of failed firms are larger than those of non-failed firms and concludes that decomposition measures may be usefully included in financial failure prediction models. This paper extends the use of decomposition measure concepts for financial failure prediction. Firstly, on a univariate basis, attributes of decomposition measures are tested for discriminating ability between failed and non-failed companies. Secondly, all decomposition measures tested are used to derive a discriminant analysis model for failure prediction. The paper concludes that (1) the stability and size of some balance sheet derived decomposition measures discriminate between failed and non-failed companies as far as four years before failure, and (2) a discriminant analysis model of balance sheet derived decomposition measures is not successful at predicting financial failure.     

A DISCRETE-VALUED RISK FUNCTION FOR MODELLING FINANCIAL DISTRESS IN PRIVATE AUSTRALIAN COMPANIES

This paper emphasises the inappropriateness of continuous measure predictors for both the logit and MDA models when dealing with the measurement errors that exist in much of the private company data used to model financial distress in that sector. Also, it is argued that the step function logit model that we get as a consequence of the necessity to categorise the predictors, may be more appropriate in explaining underlying nonlinear behaviour of firms at risk than the usual continuous response linear function. Within this context, the two models are compared using data from 140 private Australian companies. A logit model based on only three discrete-valued ratios gave an overall accuracy rate comparable to that of an existing continuous-valued multiple discriminant analysis (MDA) model based on six ratios. Of interest is the very different order of significance of the predictor ratios in the two models although neither model remains trustworthy for predictive purposes.     

A comparison of the relative costs of financial distress models: artificial neural networks,logit and multivariate discriminant analysis

This study uses two artificial neural networks (ANNs), categorical learning/instar ANNs and probabilistic (PNN) ANNs, suitable for classification and prediction type issues, and compares them to traditional multivariate discriminant analysis (MDA) and logit to examine financial distress one to three years prior to failure. The results indicate that traditional MDA and logit perform best with the lowest overall error rates. However, when the relative error costs are considered, the ANNs perform better than traditional logit or MDA. Also, as the time period moves farther away from the eventual failure date, ANNs perform more accurately and with lower relative error costs than logit or MDA. This supports the conclusion that for auditors and other evaluators interested in early warning techniques, categorical learning network and probabilistic ANNs would be useful. © 1997 John Wiley & Sons, Ltd.     

A Comparison of Neural Network, Statistical Methods, and Variable Choice for Life Insurers' Financial Distress Prediction

This study examines the effect of the statistical/mathematical model selected and the variable set considered on the ability to identify financially troubled life insurers. Models considered are two artificial neural network methods (back‐propagation and learning vector quantization (LVQ)) and two more standard statistical methods (multiple discriminant analysis and logistic regression analysis). The variable sets considered are the insurance regulatory information system (IRIS) variables, the financial analysis solvency tracking (FAST) variables, and Texas early warning information system (EWIS) variables, and a data set consisting of twenty‐two variables selected by us in conjunction with the research staff at TDI and a review of the insolvency prediction literature. The results show that the back‐propagation (BP) and LVQ outperform the traditional statistical approaches for all four variable sets with a consistent superiority across the two different evaluation criteria (total misclassification cost and resubstitution risk criteria), and that the twenty‐two variables and the Texas EWIS variable sets are more efficient than the IRIS and the FAST variable sets for identification of financially troubled life insurers in most comparisons.     

THE SIGNIFICANCE OF BASE YEAR IN DEVELOPING FAILURE PREDICTION MODELS

Most failure prediction models developed over the past fifteen years have been based on firms' financial characteristics one year before they collapsed. This article reports the results of a study employing multiple discriminant analysis on a sample of fifty-three British companies which failed over the period 1960–1971. Models were developed on various financial ratios and an industry indicator for each of the five years, prior to failure, and the results in fact show that the model developed from data five years before failure performed at least as well as that derived one year prior to bankruptcy.     

A neural network approach to the prediction of going concern status

The assessment of a firm's going concern status is not an easy task. To assist auditors, going concern prediction models based on statistical methods such as multiple discriminant analysis and logit/probit analysis have been explored with some success. This study attempts to look at a different and more recent approach—neural networks. In particular, a neural network model of the feedforward, backpropagation type was constructed to predict a firm's going concern status from six financial ratios, using a data set containing 165 non-going concerns and 165 matched going concerns. On an evenly distributed hold-out sample, the trained network model correctly predicted all 30 test cases. The results suggest that neural networks can be a promising avenue of research and application in the going concern area.     

AN EXPLORATION INTO BANKRUPTCY DISCRIMINANT MODEL SENSITIVITY

Prediction has been a central theme in much of the accounting research and theory construction and verification over the past decade. Largely ignored in such studies has been consideration of the statistical properties of accounting measures, particularly as related to the effects of those properties on the signals from prediction models that use accounting measures as inputs. This study was designed to provide preliminary insight into the magnitude of the effects of this omission, and a bankruptcy prediction model was selected to facilitate the analysis. Results indicate that the linear discriminant model (as applied to prediction of failure) is sensitive to departures of inputdata distributions from multivariate normal.     

Evaluating the Behavioural Performance of Alternative Logit Models: An Application to Corporate Takeovers Research

Abstract:  Econometric models involving a discrete outcome dependent variable abound in the finance and accounting literatures. However, much of the literature to date utilises a basic or standard logit model. Capitalising on recent developments in the discrete choice literature, we examine three advanced (or non-IID) logit models, namely: nested logit, mixed logit and latent class MNL. Using an illustration from corporate takeovers research, we compare the explanatory and predictive performance of each class of advanced model relative to the standard model. We find that in all cases the more advanced logit model structures, which correct for the highly restrictive IID and IIA conditions, provide significantly greater explanatory power than standard logit. Mixed logit and latent class MNL models exhibited the highest overall predictive accuracy on a holdout sample, while the standard logit model performed the worst. Moreover, the analysis of marginal effects of all models indicates that use of advanced models can lead to more insightful and behaviourally meaningful interpretations of the role and influence of explanatory variables and parameter estimates in model estimation. The results of this paper have implications for the use of more optimal logit structures in future research and practice.     

Modelling corporate failure: A multinomial nested logit analysis for unordered outcomes

This study evaluates the theoretical and empirical significance of the multinomial nested logit (NL) model as an advanced closed-form model for the explanation and prediction of firm financial distress. Using a four-state failure model based on Australian company samples, we estimate an NL model and test its predictive performance on a holdout sample. Comparison of model fits and out-of-sample forecasts indicate that the unordered NL model statistically outperforms a standard logit model by substantial margins. NL may even be used as an effective practical alternative to more advanced open-form models such as mixed logit in the modelling of firm financial distress.     

Off-site monitoring systems for predicting bank underperformance: a comparison of neural networks,discriminant analysis,and professional human judgment

This study compares the ability of discriminant analysis, neural networks, and professional human judgment methodologies in predicting commercial bank underperformance. Experience from the banking crisis of the 1980s and early 1990s suggest that improved prediction models are needed for helping prevent bank failures and promoting economic stability. Our research seeks to address this issue by exploring new prediction model techniques and comparing them to existing approaches. When comparing the predictive ability of all three models, the neural network model shows slightly better predictive ability than that of the regulators. Both the neural network model and regulators significantly outperform the benchmark discriminant analysis model's accuracy. These findings suggest that neural networks show promise as an off-site surveillance methodology. Factoring in the relative costs of the different types of misclassifications from each model also indicates that neural network models are better predictors, particularly when weighting Type I errors more heavily. Further research with neural networks in this field should yield workable models that greatly enhance the ability of regulators and bankers to identify and address weaknesses in banks before they approach failure. Copyright © 2001 John Wiley & Sons, Ltd.     

Binary choice models and corporate takeover

This paper utilizes four different classification procedures (binary choice models) and compares their ability to predict corporate takeovers. Specifically, the paper develops logit, probit, discriminant, and recursive partitioning, models to predict which firms will be taken over. The original classification accuracy and the validation test results indicate that the recursive partitioning model outperforms the other models (although its accuracy drops significantly in the validation test). The results also indicate the difficulty in predicting corporate takeovers.     

Predicting Corporate Failure Using a Neural Network Approach

This paper investigates the performance of Artificial Neural Networks for the classification and subsequent prediction of business entities into failed and non-failed classes. Two techniques, back-propagation and Optimal Estimation Theory (OET), are used to train the neural networks to predict bankruptcy filings. The data are drawn from Compustat data tapes representing a cross-section of industries. The results obtained with the neural networks are compared with other well-known bankruptcy prediction techniques such as discriminant analysis, probit and logit, as well as against benchmarks provided by directly applying the bankruptcy prediction models developed by Altman (1968) and Ohlson (1980) to our data set. We control the degree of ‘disproportionate sampling’ by creating ‘training’ and ‘testing’ populations with proportions of bankrupt firms ranging from 1% to 50%. For each population, we apply each technique 50 times to determine stable accuracy rates in terms of Type I, Type II and Total Error. We show that the performance of various classification techniques, in terms of their classification errors, depends on the proportions of bankrupt firms in the training and testing data sets, the variables used in the models, and assumptions about the relative costs of Type I and Type II errors. The neural network solutions do not achieve the ‘magical’ results that literature in this field often promises, although there are notable 'pockets' of superior performance by the neural networks, depending on particular combinations of proportions of bankrupt firms in training and testing data sets and assumptions about the relative costs of Type I and Type II errors. However, since we tested only one architecture for the neural network, it will be necessary to investigate potential improvements in neural network performance through systematic changes in neural network architecture.     

Bankruptcy prediction using fuzzy convolutional neural networks

We propose a combined method for bankruptcy prediction based on fuzzy set qualitative comparative analysis (fsQCA) and convolutional neural networks (CNN). Currently, CNNs are being applied to various fields, and in some areas are providing higher performance than traditional models. In our proposed method, a CNN uses calibrated variables from fuzzy sets to improve performance accuracy. In addition, there are no published studies on the effect of feature selection at the input level of convolutional neural networks. Therefore, this study compares four well-known feature selection methods used in financial distress prediction, (t-test, stepdisc discriminant analysis, stepwise logistic regression and partial least square discriminant analysis) to investigate their effect on classification performance. The results show that fuzzy convolutional neural networks (FCNN) lead to better performance than when using traditional methods.     

Forecasting Corporate Bankruptcy: Optimizing the Performance of the Mixed Logit Model

In recent studies, Jones and Hensher (2004 , 2005) provide an illustration of the usefulness of advanced probability modelling in the prediction of corporate bankruptcies, insolvencies and takeovers. Mixed logit (or random parameter logit) is the most general of these models and appears to have the greatest promise in terms of underlying behavioural realism, desirable econometric properties and overall predictive performance. It suggests a number of empirical considerations relevant to harnessing the maximum potential from this new model (as well as avoiding some of the more obvious pitfalls associated with its use). Using a three-state failure model, the unconditional triangular distribution for random parameters offers the best population-level predictive performance on a hold-out sample. Further, the optimal performance for a mixed logit model arises when a weighted exogenous sample maximum likelihood (WESML) technique is applied in model estimation. Finally, we suggest an approach for testing the stability of mixed logit models by re-estimating a selected model using varying numbers of Halton intelligent draws. Our results have broad application to users seeking to apply more accurate and reliable forecasting methodologies to explain and predict sources of firm financial distress better.     

PREDICTING PRIVATE COMPANY FAILURE

Private company failure is a significant problem that is not fully addressed by existing research. This study develops a discriminant model from data on 107 private companies. The model predicts success and failure, based on six ratios obtained from the two immediately prior years' publicly available accounting reports. Based on a hold-out sample of 40 companies a prediction with 85% accuracy was achieved. This prediction was made one year ahead. The model indicates that the retained earnings/total assets, total liabilities/total assets, and shareholders funds/total liabilities ratios are the three major predictors of bankruptcy. Overall the model's coefficients are, as expected, substantially different to those of public company models.     

Modeling default risk with support vector machines

Predicting default risk is important for firms and banks to operate successfully. There are many reasons to use nonlinear techniques for predicting bankruptcy from financial ratios. Here we propose the so-called Support Vector Machine (SVM) to predict the default risk of German firms. Our analysis is based on the Creditreform database. In all tests performed in this paper the nonlinear model classified by SVM exceeds the benchmark logit model, based on the same predictors, in terms of the performance metric, AR. The empirical evidence is in favor of the SVM for classification, especially in the linear non-separable case. The sensitivity investigation and a corresponding visualization tool reveal that the classifying ability of SVM appears to be superior over a wide range of SVM parameters. In terms of the empirical results obtained by SVM, the eight most important predictors related to bankruptcy for these German firms belong to the ratios of activity, profitability, liquidity, leverage and the percentage of incremental inventories. Some of the financial ratios selected by the SVM model are new because they have a strong nonlinear dependence on the default risk but a weak linear dependence that therefore cannot be captured by the usual linear models such as the DA and logit models.     

Bankruptcy prediction: the influence of the year prior to failure selected for model building and the effects in a period of economic decline

Using large amounts of data from small and medium‐sized industrial firms, this study examines two aspects of bankruptcy prediction: the influence of the year prior to failure selected for model building and the effects in a period of economic decline. The results show that especially models generated from the final annual report published prior to bankruptcy were less successful in the timely prediction of failure. Furthermore, it was found that economic decline coincided with the deterioration of a model's performance. With respect to the methods used, we found that neural networks had a somewhat better overall performance than multiple discriminant analysis. Copyright © 2005 John Wiley & Sons, Ltd.