Predicting Corporate Bankruptcy: An Evaluation of Alternative Statistical Frameworks

• Author: Stewart Jones,David Johnstone,Roy Wilson
• DOI: http://doi.org/10.1111/jbfa.12218
• Date: 01 January 2017
• Published date: 01 January 2017

Journal of Business Finance & Accounting

Journal of Business Finance & Accounting, 44(1) & (2), 3–34, January/February 2017, 0306-686X

doi: 10.1111/jbfa.12218

Predicting Corporate Bankruptcy: An

Evaluation of Alternative Statistical

Frameworks

Stewart Jones, David Johnstone and Roy Wilson∗

Abstract: 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).

Keywords: corporate bankruptcy prediction, binary classifiers, statistical learning

1. INTRODUCTION

The prediction of corporate bankruptcy has been of considerable interest to business

academics, corporate regulators, practitioners and financial economists over the last

five decades (Altman, 2002; Jones and Hensher, 2008). Corporate failures can impose

significant economic costs on society and cause major social dislocations through

economic downturns and recessions. The world has gone through several notable

∗Stewart Jones and David Johnstone are both at the University of Sydney, Australia. Roy Wilson is with

the Australian Centre for Commercial Mathematics, University of New South Wales, Australia. The authors

acknowledge financial assistance for this project from the Australian Research Council. Financial support

for this project was provided by the Australian Research Council. ARC A7769.

Address for correspondence: Stewart Jones, Discipline of Accounting, The University of Sydney Business

School, the University of Sydney,Codrington Building, Cnr Codrington St and Rose Lane, Darlington, NSW

2006, Australia.

e-mail: stewart.jones@sydney.edu.au

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4JONES, JOHNSTONE AND WILSON

spates of corporate collapses over the past two decades alone, including the Asian

Financial Meltdown of 1997, the Dot.Com bubble or “tech wreck” of 2000–2002; and

more recently the Global Financial Crisis of 2007–2008, the repercussions of which are

still impacting global financial markets. At the height of the GFC, the world witnessed

an unprecedented number of corporate collapses which brought the global financial

system to a dangerous precipice and spiralled many global economies into recession1

(Jones and Hensher, 2008).

Given the wider social, political and economic impacts of large-scale corporate fail-

ures across the global economy, the continual development of more robust predictive

models and frameworks has been of enduring concern to regulators, practitioners

and academics. Jones and Hensher (2004) note that corporate failure predictions

are now used in a wide number of accounting, finance and regulatory contexts,

such as monitoring the solvency of financial institutions, going concern evaluations

by corporate auditors, assessment of corporate and consumer loan security by banks

and other financial institutions, the measurement of portfolio risk and the pricing of

defaultable credit derivatives and other financial instruments exposed to credit risk

(see also Altman, 2002; Duffie and Singleton, 2003).

While an extensive literature on corporate bankruptcy prediction has emerged,

innovative modelling techniques to predict corporate bankruptcy has been slow to

develop (Jones and Hensher, 2004). Much of the corporate bankruptcy literature has

relied on quite simplistic classification models such as linear discriminant analysis

(LDA), binary logistic or probit analysis or standard form multinomial logit models

(see for example, Altman, 1968; Altman et al., 1977; Ohlson, 1980; Zmijewski, 1984;

Lau, 1987; Jones and Hensher, 2004).

The relative merits of logit, probit, LDA, and to a lesser extent neural networks, have

been examined in an extensive literature (see for example, Efron, 1975; McFadden,

1976; Ohlson, 1980; Jones, 1987; Agarwal, 1999; Altman et al., 1994).2,3 A recent

study by Bauer and Agarwal (2014) compared the performance of hazard models

with traditional bankruptcy techniques.4However, corporate bankruptcy research

has generally not explored or kept abreast of many important developments in the

statistical learning literature and related fields, which can potentially provide fruitful

avenues for future research. There is evidence that “new age” classification models

1 The corporate assets of top ten GFC related bankruptcies alone totalled more than US$ 1.42 Trillion,the

largest being the US$ 688 billion dollar bankruptcy of the investment bank Lehman Brothers, which was

the largest corporate bankruptcy filing in history (Jones and Johnstone, 2012).

2 For example, one of the most cited bankruptcy models in the business literature is the Altman Z score

model. This is an LDA model with the following fitted form: Z =1.2X1+1.4X2+3.3X3+0.6X4+

0.99X5, where the input variables X1–X

5represent financial ratios, respectively Working Capital/Total

Assets; Retained Earnings/Total Assets; Earnings Before Interest and Taxes/Total Assets; Market Value of

Equity/Book Value of TotalLiabilities; and Sales/Total Assets. When the Z score is below a certain threshold

(1.89) the company is predicted to fail (see Altman, 2002).

3 However, there are examples of more innovative modelling techniques and applications coming from

disciplines outside the business field (examples include: Frydman et al., 1985; Wilson and Sharda, 1994; Jo

et al., 1997; Olmeda and Fern´

andez, 1997; Lin and McClean, 2001; Baesens et al., 2003; Neophytou and

Molinero, 2004; Huysmans et al., 2006; Wu et al., 2007; Cort´

es et al., 2007, Hu, 2008; Sun and Li, 2008; Rafie

et al., 2012; Kim and Kang, 2012).

4 Following the approach of Jones et al. (2015), this study is limited to binary classifiers. Some studies

have used hazard model functions to predict corporate failure (see e.g., Shumway, 2001). However,

hazard/duration models are excluded from this analysis because they are not binary classifiers per se.These

models predict a single event/outcome as a function of time and other explanatory variables (see Kleinbaum

and Klein, 2012). Furthermore, this study is restricted to four years of data (which includes the year of

failure). Hazard models are more suitable when the time horizon is much longer than this.

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AN EVALUATION OF ALTERNATIVE STATISTICAL FRAMEWORKS 5

(such as AdaBoost, generalised boosting and random forests) can significantly out-

perform conventional classifiers, including logit, probit, LDA and even sophisticated

data mining techniques such as neural networks and SVMs (see Friedman, 2001;

Hastie et al., 2009; Schapire and Freund, 2012; Jones et al., 2015; Jones, 2016).5

Second, very little research has been devoted to evaluating the empirical performance,

theoretical merits and characteristics of alternative classification models, even among

the relatively narrow range of classifiers utilised in the corporate bankruptcy literature

(Jones and Hensher, 2008).6Model comparison and evaluation is hampered by the

limitations of this literature. While the corporate bankruptcy literature is extensive,

there is a great deal of heterogeneity across studies, particularly with respect to

sample sizes (which tend to be small and localised to particular jurisdictions and

industries), variable selection and definition, definitions of corporate failure, research

designs and model evaluation criteria (see Jones, 2016). This study seeks to address

some of these problems by evaluating alternative classifiers using a large sample of

US corporate bankruptcies and adopting a consistent methodological approach to

evaluating predictive performance. Jones et al. (2015) conceptualise the properties

and characteristics of the different classifiers is in terms of the trade-off between

flexibility and interpretability (Hastie et al., 2009). For instance, highly linear models that

are designed to accommodate a smaller range of explanatory variables (or reduce

a large number of predictor variables to a small optimal set of predictors) are the

most rigid on the scale, but are the most interpretable in terms of understanding the

role and influence of explanatory variables on the response outcome (for instance,

through parameter estimates and marginal effects). More general classifiers tend to

predict more accurately, but are less interpretable. The benefit from using a more

complex nonlinear classifier (such as a neural network or generalised boosting model)

should come from improved out-of-sample predictive success. As suggested in Jones

et al. (2015) a simpler more interpretable model should be preferred to a complex

model, particularly if there is little difference in predictive performance.

The major research question of this paper is to assess whether more complex classi-

fiers do in fact predict corporate bankruptcies better, particularly compared to simpler

more interpretable classifiers. Further, is this enhancement in predictive performance

sufficient enough to justify the use of a more complex model relative to a simpler

more interpretable model? An important corollary to these questions is whether

sophisticated classifiers such as AdaBoost, generalised boosting or random forests

have practical value in bankruptcy prediction, particularly in terms of implementation

feasibility and interpretability. Traditional machine learning classifiers such as neural

networks and SVMs have long been considered “black boxes”, as they are designed to

capture complex nonlinear relationships and interactions which are largely hidden in

the internal mathematics of the model system. Even if such models can predict very

well, their practical usefulness and appeal could be limited if they are too difficult to

implement or interpret in practice.

For a model to have good practical value and appeal, the models should be (1)

relatively straightforward to implement, particularly in terms of model architecture

5 One application of the generalised boosting method to corporate financial distress indicates the approach

has considerable promise as a predictive tool in this field (Cort´

es et al., 2007; and a review of boosting

literature outside of accounting and finance is provided in Jones, 2016).

6 There have been a limited number of comparative studies, and many have focused on neural networks

and other techniques.

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