Models of corporate failure prediction

The empirical literature on bankruptcy prediction has attracted the interest of researchers for many years. In fact, this field is as interesting today as it was in the 1930’s and, over the last 70 years, a remarkable body of both theoretical and empirical studies concerning this topic has been published.

These researches adopted two basic model designs: a) time-series formulations, that study the path to failure of only (normally) distressed firms; b) cross-sectional studies, based on a comparison between healthy and distressed firms. In this context, the research focus of these studies was the best prediction methods and the best failure indicators (⁷).

The first relevant studies were published in the 1930’s and 1940’s, after the Great ____________

Journal of Accounting Research 22, 59-82. LENNOX C.(1999), Indentifying Failing Companies: a revaluation of the Logit, Probit and DA approaches, Journal of Economics and Business, 51, 347-364.

(⁶) SERRANO C. (1997), Feedforward neural networks in the classification of financial information, European Journal of Finance 3, 3, 183-202; PÉREZ M. (2006), Artificial neural networks and bankruptcy forecasting: a state of the art, Neural Computing & Applications, 15, 154-163; HÄRDLE W.,LEE Y.,SCHÄFER D.,YEH Y., (2009), Variable Selection and Oversampling in the Use of Smooth Support Vector Machines for Predicting the Default Risk of Companies, Journal of Forecasting, 28, 512–534.

(⁷) In fact, many studies dealt with prediction rather than explanation. CIBINSKY P (2001), Description, Explanation, Prediction - the Evolution of Bankruptcy Studies?, Managerial Finance, vol. 27, n. 4, 29-44.

Depression, when numerous firms collapsed. As a consequence, the prediction of bankruptcy was considered important. In this period, Smith (⁸) published a pioneering study founded on ratio analysis of 29 companies from different sectors, which failed during the 1920’s. He calculated 24 ratios, even if he thought that some of them (especially: Net Earnings to Total Assets; Net Income to Net Worth; Working Capital and Fixed Assets to Total Assets; Current Ratio) were «sensitive barometers of the progress of a company».

In the same period, Fitzpatrick (⁹) published two relevant studies. In the first one, he analysed 20 companies which failed during the 1920’s, calculating 13 ratios. While in the second study, which was an extension of the previous, he compared the same 20 companies with other analogous thriving firms.

Subsequently, from the late 1960s to the present, studies combined publicly available data (i.e. financial statements) with statistical classification techniques in order to predict business failure.

Beaver (¹⁰) published a study based on a univariate approach, which represented a fundamental step in the evolution of bankruptcy prediction models. His model was based on a paired-sample design, because «each failed firm has a non-failed “mate”…» (p. 76). He calculated 30 ratios (whose selection was based on three criteria: popularity in the literature;

ratios which performed well in one of the previous studies; ratios which can be defined in terms of a cash flow concept), articulated into six groups (¹¹). After the calculation of a medium value of the ratios, he used a Dichotomus Classification Test, based on a cut-off point of each ratio, to predict failure. In fact, after the division of the original sample into two sub-samples, he established the cut-off point to classify companies. Then, he classified the companies of the first group by adopting the cut-off point of the second one. In this way, he chose the best predictive ratio, Cash Flow to Total Debt, which had the minimum classification error. In fact, this ratio was substantially constant for thriving companies.

The basic limitation of Beaver’s study was the adoption of a univariate approach, with the main implication being that each ratio is analysed autonomously. Moreover, this study represented a fundamental reference point for future researches.

A few years after Beaver’s study, Altman (¹²) proposed one of the most well-known bankruptcy prediction models, the so-called Z-score model. This model was more accurate than the previous approaches because it combined the ratio analysis with a rigorous statistical approach, the Multivariate Discriminant Analysis (MDA). The main advantage of this model was that it emphasised the correlations among ratios.

Altman analysed the financial statements of a sample of 66 companies, divided into two groups (failed and non-failed firms) and founded his research on the estimation of a linear discriminant function based on a selection of five variables.

After this pioneering study, Altman further developed his research on the topic. He

____________

(⁸) SMITH R.F. (1930), A Test Analysis of unsuccessful Industrial Companies, Bureau of Business Research, Bulletin No. 31, University of Illinois.

(⁹) FITZPATRICK P.J. (1931), Symptoms of Industrial Failure, Catholic University of American Press; FITZPATRICK

P.J. (1932), A Comparison of the Ratios of Successful Industrial Enterprises with those of Failed Companies, Certified Public Accountant, 12, October, November, December, 598-605, 656-662, 727-731.

(¹⁰) BEAVER W.H.(1966),op. cit.

(¹¹) Cash Flow ratios; Net Income ratios; Debt to Total Assets ratios; Liquid Assets to Total Assets ratios;

Liquid Assets to Current ratios; Turnover ratios.

(¹²) ALTMAN E.I. (1968), op. cit.

recently revisited his model in a Basel 2 environment (¹³).

Following these contributions, bankruptcy prediction studies have evolved (¹⁴) and a large number of models have flooded current literature (¹⁵). In this evolution, the MDA has been the main technique used to develop predictor models during the 1960’s and 1970’s. A few significant statistical approaches have been subsequently introduced such as logistic analysis and artificial neural networks.

Logistic regression analysis has been used to examine the relationship between binary or ordinal response probability and explanatory variables. Ohlson (¹⁶) was one of the first authors who used logit analysis in the context of financial distress. This approach, in line with the purpose of the discriminant analysis, assigns a weight to the independent variables and a Z score in the form of failure probability to each company included in a sample.

A neural network fundamentally implements a function f that maps a set of given input values x to some output values y: y = f(x). It consists of a large number of processing elements, neurons and the connections between them. In fact, a neural network tries to find the best possible approximation of the function f as a complex combination of elementary nonlinear functions. This approximation is designated in the neurons of the network using weights that are associated to each neuron (¹⁷) and are learned using an iterative procedure in which examples of accurate input-output associations are shown to the network. In this learning process (which means finding an appropriate set of weights), the weights are modified so that the network starts to imitate the desirable input-output behaviour. This capability of learning from examples and the derived capability of generalising new situations is the most interesting characteristic of the neural network approach.

A recent review of bankruptcy prediction studies from 1930 to present day (¹⁸) shows that MDA and neural networks are the most promising methods for bankruptcy prediction models. Nevertheless, even if the use of MDA has decreased, it remains a generally accepted standard method (¹⁹). As a consequence, different authors adopt MDA analysis as a basic ____________

(¹³) ALTMAN E.I.,HALDEMAN R.G., NARAYANAN P. (1977), Zeta Analysis, A new Model to Identify bankruptcy risk of corporations, Journal of Banking and Finance, 1, 29-54; ALTMAN E.I.,HOCHKISS E. (2005), Corporate Financial Distress and bankruptcy: Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt, Wiley, New York. ALTMAN E.I., (2002), Corporate Distress Prediction Model in a Turbulent Economic and Basel 2 Environment, NYU Working Paper No.

FIN-02-052.

(¹⁴) CORONELLA S. (2009), I modelli di previsione delle crisi aziendali: alcune riflessioni, in Rivista italiana di ragioneria e di economia aziendale, set.-ott., 503-516; MADONNA S. (2008), I modelli di scoring nella previsione delle insolvenze, in DANOVI A.,QUAGLI A. (edited by), Gestione della crisi aziendale e dei processi di risanamento, Ipsoa, Milano, 143-181;

QUAGLI A. (1990), Modelli di previsione delle insolvenze aziendali, Amministrazione e finanza, 17; TEODORI C. (1994), I modelli di previsione delle insolvenze e l’amministrazione controllata, Rivista dei dottori commercialisti, 45(1), 75-101.

(¹⁵) Examples of empirical analysis on bankruptcy prediction of Italian firms are: APPETITI S. (1984), Identifying unsound firms in Italy. An attempt to use trend variables, Journal of Banking and Finance, 8, 269–279; BARONTINI R.

(1992), L’efficacia dei modelli di previsione delle insolvenze: Risultati di una verifica empirica. Finanza, Imprese e Mercati, 1, 141–185; LAVIOLA S.,TRAPANESE M. (1997), Previsione delle insolvenze delle imprese e quantità del credito bancario: Un’analisi statistica. Temi di discussione del Servizio Studi, Banca d’Italia, 318; FOGLIA A.,LAVIOLA S.,MARULLO-REEDTZ P.

(1998), Multiple banking relationships and the fragility of corporate borrowers, Journal of Banking and Finance 22, 1441-1456;

BECCHETTI L.,SIERRA J. (2003), Bankruptcy risk and productive efficiency in manufacturing firms, Journal of Banking and Finance, 27, 2099-2120.

(¹⁶) OHLSON J.(1980), op.cit.

(¹⁷) BACK B.,LAITINEN T.,HEKANAHO J.,SERE K. (1997), The Effect of Sample Size on Different Failure Prediction Methods, Turku Centre for Computer Science, TUCS Technical Report n, 155, 1-26.

(¹⁸) BELLOVARI J.L.,GIACOMINO D.E.,AKERS M.A. (2007), Review of Bankruptcy Prediction Studies: 1930 to Present, Journal of Financial Education, 33, 1-43.

(¹⁹) DIMITRAS A.,ZANAKIS,S., ZOPOUDINIS,C. (1996), A survey of business failures with an emphasis on failure prediction methods and industrial applications, European Journal of Operational Research 90, 3, 487–513; ALTMAN E.I.,

method and neural networks as a comparative technique (²⁰).

In this first step of our research, we focused on a classical MDA approach. In the next phase, we will compare the reached results with those of other techniques such as the artificial neural network as well as introduce other variables in measuring the state of firms investigated. This will be carried out in order to include the existing (local) macroeconomic conditions as well as understand the position in the business cycle, which is an important (dynamic) factor that introduces a sort of “time dimension” into the model.