A Review and Empirical Analysis of Altman's Z‐Score Model

Edward Altman

By Edward Altman


The purpose of this paper is firstly to review the literature on the efficacy and importance of the Altman Z-Score bankruptcy prediction model globally and its applications in finance and related areas. This review is based on an analysis of 33 scientific papers published from the year 2000 in leading financial and accounting journals. Secondly, we use a large international sample of firms to assess the classification performance of the model in bankruptcy and distressed firm prediction. In all, we analyze its performance on firms from 31 European and three non-European countries. This kind of comprehensive international analysis has not been presented thus far. Except for the U.S. and China, the firms in the sample are primarily private and cover non-financial companies across all industrial sectors. Thus, the version of the Z-Score model developed by Altman(1983) for private manufacturing and non-manufacturing firms (Z”-Score Model) is used in our testing. The literature review shows that results for Z-Score Models have been somewhat uneven in that in some studies the model has performed very well, whereas in others it has been outperformed by competing models. None of the reviewed studies is based on a comprehensive international comparison, which makes the results difficult to generalize. The analysis in this study shows that while a general international model works reasonably well, for most countries, with prediction accuracy levels (AUC) of about 75%, and exceptionally well for some (above 90%), the classification accuracy may be considerably improved with country-specific estimation especially with the use of additional variables. In some country models, the information provided by additional variables helps boost the classification accuracy to a higher level.
The purpose of this paper is firstly to review the literature on the efficacy and importance of the Altman Z-Score bankruptcy prediction model globally and its applications in finance and related areas.

I. Introduction

The first multivariate bankruptcy prediction model was developed by E.I. Altman (1968) from New York. After this pioneering work, the multivariate approach to failure prediction spread worldwide among researchers in finance, banking, and credit risk. Failure prediction models are important tools for bankers, investors, asset managers, rating agencies, and even for the distressed firms themselves. The banking industry as the main provider of financing in the economy is especially interested in minimizing the level of non-performing loans in order to maximize profit on the credit activity and reduce their own risk of default. Another issue of interest for bankers is capital adequacy and an internal ratings-based approach was encouraged by Basel 2 (first version in 1999, implemented in 2004).

The Z-Score model has become a prototype for many of these internal-rate based models. Asset manager investors need to have reliable tools for the selection of companies into their portfolios. Financial distress of the companies is on the one hand detrimental to investor returns, but on the other hand, risk may give opportunities for high returns on short-sale strategies. Rating agencies assess the risk of the entities and securities issues, thus they need to have a tool to predict default. In addition, Altman (1983, 1993 and 2006) has suggested that the management of distressed firms can utilize the Z-Score model as a guide to a financial turnaround.The approach used for bankruptcy prediction has been evolving over time. Beaver (1966, 1968) used univariate analysis for selected ratios and detected that some of them had a very good predictive power. Altman (1968) moved significantly forward since he developed a multiple discriminant analysis model (MDA) called the Z-Score Model with 5 ratios.

The next two decades brought even more financial distress research (e.g. Ohlson 1980, who used the logit model, Taffler 1984, who developed a Z-score model for the UK) which was summarized by Zmijewski (1984), who used a probit approach in his own model. Dimitras et al. (1996) reviewed 47 studies on business prediction models (of which 13 were from the US and nine from the UK). They summarized the methods used (discriminant analysis was prevailing) and the variety of ratios used.

The next summary of different approaches to credit risk analysis was given by Altman and Saunders (1998). Balcaen and Ooghe (2006) reviewed models of business failure prediction and classified 43 models presented in the literature into 4 categories (univariate model: 1, risk index models: 2, MDA models: 21, conditional probability models: 19). They omitted, however, the fast growing number of models based on the option pricing theory and contingent claims (e.g. Vassalou and Xing 2004, commercialized into the KMV model) and hazard models (e.g. Shumway 2001). Kumar and Ravi (2007) reviewed 128 statistical and artificial intelligence models for the bankruptcy prediction of banks and firms, with special attention paid to the technique used in different models, pointing out that neural networks were the most popular intelligence technique. Jackson and Wood (2013) presented in their review the frequency of the occurrence of the specific forecasting techniques in the prior literature.

The top-five popular techniques were: (1) multiple discriminant analysis, (2) the logit model, (3) neural network, (4) contingent claims and (5) univariate analysis.Recent valuable reviews on the efficacy of the models have been delivered by Agarwal and Taffler (2008), Das, Hanouna and Sarin (2009) and Bauer and Agarwal (2014), taking into account the performance of accounting-based models, market-based models and hazard models. These three types of models prevail in the finance literature. According to Agarwal and Taffler (2008) there is little difference in the predictive accuracy of accounting-based and market-based models, however the usage of accounting-based models allows for a higher level of risk-adjusted return on the credit activity. In Das, Hanouna and Sarin (2009) it was shown that accounting-based models perform comparably to the Merton structural, market-based approach for CDS spread estimation.

However, the comprehensive model which used both sources of variables outperformed both of them. In Bauer and Agarwal (2014) hazard models that use both accounting and market information (Shumway 2001 and Campbell et al. 2006) were compared with two other approaches: the accounting based z-score model that was tested in Agarwal and Taffler (2008), and a contingent claims- based model using the Bharath and Shumway (2008) approach. The hazard models were superior in UK data in bankruptcy prediction accuracy (their default probabilities were close to the observed default rates), ROC analysis, and information content.In spite of the vast research on failure prediction, the original Z-Score Model introduced by Altman (1968) has been the dominant model applied all over the world. Thus, although the Z-Score Model has been in existence for more than 45 years, it is still used as a main or supporting tool for bankruptcy or financial distress prediction or analysis, both in research and practice. Our study is focused on this classic model.

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