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  • J.B. Heaton

Altman Z-Score Does Not Predict Bankruptcy

In this post, I show that the Altman Z-Score does not predict bankruptcy. In a large sample of U.S. publicly traded firms from 2010-2018, the Altman Z-Score shows no ability to classify firms accurately into those that will and will not file for bankruptcy in the next one or two years.

Bankruptcy prediction is a binary classification problem. The goal is to classify a set of firms into those that will file for bankruptcy protection within some given period of time (say one or two years) and those that will not. Early work[1] tended to study whether firms that fail had bad financial ratios. This work was suggestive but not predictive. We are not so much interested in the likelihood of having bad financial ratios given failure; we are interested in the likelihood of failure given bad financial ratios or other data.

The bankruptcy prediction problem is made more complicated by the fact that the decision to file for bankruptcy is not a simple function of any particular variable. For example, it often is easy to determine whether a particular company is or is not insolvent at a particular point in time if publicly-traded equity and debt prices are available. Insolvency, however, does not itself necessitate a bankruptcy filing.

Perhaps the best-known bankruptcy prediction model is that created by Edward I. Altman.[2] Altman (1968) sought to advance bankruptcy prediction by using discriminant analysis – a statistical classification method – to optimally weight multiple financial ratios that might predict bankruptcy. Altman engaged in a data mining exercise to find a linear combination of five financial ratios: (1) working capital/total assets; (2) retained earnings/total assets; (3) earnings before interest and taxes/total assets; (4) market value equity/book value of total debt; and (5) sales/total assets.

Altman claimed great success in distinguishing firms that would become bankrupt from those that would not, but the success of his method was only in distinguishing a hand-picked number (33 in his 1968 paper) of bankrupt firms from an equal number of industry- and size-matched non-bankrupt firms. This dramatically but unrealistically simplified the classification problem. It is relatively easy to distinguish bankrupt from non-bankrupt firms when the number of each kind of firms is the same. The real problem is to classify firms in a world where far fewer than 50% of firms go bankrupt.

Scholars criticized Altman’s work on this ground almost from the start. As one author wrote in 1970 in the Journal of Finance, the Altman Z-scores were “largely descriptive statements devoid of predictive content ... Altman demonstrates that failed and non-failed firms have dissimilar ratios, not that ratios have predictive power. But the crucial problem is to make an inference in the reverse direction, i.e., from ratios to failures.”[3] Despite criticisms of the Altman Z-Score – and largely as a result of Altman’s promotion of his method – the method remains in use among credit analysts and insolvency practitioners.


All data is from Bloomberg Terminal. The set of publicly traded firms starts with the Russell 3000 firms for each year end 2010 to 2018. I then require that each firm have data available for the following variables: total liabilities, total stock market return for the year, year-end stock price, year-end market cap, one year historical volatility, short interest ratio (ratio of shares short to total shares), and the Altman Z-Score. I remove financial institutions (banks and insurers) from the sample since the Altman Z-Score is not designed for such firms and since such some firms are likely not subject to bankruptcy being considered “too big to fail,” including JPMorgan Chase, Citigroup, Bank of America, Goldman Sachs, Wells Fargo, Bank of New York Mellon, Morgan Stanley, State Street. I obtain bankruptcy dates three sources: (1) Bloomberg Terminal; (2) the UCLA-LoPucki Bankruptcy Research Database,[4] and (3) searches on sec.gov for firms that are shown with a “Q” ticker designation on Bloomberg but do not otherwise appear in the two previous sources. The final dataset contains 17,307 firm-year observations. There are 69 bankruptcies in the sample, reflecting the serious “class imbalance” problem in bankruptcy detection: far more firms do not go bankrupt that do.

Evaluation of the Altman Z-Score

The inability of the Altman Z-Score to predict bankruptcy within 2 years is reflected in Figures 1-3 below. Each figure is a scatterplot of the incidence of bankruptcy or non-bankruptcy and the Altman Z-Score ("AZS"). A "1" indicates a bankruptcy filing within the time period and a "0" indicates no bankruptcy filing within that period. Figure 1 plots filings within 1 year against AZS. The range of bankruptcy filings within 1 year has a relatively small range of Z-Scores, but as Table 1 shows, these firms do not have the worst Z-Scores, nor does the range of Z-Scores they exhibit distinguish firms that will file for bankruptcy in one year versus those that will not.

Figure 1

Table 1

Figures 2 and 3 show the same problem for predicting bankruptcy in 2 years (Figure 1) but later than 1 year and in predicting a bankruptcy within 2 years (Figure 3). In each case, the range of bankruptcy filings within 1 year has a relatively small range of Z-Scores, but as Table 1 shows, these firms do not have the worst Z-Scores, nor does the range of Z-Scores they exhibit distinguish firms that will file for bankruptcy in one year versus those that will not.

Figure 3

Table 2 breaks down the serious misclassification problem of the AZS. The traditional predictive breakpoint for a 2-year bankruptcy prediction is around 2 (1.81 in the 1968 paper) where a score below that breakpoint is a bankruptcy predictor. Table 2 shows, however, that 98% of firms with AZS < 2.0 do not file for bankruptcy within 2 years. Even Z < 0 cannot predict bankruptcy, assigning that score to firms where - in this large sampling - over 96% of firms with Z < 0 do not file for bankruptcy within 2 years.

Table 2

Why the AZS Fails

Our research finds that the AZS lacks predictive ability because it does not capture market information. Only one variable in the AZS - market value of equity/book value of total debt - introduces any market evidence. This signal is very weak, however, both because book value of debt overstates market value of debt for distressed firms and because other market information is far more important in creating a predictive bankruptcy model. In OLS and probit models, for example, the AZS is not statistically significant when introduced in models with better feature generation using market variables.


[1] Beaver, W.H. 1966. Financial Ratios as Predictors of Failure. Journal of Accounting Research, 1966, 71-111. Beaver, W.H. 1968. Market Prices, Financial Ratios, and the Prediction of Failure. Journal of Accounting Research, 6(2), 179-192. One early author recognized the problem, but his work was largely overlooked. See Tamari, M. 1966. Financial Ratios as a Means of Forecasting Bankruptcy. Management International Review, 6(4), 15-21.

[2] E.I. 1968. Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. Journal of Finance, 23(4), 589-609.

[3] Johnson, C.G. 1970. Ratio Analysis and the Prediction of Firm Failure. Journal of Finance, 25(5), 1166-1168.) Altman's defense was unpersuasive. Altman, E.I. 1970. Ratio Analysis and the Prediction of Firm Failure: A Reply. Journal of Finance, 25(5), 1169-1172. A number of later papers followed Beaver and Altman into the same error. See, for example, Deakin, E.B. 1972. A Discriminant Analysis of Predictors of Business Failure. Journal of Accounting Research, 10(1), 167-179; Wilcox, J.W. 1973. A Prediction of Business Failure Using Accounting Data. Journal of Accounting Research, 11, 163-179.

[4] See https://lopucki.law.ucla.edu/.

A Sampling of Additional Relevant Research Bankruptcy Prediction Research Not Cited Above (Chronological):

Moyer, R.C. 1977. Forecasting Financial Failure. Financial Management, 6(1), 11-17.

Altman, E.I. 1978. Examining Moyer's Re-Examination of Forecasting Financial Failure. Financial Management, 7(4), 76-79.

Altman, E.I. and R.A. Eisenbeis. 1978. Financial Applications of Discriminant Analysis: A Clarification. Journal of Financial and Quantitative Analysis, 13(1), 185-195.

Largay, III, J.A., and C. Stickney. 1980. Cash Flows, Ratio Analysis and the W.T. Grant Company Bankruptcy. Financial Analysts Journal, 36(4), 51-54.

Zimmer, I. 1980. A Lens Study of the Prediction of Corporate Failure by Bank Loan Officers. Journal of Accounting Research, 18(2), 629-636.

Altman, E.I. and J. Spivack. 1983. Prediction Bankruptcy: The Value Line Relative Financial Strength System v. the Zeta(R) Bankruptcy Classification Approach. Financial Analysts Journal, 39(6), 60-67.

Zmijewski, M.E. 1984. Methodological Issues Related to the Estimation of Financial Distress Prediction Models. Journal of Accounting Research, 22, 59-82.

Casey, C. and N. Bartczak. 1985. Using Operating Cash Flow to Predict Financial Distress: Some Extensions. Journal of Accounting Research, 23(1), 384-405.

Gentry, J.A., P. Newbold, and D.T. Whitford. 1985. Predicting Bankruptcy: If Cash Flow's Not the Bottom Line, What Is? Financial Analysts Journal, 41(5), 47-56.

Shaked, I. 1985. Measuring Prospective Probabilities of Insolvency: An Application to the Life Insurance Industry. Journal of Risk and Insurance, 52(1), 59-80.

Chiang, R. 1987. Some Results on Bond Yield and Default Probability. Southern Economic Journal, 53(4), 1037-1051.

Gombola, M.J., M.E. Haskins, J.E. Ketz, and D.D. Williams. 1987. Cash Flow in Bankruptcy Prediction. Financial Management, 16(4), 55-65.

Lau, A.H-L. 1987. A Five-State Financial Distress Prediction Model. Journal of Accounting Research, 25(1), 127-138.

Zavgren, C.V. and G.E. Friedman. 1988. Are Bankruptcy Prediction Models Worthwhile? Management International Review, 28(1), 34-44.

Tam, K.Y. and M.Y. Kiang. 1992. Managerial Applications of Neural Networks: The Case of Bank Failure Predictions. Management Science, 38(7), 926-947.

Shumway, T. 2001. Forecasting Bankruptcy More Accurately: A Simple Hazard Model. Journal of Business, 74(1), 101-124.

Kealhofer, S. 2003. Quantifying Credit Risk I: Default Prediction. Financial Analysts Journal, 59(1), 30-44.

Jones, S. and D.A. Hensher. 2004. Predicting Firm Financial Distress: A Mixed Logit Model. Accounting Review, 79(4), 1011-1038.

Hanson, S. and T. Schuermann. 2006. Confidence Intervals for Probabilities of Default. Journal of Banking & Finance, 30, 2281-2301.

Duffie, D., L. Saita, and K. Wang. 2007. Multi-Period Corporate Default Prediction with Stochastic Covariates. Journal of Financial Economics, 83, 635-665.

Campbell, J.Y., J. Hillscher, and J. Szilagyi. 2008. In Search of Distress Risk. Journal of Finance, 63(6), 2899-2939.

Blochinger, A. 2012. Validation of Default Probabilities. Journal of Financial and Quantitative Analysis, 47(5), 1089-1123.

Duan, J-C, J. Sun, and T. Wang. 2012. Multiperiod Corporate Default Prediction - A Forward Intensity Approach. Journal of Econometrics, 170, 191-209.

Atkeson, A.G., A.L. Eisfeldt, and P-O Weill. 2017. Measuring the Financial Soundness of U.S. Firms: 1926-2012. Research in Economics, 71, 613-635.

Jovan, M. and A. Ahcan. 2017. Default Prediction with the Merton-Type Structural Model Based on the NIG Levy Process. Journal of Computational and Applied Mathematics, 311, 414-422.

Mare, D.S., F. Moreira, R. Rossi. 2017. Nonstationary Z-Score Measures. European Journal of Operations Research, 260, 348-358.

Duan, J-C., B. Kim, W. Kim, and D. Shin. 2018. Default Probabilities of Privately Held Firms. Journal of Banking and Finance, 94, 235-250.

Le, T., M.Y. Lee, J.R. Park, and S.W. Baik. 2018. Oversampling Techniques for Bankruptcy Prediction: Novel Features from a Transaction Data Set. Symmetry, 10.

Miao, H., S. Ramchander, P. Ryan, and T. Wang. 2018. Default Prediction Models: The Role of Forward-Looking Measures of Returns and Volatility. Journal of Empirical Finance, 46, 146-162.

Agrawal, K. and Y. Maheshwari. 2019. Efficacy of Industry Factors for Corporate Default Prediction. IIMB Management Review, 31, 71-77.

Li, L. and R. Faff. 2019. Predicting Corporate Bankruptcy: What Matters? International Review of Economics and Finance, 62, 1-19.

Son, H., C. Hyun, D. Phan, and H.J. Hwang. 2019. Data Analytic Approach for Bankruptcy Prediction. Expert Systems with Applications, 138.