Review of Accounting Studies

, Volume 9, Issue 1, pp 5–34 | Cite as

Assessing the Probability of Bankruptcy

  • Stephen A. HillegeistEmail author
  • Elizabeth K. Keating
  • Donald P. Cram
  • Kyle G. Lundstedt


We assess whether two popular accounting-based measures, Altman’s (1968) Z-Score and Ohlson’s (1980) O-Score, effectively summarize publicly-available information about the probability of bankruptcy. We compare the relative information content of these Scores to a market-based measure of the probability of bankruptcy that we develop based on the Black–Scholes–Merton option-pricing model, BSM-Prob. Our tests show that BSM-Prob provides significantly more information than either of the two accounting-based measures. This finding is robust to various modifications of Z-Score and O-Score, including updating the coefficients, making industry adjustments, and decomposing them into their lagged levels and changes. We recommend that researchers use BSM-Prob instead of Z-Score and O-Score in their studies and provide the SAS code to calculate BSM-Prob.

bankruptcy prediction option-pricing models Z-Score O-Score 


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  1. Altman, E. (1968). “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy.” Journal of Finance 23, 589–609.Google Scholar
  2. Barth, M., W. Beaver and W. Landsman. (1998). “Relative Valuation Roles of Equity Book Value and Net Income as a Function of Financial Health.” Journal of Accounting and Economics 25, 1–34.Google Scholar
  3. Beaver, W. (1966). “Financial Ratios as Predictors of Bankruptcy.” Journal of Accounting Research 6, 71–102.Google Scholar
  4. Beaver, W. (1968). “Market Prices, Financial Ratios, and the Prediction of Failure.” Journal of Accounting Research 8, 179–192.Google Scholar
  5. Beck, N., J. Katz and R. Tucker. (1998). “Taking Time Seriously: Time-Series-Cross-Section Analysis with a Binary Dependent Variable.” American Journal of Political Science 42, 1260–1288.Google Scholar
  6. Begley, J., J. Ming and S. Watts. (1996). “Bankruptcy Classification Errors in the 1980's: An Empirical Analysis of Altman's and Ohlson's Models.” Review of Accounting Studies 1, 267–284.Google Scholar
  7. Berger, P., E. Ofek and I. Swary. (1996). “Investor Valuation of the Abandonment Option.” Journal of Financial Economics 42, 257–287.Google Scholar
  8. Billings, B. (1999). “Revisiting the Relation between the Default Risk of Debt and the Earnings Response Coefficient.” Accounting Review 74:4, 509–522.Google Scholar
  9. Black, F. and J. Cox. (1976). “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions.” Journal of Finance 31:2, 351–367.Google Scholar
  10. Black, F. and M. Scholes. (1973). “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 7, 637–654.Google Scholar
  11. Burgstahler, D., J. Jiambalvo and E. Noreen. (1989). “Changes in the Probability of Bankruptcy and Equity Value.” Journal of Accounting and Economics 11, 207–224.Google Scholar
  12. Campbell, J., M. Lettau, B. Malkiel and Y. Xu. (2001). “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk.” Journal of Finance 56:1, 1–43.Google Scholar
  13. Cheung, J. (1991). “A Review of Option-Pricing Theory in Accounting Research.” Journal of Accounting Literature 10, 51–84.Google Scholar
  14. Core, J. and C. Schrand. (1999). “The Effect of Accounting-Based Debt Covenants on Equity Valuation.” Journal of Accounting and Economics 27:1, 1–34.Google Scholar
  15. Dambolena, I. and S. Khoury. (1980). “Ratio Stability and Corporate Failure.” Journal of Finance 35:4, 1017–1026.Google Scholar
  16. Delaney, K. (1992). Strategic Bankruptcy. Berkeley, CA: University of California Press.Google Scholar
  17. Dhaliwal, D., K. Lee and N. Fargher. (1992). “The Association between Unexpected Earnings and Abnormal Security Returns in the Presence of Financial Leverage.” Contemporary Accounting Research 8, 20–41.Google Scholar
  18. Dhaliwal, D. and S. Reynolds. (1994). “The Effect of the Default Risk of Debt on the Earnings Response Coefficient.” Accounting Review 69:2, 412–419.Google Scholar
  19. Dichev, I. (1998). “Is the Risk of Bankruptcy a Systematic Risk?” Journal of Finance 53:3, 1131–1147.Google Scholar
  20. Fama, E. and K. French. (1997). “Industry Costs of Equity.” Journal of Financial Economics 43:2, 153–193.Google Scholar
  21. Francis, J. (1990). “Corporate Compliance with Debt Covenants.” Journal of Accounting Research 28, 326–347.Google Scholar
  22. Geske, R. (1977). “The Valuation of Corporate Liabilities as Compound Options.” Journal of Financial and Quantitative Analysis 12:4, 541–552.Google Scholar
  23. Griffin, J. and M. Lemmon. (2002). “Book-to-Market Equity, Distress Risk, and Stock Returns.” Journal of Finance 57:5, 2317–2336.Google Scholar
  24. Han, B., R. Jennings and J. Noel. (1992). “Communication of Nonearnings Information at the Financial Statements Release Date.” Journal of Accounting and Economics 15:1, 63–86.Google Scholar
  25. Lo, A. (1986). “Logit versus Discriminant Analysis: A Specification Test and Application to Corporate Bankruptcies.” Journal of Econometrics 31, 151–178.Google Scholar
  26. Lys, T. (1984). “Mandated Accounting Changes and Debt Covenants: The Case of Oil and Gas Accounting.” Journal of Accounting and Economics 7, 39–65.Google Scholar
  27. McDonald, R. (2002). Derivative Markets. Boston, MA: Addison Wesley.Google Scholar
  28. McFadden, D. (1976). “A Comment on Discriminant Analysis versus Logit Analysis.” Annals of Economic and Social Measurement 5, 511–523.Google Scholar
  29. Merton, R. (1974). “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance 29, 449–470.Google Scholar
  30. Ohlson, J. (1980). “Financial Ratios and the Probabilistic Prediction of Bankruptcy.” Journal of Accounting Research 19, 109–131.Google Scholar
  31. Opler, T. and S. Titman. (1994). “Financial Distress and Corporate Performance.” Journal of Finance 49:3, 1015–1040.Google Scholar
  32. Palepu, K. (1986). “Predicting Takeover Targets: A Methodological and Empirical Analysis.” Journal of Accounting and Economics 8, 3–35.Google Scholar
  33. Platt, H. and M. Platt. (1991). “A Note on the Use of Industry-Relative Ratios in Bankruptcy Prediction.” Journal of Banking and Finance 15, 1183–1194.Google Scholar
  34. Rogers, W. (1993). “Regression Standard Errors in Clustered Samples.” Stata Technical Bulletin 13, 88–94.Google Scholar
  35. Sharpe, W. (1982). “Factors in New York Stock Exchange Security Returns.” Journal of Portfolio Management 8:4, 5–19.Google Scholar
  36. Shumway, T. (2001). “Forecasting Bankruptcy More Accurately: A Simple Hazard Model.” Journal of Business 74:1, 101–124.Google Scholar
  37. Sloan, R. (1996). “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows About Future Earnings?” Accounting Review 71:3, 289–315.Google Scholar
  38. Stone, M. (1991). “Firm Financial Stress and Pension Plan Continuation/Replacement Decisions.” Journal of Accounting and Public Policy 10, 175–206.Google Scholar
  39. Subramanyam, K. and J. Wild. (1996). “The Going Concern Assumption and the Informativeness of Earnings.” Contemporary Accounting Research 13, 251–274.Google Scholar
  40. Vassalou, M. and Y. Xing. (2004). “Default Risk in Equity Returns.” Journal of Finance 59:2, April 2004.Google Scholar
  41. Vuong, Q. (1989). “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses.” Econometrica 57:2, 307–333.Google Scholar
  42. Warren, S. (2003). “Asbestos Quagmire.” Wall Street Journal Jan. 27, B1.Google Scholar
  43. Zmijewski, M. (1984). “Methodological Issues Related to the Estimation of Financial Distress Prediction Models.” Journal of Accounting Research Supplement, 59–86.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Stephen A. Hillegeist
    • 1
    Email author
  • Elizabeth K. Keating
    • 2
  • Donald P. Cram
    • 3
  • Kyle G. Lundstedt
    • 4
  1. 1.Kellogg School of ManagementNorthwestern UniversityEvanston
  2. 2.Kennedy School of GovernmentHarvard UniversityCambridge
  3. 3.College of Business and EconomicsCalifornia State UniversityFullerton
  4. 4.VaRisk, Inc.San Francisco

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