## Abstract

Using Ohlson’s (J Account Res 18(1):109–131, 1980) measure of bankruptcy risk (O-Score), Dichev (J Fin 53(3):1131–1147, 1998) documents a bankruptcy risk anomaly in which firms with high bankruptcy risk earn lower than average returns. This study first demonstrates that the negative association between bankruptcy risk and returns does not generalize to an alternative measure of bankruptcy risk. Then, by examining the nine individual components of O-Score, I find that funds from operations (FFO) is the only component that is associated with returns. Furthermore, I show that the return-predictive power of FFO is due to cash flows from operations. Taken as a whole, this study provides evidence that Dichev’s bankruptcy risk anomaly is a manifestation of investors’ under (over)-pricing of cash flows (accrual) component of earnings, i.e., the accrual anomaly documented by Sloan (Account Rev 71(3):289–316, 1996).

This is a preview of subscription content, log in to check access.

## Notes

- 1.
One exception is Campbell et al. (2008), who find that stocks with high bankruptcy risk have delivered low returns since 1981. Their measure of bankruptcy risk utilizes accounting information as well as market information and lies outside the scope of this study.

- 2.
The results in Houge and Loughran (2000) and Pincus et al. (2007) suggest that there may be an accrual anomaly and a cash flow anomaly and that they do not always occur together, i.e., there is no mechanical relationship going on such that if one is present, the other must also be present. Section 4.4 investigates whether the negative association between O-Score and returns would disappear when Sloan’s original accrual measure is employed.

- 3.
Unlike the Compustat Industrial File, in which all data were displayed in U.S. dollars, the Fundamental File displays data for Canadian companies (dual listed or not) using Canadian dollars.

- 4.
More precisely, Griffin and Lemmon find that the negative association between Ohlson’s (1980) measure of bankruptcy risk and subsequent returns is primarily from growth firms, suggesting that the bankruptcy risk anomaly is likely to occur as a result of a high degree of information asymmetry among growth firms. However, I repeat my analysis using small and large firms as well as growth and value firms because growth firms tend to be small and Kothari (2001) documents that evidence of market inefficiency tends to be more pronounced among small firms.

- 5.
Firms listed in AMEX or NASDAQ tend to be smaller than those in NYSE. Hence using the median of NYSE size distribution leads me to classify less than 20 % of firm-years to the subsample of large firms. Thus I employ the first quintile of NYSE size distribution. In any case, the tenor of results remains unchanged when I use the median as a size cutoff.

- 6.
The data library is available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.

- 7.
- 8.
The average annual bankruptcy rate during the period of 1980 through 2000 was 0.97 % among the industrial firms in the intersection of the CRSP and Compustat databases (Hillegeist et al. 2004, Table 1, p. 12).

- 9.
A decline of book-to-market from the second highest

*O*-*Score*decile portfolio to the highest decile portfolio is much milder in Dichev because he winsorizes all the variables at the 1st and 99th percentile, whereas I use the variables without any adjustment. I intentionally do not follow Dichev in this respect due to the concern raised by Kothari et al. (2005), who demonstrate that data deletion induces a spurious association between subsequent returns and ex ante information variables. - 10.
Note that

*BSM*-*Prob*is a measure based on market prices. If the market is not adequately anticipating bankruptcy probabilities, then*BSM*-*Prob*may not show the bankruptcy anomaly even if the anomaly exists. I cannot confirm or refute this possibility. - 11.
I include value-weighted portfolio analysis because Fama (1998) finds that, when value-weighted returns are examined, evidence of stock market inefficiency shrinks substantially and typically becomes statistically unreliable.

- 12.
- 13.
The Pearson (Spearman) correlation coefficient is −0.74 (−0.85).

- 14.
Note that cash flows from operations could be derived from reported funds from operations for observations on pre-SFAS No. 95 regime, but it is standard practice to adopt Sloan’s definitions of accruals (and cash flows from operations, if applicable) among studies that examine the accrual anomaly.

- 15.
I want to express my gratitude to an anonymous referee for raising this question.

- 16.
There are cases where the iterative process cannot solve the two equations. This occurs because of the boundary condition, which requires solutions of the equations to be positive. Accordingly, a few observations with valid data are lost; the number of lost observations is less than 0.01 % of the total number of firm-years in my sample. Thus I do not expect that this deletion will make any change in the tenor of the results.

## References

Abarbanell, J. S., & Bushee, B. J. (1998). Abnormal returns to a fundamental analysis strategy.

*The Accounting Review,**73*(1), 19–45.Alford, A. W., Jones, J. J., & Zmijewski, M. E. (1994). Extensions and violations of the statutory SEC form 10-K filing requirements.

*Journal of Accounting and Economics,**17*(1–2), 229–254.Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy.

*The Journal of Finance,**23*(4), 589–609.Anginer, D. & Yildizhan, C. (2010).

*Is there a distress risk anomaly? Corporate bond spread as a proxy for default risk*. Working paper, World Bank and University of Georgia. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1616477.Begley, J., Ming, J., & Watts, S. (1996). Bankruptcy classification errors in the 1980 s: An empirical analysis of Altman’s and Ohlson’s models.

*Review of Accounting Studies,**1*(4), 267–284.Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities.

*Journal of Political Economy,**81*(3), 637–654.Campbell, J. Y., Hilscher, J., & Szilagyi, J. (2008). In search of distress risk.

*The Journal of Finance,**63*(6), 2899–2939.Campbell, J. Y., & Vuolteenaho, T. (2004). Bad beta, good beta.

*The American Economic Review,**94*(5), 1249–1275.Chava, S., & Purnanandam, A. (2010). Is default risk negatively related to stock returns?

*The Review of Financial Studies,**23*(6), 2523–2559.Collins, D. W., & Hribar, P. (2000). Earnings-based and accrual-based market anomalies: One effect or two?

*Journal of Accounting and Economics,**29*(1), 101–123.Desai, H., Rajgopal, S., & Venkatachalam, M. (2004). Value-glamour and accruals mispricing: One anomaly or two?

*The Accounting Review,**79*(2), 355–385.Dichev, I. D. (1998). Is the risk of bankruptcy a systematic risk?

*The Journal of Finance,**53*(3), 1131–1147.Fama, E. F. (1998). Market efficiency, long-term returns, and behavioral finance.

*Journal of Financial Economics,**49*(3), 283–306.Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns.

*The Journal of Finance,**47*(2), 427–465.George, T. J., & Hwang, C. Y. (2010). A resolution of the distress risk and leverage puzzles in the cross section of stock returns.

*Journal of Financial Economics,**96*(1), 56–79.Griffin, J. M., & Lemmon, M. L. (2002). Book-to-market equity, distress risk, and stock returns.

*The Journal of Finance,**57*(5), 2317–2336.Hillegeist, S., Keating, E., Cram, D., & Lundstedt, K. (2004). Assessing the probability of bankruptcy.

*Review of Accounting Studies,**9*(1), 5–34.Houge, T., & Loughran, T. (2000). Cash flow is king? Cognitive errors by investors.

*Journal of Psychology & Financial Markets,**1*(3–4), 161–175.Hribar, P., & Collins, D. W. (2002). Errors in estimating accruals: Implications for empirical research.

*Journal of Accounting Research,**40*(1), 105–134.Kothari, S. P. (2001). Capital markets research in accounting.

*Journal of Accounting and Economics*,*31*(1–3), 105–231.Kothari, S. P., Sabino, J. S., & Zach, T. (2005). Implications of survival and data trimming for tests of market efficiency.

*Journal of Accounting and Economics,**39*(1), 129–161.Lakonishok, J., Shleifer, A., & Vishny, R. W. (1994). Contrarian investment, extrapolation, and risk.

*The Journal of Finance,**49*(5), 1541–1578.Lamont, O. A., & Thaler, R. H. (2003). Can the market add and subtract? Mispricing in tech stock carve-outs.

*Journal of Political Economy,**111*(2), 227–268.McDonald, R. L. (2002).

*Derivative markets*. Boston, MA: Addison-Wesley.Mendenhall, R. R. (2004). Arbitrage risk and post-earnings-announcement drift.

*Journal of Business,**77*(4), 875–894.Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates.

*The Journal of Finance,**29*(2), 449–470.Narayanamoorthy, G. (2006). Conservatism and cross-sectional variation in the post-earnings announcement drift.

*Journal of Accounting Research,**44*(4), 763–789.Ohlson, J. A. (1980). Financial ratios and the probabilistic prediction of bankruptcy.

*Journal of Accounting Research,**18*(1), 109–131.Pincus, M., Rajgopal, S., & Venkatachalam, M. (2007). The accrual anomaly: international evidence.

*The Accounting Review*,*82*(1), 169–203.Ritter, J. R., & Welch, I. (2002). A review of IPO activity, pricing, and allocations.

*The Journal of Finance,**57*(4), 1795–1828.Shumway, T. (2001). Forecasting bankruptcy more accurately: A simple hazard model.

*Journal of Business*,*74*(1), 101–124.Sloan, R. G. (1996). Do stock prices fully reflect information in accruals and cash flows about future earnings?

*The Accounting Review,**71*(3), 289–315.Vassalou, M., & Xing, Y. (2004). Default risk in equity returns.

*The Journal of Finance,**59*(2), 831–868.

## Acknowledgments

This study is based on a chapter of my dissertation at the University of British Columbia. I am grateful to members of my dissertation committee: Sandra Chamberlain (co-chair), Kin Lo (co-chair), and Kai Li for their guidance and direction. Also, I gratefully acknowledge Jim Ohlson (editor), an anonymous referee, Darlene Bay, Joy Begley, Larry Brown, Duane Kennedy, James Moore, Michael Shih, Dan Simunic, Samir Trabelsi, and seminar participants at Brock University, Georgia State University, McMaster University, National University of Singapore, University of Alberta, University of British Columbia, the 2010 Canadian Academic Accounting Association annual meeting, and the 2011 American Accounting Association annual meeting for helpful comments and suggestions. Any errors are my own.

## Author information

### Affiliations

### Corresponding author

## Appendices

### Appendix 1

### Estimation of Hillegeist et al.’s (2004) *BSM*-*Prob*

Hillegeist et al. (2004) modify the original option-pricing equation as follows:

where *N(d*
_{1}
*)* and *N(d*
_{2}
*)* are the standard cumulative normal distribution of *d*
_{1} and *d*
_{2}, respectively, and

and

*V*
_{
E
} is the current market value of equity; *V*
_{
A
} is the current market value of assets; *X* is the face value of debt maturing at time *T*; *r* is the continuously compounded risk-free rate; *δ* is the dividend rate expressed in terms of *V*
_{
A
}; and *σ*
_{
A
} is the standard deviation of assets returns. They make two modifications to the traditional option-pricing model. The *V*
_{
A
}
*e*
^{−δT} term accounts for the reduction in the value of the assets due to the dividends that are distributed before time T. The addition of the *(*1 − *e*
^{−δT}
*)V*
_{
A
} term is necessary because it is the equity holders who receive the dividends.

Under the BSM model, the probability of bankruptcy is simply the probability that the market value of assets, *V*
_{
A
}, is less than the face value of the liabilities, *X*, at time *T*. The BSM model assumes that the natural log of future asset values is distributed normally as follows:

where *μ* is the continuously compounded expected return on assets. Then, as shown in McDonald (2002, p. 604), the probability that *V*
_{
A
}
*(T)* < *X* is, as follows:

Equation (5) shows that the probability of bankruptcy is a function of the distance between the current value of the firm’s assets and the face value of its liabilities ln(*V*
_{
A
}
*/X*) adjusted for the expected growth in asset values (*μ* − *δ*) relative to asset volatility (*σ*
_{
A
}). Note that the value of the call option in Eq. (1) is not a function of *μ* because Eq. (1) is derived under the assumption of risk-neutrality. However, the probability of bankruptcy depends upon the actual distribution of future asset values, which is a function of *μ*.

To empirically estimate *BSM*-*Prob* from Eq. (5), the market value of assets, *V*
_{
A
}, asset volatility, *σ*
_{
A
}, and the expected return on assets, *μ*, need to be estimated because these values are not directly observable. In the first step, Hillegeist et al. (2004) estimate the values of *V*
_{
A
} and *σ*
_{
A
} by simultaneously solving Eq. (1) and the following optimal hedge equation^{Footnote 16}:

*V*
_{
E
} is set equal to the total market value of equity at the end of the firm’s fiscal year ending in calendar year *t*−1. *σ*
_{
E
} is computed using daily return data from the CRSP over the entire fiscal year ending in calendar year *t*−1. The strike price *X* is set equal to the book value of total liabilities, *T* equals one year, and *r* is the one-year Treasury bill rate. The dividend rate, *δ*, is the sum of common and preferred dividends divided by the sum of the market value of equity plus total liabilities at the end of the fiscal year. Note that all applicable accounting data are from financial statements with fiscal years ending calendar year *t*−1 so that *BSM*-*Prob* is estimated on an *ex ante* basis.

In the second step, the expected market return on assets, *μ*, is estimated based on the actual return on assets during the previous year as follows:

where *dividends* is the sum of the common and preferred dividends declared during the year. Note that this process is based on the estimates of *V*
_{
A
} that were computed in the first step. When expected returns are below the risk-free rate (above one), Hillegeist et al. (2004) set them equal to the risk-free rate (one).

### Appendix 2

### An association of a variable with a score: an econometric interpretation

Without a loss of generality, suppose that there are *n* firms and each firm has its score S, which is a linear combination of *k* components (e.g., accounting variables). Using matrices, I can express scores for *n* firms as:

where **S** = *n* × 1, **X** = *n* × *k*, and **α** = *k* × 1. Then, an association of a variable Y (e.g., returns) with the score S can be written as:

where **Y** is *n* × 1. Substituting (8) into (9), I obtain:

With respect to the numerator (**α**’**X**’**Y)**, since **α** ≠ **0**, the following holds:

The denominator (**α**’**X**’**Xα)** is nonzero as long as **X**’**X** is positive definite (i.e., rank (**X**) = k). This condition is satisfied as long as one component of the score is not a linear combination of the other components. Thus it follows that, in a regression of variable Y on X (the component of the score), the resulting coefficients is a nonzero vector:

Therefore, when there is an association between a variable and a score, it must be true that one or more components of the score have nontrivial associations with the variable, holding all other components constant.

## Rights and permissions

## About this article

### Cite this article

Kim, S. What is behind the magic of O-Score? An alternative interpretation of Dichev’s (1998) bankruptcy risk anomaly.
*Rev Account Stud* **18, **291–323 (2013). https://doi.org/10.1007/s11142-012-9206-7

Published:

Issue Date:

### Keywords

- Market efficiency
- Bankruptcy risk
- Funds from operations
- Cash flows
- Accruals

### JEL Classification

- G14
- G33
- M41