Review of Accounting Studies, 9, 5–34, 2004
# 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Assessing the Probability of Bankruptcy
STEPHEN A. HILLEGEIST* firstname.lastname@example.org
Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Room 6223, Evanston,
ELIZABETH K. KEATING
Kennedy School of Government, Harvard University, Littauer 115, 79 JFK St., Cambridge, MA 02138
DONALD P. CRAM
College of Business and Economics, California State University, Fullerton, 800 N. State College Blvd.,
LH-360, Fullerton, CA 92834
KYLE G. LUNDSTEDT
VaRisk, Inc., 116 Lyon St., San Francisco, CA 94117
Abstract. 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.
Keywords: bankruptcy prediction, option-pricing models, Z-Score, O-Score
JEL Classiﬁcation: M41, G1, C41, C52
Academics in the ﬁelds of accounting and ﬁnance have actively studied bankruptcy
prediction since the work of Beaver (1966, 1968) and Altman (1968). With few
exceptions, this literature has relied on accounting-based measures as the predictor
variables. More recent studies have used proxies for the probability of bankruptcy
(PB) as an independent variable rather than as the dependent variable. These latter
studies frequently obtain their PB proxies from the existing bankruptcy prediction
literature, and hence, have relied on accounting-based measures. Many of these
studies have used composite measures that statistically combine several different
accounting variables, with Altman’s (1968) Z-Score and an O-Score derived from
Ohlson’s (1980) Model 1 being the most popular.
This paper assesses the
performance of these accounting-based composite measures in explaining the
cross-sectional variation in the actual probability of bankruptcy.
We compare their
performance to a market-based PB measure that is derived from the Black–Scholes–
Merton option-pricing model.