On the Relationship between Accounting
Risk and Return: Is There a
(Bowman) Paradox?
Ivan E. Brick,
1
Oded Palmon,
1
and Itzhak Venezia
2
1
Rutgers Business School – Newark and New Brunswick, Rutgers University
2
The Hebrew University and the Center for Academic Studies, Or-Yehuda, Israel
Bowman’s (1980, 1982, 1984) finding of a negative relationship between the means and variances of accounting
returns (the Bowman Paradox) spurred a considerable literature analyzing this phenomenon. The sign of the
relationship between the mean return on equity (ROE) and its standard deviation remains unresolved. Concerns
were raised about ROE measurement and statistical techniques used in establishing the paradox. The papers
critiquing (and supporting) it were mostly limited in scope, studied only short periods of time and provided limited
robustness checks. In addition, no paper considered the effect of issuances and repurchase of stocks on the
measurement of ROE. This study revisits the Paradox and addresses the above mentioned deficiencies in prior
research. We use data from longer periods, control for size and leverage and provide additional robustness checks.
We conclude that a positive relationship between mean ROE and its standard deviation is far more likely than a
negative one.
Keywords: Risk-return relationship; accounting and financial ratios; accruals; Bowman Paradox; issuances and
purchases of equity
Introduction
In his seminal papers, Bowman (1980, 1982, 1984),
surprisingly finds a negative relationship between the
mean and standard deviation of the return on equity (the
“Bowman Paradox”).
1
This finding has spurred an exten-
sive debate between its proponents and opponents. The
validity of this paradox carries great importance for
practitioners as well as academics in the accounting and
strategy areas. The accounting literature since Ball and
Brown (1968, 1969), has argued that accounting data
convey information that should be reflected in stock
prices.
2
Being one of the more prominent accounting
ratios used to measure profitability, one would expect a
positive risk-return relationship in the return on equity
(ROE), similar to that observed in stock returns.
3
A
negative correlation between risk and return of account-
ing profitability measures may therefore cast doubt on
how well they represent financial information.
This Paradox has also challenged researchers to put
forth managerial theories that attempt to explain it and to
explore its managerial implications. Indeed the challenge
was met with extensive research (in their review, Nickel
and Rodriguez, 2002, cite about 40 papers), most of
which comes from researchers in the strategy, behavior,
or management branches of business administration.
4
Along with the support, the Paradox has been subject
also to heavy criticism, mainly arguing that it can be
Correspondence: Ivan E. Brick, Rutgers Business School – Newark and
New Brunswick, Rutgers University, 1 Washington Park, Newark, NJ
07102, USA. E-mail: ibrick@andromeda.rutgers.edu
1
Risk and return in these studies are measured, respectively, as
the ex-post volatility and average of the ROE.
2
However, Lev (1989) does not find a statistical relationship
between accounting earnings and stock returns. He argues that
one reason for the lack of statistical power of earnings is that the
accounting measures used in empirical tests do not accurately
reflect expected returns.
3
Financial theories argue that risk and return on stocks are posi-
tively related (see, for example, Brealey et al., 2008, and Ross
et al., 2011). These theories, however, do not require accounting
measures to also carry this property.
4
The original explanation of Bowman (1980), for the paradox is
that losing firms take higher risks to escape their hardship. We
elaborate on further explanations in the literature review below.
European Management Review, Vol. 12, 99–111 (2015)
DOI: 10.1111/emre.12045
© 2015 European Academy of Management