On the Relationship between Accounting Risk and Return: Is There a (Bowman) Paradox?

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.