Don’t Fear the Four
November 13, 2023You’ve heard of claustrophobia, agoraphobia, and arachnophobia. Now there’s quadrophobia: fear of the number four.
Yao Shen, PhD, Bert W. Wasserman Department of Economics and Finance
According to a paper co-authored by Assistant Professor Yao Shen, PhD (Bert W. Wasserman Department of Economics and Finance), and published in the Journal of Financial and Quantitative Analysis, financial firm managers have an incentive to round up data on earnings per share (EPS) because of how numbers are conventionally rounded. EPS data is rounded to the nearest cent, with half-cent (.5) earnings rounded up and earnings of less than a half-cent rounded down. Thus if EPS is 13.4 cents, for example, it would normally be rounded down to 13 cents. But if managers increase EPS by just a tenth of a cent to 13.5, that manipulation results in a full one-cent increase in total earnings.
Dr. Shen and her co-authors found that the incidence of “quadrophobia,” as they term the under-representation of the number four in the first post-decimal digit in EPS data, is higher when executive compensation is more closely linked to the firm’s stock price. They further found that quadrophobia can be used to predict the likelihood that a firm will be named as defendants in SEC Accounting and Auditing Enforcement Releases and be sued in class-action securities fraud litigation.