A study shows that when the number 4 doesn’t show up as often as the first digit after a decimal point, it could be a red flag about earnings, according to an article in The Wall Street Journal. Unusually low rates of the number 4 in that first digit spot could indicate that a company is propping up its results by a 10th of cent everywhere it can. While that might seem like much, it could potentially increase earnings per share by a full cent—a substantial rounding up, as a manipulation of 13.4 cents earnings to 13.5 cents can be reported as 14 cents earnings per share. The study, which was conducted by Nadya Malenko of University of Michigan with Joseph Grundfest at Stanford University and Yao Shen from Baruch College, calls this phenomenon “quadrophobia.” While managers are motivated to round up where they can, doing so too aggressively could result in violations.
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Using Compustat data, the researchers analyzed a sample of over 15,000 companies and found that the number 4 was significantly underrepresented in the 10th spot, appearing only 8.7% of the time. If the company had analyst coverage, the number 4 showed up 8.2% of the time, though when the rounding offered companies the chance to meet or beat expectations, representation dropped to only 7.2% of the time. That bears the question of whether managers were reworking their numbers in order to push their earnings per share higher. And 4 wasn’t the only underrepresented number; 2 and 3 were as well, while 5, 6, 7, 8, and 9 were overrepresented, the article reports.
The study also found that there was a correlation between quadraphobia and the companies that were more likely to be forced to redo their financial statements, be sued in securities-fraud cases, and be listed as defendants in SEC violations. In addition, quadraphobia appeared more significant at companies where upper management’s compensation depends on stock price. “Overall, quadrophobia appears to signal an aggressive financial reporting culture,” Dr. Malenko told The Journal. And the study’s findings are in line with other research that shows that managers’ incentives influence the reporting and disclosure choices they make.
And while investors might miss the manipulated rounding in the short-term, over the long run they generally catch on; companies that match or exceed their earnings expectations thanks to rounding up then go on to underperform companies that round down three, six, and twelve months out. It could be that “rounding up firms experience a deterioration of their overall performance,” in the wake of the manipulation, the researchers contend, but investors would be wise to look for the number 4 in their portfolio’s earnings reports.
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