The paper is titled Quadrophobia due to management's apparent fear/avoidance of the number "4" as the third decimal in its earnings per share (EPS) reports. If the third decimal number is a four, the EPS number gets rounded down. The paper's authors scoured the universe of US public financial statements, however, and found that the number four (when dividing income by weighted average shares outstanding) is absent as the third decimal number by a statistically significant amount.
Why might this be the case? When management is close to rounding up its EPS number to the nearest penny (and having a four as the third decimal is as close as you can get), it will make the accounting adjustments it needs to in order to get there. Of course, not all companies engage in this sort of practice. But the authors found that the incidences of quadrophobia increase for companies that gain analyst coverage and where earnings come in close to analysts forecasts. Startlingly, the authors also found that persistent quadrophobes actually turn out to be more likely to be sued by the SEC!
What can the investor do with this knowledge? For one thing, it should reinforce the notion that one should not buy/sell a company if it beats/misses short-term earnings by a few pennies here and there. One might be tempted to check the third decimal of the companies in one's portfolio, but unfortunately even if the number four is absent from these calculations, the results for any one company would not be significant enough to draw any conclusions. As a whole, using EPS as a measure of a company's health has some definite drawbacks, and so investors would be wise to focus on other measures.