A recent study finds that, as a general matter, forecasts from stock analysts of corporate earnings in which the numbers are rounded to the nearest zero or five not only prove to be significantly more inaccurate than those that strive for penny precision, but turn out to be significantly more upwardly biased as well.

The sharpest differences in both respects occur in companies with annual earnings per share of less than $10.

According to the laws of probability, numbers ought to end with the digit zero 10 percent of the time. But in stock analysts’ forecasts of annual corporate earnings, zero occupies that final slot about 26 percent of the time, more than two and a half times what would randomly be expected, while zeros and fives together account for almost half the final digits.

In an era when a stock can take a beating if earnings fall a penny short of analysts' predictions, the study tried to determine which factors influence whether forecasters seek precision to the penny or round off, and how their choice affects investors.

The new research, by Patricia M. Dechow of the University of California, Berkeley and Haifeng You of the Hong Kong University of Science and Technology, finds that rounded estimates for firms with earnings per share of less than a dollar (amounting to about 26 percent of the sample) are on average about 70 percent more inaccurate than unrounded ones and almost 125 percent more upwardly biased. For companies with annual earnings per share between $1 and $10 (accounting for about 61 percent of the study's total sample), rounded estimates are on average about 40 percent more inaccurate and 68 percent more upwardly biased than those that are unrounded.

The study appears in the November/December issue of the American Accounting Association journal The Accounting Review.

The study also finds that the market takes rounding into account in its response to analysts' forecasts, with investors responding less to earnings surprises when forecasts were rounded than when they were not. Investors also anticipate the upward bias of rounded forecasts, though not fully.

Given the importance that attaches to forecast accuracy in contemporary markets, previous research on rounding has sought the reasons for rounding in limitations of the stock pickers and their resources. It found that analysts who rounded tended to work for small brokerage firms, to have relatively poor prior records of accuracy, to update their forecasts only infrequently, to have long forecast horizons, and to follow an above-average number of firms from multiple industries.

The new research confirms these findings, and interestingly also corroborates the counterintuitive earlier discovery that experienced analysts tend to round more often than less seasoned colleagues, perhaps "because they are compensated less for accuracy as their tenure with the firm increases."

But individual characteristics of the analysts, the new study finds, have only one third the explanatory power for rounding that the firms being analyzed have, through company features that motivate precision-seeking as opposed to rounding.

In the words of the study, "Analyst incentives impact the likelihood of rounding....Analysts can choose to be less informed about a particular stock and this choice affects how certain they feel about their forecasts, and, as a consequence, their decision to round...Analysts have limited time and so will rationally focus their forecasting efforts on firms for which the benefits of doing so are the highest."

As to which firms yield the most benefits, the study identifies the following firms:

Firms whose earnings per-share number is relatively small
Approximately 34 percent of forecasts are rounded when annual EPS is a dollar or less, in contrast to 49 percent when it is from $1 to $10 and 60% when it is from $10 to $100. According to the authors, "As the level of EPS increases (1) the economic importance of the penny digit declines and so is less relevant to investors, and (2) the precision of the analyst's information is not as likely to hold to the penny."

Firms with high stock-trading volume
The authors explained that a high-volume stock "offers greater opportunities for trades to pass through the brokerage division. Analysts who provide more informative research are likely to generate more trading business, and this can benefit the analyst...In contrast, low trading volume offers fewer brokerage fee opportunities."

Growth companies
Although assessing the prospects of growth firms "requires the analyst to exert effort and incur higher information-gathering costs to determine potential future opportunities...investors are also more interested in growth companies because of the greater potential gains, and this creates an increased demand for analyst guidance...Low-growth firms are likely to be less lucrative for the employers of analysts, and so we expect less forecasting effort."

Companies that offer investment-banking business opportunities
Although it might be assumed (and, in fact, has been assumed by regulators) that the potential to procure investment-banking business for their employers leads analysts to inflate the prospects of a stock, the study finds that it inspires the extra effort required of precise forecasts. In the words of the study, "Firms that are raising financing frequently select the investment bank that has a favorable analyst following the firm to underwrite the deal. Understanding this relation, an analyst who is covering a firm that is likely to need financing is likely to exert more effort in forecasting [and will be] less likely to round forecasts."

Small companies or those with few business segments
The tendency to round increases with company size and complexity. In the words of the study, "larger firms are more complex than small firms, making them more difficult to analyze and value. In addition, if an analyst does provide an informative report, then this information is likely to be quickly dispelled among market participants and not necessarily captured by the analysts' brokerage division." As for number of segments, "companies with complicated business models require more effort to understand and therefore impose more costs on analysts...Controlling for firm size, firms with more business segments will have more rounded forecasts."

What practical lessons can investors derive from the study? "Generally to be a little wary of rounded analyst forecasts, particularly for small companies or high-growth firms with heavily traded stocks (especially if they're likely to want to raise money soon) or simply companies with low earnings per share,” Dechow said. “Those are all characteristics that should motivate precise forecasts. If they don't, it could very well be a tip-off to hurried or cursory analysis."

Entitled "Analysts' Motives for Rounding EPS Forecasts," the study appears in the November/December issue of The Accounting Review, published six times a year by the American Accounting Association, a worldwide organization devoted to excellence in accounting education, research and practice.

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