Rounding off numbers to zero or five for earnings forecasts can help to simplify and communicate their value, but it is not the most accurate form of measurement. Previous research has suggested that analysts who round off are less informed than other analysts. Patricia M Dechow and Haifeng You suggest that is only part of the story. They extended the literature and found that rounded forecasts are not only less accurate but also significantly more upwardly biased. Furthermore, they also show that analyst incentives impact the likelihood of rounding and analysts may choose to be less informed.

“Given that earnings per share is a widely used input in equity valuation and investment decision making, it would seem the economic importance of a precise forecast would dwarf the benefits of providing a rounded number that is easy to remember,” they said.

However, “analysts may rationally decide not to provide a forecast precise to the penny even when the information to help them do so is readily available because exerting effort on this would be costly to them. They have limited time and so they will rationally focus forecasting efforts on firms in which the benefits from doing so are highest.”

This was confirmed in tests on more than 800,000 analyst forecasts from 1984-2009, in which 46.30 per cent were rounded to zero or five. The authors identified several scenarios that led to rounding.

First, as the magnitude of earnings per share increased, the precise penny figure became more difficult and therefore more costly to forecast and it was also seemingly less important. So while 34 per cent of forecasts priced below $1 were rounded, some 60 per cent of those priced between $10 and $100 were rounded.

Compensation also came into play. Analysts were more likely to round for firms that generated less brokerage fees since there was less benefit in exerting additional effort to find a precise figure. On the other hand, they exerted more effort in forecasting earnings for firms that had potential investment banking clients who could generate revenue for the analyst’s employer, or firms that were raising more external financing.

Analysts were also more likely to round when firms were larger and more complex, since these required greater effort.

Interestingly for investors, rounding tended to skew in one direction. “Our results suggest rounded forecasts are more optimistically biased than other forecasts. When analysts round, they tend to round up,” the authors said.

The findings offer strong evidence that firm characteristics are driving rounding off even more strongly than analyst characteristics which had been the focus of previous studies.

For investors, that means some caution is in order.

One implication of rounding is that it provides more “noisy” information on stocks. “If investors understand that rounded forecasts contain more noise, then they should place a lower weight on these forecasts in forming their expectations. Our results are consistent with this prediction as rounded forecasts had lower earnings response coefficients than other forecasts,” the authors said.

But investors did not fully adjust to the optimistic bias in earnings expectations found in rounded forecasts. “On average, rounded forecasts had a small but significantly lower announcement return than other forecasts. This suggests the optimistic bias in rounded forecasts may not be always fully anticipated by investors,” they said.