Small numbers are processed on a linear scale, while large numbers are processed on a logarithmic one. Due to this, financial analysts are more optimistic about small price stocks than about large price stocks even after controlling for differences in risk factors

Behavioral bias in number processing: Evidence from analysts’ expectations. Tristan Roger, Patrick Roger, Alain Schatt. Journal of Economic Behavior & Organization, Volume 149, May 2018, Pages 315-331. https://doi.org/10.1016/j.jebo.2018.02.026

Highlights

•    Research in neuropsychology shows that the human brain processes small and large numbers differently.
•    Small numbers are processed on a linear scale, while large numbers are processed on a logarithmic scale.
•    We show that financial analysts process small prices and large prices differently.
•    Analysts are more optimistic about small price stocks than about large price stocks even after controlling for differences in risk factors.
•    A deeply-rooted behavioral bias in number processing drives analysts return expectations.

Abstract: Research in neuropsychology shows that individuals process small and large numbers differently. Small numbers are processed on a linear scale, while large numbers are processed on a logarithmic scale. In this paper, we show that financial analysts process small prices and large prices differently. When they are optimistic (pessimistic), analysts issue more optimistic (pessimistic) target prices for small price stocks than for large price stocks. Our results are robust when controlling for the usual risk factors such as size, book-to-market, momentum, profitability and investments. They are also robust when we control for firm and analyst characteristics, or for other biases such as the 52-week high bias, the preference for lottery-type stocks and positive skewness, and the analyst tendency to round numbers. Finally, we show that analysts become more optimistic after stock splits. Overall, our results suggest that a deeply-rooted behavioral bias in number processing drives analysts’ return expectations.