Numerosity: Forward and Reverse Stock Splits

Abstract

Individuals have a tendency to fixate on large numbers and ignore other relevant information in their decision making process. The numerosity heuristic, a cognitive bias, is the first behavioral hypothesis to explain why investors prefer to receive more shares (rather than less shares) in a stock split even though the aggregate economic value is the same. For forward splits, after controlling for the positive signaling of improved earnings growth and liquidity from the split announcement, the stock price reacts positively to the larger number of shares issued. More importantly, the use of a dual class numerosity model can explain why most conventional hypotheses fail to explain the negative stock price reaction to reverse splits. Given a typical bearish outlook associated with a reverse stock split, investors’ cognitive resources have already been conditioned to derive a systematic conclusion to sell the stock at the higher price. Focusing only on large stock price numerosity, investors are incorrectly inferring a higher investment value. As the high numerosity encourages bearish investors to sell at the higher perceived investment value, the stock returns react more negatively to the higher post-reverse split price level. In both forward and reverse split cases, investors react to high numerosity.

Keywords:

• Numerosity
• Stock split
• Reverse split
• Behavioral bias
• Cognitive bias