A Quantitative Behavioral Model and its Implications for Market Volatility, Underreaction, and Overreaction

This paper develops a model of weight assignments using a pseudo-Bayesian approach that reflects investors' behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors' conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors' behavioral biases. Using this model, we can show that while learning may contribute to market anomalies, anomalies still exist even after the learning process has been completed. In particular, we can deduce the following: (1) Excess market volatility will result from investors' biased heuristics. It is the representative heuristic, rather than the conservative heuristic, which contributes to excess volatility in the market. In addition, excess volatility is more prominent when the discount rate is small. (2) Through a misapplication of Bayes' rule, investors' behavioral biases lead to short-term underreaction and long-term overreaction in the market. The more conservative/representative the heuristic, the larger the magnitude of the return auto-correlation and the larger is the contrarian/momentum trading profit. Further analysis shows that the representative heuristic contributes to the contrarian trading profit and the conservative heuristic contributes to the momentum trading profit. In addition, the smaller the discount rate, the larger the contrarian/momentum profit. (3) Investors' behavioral biases induce a magnitude effect in the under- and overreaction phenomena, i.e., the more severe the earnings shock, the larger the market autocorrelation and the larger the momentum/contrarian trading profit. (4) The magnitude effect described in (3) is convex in nature