Overconfidence, Short-Sale Constraints, and Stock Valuation

Abstract

There is a recent renaissance in the research of investor differences of opinion and short-sale constraints. This literature usually assumes that investor opinion is generated from an exogenous distribution and hence does not link opinion divergence and stock valuation to stock fundamentals. In addition, most theories simply model short-sale constraints as short-sale prohibition. This paper develops a stock market model based on investor overconfidence and short-sale constraints, in which overconfidence generates differences of opinion and the degree of short-sale constraints is variable. In the model, after receiving private signals, overconfident investors and rational investors exchange one risky asset with which there is a restriction in maximum number of shortable shares. In equilibrium, conditional on private signals, stocks can be overvalued or undervalued. How stocks are mispriced depends on whether private signals are favorable or adverse and, accordingly, what investors are bound by short-sale constraints. However, due to the asymmetry in under- and overvaluation introduced by short-sale constraints, on average, stocks are overvalued. The model produces a distribution of investor differences of opinion that is correlated with stock fundamentals, which explains the cross-sectional differences in opinion divergence. The models also examines the effects of investor overconfidence and short-sale constraints on opinion divergence, trading volume, and short interest. It shows that a variation in overconfidence induces a negative correlation between subsequent stock returns and opinion divergence, trading volume, or short interest. In contrast, a variation in short-sale constraints generates a positive correlation between subsequent stock returns and trading volume or short interest but has no effects on opinion divergence. These relationships provide an explanation for a number of stylized facts in the cross-section. After we further incorporate multiple assets whose payoffs share a common factor, the model gives many implications for the time-series behavior of aggregate returns. It explains the ability of cross-sectional averages of firm valuation measures (such as book-to-market equity and dividend yield) to forecast market returns and returns of various portfolios. It also provides an explanation for the stronger predictability of equal-weight market returns than value-weight market returns. Finally, we suggest a number of new predictors of aggregate returns, including cross-sectional averages of opinion divergence, of trading volume, and of short interest, and cross-sectional dispersions of firm misvaluation and of opinion divergence.