What Determines the Stock Price and the Informative Efficiency: The Omitted Information Frequency Observed

Abstract

This paper investigates the determination of the price system of the stock market. Different from previous studies, we emphasize the concept of the ”observational frequency” of information. This paper allows each informed investor to observe more than one kind of information. There are I kinds of information x1, x2,...x(subscript I) available in a competitive stock market. Since there exists information asymmetry among investors, the market information are respectively observed f1, f2,..., f(subscript I) times by N constant risk-averse traders to form a more precise estimate for the expected value of the risky asset, v, to buy the shares to maximize their own expected utility, and then to determine the stock market equilibrium simultaneously. Our main findings are as follows. First, we propose that the equilibrium price, trading quantity, and the expected utility of investors depend not only on realized value of the information but also on the observational frequencies and the precisions of the market information. The competitive equilibrium price is equal to the rational expectations equilibrium price, which aggregates all the market information according to their observational frequencies and the precisions of the market information. Second, the fully-informed economy equilibrium is a special case of the competitive equilibrium (or the rational expectations equilibrium) only when the observational frequencies of all the market information are just equal and it serves as a sufficient statistic for all the market information about the intrinsic value of the risky asset. Finally, we prove that the heterogeneity in the observational frequency of information is impossibility for informationally efficiency. Since the observational frequencies among the market information are not uniform, the equilibrium price still aggregates the market information but will not break down as the case described by Grossman (1976).