Abstract
The traditional model in the competitive stock market assumes that the observational frequency of information is uniform, and concludes that the stock market equilibrium price which aggregates market information provides a sufficient statistic reflecting all the private information in the market. However, we are the first to assume that the observational frequency of an information is not uniform. Actually, information is heterogeneous among market participants, and there is an information asymmetry among investors. The main purpose of this study is to explore the relationship among information precision, the observational frequency of information and the stock market equilibrium. The study analyze the determination of the price system in a competitive stock market, where there are l sources of information which are respectively observed f1, f2, …, fI times by risk-averse traders. Each informed investor uses information observed to form an estimate for the expected value of the firm’s true value, , and to make decisions to buy the shares to maximize his own expected utility, and hence, determine the stock market equilibrium. Our main findings are as follows: Firstly, we found that the competitive equilibrium price is equal to the rational expectations equilibrium price. Only when the observational frequencies of each piece of market information are equal, will the fully-informed equilibrium become a special case of competitive equilibrium. Secondly, we found that the market equilibrium price aggregates all the market information, contingent on each observational frequency and its precision. The market equilibrium condition and the expected utility depend not only on the realized information, but also on the observational frequency and the precision of information. The market equilibrium price will fully reflect the precision and the observational frequency of information about the future value of asset. The stock price response to an unexpected change of information is positively related to the observational frequency and the precision of that information. We found that, the heterogeneity of belief about the true value of the risky asset among investors will lead to different regimes of market equilibrium. Thirdly, when the observational frequency of each piece of market information is uniform, Grossman’s model (1976) is mathematically equivalent to a special case of our model, and the market equilibrium price could act as a sufficient statistic for all the private information about the intrinsic value of the risky asset. However, the observational frequencies of market information with asymmetry are usually not uniform such that traders still have an incentive to collect costly information. Finally, further research could investigate how accurate the market equilibrium price is as a sufficient statistic for all the market information.
Key words: Information precision, observational frequency of information, stock market equilibrium, information value.
