Stock Price Consistency in a Market with Heterogeneous Investors

This paper examines an idealized dynamic model of a market for a single stock. The model assumes a finite number of investor classes, the members of each class having essentially infinite wealth. All investors are assumed to be risk neutral, but members of different classes may discount future income differently. All investors have access to the same substantive information, but members of different classes may arrive at different(subjective) probability assessments on the basis of that information. We characterize the class of potential mechanisms for pricing the stock that satisfy a basic market equilibrium condition. These we call consistent price schemes. We find that a price scheme is consistent if and only if it satisfies a simple (martingale-like) condition between prices in consecutive periods. Moreover, if there are any (finite) consistent price schemes, then there is one which is minimal. The existence of this minimal consistent scheme is demonstrated constructively, and the construction is animated as an infinite sequential bidding procedure. This minimal consistent price typically will exceed every investors expected present worth of future dividends. We consider the special case of a single class, and find that the minimal consistent scheme prices the stock at the investors (unanimous) expected present worth of future dividends. For the general model, the investor on the margin is identified, and we discuss the extent to which the original heterogeneous market is equivalent to a market with a homogeneous population of these typical investors. A simple example, illustrating all of our basic concepts and results, is presented. Connections are made with a recent paper by Samuelson [10] , with the efficient-market hypothesis, and with the fundamentalist theory of stock valuation. The mathematical methods used are those of dynamic programming, and the connection between our model and a sequential decision process is discussed at some length.