ON THE EFFICIENCY OF COMPETITIVE STOCK MARKETS WHERE TRADES HAVE DIVERSE INFORMATION

Abstract

I HAVE SHOWN elsewhere that competitive markets can be over-informationally efficient. (See Grossman [1975] for this and a review of other work in this area.) If competitive prices reveal too much information, traders may not be able to earn a return on their investment in This was demonstrated for a market with two types of traders, and uninformed. Informed traders learn the true underlying probability distribution which generates a future price, and they take a position in the market based on this When all informed traders do this, current prices are affected. traders invest no resources in collecting information, but they know that current prices reflect the information of informed traders. Uninformed traders form their beliefs about a future price from the information of informed traders which they learn from observing current prices. In the above framework, prices transmit However, it is often claimed that prices aggregate In this paper we analyze a market where there are n-types of informed traders. Each gets a piece of information. In a simple model we study the operation of the price system as an aggregator of the different pieces of We consider a market where there are two assets; a risk free asset and a risky asset. Each unit of the risky asset yields a return of P1 dollars. P1 will also be referred to as the price of the risky asset in period 1. In period 0 (the current period), each trader gets information about P1 and then decides how much of risky and non-risky assets to hold. This determines a current price of the risky asset, P0, which will depend on the information received by all traders. We assume that the ith trader observes yj, where yi = PI + ,E. There is a noise term, 'E, which prevents any trader from learning the true value of P1. The current equilibrium price is a function of (Y1Y25 ... Yn); write it as PO(Y,Y2, ... 5Yn). The main result of this paper is that when there are n-types of traders (n > 1), PO reveals information to each trader which is of higher quality than his own That is, the competitive system aggregates all the market's information in such a way that the equilibrium price summarizes all the information in the