Speculative Markets With an Unknown Number of Insiders

This paper analyzes how uncertainty about the number of informed traders in a market alters the market characteristics. Increasing the uncertainty about the number of informed traders while holding the expected number of informed traders constant: (i) increases the residual price uncertainty in the market; (ii) increases the total expected volume of informed trade and profits earned by insiders; and (iii) significantly prolongs the impact of an information event by extending the expected trade horizon of insiders and the time over which market liquidity is depressed. These results are compared with those found in experimental asset markets with a similar information structure. The model confirms several of the broad experimental conclusions and provides new insights in some important dimensions, particularly with respect to the behavior of (unknown) monopolist insiders. How should traders who expend resources to generate private information to use when trading allocate their resources? One branch of literature, beginning with Kyle (1985), offers a clear prescription: seek to acquire unique information from which one can earn monopoly rents. This branch of literature, among other things, provides a theoretical foundation for the intuition that, in financial markets, private information is valuable while public information is not. Public information, being already reflected in prices, doesn’t lend itself to profitable trading strategies. Private information, in constrast, allows one to trade strategically and earn positive profits (on average) while the price adjusts to incorporate the information (Kyle (1985)). The value of private information depends largely on whether it is known to one or many. Holden and Subrahmanyam (1992), for example, show that information shared by as few as two insiders may not yield any trading profits. Foster and Viswanathan (1996) show that traders with correlated private signals will trade aggressively on the common component of their signals and strategically on the unique component. Expected total insider profits are always lower than those of a monopolist insider, but they are the lowest when the insiders have highly correlated signals. It would appear to follow, then, that traders could maximize their collective profits by minimizing the competition among themselves by, for example, focusing their information gathering efforts in different arenas. This paper shows that this conclusion may be incorrect. While traders who acquire “information monopolies” will earn monopoly rents, higher profits Fama (1991) reviews the literature on market efficiency. In general, most U.S. financial markets show evidence of semi-strong form market efficiency. That is, trading strategies based on public information (including price histories) are rarely profitable. See also Back, Cao and Willard (2000) who solve the continuous time analog of the earlier discrete time models.