Informed Trading When Information Becomes Stale

This paper characterizes informed trade when speculators can acquire distinct signals of varying quality about an asset’s value at different dates. The most reasonable characterization of private information about stocks is that while information is longlived, new information will arrive over time, information that may be acquired by others. Hence, while a speculator may know more than others at a moment, in the future, his information will become stale, but not valueless. In an environment that allows for arbitrary correlations among signals, we characterize equilibrium outcomes including trading, prices, and profits. We provide explicit numerical characterizations for different informational environments. ONE OF THE MOST IMPORTANT OPEN QUESTIONS in theoretical market microstructure finance is: How do informed speculators trade in a dynamic environment when different speculators receive distinct signals at different dates? The most interesting and reasonable characterization of private information about stocks is that, while information is long-lived, new information will arrive over time and this information may be acquired by other speculators. In practice, individuals only periodically engage in detailed research on a particular stock. At the moment a speculator does this research, he may know that he is better informed than everyone else with regard to the stock, but he also knows that in the future, his information will become dated, and others will acquire fresher information. Still, the speculator can continue to trade profitably on his information in the future; that is, even though his information will become stale, it will still have value. An informed speculator must determine how intensively to trade on his information at each date. To do this he must use the information contained in both his signal and market prices to forecast (i) the information that each differentially informed agent has about the asset value, and (ii) the trades of other informed agents, because those trades influence prices. In such an environment, one wishes to determine how the strategic interplay among differentially ∗Bernhardt is with the Department of Economics, University of Illinois at Urbana-Champaign. Miao is with the Department of Economics, Boston University. We thank Shmuel Baruch, Oleg Bondarenko, Larry Epstein, Terrence Henderschott, Eric Hughson, Leslie Marx, and a particularly conscientious referee for helpful comments. We are especially grateful to Motohiro Sato. Our analysis was tremendously facilitated by Motohiro Sato’s extended solution to a homework problem in a market microstructure finance course at Queen’s University in 1997.