Optimal Informed Trading in a Quote-Driven Market

This paper presents a model of a quote-driven market with asymmetric information. The model is similar to the Glosten-Milgrom (1985) model, except that we allow the informed trader to optimally time his trades, rather than employing a probabilistic selection process for informed and uninformed trades. The contribution of the paper is to show that the probabilistic arrival process is a robust assumption: in equilibrium, informed trades and uninformed trades do arrive randomly, and the informed trader’s information is revealed only gradually to the market. Cross-sectionally, a larger intensity of liquidity trading implies a larger intensity of informed trading but a lower bidask spread. Preliminary and Incomplete ∗John M. Olin School of Business, Washington University in St. Louis, St. Louis, MO 63130, and David Eccles School of Business, University of Utah, Salt Lake City, UT 84112, respectively. Bagehot (1971) was probably the first to make the point that asymmetric information alone can explain the bid-ask spread. His argument was that market makers, who must stand ready to trade with anonymous traders, lose to informed traders. This is because the informed traders transact only when the price does not reflect the information that they possess. Market makers offset these losses with profits earned from liquidity traders, who are willing to pay a premium for immediacy. Glosten and Milgrom (1985) (and its static antecedent Copeland and Galai (1983)) formalized the adverse selection problem faced by the market makers in a quote-driven environment. There, competitive risk neutral market makers post the bid and ask prices at which they are ready to trade one unit of stock. Liquidity traders and informed traders arrive randomly, one at a time, and submit their orders. Given any positive rate of informed trader activity, it is shown that there is a positive spread. In Glosten and Milgrom (1985), however, the behavior of the informed traders does not appear to be consistent with profit maximization. On one hand, the informed traders enjoy what Bagehot (1971) called the option not to trade (which they exercise when the “true” price is within the spread), but on the other hand they ignore the option to time their trades. To illustrate their theory, Glosten and Milgrom (1985) provide an example involving a pool of potential traders, some of which are informed, with traders being randomly selected to arrive at the trading post. O’Hara (1995, p. 59) discusses this issue as follows: How traders actually arrive at the market is an important issue. Informed traders profit from trading if prices are not at full-information levels, and so any informed trader will prefer to trade as much (and as often) as possible. Since such behavior would quickly indicate the information of the informed, the market maker would quickly (perhaps instantly) adjust prices to reflect this information . . . One way to avoid this instantaneous revelation outcome is to assume that traders are chosen probabilistically . . . The purpose of this paper is to show that the premise that informed traders prefer to trade as much and as often as possible may be unfounded. Abstinence from trading can be a virtue because prices can become more favorable and/or less sensitive to new orders when trading is delayed. This same phenomenon appears in the model of Kyle (1985) when there are multiple