Strategic trading in a dynamic noisy market

This paper studies a dynamic model of a financial market with a strategic trader. In each period the strategic trader receives a privately observed endowment in the stock. He trades with competitive market makers to share risk. Noise traders are present in the market. After receiving a stock endowment, the strategic trader is shown to reduce his risk exposure either by selling at a decreasing rate over time, or by selling and then buying back some of the shares sold. When the time between trades is small, the strategic trader reveals the information regarding his endowment very quickly. ∗MIT and NBER. I thank Anat Admati, Denis Gromb, Pete Kyle, Andy Lo, Lee-Bath Nelson, Paul Pfleiderer, Jose Scheinkman, Matt Spiegel, René Stulz, Rangarajan Sundaram, Jean Tirole, Jiang Wang, Ingrid Werner, Jeff Zwiebel, seminar participants at Chicago, Harvard, LSE, MIT, UCSD, and participants at the Western Finance Association, NBER market microstructure, and European Econometric Society conferences for very helpful comments. I am especially grateful to Avanidhar Subrahmanyam for many valuable comments and suggestions. I thank Muhamet Yildiz for excellent research assistance. Large traders, such as dealers, mutual funds, and pension funds, play an important role in financial markets.1 Many empirical studies show that these agents’ trades have a significant price impact.2 Recent studies also show that large traders execute their trades slowly, over several days, presumably to reduce their price impact.3 These studies raise a number of theoretical questions. For instance, what dynamic strategies should large traders employ to minimize their price impact? In particular, how quickly should they execute their trades? How quickly does the price adjust to reflect the presence of a large trader? Given the importance of large traders, an analysis of their dynamic strategies is relevant for understanding the daily and weekly behavior of returns, volume, and bid-ask spreads. It is also relevant for comparing trading mechanisms, in terms of liquidity provided to large traders, and information revealed in prices. An analysis of large traders’ dynamic strategies requires an assumption about their motives to trade. Trading motives are generally divided into “informational” motives, arising from private information about asset payoffs, and “allocational” motives, such as risk-sharing, portfolio rebalancing, and liquidity. In a seminal paper, Kyle (1985) studies the dynamic strategy of a large trader with informational motives (an “insider”). The insider is risk-neutral and trades with risk-neutral market makers. Market makers agree to trade because they cannot distinguish the insider from noise traders who are also present in the market. Kyle shows that the insider reveals his information slowly, until the time when it is publicly announced.4 If most large trades were motivated by information, large traders would significantly outperform the market. However, many empirical studies show that large traders do not significantly outperform, and may even underperform, the market. Moerover, this performance is in spite of high portfolio turnover.5 Therefore, allocational motives must be important. The dynamic strategies of large traders with allocational motives have received comparatively less attention. The problem has some similarities with the case of informational motives. For instance, a large trader who wants to sell in order to hedge a risky position, has private information that he will sell and that the price will fall. This is similar to an insider who has private information that the price will fall because of a negative earnings announcement. The crucial difference, however, is that the time of the earnings announcement is exogenous, while the time at which the large trader sells is endogenous. Therefore, the large trader’s speed of trade execution cannot be deduced from the insider’s, since the latter