Optimal Liquidity Trading

A liquidity trader wishes to trade a fixed number of shares within a certain time horizon and to minimize the mean and variance of the costs of trading. Explicit formulas for the optimal trading strategies show that risk-averse liquidity traders reduce their order sizes over time and execute a higher fraction of their total trading volume in early periods when price volatility or liquidity increases. In the presence of transaction fees, traders want to trade less often when either price volatility or liquidity goes up or when the speed of price reversion declines. In the multi-asset case, price effects across assets have a substantial impact on trading behavior.We are grateful to Prajit Dutta and Larry Glosten for numerous conversations and comments and to Marc Lipson for help with the Plexus data. Comments and suggestions of the referee and the editor, Josef Zechner, helped us improve the paper. We also thank the participants of the Chicago Board of Trade 13th Annual European Futures Research Symposium 2000 and the participants of the EFA Annual Meetings 2001.