A Theory of Optimal Institutional Trading

I develop a theory of optimal trading by an institutional trader who receives a parent order (i.e., an overall trading request) from a fund manager to buy a specific quantity of a particular stock over a specified time horizon. The trader selects child orders to be submitted each period over the allotted time horizon to a limit order book market. Child orders can be either market orders or limit orders. Limit order prices can be selected from any price on a penny price grid. An unexecuted limit order can be cancelled at any time. The trader’s objective is to minimize the disutility of the fund manager. In the base version of the theory, all child orders are of unit size. I derive an analytic solution for the optimal trading strategy and show that it involves “dynamic aggressiveness.” This means that if the current period limit order executes (doesn’t execute), then the next limit order optimally has a weakly less (weakly more) aggressive price. Next, I extend the theory to: (1) permit child orders of any size, (2) allow the fund manager to have private information about future stock prices, (3) allow the fund manager to be risk averse, and (4) allow four alternative metrics for computing execution cost. I calibrate the model to real-world data and optimize it numerically. I find that if the fund manager has a large disutility parameter for underfills, then the optimal strategy involves a sequence of limit orders early on and switches to a sequence market orders later on to guarantee purchasing the parent order. Conversely, if the fund manager has a zero disutility parameter for underfills, then the optimal strategy involves a sequence of limit orders with low price aggressiveness, such that each individual trade will earn the spread. If a fund manager is relatively informed and/or highly risk averse, then the optimal strategy is relatively front-loaded in time and switches to market orders relatively early so as to trade before price moves in the predicted direction and/or to reduce risk. Conversely, if the fund manager is uninformed and has low risk aversion, then the optimal strategy is spread out over time and switches to market orders later. I find that the optimal trading strategy frequently involves dynamic aggressiveness and frequently beats two benchmark trading strategies from the existing literature. Finally, I discuss empirical predictions of the theory and how they can be tested.