Optimal Portfolio Execution Using Market and Limit Orders

Abstract

We investigate trade execution strategies that maximize expected exponential utility. In contrast to existing literature our strategy dynamically executes both market and limit orders. We derive a Hamilton-Jacobi-Bellman equation for the optimal combination of these order types and solve it numerically. We show that limit orders have a significant impact on the optimal strategy, and discuss the utility gains with respect to pure market order strategies. Our findings indicate an inverse relation between the speed at which market orders are submitted and the likelihood of limit orders being filled. For limit orders, we find that the optimal price moves away from the market price when any of the following hold: i) trade execution is not urgent, ii) the portfolio is relatively small, iii) the agent is not very risk averse. Finally, the optimal size of limit orders is largest for moderate portfolio sizes and long time horizons.

Keywords: Optimal portfolio execution, liquidity effects, market order, limit order, HJB equation, partial integro-differential equation, ADI method

JEL Classification: C61, G11, G12