Theory of optimal transaction implementation

In a securities market, the initiator of a large transaction can expect the realized price of his trade to be inferior to the current market price immediately prior to his appearance in the market. This "transaction implementation cost" phenomenon is a major concern of institutional money managers, both in portfolio selection and in trade implementation strategy. A considerable amount of current research in finance theory deals with modeling and prediction of these costs for equities trading, and commercial products and services have become available for probabilistically estimating real time transaction implementation costs versus transaction size on a stock-specific basis. An earlier paper described the concept of satisfaction- or preference-based trading, with optimization of trade matching on the basis of mutual preference. A market structure based upon this design will shortly begin trading listed equities on the Pacific Exchange, under the trade name OptiMark/sup TM/. The Nasdaq market is expected to begin trading using the OptiMark system in 1999, followed by the Osaka Securities Exchange in 2000. A prima facie benefit of this approach is the ability to specify trading strategies that explicitly account for transaction implementation cost estimates. We present the underlying theoretical framework that unites these concepts of preference-based trading and probabilistic transaction cost estimation. In particular, we develop an analytical generalization of the current market structure constructs of market orders and limit orders. We describe a feasible optimization problem whose solution yields optimal preference profiles, given current market conditions (as reflected by the probability distribution of transaction implementation cost) and a trader-specified coefficient of urgency. This enables seamless integration of the functions of portfolio selection (the purview of modern portfolio theory) and transaction implementation.