David vs Goliath (You against the Markets), A Dynamic Programming Approach to Separate the Impact and Timing of Trading Costs

摘要

To trade, or not to trade, that is the question! Whether an optimizer can yield the answer, Against the spikes and crashes of markets gone wild. To quench one's thirst before liquidity runs dry, Or wait till the tide of momentum turns mild. A trader's conundrum is whether (and how much) to trade during a giveninterval or wait for the next interval when the price momentum is morefavorable to his direction of trading. We develop a fundamentally differentstochastic dynamic programming model of trading costs based on the Bellmanprinciple of optimality and show that trading costs are a zero sum game. Builton a strong theoretical foundation, this model can provide insights to marketparticipants by splitting the overall move of the security price during theduration of an order into the Market Impact (price move caused by theiractions) and Market Timing (price move caused by everyone else) components.Plugging different distributions of prices and volumes into this framework canhelp traders decide when to bear higher Market Impact by trading more in thehope of offsetting the cost of trading at a higher price later. We deriveformulations of this model under different laws of motion of the securityprices. We start with a benchmark scenario and extend this to include multiplesources of uncertainty, liquidity constraints due to volume curve shifts andrelate trading costs to the spread.