  Addressing the ongoing examination of high-frequency trading practices in
financial markets, we report the results of an extensive empirical study
estimating the maximum possible profitability of the most aggressive such
practices, and arrive at figures that are surprisingly modest. By "aggressive"
we mean any trading strategy exclusively employing market orders and relatively
short holding periods. Our findings highlight the tension between execution
costs and trading horizon confronted by high-frequency traders, and provide a
controlled and large-scale empirical perspective on the high-frequency debate
that has heretofore been absent. Our study employs a number of novel empirical
methods, including the simulation of an "omniscient" high-frequency trader who
can see the future and act accordingly.
