Optimal Transaction Filters under Transitory Trading Opportunities: Theory and Empirical Illustration

Abstract

If transitory profitable trading opportunities exist, filter rules are used in practice to mitigate transaction costs. The filter size is difficult to determine a priori. Our paper uses a dynamic programming framework to design a filter that is optimal in the sense of maximizing expected returns after transaction costs. The optimal filter size depends crucially on the degree of persistence of the profitable trading opportunities, on transaction cost, and on the standard deviation of shocks. We apply our theoretical results to foreign exchange trading by parameterizing the moving average strategy often employed in foreign exchange markets. The parameterization implies the same decisions as the moving average rule, in the absence of transaction costs, but has the advantage of translating the buy/sell signal into the same units as the transaction costs so that the optimal filter can be calculated. Application to daily dollar-yen trading demonstrates that the optimal filter can differ dramatically from a naïve filter equal to the transaction cost. We confirm that daily moving average foreign exchange trading generates positive returns that disappear after accounting for transaction costs. However, when the optima