  We extend the framework of trading strategies of Gatheral [2010] from single
stocks to a pair of stocks. Our trading strategy with the executions of two
round-trip trades can be described by the trading rates of the paired stocks
and the ratio of their trading periods. By minimizing the potential cost
arising from cross-impacts, i.e., the price change of one stock due to the
trades of another stock, we can find out an optimal strategy for executing a
sequence of trades from different stocks. We further apply the model of the
strategy to a specific case, where we quantify the cross-impacts of traded
volumes and of time lag with empirical data for the computation of costs. We
thus picture the influence of cross-impacts on the trading strategy.
