We extend the framework of trading strategy for single stocks from Gatheral [2010] 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 our strategic model to a special pair of stocks, where the impacts of traded volumes and the cross-impacts of time lag are quantified with empirical data. We thus provide a view of how the cross-impact influences the trading strategy for a pair of stocks, although the trading strategy is to be improved by containing the cost of self-impact and to be extended to more than two stocks in a portfolio.
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