We show that exploitable lead-lag relations of the order of a few hundred milliseconds exist in the three pairings between the S&P 500, FTSE 100, and DAX futures contracts. These relations exhibit clear intra-daily patterns, particularly around the US open, the European close, and the announcement of macroeconomic data. Using this information, we forecast mid-quote changes in lagging contracts with a directional accuracy in excess of 85%. A simple statistical arbitrage strategy exploiting these relations yields economically significant profits which are robust to market impact costs and the bid-ask spread. However, returns are sensitive to the risk of slippage, and the most profitable trading opportunities rarely exist for longer than 300 milliseconds. Hence, we highlight price slippage and infrastructure costs as the most significant limits to arbitrage in this market setting. Overall, our results accord with the view that informational inefficiencies incentivize arbitrageurs to appropriate pricing anomalies.