There is an extensive literature claiming that it is often difficult to make use of arbitrage opportunities in financial markets. This paper provides a new reason why existing arbitrage opportunities might not be seized. We consider a world with short-lived securities, no short-selling constraints and no transaction costs. We show that to exploit all existing arbitrage opportunities, traders should pay attention to all financial markets simultaneously. The paper gives a general result stating that failure to do so will leave some arbitrage opportunities unexploited with probability one.