The textbook description of arbitrage suggests that it is a straightforward matter of taking offsetting positions in different securities and realizing the arbitrage profit. Such descriptions, however, typically ignore the transaction costs that give rise to the arbitrage opportunity in the first place. Taking proper account of these transactions costs may considerably complicate the problem, particularly when, as is usually the case, the arbitrage potential is restricted.' This article is concerned withoptimal arbitrage strategies with transaction costs when the arbitrage potential is restricted by position limits. The particular case we shall analyze is the Standard and Poor's (SP the corresponding figure for the S&P 500 portfolio for the same period was