Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities

We derive the optimal investment policy of a risk-averse investorin a market where there is a textbook arbitrage opportunity,but where liabilities must be secured by collateral. We findthat it is often optimal to underinvest in the arbitrage bytaking a smaller position than collateral constraints allow.Even when the optimal policy is followed, the arbitrage portfoliotypically experiences losses before the final convergence date.In fact, its initial performance may be indistinguishable fromthat of a conventional portfolio with a poor track record. Theseresults have important implications for the role of arbitrageursin financial markets.