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

Abstract

We derive the optimal investment policy of a risk-averse investor in a market where there is a textbook arbitrage opportunity, but where liabilities must be secured by collateral. We find that it is often optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow. Even when the optimal policy is followed, the arbitrage portfolio typically experiences losses before the final conver- gence date. In fact, its initial performance may be indistinguishable from that of a conventional portfolio with a poor track record. These results have important impli- cations for the role of arbitrageurs in financial markets. So there's an arbitrage. So what? This desk has lost a lot of money on arbitrages. Arbitrages aren't particularly great trades. — Treasury bond trader at a major Wall Street investment bank