Facing an Arbitrage Opportunity: Trade or Wait?

In traditional thinking, an arbitrageur will trade immediately once an arbitrage opportunity appears. Is this the best strategy for the arbitrageur or it is even better to wait for the best time to trade so as to achieve the maximum profit? To answer this question, this paper studies the optimal trading strategies of an arbitrageur in a dynamic economy where the arbitrageur’s trades affect prices, and the arbitrageur faces competition from other arbitrageurs exploiting the same mispricings. The proposed model considers fixed and proportional transaction costs, and closed form expressions for the threshold values in the optimal policies are provided. The theoretical and numerical results answer how the timing of the trade and the trade size depend on the magnitudes of the fixed and proportional transaction costs, the dynamics of the arbitrage opportunity, the interest rate, the market impact, and the level of competition. Furthermore, this study numerically studies how the trading horizon and the trader’s risk attitude affect the arbitrageurs’ decision. With competition, the start-to-trade threshold approaches the proportional cost. Our paper provides a new perspective on the existing empirical literature testing for the existence of arbitrage opportunities.