I develop an equilibrium model of convergence trading and its impact on asset prices. Arbitrageurs optimally decide how to allocate their limited capital over time. Their activity reduces price discrepancies, but their activity also generates losses with positive probability, even if the trading opportunity is fundamentally riskless. Moreover, prices of identical assets can diverge even if the constraints faced by arbitrageurs are not binding. Occasionally, total losses are large, making arbitrageurs' returns negatively skewed, consistent with the empirical evidence. The model also predicts comovement of arbitrageurs' expected returns and market liquidity.