We develop a model in which long-term swap spreads are determined by end users’ demand for swaps, constrained dealers’ supply of swaps, and the risk of future imbalances between demand and supply. Exploiting the sign restrictions implied by our model, we estimate these unobserved demand and supply factors using data on swap spreads and a proxy for dealers’ swap arbitrage positions. We find that demand and supply play equally important roles in driving the observed variation in swap spreads. Yet, as predicted by the model, demand plays a more important role in shaping the expected returns on swap spread arbitrage, which embed a premium for bearing future demand-supply imbalance risk. Hedging activity from mortgage investors seems to play a key role in driving the demand for swaps. By contrast, the supply of swaps is closely linked to proxies for the tightness of dealers’ constraints. Finally, our analysis helps explain the relationship between swap spreads and other no-arbitrage violations.