Self-fulfilling crises, where investors’ expectations of a default cause a default, are a defining feature of sovereign debt markets. However, we show that a selffulfilling crisis creates an arbitrage opportunity. Suppose that there are two equilibria in an economy: a self-fulfilling crisis where investors do not rollover the debt and default happens and a non-crisis where investors rollover the debt and default does not happen. In the self-fulling crisis, a large investor or coalition of small investors with sufficient resources could bid up the sovereign debt to its non-crisis equilibrium price. This price results in zero profits on the purchase of the new issuance and a gain for existing debt holders. We propose an equilibrium refinement based on absence of this arbitrage opportunity and show that (i) there is a unique equilibrium which survives the refinement, and (ii) in the unique equilibrium the sovereign does not default due to rollover risk. Further, we show that the possibility of indeterminacy increases when resource constraints are tight or the country’s debt is large relative to investor resources. Last, we extend our model to allow investors to participate in credit-default swap (CDS) markets. Contrary to conventional wisdom, we find the ability to trade in CDS markets can dampen indeterminacy by allowing investors to sell CDS protection and use those proceeds to execute the arbitrage trade. JEL Classification: F34, E44, G12, G15