The debate about the appropriate choice of exchange rate regime is fundamental in international economics. This paper develops a small open-economy model with balance sheet effects and compares the performance of fixed and flexible exchange rate regimes. The model is solved up to a second-order approximation which allows us to address the issue of risk and welfare rigorously. The paper identifies threshold levels of the debt-to-GDP ratio above which fixed exchange rate regimes are welfare superior to monetary policy rules that imply flexible exchange rate regimes. The results suggest that emerging market economies that suffer from a relatively high level of indebtedness and are constrained in their pursuit of optimal monetary policy, could find it beneficial to opt for a fixed exchange rate regime.