Exchange rate policies depend on portfolio choices, and portfolio choices depend on anticipated exchange rate policies. This opens the door to multiple equilibria in policy regimes. We construct a model in which agents optimally choose to denominate their assets and liabilities either in domestic or in foreign currency. The monetary authority optimally chooses to float or to fix the currency, after portfolios have been chosen. We identify conditions under which both fixing and floating are equilibrium policies: if agents expect fixing and arrange their portfolios accordingly, the monetary authority validates that expectation; the same happens if agents initially expect floating. We also show that a flexible exchange rate Pareto-dominates a fixed one. It follows that social welfare would rise if the monetary authority could precommit to floating.