The majority of households across emerging market economies are excluded from the financial markets and cannot smooth consumption. I analyze the implications of this for optimal monetary policy and the corresponding choice of domestic versus external nominal anchor in a small open economy framework with nominal rigidities, aggregate uncertainty and financial exclusion. I find that, if set optimally, monetary policy smooths the consumption of financially excluded agents by stabilizing their income. Even though Consumer Price Index (CPI) inflation targeting approximates optimal monetary policy when financial inclusion is high, targeting the exchange rate is appropriate if financial inclusion is limited. Nominal exchange rate stability, upon shocks that create trade-offs for monetary policy, directly stabilizes the import component of financially excluded agents' consumption baskets, which smooths their consumption and reduces macroeconomic volatility. This study provides a counterpoint to Milton Friedman's long-standing argument for a float.