We study the role of heterogeneity in the transmission of foreign shocks. We build a Heterogeneous-Agent New-Keynesian Small Open Model Economy (HANKSOME) that experiences a current account reversal. Households' portfolio composition and the extent of foreign currency borrowing are key determinants of the magnitude of the contraction in consumption associated with a sudden stop in capital inflows. The contraction is more severe when households are leveraged and owe debt in foreign currency. In this setting, the revaluation of foreign debt causes a larger contraction in aggregate consumption when debt and leverage are concentrated among poorer households. Closing the output gap via an exchange-rate devaluation may therefore be detrimental to household welfare due to the heterogeneous impact of the foreign debt revaluation. Our HANKSOME framework can rationalize the observed fear of floating in emerging market economies, even in the absence of contractionary devaluations.