This paper characterizes analytically the adjustment of an open economy with a stock collateral constraint to fundamental and nonfundamental shocks. In the model, external borrowing is limited by the value of physical capital. Three results are established: (1) Adjustment to external shocks is nonlinear. In response to small negative output shocks, the economy adjusts as prescribed by the intertemporal approach to the current account, with increases in debt, deficits in the trade and current account balances, and no significant movement in the price of collateral. By contrast, in response to large negative output shocks the economy experiences a sudden stop with debt deleveraging, trade and current account reversals, and a Fisherian deflation of asset prices. (2) Generically, weak fundamentals (low output and high external debt) give rise to multiple equilibria. (3) In this case, the economy is prone to self-fulfilling sudden stops driven by downward revisions of expectations about the value of collateral.