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The recent financial crisis has shown that short-term collateralized borrowing may be highly unstable in times of stress. The present paper develops a dynamic equilibrium model and shows that this instability can be a consequence of market-wide changes in expectations, but does not have to be. We derive a liquidity constraint and a collateral constraint that determine whether such expectations-driven runs are possible and show that they depend crucially on the microstructure of particular funding markets that we examine in detail. In particular, our model provides insights into the differences between the tri-party repo market and the bilateral repo market, which were both at the heart of the recent financial crisis.