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Non-technical summaryThe stability of the financial system is a key concern to central bankers. A particular aspect that has received much attention recently is the wholesale funding of banks. Before the financial crisis, banks funded themselves increasingly with short-term debt. However, such funding dried up as economic news deteriorated. This dark side of wholesale funding in part inspired the Basel III regulation.Specifically, a Liquidity Coverage Ratio (LCR) and a Net Stable Funding Ratio (NSFR) require banks to maintain a minimum level of liquidity.In this paper, I study rollover risk in wholesale funding markets. Investors may roll over funding to their intermediaries after receiving some noisy information about their solvency. My setup has two noteworthy features. First, financial intermediaries are allowed to hold precautionary liquidity in order to prepare for the possible future drying up of funding. That is, intermediaries choose how much liquidity to hold initially, while the remainder is invested in illiquid projects with high expected returns. Second, a fire sale occurs when intermediaries liquidate their projects jointly.This paper derives two results. The first is technical and states that the methods previously used to ensure a unique equilibrium require refinement. Uniqueness matters, since it puts subsequent policy implications on a strong theoretical footing. The second result is the inefficiency of private liquidity holdings. Since intermediaries free ride on the liquidity holdings of other intermediaries, there is excessive liquidation. By contrast, a macroprudential authority understands the systemic nature of liquidity, whereby one intermediary's holdings mitigate the risk of fire sales for other intermediaries. Imposing a macroprudential liquidity buffer restores efficiency.Finally, I link this welfare result to the regulatory debate of Basel III. I argue why this set-up provides a theoretical foundation for the Liquidity Coverage Ratio. It follows a brief discussion about requiring intermediaries to hold additional liquidity versus creating a systemic liquidity fund that all intermediaries contribute to. While the proposed set-up also provides some support for the Net Stable Funding Ratio, I describe how the current set-up could be extended to address the trade-offs associated with the NSFR more directly.2