Banks act as maturity transformers, who take liquid deposit and invest in illiquid assets. In this classical framework, we introduce uncertainty in the asset returns. We show that banks can insure individuals against the risk of illiquidity at the cost of increasing the riskIness of their portfolios. In an open financial market, they can better diversify their portfolio and decrease its risk. In that way, they can also increase the level of insurance against the risk of illiquidity. This improves individual welfare, but the banks' short-term deposit-reserve ratio and the fragility of the financial system result higher in an open economy than in an autarchic regime. For this reason, the mechanism of deposit insurance against bank runs becomes more difficult to implement by each country's central bank.
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