Banks' liquidity management and systemic risk

We study a novel mechanism to explain the interaction between banks’ liquidity
management and the emergence of systemic financial crises, in the form of self-fulfilling
runs. To this end, we develop an environment where banks offer insurance to their
depositors against both idiosyncratic and aggregate real shocks, by holding a portfolio
of liquidity and productive but illiquid assets. Moreover, banks’ asset portfolios and the
probability of a depositors’ self-fulfilling run are jointly determined via a “global game”.
We characterize the sufficient conditions under which there exists a unique threshold
recovery rate, associated with the early liquidation of the productive assets, below which
the banks first employ liquidity and then liquidate, in order to finance depositors’ early
withdrawals. Ex ante, the banks hold more liquidity than in a full-information economy,
where there are no self-fulfilling runs and risk is only due to idiosyncratic and aggregate
real shocks.