Will an Optimal Deposit Insurance Always Decrease the Probability of Systematic Banking Crisis?

In this paper we show that a deposit insurance can increase the probability of systematic banking crisis, even though it is optimally designed and does not induce any moral hazard. This is driven by the possibility of contagious bank runs. We prove that contagion only occurs if the correlation between the portfolios of banks is high enough. Without a deposit insurance contagious bank runs can impose such great losses on banks, that banks sometimes choose less correlated portfolios to avoid contagion altogether. An optimal deposit insurance eliminates this incentive and thus the correlation of portfolios and with it the probability of systematic banking crisis can increase