Will an optimal deposit insurance always increase financial stability?

In this paper we show that deposit insurance can increase the probability of systemic banking crisis, even though it is optimally designed and its premium is risk related. 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 deposit insurance contagious bank runs can impose such great losses on banks, that banks choose less correlated portfolios to avoid contagion altogether. Optimal deposit insurance eliminates this incentive and thus the correlation of portfolios and with it the probability of systemic banking crisis can increase.