We carry out a quantitative analysis of the financing measures proposed for the European Deposit Insurance Scheme (EDIS) regarding the target level of the fund and the contribution scheme of member entities. We estimate the loss distribution of the EDIS considering different sources of systemic risk associated with the correlations between bank assets and we analyse the sensitivity of the results to bank portfolio risk. Our findings show how the interconnection between banks of different countries has an important influence on accumulated losses in the tail of the distribution. Likewise deterioration in the quality of bank portfolios produces a significant reduction in the fund's loss-absorbing capacity, which calls into question its soundness in times of economic recession. Finally, the contribution scheme provides more equitable risk measures and may be an appropriate incentive to reduce moral hazard in the Banking Union.