Banks are exposed globally to risk either directly through their portfolio and funding, or indirectly through their affiliates and the structure of their banking group. Therefore, it is crucial to consider the global framework in which banks operate in order to assess banking stability. In this paper, I first develop a theoretical model to focus on the impact of international integration on the resilience of banks. Starting from an accounting identity, I derive the volatility of bank's equity as a function of asset returns, funding costs, foreign exchange rate and leverage. In particular, I ask how the variance co-variance matrix between each component of the balance sheet impacts the volatility of equity returns. This model introduces a banking theory on international diversification where three main channels are identified: the global financial cycle channel; the within channel of assets and liabilities; and the foreign exchange rate channel. In the second part of the paper, I depict the financial evolution of international integration between the US and the Euro area from 2000 to 2015, estimating conditional correlations between asset returns, funding costs and exchange rate fluctuations. Focusing on this period, the model predicts that international diversification improves the resilience of banks even during periods of strong international integration such as 2008. Finally, this exercise brings to light some common patterns between what the theoretical model predicts and what the euro area banks actually do.