European banks straddling borders: Risky or rewarding?

•Business cycles across European countries are not perfectly synchronized, providing room for risk reduction by banks via cross-border operations.•Considering all foreign activities of 61 European banks, including those via branches and direct lending, European banks invest 40.4% of their assets outside their home country.•Cross-border banking decreases banks’ insolvency risk and results in more stable returns.•The results contribute to policy discussions on the progress of the single European banking market, and on the treatment of cross-border lending in the regulatory framework and in supervision.