We suggest that foreign banks may represent a trade-off for their developing country hosts. A portfolio model is developed to show that a more diversified international bank may be one of lower overall risk and less susceptible to funding shocks but may react more to shocks that affect expected returns in a particular host country. Foreign banks have become particularly important in Latin America where we find strong support for these theoretical predictions using a dataset of individual Latin American banks in eleven countries. Moreover, we find no significant difference between the size of the response of foreign banks to a negative liquidity shock and a positive opportunity shock: in both cases the market share of foreign banks in credit increases.