This paper develops a dynamic continuous-time model in which international risk sharing can yield substantial welfare gains through its positive effect on expected consumption growth. The mechanism linking global diversification to growth is an attendant world portfolio shift from safe, but low-yield, capital into riskier, high-yield capital. The presence of these two types of capital is designed to capture the idea that growth depends on the availability of an ever-increasing array of specialized, and hence inherently risky, production inputs. A partial calibration exercise based on Penn World Table consumption data implies steady-state welfare gains from global financial integration, which for some regions amount to several times initial wealth.