International risk sharing is better than you think, or exchange rates are too smooth

Exchange rates depreciate by the difference between domestic and foreign marginal utility growth or discount factors. Exchange rates vary a lot, as much as 15% per year. However, equity premia imply that marginal utility growth varies much more, by at least 50% per year. Therefore, marginal utility growth must be highly correlated across countries: international risk sharing is better than you think. Conversely, if risks really are not shared internationally, exchange rates should vary more than they do: exchange rates are too smooth. We calculate an index of international risk sharing that formalizes this intuition. We treat carefully the realistic case of incomplete capital markets. We contrast our estimates with the poor risk sharing suggested by consumption data and home-bias portfolio calculations.