This paper develops a two-country monetary DSGE model in which households choose a portfolio of home and foreign equities, and a forward position in foreign exchange. Some nominal goods prices are sticky. Trade in these assets achieves the same allocations as trade in a complete set of nominal state-contingent claims in our linearized model. When there is a high degree of price stickiness, we show that not much equity diversification is required to replicate the complete-markets equilibrium when agents are able to hedge foreign exchange risk sufficiently. Moreover, temporarily sticky nominal goods prices can have large effects on equity portfolios even when dividend processes are very persistent.