Demand shocks have been shown to be an important determinant of firm sales' variation across different markets. The key insight of this paper is that, in presence of incomplete financial markets, firms can reduce demand risk through geographical diversification. I first develop a general equilibrium trade model with monopolistic competition, characterized by stochastic demand and risk-averse entrepreneurs, who exploit the imperfect correlation of demand across countries to lower the variance of their total sales. Despite its complexity, I provide a novel analytical characterization of the firms problem and show that both entry and trade flows to a market are affected by its risk-return profile, which in turn depends on the multilateral covariance of the country's demand with all other markets. Moreover, I show that welfare gains from trade can be significantly higher than the gains predicted by standard models which neglect firm level risk. After a trade liberalization, risk-averse firms boost exports to countries that offer better diversification benefits. Hence, in these markets foreign competition becomes stronger, lowering the price level more. Therefore, countries with better risk-return profiles gain more from international trade, while riskier markets reap lower gains. I then use data on Portuguese firm-level international trade flows, from 1995 to 2005, to provide evidence that exporters behave in a way consistent with my model's predictions. Finally, policy counterfactuals reveal that, for the median country in the sample, the risk diversification channel increases welfare gains from trade by 15% relative to traditional models with risk neutrality.