We present and test a model relating a firm's idiosyncratic cost, its exporting status, and the volatilities of its domestic and export sales. In prior models of trade, supply costs for domestic and exports were linear and thus additively separable. We introduce a nonlinear cost function in order to link the domestic and export supply costs. This theoretical contribution has two new implications for the exporting firm. First, the demand volatility in the foreign market now directly affects the firm's domestic sales volatility. Second, firms hedge domestic demand volatility with exports. The model has several testable predictions. First, larger firms have lower total and domestic sales volatilities. Second, foreign market volatility increases domestic sales volatilities for exporters. Third, exporters allocate output across both markets in order to reduce total sales volatility. We find evidence for these predictions with Danish firms operating between 1992 and 2006.