Using firm and industry data, we unveil two empirical regularities: (i) Demand uncertainty not only reduces export probabilities but also decreases export quantities and increases export prices; (ii) The most productive exporters are more affected by higher industry-wide expenditure volatility than are the least productive exporters. We rationalize these regularities by developing a new firm-based trade model wherein managers are risk averse. Higher volatility induces the reallocation of export shares from the most to the least productive incumbents. Greater skewness of the demand distribution and/or higher trade costs weaken this effect. Our results hold for a large class of consumer utility functions.