Does demand volatility matter for exports? How do exporting firms deal with skewed demand? A simple model of downside risk aversion shows that on average exporters increase export prices and reduce export volumes when demand volatility in destination markets increases. They behave the opposite way when demand skewness rises. We find that the moments of the demand distribution also affect the number of exporting firms and the industry supply. These adjustments may lead some firms to increase their exports when demand volatility increases. These theoretical predictions are put to the test by using French firm-level exports across destination markets with different levels of demand volatility and skewness. The firm-level results, over the period 2000-2009, are consistent with our predictions.