Optimal protective responses to long-term risks depend on rational perceptions of ambiguous risks and uncertain time horizons. Our study examined the joint influence of uncertain delay and risk in an original sample of business owners and managers. We found that many subjects disliked uncertainty in the timing of an outcome, a reaction we term ``lottery timing risk aversion.'' Such aversion to uncertain timing was positively related to aversion to ambiguous probabilities for lotteries involving storm damage risks. This association suggests that uncertainty may be processed similarly in both the risk and time dimensions.