This article investigates under what conditions an increase in ambiguity reduces demand for an uncertain asset (or raises demand for coinsurance). We find that the comparative statics of ambiguity and of risks have structural similarities under the smooth ambiguity aversion model (Klibanoff, Marinacci, and Mukerji, (2005)). The determinant condition on ambiguity preferences is analogous to that on risk preferences. However, the comparative statics have fundamental differences under the α-maxmin model (Ghirardato, Maccheroni, and Marinacci, 2004). When relative risk aversion is less than 1, only an increase in ambiguity, which broadens support for an investor's belief in the probability of the return distribution in the manner of a strong increase in risk, can reduce demand for an uncertain asset.