This paper investigates the role of basis risk in decisions to buy derivatives that protect against drought risk. We conducted a discrete choice experiment on a sample of Ethiopian farmers. The results suggest that there is an inverted U-shaped relationship between the contractual frequency of severe drought and the market share of insurance. In other words, when the contractual frequency differs from the average perceived frequency, demand decreases. This relationship is not verified for moderate drought insurance. These findings point to the necessity to design insurance for moderate drought events and for risk aggregators that can diversify the idiosyncratic risk component.