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The low observed uptake of non-subsidised index-based insurance policies in developing countries has been puzzling researchers for about a decade. This paper analyses the role of drought frequency in farmers' demand for index-based insurance in developing countries. While it is typically assumed that an increase in exposure to risk would result in higher demand for index insurance, this paper finds the opposite: an increase in drought frequency may result in lower demand for index insurance under fairly standard conditions. In an expected utility model, we show that the demand for insurance is an inverted U function of drought frequency. We further show that downside basis risk decreases insurance demand under frequent drought conditions. It implies that insurance against similar but more frequent events cannot meet large demand from farmers. To check the empirical relevance of these effects, we conduct an insurance field experiment in Burkina Faso with 205 farmers. We analyse insurance demand for different drought frequencies, different levels of basis risks and different loading factors through incentivised lottery choices. This analysis confirms that for higher drought frequencies, insurance demand is lower. Insurance demand also decreases with basis risk and the loading factor.