We play a series of incentivised laboratory games with risk-exposed co-operativised Guatemalan coffee farmers to understand the demand for index-based rainfall insurance. We estimate an explicit utility curve for every player and hence predict expected utility demand under counterfactual scenarios. Using these estimates, we provide a precise money-metric decomposition of the extent to which the low observed demand for index insurance is driven by expected utility theory, or by behavioural issues arising from a prospect-style utility structure. Our results suggest that consumers value probabilistic insurance using a prospect-style utility function that is concave both in probabilities and in income.