We investigate the extent to which climate change will result in insurable and uninsurable losses for farmers in India. Shifts in the distributions of temperature and precipitation may increase the volatility of farmers' yields, leading to rising but insurable risk, and/or reduce mean yields and thus cause permanent reductions in the returns to farming. We use a multi-run climate model to predict the future distribution of yields at the district level for sixteen major crops. For the average district, we project a sharp decline in mean agricultural revenue, but relatively small shifts in volatility. This is because weather draws resulting in extremely low agricultural revenue -- what had once been 1-in-100-year events -- are predicted to become the norm by the end of the century, implying substantial uninsurable losses from the changing climate.