Droughts are amongst the most damaging natural hazard with cascading impacts across multiple sectors of the economy and society. Improved forecasting of drought conditions ahead of time can significantly improve strategic planning to mitigate the impacts and enhance resilience. Though significant progress in forecasting approaches has been made, the current approaches focus on the overall improvement of the forecast, with less attention on the extremeness of drought events. In this paper, we focus on improving the accuracy of forecasting extreme and severe drought events by introducing a novel loss function Surrogate Quantile and Shape loss (SQUASH) that combines weighted quantile loss and dynamic time-warping-based shape loss. We show the effectiveness of the proposed loss functions for imbalanced time-series drought forecasting tasks on two regions in India and the USA.