Data-driven stochastic programming aims to find a procedure that transforms time series data to a near-optimal decision (a prescriptor) and to a prediction of this decision's expected cost under the unknown data-generating distribution (a predictor). We propose a meta-optimization problem to find the least conservative predictors and prescriptors subject to constraints on their out-of-sample disappointment. Leveraging tools from large deviations theory, we prove that the best predictor-prescriptor pair is obtained by solving a distributionally robust optimization problem.