Bayesian predictive distributions quantify uncertainty about out-of-sample values of a random process conditional only on observed data; uncertainty regarding model-specific parameters being integrated out via the usual probability calculus. While immensely useful, application of Bayesian prediction is model specific and its statistical validity is most relevant under the so-called M-closed worlds interpretation of model specification. Herein, we propose a novel method for constructing Bayesian predictive distributions that explicitly acknowledges that practitioners operate in an M-open world. This new approach is not based upon a given model, but is instead driven by a user-supplied concept of predictive performance loss. To develop such machinery in the Bayesian paradigm, we rely on the principles underlying approximate Bayesian computation. Specifically, construction of prediction distributions is carried out using simulation, summary statistics that minimize predictive loss over a pre- specified training period, and a tolerance level that captures our risk aversion to predictive loss.