Abstract
This study establishes a nontrivial upper bound on the out-of-sample R² (R²_OOS) in return forecasting. In particular, we define a coin-flip oracle model that, under the same directional accuracy, theoretically outperforms practical models in terms of MSE. The R²_OOS of the oracle model, whose analytical expression is a quadratic function of directional accuracy, can therefore serve as a tractable upper bound on the actual R²_OOS. Empirical analyses across multiple forecasting scenarios reveal that the R²_OOS values of common predictive models are fundamentally bounded by this quadratic function.