A Nontrivial Upper Bound on the Out-of-Sample R2 in Return Forecasting

Battle Count: 134

Highly relevant to quantitative trading as it establishes fundamental theoretical limits on return forecasting performance (R²_OOS), directly informing realistic expectations for trading strategy development. The quadratic relationship between directional accuracy and R²_OOS provides a practical benchmark for evaluating whether a forecasting model is performing near its theoretical ceiling. The metric disconnect finding (negative R² with positive directional accuracy) is particularly important for strategy design. However, the paper is primarily theoretical/evaluative rather than providing actionable trading signals or portfolio construction methods.

The theoretical derivation involves moderately complex algebra (MSE decomposition, law of total expectation, conditional independence assumptions). The empirical implementation is straightforward: estimate κ via GARCH(1,1) volatility, compute directional accuracy, and plot (2DA-1)² vs R²_OOS/κ̂. The 10 baseline models are standard and well-documented. The main complexity lies in understanding the theoretical framework and correctly implementing the κ estimation with proper trimming.

Data and code are publicly available on GitHub (https://github.com/Zhang-Cheng-76200/R2DA). The methodology is fully specified with analytical derivations. Data is sourced from Yahoo Finance (publicly accessible). Model configurations are detailed in Table A3. However, the paper is a single-author work with no external validation, and the κ estimation depends on GARCH(1,1) volatility estimates which may vary across implementations.