A Nontrivial Upper Bound on the Out-of-Sample $R^2$ in Return Forecasting
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914447353708544 |
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| author | Zhang, Cheng |
| author_facet | Zhang, Cheng |
| contents | This study establishes a nontrivial upper bound on the out-of-sample $R^2$ ($R^2_{\text{OOS}}$) 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 $R^2_{\text{OOS}}$ 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 $R^2_{\text{OOS}}$. Empirical analyses across multiple forecasting scenarios reveal that the $R^2_{\text{OOS}}$ values of common predictive models are fundamentally bounded by this quadratic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Nontrivial Upper Bound on the Out-of-Sample $R^2$ in Return Forecasting Zhang, Cheng Econometrics Statistical Finance Applications This study establishes a nontrivial upper bound on the out-of-sample $R^2$ ($R^2_{\text{OOS}}$) 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 $R^2_{\text{OOS}}$ 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 $R^2_{\text{OOS}}$. Empirical analyses across multiple forecasting scenarios reveal that the $R^2_{\text{OOS}}$ values of common predictive models are fundamentally bounded by this quadratic function. |
| title | A Nontrivial Upper Bound on the Out-of-Sample $R^2$ in Return Forecasting |
| topic | Econometrics Statistical Finance Applications |
| url | https://arxiv.org/abs/2602.07841 |