Paper: arXiv 2602.07841

Authors: Cheng Zhang

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a neat theoretical derivation for an upper bound on out-of-sample R2 using a coin-flip oracle model based on directional accuracy. The math is elegant and tractable, accompanied by clear empirical validation on weekly asset returns and a public GitHub link for reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Establish Nontrivial Upper Bound for Out-of-Sample R² in Return Forecasting] --> B[Define Coin-Flip Oracle Model based on Directional Accuracy]
    B --> C[Derive Analytical Expression: Quadratic Function of Directional Accuracy]
    D[Inputs: Multiple Forecasting Scenarios & Equities Data] --> E[Empirical Analysis: Compare Common Predictive Models against Oracle Model]
    C --> E
    E --> F[Key Outcome: R²_OOS of Practical Models is Fundamentally Bounded by Oracle Quadratic Function]

Cited References (18)

  1. Reprint of: Generalized Autoregressive Conditional Heteroskedasticity (2023) — link
  2. Empirical Asset Pricing via Machine Learning (2018) — link
  3. Why is it so difficult to outperform the random walk in exchange rate forecasting? (2013) — link
  4. A Comprehensive Look at the Empirical Performance of Equity Premium Prediction (2009) — link
  5. Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average? (2008) — link
  6. Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics (2006) — link
  7. A Multiple Indicators Model for Volatility Using Intra-Daily Data (2003) — link
  8. Predictability of Stock Returns: Robustness and Economic Significance (1995) — link
and 10 more
  1. Some Properties of Absolute Return, An Alternative Measure of Risk (1995) — link
  2. Expected stock returns and volatility (1987) — link
  3. On Estimating the Expected Return on the Market: An Exploratory Investigation (1980) — link
  4. Modeling Financial Return Dynamics by Decomposition (2007)
  5. Why is it so difficult to beat the random walk forecast of exchange rates ? (2001)
  6. Economic Forecast Evaluation: Profits versus the Conventional Error Measures (1991)
  7. Do they fit out of sample (1983)
  8. L2 α = 0 . 1, Adam
    1. Forecasting: theory and practice
    1. Pockets of predictability

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.