Paper: arXiv 2609.26303

Authors: Masoud Soleimani

Abstract

Forecasters often score the same units per date against one standardized realized outcome. We show that every standardized forecast splits exactly into a component aligned with this common target and a component uncorrelated with it. Three consequences follow: forecast-error correlation largely mirrors forecast correlation and is therefore a poor measure of diversity; an equally weighted combination beats a no-information forecast only when average alignment is large relative to the combination’s dispersion; and the gain from adding a forecaster separates into genuine improvement and mere dilution, which equal-weight admission can mistakenly reward. We develop a cautious selection rule, study it in simulations, and apply it to language-model forecasts of US equity rankings and mechanical signals ranking exchange-traded funds. Selection removes most dilution losses, but no combination beats the no-information forecast.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical decomposition of forecast alignment and its implications for combination, backed by simulations and real-world applications. The theoretical contributions are significant, and the empirical sections provide solid validation, even if the ’null findings’ are somewhat counterintuitive.

Research Flowchart

  flowchart TD
    A[Research Goal: Understand cross-sectional forecast dynamics] --> B{Key Concepts: Target alignment, Dilution, Forecast selection};
    B --> C[Methodology: Decompose standardized forecasts into aligned/uncorrelated components];
    C --> D{Data/Inputs: Language model forecasts (US equity), Mechanical signals (ETFs)};
    D --> E[Computational Processes: Analyze forecast-error correlation, Simulate combination strategies, Apply cautious selection rule];
    E --> F[Key Findings: Forecast-error correlation mirrors forecast correlation; Equal-weight combination effectiveness depends on alignment/dispersion; Cautious selection removes dilution losses but no combination beats no-information forecast.];