Paper: arXiv 2501.03938

Abstract

We study how much the in-sample performance of trading strategies based on linear predictive models is reduced out-of-sample due to overfitting. More specifically, we compute the in- and out-of-sample means and variances of the corresponding PnLs and use these to derive a closed-form approximation for the corresponding Sharpe ratios. We find that the out-of-sample “replication ratio” diminishes for complex strategies with many assets based on many weak rather than a few strong trading signals, and increases when more training data is used. The substantial quantitative importance of these effects is illustrated with a simulation case study for commodity futures following the methodology of Gârleanu and Pedersen, and an empirical case study using the dataset compiled by Goyal, Welch and Zafirov.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper is mathematically dense, deriving closed-form approximations for Sharpe ratios using advanced statistical models, yet it validates these with concrete empirical and simulation case studies using real financial datasets.

Research Flowchart

  flowchart TD
  A["Research Goal: Quantify OOS Sharpe<br>ratio decay from in-sample overfitting"] --> B["Methodology: Closed-form approximation<br>for in- & out-of-sample Sharpe ratios"]
  B --> C[""Data & Models:
      - Simulation (Commodity Futures)
      - Empirical (Goyal, Welch, Zafirov dataset)""]
  C --> D["Computational Process:<br>Derive replication ratio<br>(OOS / In-Sample Sharpe)"]
  D --> E[""Key Findings:
      - OOS replication ratio decreases with<br>complexity (many assets, weak signals)
      - Increases with more training data
      - Quantified via Gârleanu & Pedersen simulation & empirical study""]