In-Sample and Out-of-Sample Sharpe Ratios for Linear Predictive Models
ArXiv ID: 2501.03938 “View on arXiv”
Authors: Unknown
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.
Keywords: Overfitting, In-Sample vs Out-of-Sample, Replication Ratio, Linear Predictive Models, Commodity Futures, Commodities
Complexity vs Empirical Score
- Math Complexity: 8.0/10
- Empirical Rigor: 7.5/10
- Quadrant: Holy Grail
- Why: 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.
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""]