In-Sample and Out-of-Sample Sharpe Ratios for Linear Predictive Models

Antoine Jacquier, Johannes Muhle-Karbe and Joseph Mulligan

Papers from arXiv.org

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 G\^arleanu and Pedersen, and an empirical case study using the dataset compiled by Goyal, Welch and Zafirov.

Date: 2025-01, Revised 2025-07
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