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

Author

Listed:
  • Antoine Jacquier
  • Johannes Muhle-Karbe
  • Joseph Mulligan

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.

Suggested Citation

  • Antoine Jacquier & Johannes Muhle-Karbe & Joseph Mulligan, 2025. "In-Sample and Out-of-Sample Sharpe Ratios for Linear Predictive Models," Papers 2501.03938, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2501.03938
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    References listed on IDEAS

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    1. R. David Mclean & Jeffrey Pontiff, 2016. "Does Academic Research Destroy Stock Return Predictability?," Journal of Finance, American Finance Association, vol. 71(1), pages 5-32, February.
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