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A Bayesian Approach to Measurement of Backtest Overfitting

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  • Jiří Witzany

    (Department of Banking and Insurance, Faculty of Finance and Accounting, University of Economics, W. Churchill Sq. 4, 130 67 Prague, Czech Republic)

Abstract

Quantitative investment strategies are often selected from a broad class of candidate models estimated and tested on historical data. Standard statistical techniques to prevent model overfitting such as out-sample backtesting turn out to be unreliable in situations when the selection is based on results of too many models tested on the holdout sample. There is an ongoing discussion of how to estimate the probability of backtest overfitting and adjust the expected performance indicators such as the Sharpe ratio in order to reflect properly the effect of multiple testing. We propose a consistent Bayesian approach that yields the desired robust estimates on the basis of a Markov chain Monte Carlo (MCMC) simulation. The approach is tested on a class of technical trading strategies where a seemingly profitable strategy can be selected in the naïve approach.

Suggested Citation

  • Jiří Witzany, 2021. "A Bayesian Approach to Measurement of Backtest Overfitting," Risks, MDPI, vol. 9(1), pages 1-22, January.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:1:p:18-:d:476849
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    References listed on IDEAS

    as
    1. Campbell R. Harvey & Yan Liu, 2020. "False (and Missed) Discoveries in Financial Economics," Journal of Finance, American Finance Association, vol. 75(5), pages 2503-2553, October.
    2. Marcos López de Prado & Michael J. Lewis, 2019. "Detection of false investment strategies using unsupervised learning methods," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1555-1565, September.
    3. Isaiah Andrews & Maximilian Kasy, 2019. "Identification of and Correction for Publication Bias," American Economic Review, American Economic Association, vol. 109(8), pages 2766-2794, August.
    4. Andrew Y Chen & Tom Zimmermann & Jeffrey Pontiff, 2020. "Publication Bias and the Cross-Section of Stock Returns," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 10(2), pages 249-289.
    5. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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