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Noise Fit, Estimation Error and a Sharpe Information Criterion

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  • Dirk Paulsen
  • Jakob Sohl

Abstract

When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise fit and estimation error. We then show (2) how to use the adjusted Sharpe ratio as model selection criterion analogously to the Akaike Information Criterion (AIC). Selecting a model with the highest adjusted Sharpe ratio selects the model with the highest estimated out-of-sample Sharpe ratio in the same way as selection by AIC does for the log-likelihood as measure of fit.

Suggested Citation

  • Dirk Paulsen & Jakob Sohl, 2016. "Noise Fit, Estimation Error and a Sharpe Information Criterion," Papers 1602.06186, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1602.06186
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    References listed on IDEAS

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    1. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    2. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    3. Hutton, James E. & Nelson, Paul I., 1984. "Interchanging the order of differentiation and stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 371-377, November.
    4. Robert Novy-Marx, 2015. "Backtesting Strategies Based on Multiple Signals," NBER Working Papers 21329, National Bureau of Economic Research, Inc.
    5. Bossaerts, Peter & Hillion, Pierre, 1999. "Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn?," The Review of Financial Studies, Society for Financial Studies, vol. 12(2), pages 405-428.
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    Cited by:

    1. Vukovic, Darko & Vyklyuk, Yaroslav & Matsiuk, Natalia & Maiti, Moinak, 2020. "Neural network forecasting in prediction Sharpe ratio: Evidence from EU debt market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).

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