Noise fit, estimation error and a Sharpe information criterion

Dirk Paulsen, Jakob Söhl

Research output: Contribution to journalArticleScientificpeer-review

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 a measure of fit.

Original languageEnglish
Pages (from-to)1027-1043
Number of pages17
JournalQuantitative Finance
Volume20
Issue number6
DOIs
Publication statusPublished - 2020

Keywords

  • AIC
  • Akaike information criterion
  • Backtesting
  • Estimation error
  • Model selection
  • Noise fit
  • Overfit
  • Sharpe ratio
  • Sharpe ratio information criterion
  • SRIC

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