Noise fit, estimation error and a Sharpe information criterion

Paulsen, Dirk; Söhl, J.

Noise fit, estimation error and a Sharpe information criterion

Journal article (2020)

Authors

Dirk Paulsen John Street Capital LLP, London

J. Söhl Statistics -

Research Group

Statistics () (TU Delft)

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

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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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.

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