Noise fit,estimation error and a Sharpe information criterion |
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Authors: | Dirk Paulsen Jakob Söhl |
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Affiliation: | 1. John Street Capital LLP, London, UKdirk.h.paulsen@gmail.comhttps://orcid.org/0000-0002-0799-3055;3. TU Delft, Delft, The Netherlandshttps://orcid.org/0000-0002-0831-1714 |
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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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Keywords: | Model selection Sharpe ratio Akaike information criterion AIC Backtesting Noise fit Overfit Estimation error Sharpe ratio information criterion SRIC |
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