We derive (1) an unbiased estimator for the out-of-sample Sharpe ratio when the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space . The estimator corrects the in-sample Sharpe ratio for both : noise fit and estimation error. We then show (2) how to use the corrected Sharpe ratio as model selection criterion analogous to the Akaike Information Criterion (AIC). Selecting a model with the highest corrected 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.
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.
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We derive (1) an unbiased estimator for the out-of-sample Sharpe ratio when the
When the
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. The estimator corrects the in-sample Sharpe ratio for both
, 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
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corrected
adjusted
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analogous
analogously
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corrected
adjusted