When optimizing the Sharpe ratio over a k-dimensional parameter space the thus obtained in-sample Sharpe ratio tends to be higher than what will be captured out-of-sample. For two reasons: the estimated parameter will be skewed towards the noise in the in-sample data (noise fitting) and, second, the estimated parameter will deviate from the optimal parameter (estimation error). This article derives a simple correction for both. Selecting a model with the highest corrected Sharpe  selects the model with the highest expected out-of-sample Sharpe  in the same way as selection by Akaike Information Criterion does for the log-likelihood as measure of fit.
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.
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When optimizing the Sharpe ratio
We derive (1) an unbiased estimator for the out-of-sample Sharpe ratio when the in-sample Sharpe ratio is obtained by optimizing
R
the thus obtained
. The estimator corrects the
R
tends to be higher than what will be captured out-of-sample. For two reasons: the estimated parameter will be skewed towards the noise in the in-sample data (noise fitting) and, second, the estimated parameter will deviate from the optimal parameter (estimation error). This article derives a simple correction for both.
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).
A
ratio
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expected
estimated
A
ratio
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Akaike Information Criterion
AIC