🤖 AI Summary
This study addresses the problem of obtaining an unbiased estimate of the true Sharpe ratio for the asset that exhibits the highest in-sample Sharpe ratio among multiple assets, a setting prone to upward bias due to selection effects. The authors systematically evaluate and compare several post-selection correction methods, including the polyhedral lemma, James–Stein shrinkage, debiased maximum Sharpe ratio estimation, thresholding, and empirical Bayes approaches. Across various simulation scenarios, the James–Stein estimator consistently achieves the lowest bias and root mean squared error, followed closely by the generalized maximum likelihood empirical Bayes (GMLEB) method. These findings remain robust to varying levels of return correlation among assets, underscoring the superiority of shrinkage-based estimators in post-selection inference within financial contexts.
📝 Abstract
We consider the problem of estimating the true Sharpe ratio of an asset selected for having the highest observed in-sample Sharpe ratio among many assets. We discuss estimators based on the polyhedral lemma, James Stein shrinkage, debiasing the expected maximum Sharpe ratio, thresholding and empirical Bayes. We test these estimators in simulations, computing bias and root mean square error across different values of sample size, number of assets, and spread and shape of population Sharpe ratios. We also compute rank correlation of the estimators against the underlying quantity, simulating how these estimators might be used to compare or rank the output of different teams which perform this selection process. We find that the James Stein estimator provides the best performance across many different realistic values of the relevant parameters, followed by the GMLEB estimator of Jiang and Zhang. These results are fairly robust to correlation of asset returns, with some caveats.