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.

翻译：我们考虑估计某个资产真实夏普比率的问题，该资产因在众多资产中具有最高的样本内观测夏普比率而被选中。我们讨论了基于多面体引理、詹姆斯-斯坦因收缩、期望最大夏普比率去偏、阈值化以及经验贝叶斯的估计量。我们通过模拟测试了这些估计量，在样本量、资产数量、总体夏普比率的分布范围和形状等不同参数值下计算了偏差和均方根误差。我们还计算了这些估计量与潜在真实值之间的秩相关系数，模拟了这些估计量如何用于比较或排序执行此选择过程的不同团队的输出结果。我们发现，詹姆斯-斯坦因估计量在相关参数的多种实际取值下表现最佳，其次是江和张提出的GMLEB估计量。这些结果对资产收益的相关性具有相当稳健性，但存在一些注意事项。