An Estimation Error Corrected Sharpe Ratio Using Bootstrap Resampling

The Sharpe ratio is a common financial performance measure that represents the optimal risk versus return of an investment portfolio, also defined as the slope of the capital market line within the mean-variance Markowitz efficient frontier. Obtaining sample point and confidence interval estimates for this metric is challenging due to both its dynamic nature and issues surrounding its statistical properties. Given the importance of obtaining robust determinations of risk versus return within financial portfolios, the purpose of the current research was to improve the statistical estimation error associated with Sharpe’s ratio, offering an approach to point and confidence interval estimation which employs bootstrap resampling and computational intelligence. This work also extends prior studies by minimizing the ratio’s statistical estimation error first by incorporating the common assumption that the ratio’s loss function is the squared error and second by correcting for overestimation through an approach that recognizes that the negative covariance between the variables representing the estimate of the Sharpe ratio and the standard deviation can be used for corrective purposes. Results of an accompanying empirical simulation study indicated improved relative efficiency of point estimates and the coverage probability, coverage error, length, and relative bias of confidence intervals.