Inference for the Difference of Two Independent KS Sharpe Ratios under Lognormal Returns

A higher-order likelihood-based asymptotic method to obtain inference for the difference between two KS Sharpe ratios when gross returns of an investment are assumed to be lognormally distributed is proposed. Theoretically, our proposed method has $O\left(n^{-3/2}\right)$ distributional accuracy, whereas conventional methods for inference have $O\left(n^{-1/2}\right)$ distributional accuracy. Using an example, we show how discordant confidence interval results can be depending on the methodology used. We are able to demonstrate the accuracy of our proposed method through simulation studies.