A note on Guo and Xiao's (2016) results on monotonic functions of the Sharpe ratio

In this note, we point out that the recent finding of Guo and Xiao (2016) that several performance measures are monotonic functions of the Sharpe ratio under the family of location-scale distributions is not fully original but has already been covered by the earlier theoretical studies of Schuhmacher and Eling (2011, 2012) and Schuhmacher and Auer (2014).