A note on the relationships between some risk-adjusted performance measures


  • Donald Lien

    Corresponding author
    1. The University of Texas—San Antonio, San Antonio, Texas
    • Department of Economics, University of Texas—San Antonio, 6900 North Loop 1604 West, San Antonio, Texas 78249-0633
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Assuming portfolio returns are normally distributed, it is shown that both Sortino ratio (SR) and upside potential ratio (UPR) are monotonically increasing functions of the Sharpe ratio. As a result, all three risk-adjusted performance measures provide identical ranking among investment alternatives. The effects of skewness and kurtosis are then evaluated within the Edgeworth-Sargan density family. For the Sortino ratio, the above conclusion remains valid in the presence of negative skewness or excessive kurtosis. Similar results apply to the UPR with modifications. For all other cases, both SR and UPR provide exactly opposite ranking among investment alternatives to that suggested by the Sharpe ratio when the Sharpe ratio is large. Applications to futures hedging are discussed. Specifically, it is found that the Sharpe ratio may frequently lead to a smaller futures position than the other two ratios. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:483–495, 2002