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

✍ Scribed by Donald Lien

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
100 KB
Volume
22
Category
Article
ISSN
0270-7314

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✦ Synopsis

Abstract

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. Β© 2002 Wiley Periodicals, Inc. Jrl Fut Mark
22:483–495, 2002

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