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2006 | OriginalPaper | Chapter

21. A note on the relationship among the portfolio performance indices under rank transformation

Authors : Ken Hung, Chin-Wei Yang, Dwight B. Means Jr.

Published in: Encyclopedia of Finance

Publisher: Springer US

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Abstract

This paper analytically determines the conditions under which four commonly utilized portfolio measures (the Sharpe index, the Treynor index, the Jensen alpha, and the Adjusted Jensen’s alpha) will be similar and different. If the single index CAPM model is appropriate, we prove theoretically that well-diversified portfolios must have similar rankings for the Treynor, Sharpe indices, and Adjusted Jensen’s alpha ranking. The Jensen alpha rankings will coincide if and only if the portfolios have similar betas. For multi-index CAPM models, however, the Jensen alpha will not give the same ranking as the Treynor index even for portfolios of large size and similar betas. Furthermore, the adjusted Jensen’s alpha ranking will not be identical to the Treynor index ranking.

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Title: A note on the relationship among the portfolio performance indices under rank transformation
Authors: Ken Hung
Chin-Wei Yang
Dwight B. Means Jr.
Publisher: Springer US
Book: Encyclopedia of Finance
Print ISBN: 978-0-387-26284-0

Electronic ISBN: 978-0-387-26336-6

Copyright Year: 2006
DOI: https://doi.org/10.1007/978-0-387-26336-6_47