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Encyclopedia of Finance pp 470–476Cite as

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

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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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Author information

Authors and Affiliations

  1. National Dong Hwa University, Hualien, Taiwan

    Ken Hung

  2. Clarion University, Clarion, USA

    Chin-Wei Yang

  3. Consultant, New York, USA

    Dwight B. Means Jr.

Authors
  1. Ken Hung
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  2. Chin-Wei Yang
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  3. Dwight B. Means Jr.
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Editor information

Editors and Affiliations

  1. Rutgers University, New Brunswick/Piscataway, USA

    Cheng-Few Lee

  2. San Francisco State University, San Francisco, USA

    Alice C. Lee

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© 2006 Springer Science+Business Media, Inc.

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Hung, K., Yang, CW., Means, D.B. (2006). A note on the relationship among the portfolio performance indices under rank transformation. In: Lee, CF., Lee, A.C. (eds) Encyclopedia of Finance. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-26336-6_47

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  • DOI: https://doi.org/10.1007/978-0-387-26336-6_47

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-26284-0

  • Online ISBN: 978-0-387-26336-6

  • eBook Packages: Business and Economics

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