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A Critical Evaluation of the Portfolio Performance Indices Under Rank Transformation

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Encyclopedia of Finance

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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 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. Texas A&M International University, Laredo, TX, USA

    Ken Hung

  2. Clarion University of Pennsylvania, Clarion, PA, USA

    Chin-Wei Yang, Matthew Brigida & Dwight B. Means Jr.

  3. National Chung cheng University, Chia-yi, Taiwan, Republic of China

    Chin-Wei Yang

Authors
  1. Ken Hung
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  2. Chin-Wei Yang
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  3. Matthew Brigida
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  4. Dwight B. Means Jr.
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Corresponding author

Correspondence to Ken Hung .

Editor information

Editors and Affiliations

  1. Dept. Finance, Rutgers University, Rockafeller Road 94, New Brunswick, 08854-8054, New Jersey, USA

    Cheng-Few Lee

  2. College of Business, San Francisco State University, Holloway Ave. 1600, San Fransisco, 94132, California, USA

    Alice C. Lee

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Hung, K., Yang, CW., Brigida, M., Means, D.B. (2013). A Critical Evaluation of the Portfolio Performance Indices Under Rank Transformation. In: Lee, CF., Lee, A. (eds) Encyclopedia of Finance. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5360-4_22

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  • DOI: https://doi.org/10.1007/978-1-4614-5360-4_22

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4614-5359-8

  • Online ISBN: 978-1-4614-5360-4

  • eBook Packages: Business and Economics

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