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A Critical Evaluation of the Portfolio Performance Indices Under Rank Transformation

In: Encyclopedia of Finance

Author

Listed:
  • Ken Hung

    (Texas A&M International University)

  • Chin W. Yang

    (Clarion University of Pennsylvania
    National Chung Cheng University)

  • Matthew Brigida

    (SUNY Polytechnic Institute)

  • Dwight B. Means

    (Clarion University of Pennsylvania)

Abstract

This chapter 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.

Suggested Citation

  • Ken Hung & Chin W. Yang & Matthew Brigida & Dwight B. Means, 2022. "A Critical Evaluation of the Portfolio Performance Indices Under Rank Transformation," Springer Books, in: Cheng-Few Lee & Alice C. Lee (ed.), Encyclopedia of Finance, edition 0, chapter 22, pages 761-771, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-91231-4_22
    DOI: 10.1007/978-3-030-91231-4_22
    as

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