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Don’t use quotients to calculate performance

Author

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  • Fernando Gómez-Bezares
  • Fernando R. Gómez-Bezares
  • David McMillan

Abstract

Quotients, ratios, are among the most applied tools for measuring performance of mutual funds and investment portfolios, the Jensen index being an exception to the general rule. In this paper, we show some problems that arise when quotients are applied, closely related to their statistical meaning, which is too often forgotten. We also raise some advantages of the use of linear penalization, introducing a little known methodology for performance measurement. With this purpose, this paper’s approach is comprehensive: we conceptually analyze performance indexes’ geometric and statistical meaning, complementing this with a numerical example and empirical testing that confirm our view. This paper’s main contribution is to demonstrate and empirically test how the use of quotients to measure performance may create problems due to their denominators, which may be solved by applying linear penalization.

Suggested Citation

  • Fernando Gómez-Bezares & Fernando R. Gómez-Bezares & David McMillan, 2015. "Don’t use quotients to calculate performance," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1065584-106, December.
    • Handle: RePEc:taf:oaefxx:v:3:y:2015:i:1:p:1065584
    DOI: 10.1080/23322039.2015.1065584
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    References listed on IDEAS

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    1. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, May.
    2. Jensen, Michael C, 1969. "Risk, The Pricing of Capital Assets, and the Evaluation of Investment Portfolios," The Journal of Business, University of Chicago Press, vol. 42(2), pages 167-247, April.
    3. Charles Hodges & Walton Taylor & James Yoder, 2003. "Beta, the Treynor ratio, and long-run investment horizons," Applied Financial Economics, Taylor & Francis Journals, vol. 13(7), pages 503-508.
    4. Eugene F. Fama & Kenneth R. French, 2010. "Luck versus Skill in the Cross‐Section of Mutual Fund Returns," Journal of Finance, American Finance Association, vol. 65(5), pages 1915-1947, October.
    5. Ferruz Agudo, Luis & Sarto Marzal, José Luis, 2004. "An analysis of Spanish investment fund performance: some considerations concerning Sharpe's ratio," Omega, Elsevier, vol. 32(4), pages 273-284, August.
    6. Choong Tze Chua & Winston Koh, 2007. "Measuring investment skills of fund managers," Applied Financial Economics, Taylor & Francis Journals, vol. 17(16), pages 1359-1368.
    7. Craig Israelsen, 2005. "A refinement to the Sharpe ratio and information ratio," Journal of Asset Management, Palgrave Macmillan, vol. 5(6), pages 423-427, April.
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    Cited by:

    1. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2017. "Analysing assets’ performance inside a portfolio: From crossed beta to the net risk premium ratio," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1270251-127, January.

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