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A strong case to calculate the Treynor ratio using log-returns

Author

Listed:
  • Ziemowit Bednarek

    (California Polytechnic State University at San Luis Obispo)

  • Oleksandr Firsov

    (Orfalea College of Business)

  • Pratish Patel

    (California Polytechnic State University at San Luis Obispo)

Abstract

Both of the building blocks of the Treynor ratio (TR), the expected return and the portfolio beta, depend on the investment horizon. This raises a natural question: how to compare two portfolios using TR over different horizons? Previous studies show that there may be a ranking reversal. That is, one portfolio may look attractive at a short horizon but not at a longer horizon. We theoretically show that the ranking reversal is due to the compounding of simple returns. We propose to calculate the TR using log-returns, not simple returns. Since the multi-period log-returns are additive, there is no ranking reversal. We empirically corroborate the theory using portfolio of bonds, large and small stocks. Using robust bootstrapped estimates, we are the first to provide TR of several popular test assets over a long horizon (up to 30 years).

Suggested Citation

  • Ziemowit Bednarek & Oleksandr Firsov & Pratish Patel, 2017. "A strong case to calculate the Treynor ratio using log-returns," Journal of Asset Management, Palgrave Macmillan, vol. 18(4), pages 317-325, July.
    • Handle: RePEc:pal:assmgt:v:18:y:2017:i:4:d:10.1057_s41260-017-0040-0
    DOI: 10.1057/s41260-017-0040-0
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    References listed on IDEAS

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    1. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    2. 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.
    3. Jea, Rong & Lin, Jin-Lung & Su, Chao-Ton, 2005. "Correlation and the time interval in multiple regression models," European Journal of Operational Research, Elsevier, vol. 162(2), pages 433-441, April.
    4. Levhari, David & Levy, Haim, 1977. "The Capital Asset Pricing Model and the Investment Horizon," The Review of Economics and Statistics, MIT Press, vol. 59(1), pages 92-104, February.
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