IDEAS home Printed from https://ideas.repec.org/a/pal/assmgt/v18y2017i4d10.1057_s41260-017-0040-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/s41260-017-0040-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1057/s41260-017-0040-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Edna Schechtman & Amit Shelef, 2018. "Correlation and the time interval over which the variables are measured – A non-parametric approach," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-9, November.
    2. George G. Kaufman, 1980. "Duration, Planning Period, And Tests Of The Capital Asset Pricing Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 3(1), pages 1-9, March.
    3. Javier Bianchi & Enrique G. Mendoza, 2018. "Optimal Time-Consistent Macroprudential Policy," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 588-634.
    4. R. Anton Braun & Tomoyuki Nakajima, 2011. "Making the Case for a Low Intertemporal Elasticity of Substitution," KIER Working Papers 788, Kyoto University, Institute of Economic Research.
    5. Luo, Yulei & Young, Eric R., 2016. "Induced uncertainty, market price of risk, and the dynamics of consumption and wealth," Journal of Economic Theory, Elsevier, vol. 163(C), pages 1-41.
    6. Taisuke Nakata & Hiroatsu Tanaka, 2020. "Equilibrium Yield Curves and the Interest Rate Lower Bound," CARF F-Series CARF-F-482, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Semenov, Andrei, 2021. "Measuring the stock's factor beta and identifying risk factors under market inefficiency," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 635-649.
    8. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    9. Zsofia Barany & Nicolas Coeurdacier & Stéphane Guibaud, 2015. "Fertility, Longevity and International Capital Flows," Working Papers hal-01164462, HAL.
    10. Masakatsu Okubo, 2011. "The Intertemporal Elasticity of Substitution: An Analysis Based on Japanese Data," Economica, London School of Economics and Political Science, vol. 78(310), pages 367-390, April.
    11. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    12. David N. DeJong & Emilio Espino, 2007. "The Cyclical Behavior of Equity Turnover," Working Paper 294, Department of Economics, University of Pittsburgh, revised Jun 2010.
    13. Suleyman Basak & Hongjun Yan, 2010. "Equilibrium Asset Prices and Investor Behaviour in the Presence of Money Illusion," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 914-936.
    14. Rieger, Marc Oliver & Wang, Mei, 2012. "Can ambiguity aversion solve the equity premium puzzle? Survey evidence from international data," Finance Research Letters, Elsevier, vol. 9(2), pages 63-72.
    15. Chabakauri, Georgy, 2010. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 43142, London School of Economics and Political Science, LSE Library.
    16. Marc Oliver Rieger & Thorsten Hens & Mei Wang, 2013. "International Evidence on the Equity Premium Puzzle and Time Discounting," Multinational Finance Journal, Multinational Finance Journal, vol. 17(3-4), pages 149-163, September.
    17. Emi Nakamura & Jón Steinsson & Robert Barro & José Ursúa, 2013. "Crises and Recoveries in an Empirical Model of Consumption Disasters," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 35-74, July.
    18. Francisco Azeredo, 2014. "The equity premium: a deeper puzzle," Annals of Finance, Springer, vol. 10(3), pages 347-373, August.
    19. Chen, Long & Petkova, Ralitsa & Zhang, Lu, 2008. "The expected value premium," Journal of Financial Economics, Elsevier, vol. 87(2), pages 269-280, February.
    20. Laimutė Urbšienė & Andrius Bugajevas & Marekas Pipiras, 2016. "The Impact Of Investment Horizon On The Return And Risk Of Investments In Securities In Lithuania," Organizations and Markets in Emerging Economies, Faculty of Economics, Vilnius University, vol. 7(2).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pal:assmgt:v:18:y:2017:i:4:d:10.1057_s41260-017-0040-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.