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

Ziemowit Bednarek (), Oleksandr Firsov and Pratish Patel
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Ziemowit Bednarek: California Polytechnic State University at San Luis Obispo
Oleksandr Firsov: Orfalea College of Business

Journal of Asset Management, 2017, vol. 18, issue 4, No 5, 317-325

Abstract: 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).

Keywords: Beta; Treynor ratio; investment horizon; portfolio allocation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1057/s41260-017-0040-0

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