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Evaluation by the Aumann and Serrano performance index and Sharpe ratio: Bitcoin performance

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  • Jiro Hodoshima
  • Nana Otsuki

Abstract

We compare Bitcoin performance based on the Aumann and Serrano performance index and Sharpe ratio assuming that asset returns follow the class of discrete normal mixture distributions. The Aumann and Serrano performance index can take into account higher moments of the underlying distribution of assets and is relevant for risk-averse investors. We evaluate Bitcoin performance based on the Aumann and Serrano index relative to the performance of other assets. Our evaluation shows that Bitcoin is rated highly by the Sharpe ratio but rated very poorly by the Aumann and Serrano index. We also find some stock assets can beat Bitcoin by the Sharpe ratio when an investment horizon is monthly.

Suggested Citation

  • Jiro Hodoshima & Nana Otsuki, 2019. "Evaluation by the Aumann and Serrano performance index and Sharpe ratio: Bitcoin performance," Applied Economics, Taylor & Francis Journals, vol. 51(39), pages 4282-4298, August.
    • Handle: RePEc:taf:applec:v:51:y:2019:i:39:p:4282-4298
    DOI: 10.1080/00036846.2019.1591601
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    Citations

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    Cited by:

    1. Parthajit Kayal & G. Balasubramanian, 2021. "Excess Volatility in Bitcoin: Extreme Value Volatility Estimation," IIM Kozhikode Society & Management Review, , vol. 10(2), pages 222-231, July.
    2. Jiro Hodoshima & Tetsuya Misawa & Yoshio Miyahara, 2020. "Stock Performance Evaluation Incorporating High Moments and Disaster Risk: Evidence from Japan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(2), pages 155-174, June.
    3. Jiro Hodoshima & Toshiyuki Yamawake, 2020. "The Aumann–Serrano Performance Index for Multi-Period Gambles in Stock Data," JRFM, MDPI, vol. 13(11), pages 1-18, November.
    4. Lu, Richard & Horng, Tzyy-Leng & Horng, Min-Sun & Wang, Amy Z.-H., 2023. "A performance evaluation of portfolio insurance under the Black and Scholes framework: An application of the economic index of riskiness," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 269-276.

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