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Notes on Fano Ratio and Portfolio Optimization

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  • Zura Kakushadze
  • Willie Yu
Abstract
We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the Fano ratio (which, unlike the Sharpe ratio, is independent of the time horizon). Thus, for long-only portfolios optimizing the Fano ratio generally results in a more diversified and less skewed portfolio (compared with optimizing the Sharpe ratio). We give an explicit algorithm for such optimization. We also discuss (Fano-ratio-inspired) long-short strategies that outperform those based on optimizing the Sharpe ratio in our backtests.

Suggested Citation

  • Zura Kakushadze & Willie Yu, 2017. "Notes on Fano Ratio and Portfolio Optimization," Papers 1711.10640, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1711.10640
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    References listed on IDEAS

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    1. Zura Kakushadze & Willie Yu, 2016. "Statistical Industry Classification," Journal of Risk & Control, Risk Market Journals, vol. 3(1), pages 17-65.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    9. Cheng-Few Lee & John C. Lee (ed.), 2015. "Handbook of Financial Econometrics and Statistics," Springer Books, Springer, edition 127, number 978-1-4614-7750-1, June.
    10. Zura Kakushadze, 2016. "On Origins of Bubbles," Papers 1610.03769, arXiv.org, revised Jul 2017.
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    12. Bai, Zhidong & Wang, Keyan & Wong, Wing-Keung, 2011. "The mean-variance ratio test--A complement to the coefficient of variation test and the Sharpe ratio test," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1078-1085, August.
    13. Zura Kakushadze, 2016. "101 Formulaic Alphas," Papers 1601.00991, arXiv.org, revised Mar 2016.
    14. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    15. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    16. Zura Kakushadze, 2017. "On Origins of Bubbles," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 1-30.
    17. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.
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    Cited by:

    1. Zura Kakushadze & Willie Yu, 2018. "Betas, Benchmarks and Beating the Market," Papers 1807.09919, arXiv.org.

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