IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/120203.html
   My bibliography  Save this paper

Sortino(γ): a modified Sortino ratio with adjusted threshold

Author

Listed:
  • Kroll, Yoram
  • Marchioni, Andrea
  • Ben-Horin, Moshe

Abstract

A portfolio’s Sortino ratio is strongly affected by the risk-free vs. risky assets mix, except for the case where the threshold, T is equal to the risk-free rate. Therefore, if T differs from the risk-free rate, the portfolio’s Sortino ratio could potentially be increased by merely changing the mix of the risk-free and the risky components. The widely used Sharpe ratio, on the other hand, does not share this caveat. We introduce a modified Sortino ratio, Sortino(γ), which is invariant with respect to the portfolio’s risk-free vs. risky assets mix, and hence eliminates the above deficiency. The selected threshold T(γ), mimics the portfolio composition in the sense that it equals to the risk-free rate plus γ times the portfolio’s equity risk premium. Higher selected γ reflects higher risk/loss aversion. We propose a procedure for optimizing the composition of the risky portion of the portfolio to maximize the Sortino(γ) ratio. In addition, we show that Sortino(γ) is consistent with first and second order stochastic dominance with riskless asset rules.

Suggested Citation

  • Kroll, Yoram & Marchioni, Andrea & Ben-Horin, Moshe, 2024. "Sortino(γ): a modified Sortino ratio with adjusted threshold," MPRA Paper 120203, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:120203
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/120203/1/MPRA_paper_120203.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Josep Perello, 2006. "Downside Risk analysis applied to Hedge Funds universe," Papers physics/0610162, arXiv.org, revised Apr 2007.
    2. Christian Pedersen & Stephen Satchell, 2002. "On the foundation of performance measures under asymmetric returns," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 217-223.
    3. Balder, Sven & Schweizer, Nikolaus, 2017. "Risk aversion vs. the Omega ratio: Consistency results," Finance Research Letters, Elsevier, vol. 21(C), pages 78-84.
    4. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    5. Levy, Haim & Kroll, Yoram, 1976. "Stochastic Dominance with Riskless Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(5), pages 743-777, December.
    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. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    2. Christian Bach, 2011. "Conservatism in Corporate Valuation," CREATES Research Papers 2011-32, Department of Economics and Business Economics, Aarhus University.
    3. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    4. Michele Costola & Massimiliano Caporin, 2016. "Rational Learning For Risk-Averse Investors By Conditioning On Behavioral Choices," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-26, March.
    5. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    6. Shi, Huai-Long & Zhou, Wei-Xing, 2022. "Factor volatility spillover and its implications on factor premia," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    7. Muhammad Kashif & Thomas Leirvik, 2022. "The MAX Effect in an Oil Exporting Country: The Case of Norway," JRFM, MDPI, vol. 15(4), pages 1-16, March.
    8. Michel Fliess & Cédric Join, 2009. "Systematic risk analysis: first steps towards a new definition of beta," Post-Print inria-00425077, HAL.
    9. Radosław Kurach, 2013. "Does Beta Explain Global Equity Market Volatility – Some Empirical Evidence," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 7(2), June.
    10. Shi, Yun & Cui, Xiangyu & Zhou, Xunyu, 2020. "Beta and Coskewness Pricing: Perspective from Probability Weighting," SocArXiv 5rqhv, Center for Open Science.
    11. Abugri, Benjamin A. & Dutta, Sandip, 2014. "Are we overestimating REIT idiosyncratic risk? Analysis of pricing effects and persistence," International Review of Economics & Finance, Elsevier, vol. 29(C), pages 249-259.
    12. Sree Vinutha Venkataraman, 2023. "A remark on mean‐semivariance behaviour: Downside risk and capital asset pricing," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(3), pages 2683-2695, July.
    13. Hany Shawky & Ronald Forbes & Alan Frankle, 1983. "Liquidity Services and Capital Market Equilibrium: The Case for Money Market Mutual Funds," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 6(2), pages 141-152, June.
    14. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    15. Debabrata Mukhopadhyay & Nityananda Sarkar, 2021. "A Starting Note: Do Green Indices Outperform BSESENSEX and Energy Indices in India? Some Evidence on Investors’ Commitment Towards Green Investing," International Econometric Review (IER), Econometric Research Association, vol. 13(2), pages 41-58, June.
    16. Mohamed Es-Sanoun & Jude Gohou & Mounir Benboubker, 2023. "Testing of Herd Behavior In african Stock Markets During COVID-19 Pandemic [Essai de vérification du comportement mimétique dans les marchés boursiers africains au cours de la crise de covid-19]," Post-Print hal-04144289, HAL.
    17. Sabur Mollah & Asma Mobarek, 2009. "Market volatility across countries – evidence from international markets," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 26(4), pages 257-274, October.
    18. Shaikh, Salman, 2013. "Investment Decisions by Analysts: A Case Study of KSE," MPRA Paper 53802, University Library of Munich, Germany.
    19. Ali K. Ozdagli, 2012. "Financial Leverage, Corporate Investment, and Stock Returns," The Review of Financial Studies, Society for Financial Studies, vol. 25(4), pages 1033-1069.
    20. Boes, M.J., 2006. "Index options : Pricing, implied densities and returns," Other publications TiSEM e9ed8a9f-2472-430a-b666-9, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Performance ratios; Sortino ratio; Risk aversion; Loss aversion; FSDR rule; SSDR rule;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • G0 - Financial Economics - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:120203. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.