IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/82737.html
   My bibliography  Save this paper

Farinelli and Tibiletti ratio and Stochastic Dominance

Author

Listed:
  • Niu, Cuizhen
  • Wong, Wing-Keung
  • Zhu, Lixing

Abstract

Farinelli and Tibiletti (F-T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F-T ratios are ratios of average gains to average losses with respect to a target, each raised by a power index, p and q. In this paper, we establish the consistency of F-T ratios with any nonnegative values p and q with respect to first-order stochastic dominance. Second-order stochastic dominance does not lead to F-T ratios with any nonnegative values p and q, but can lead to F-T dominance with any p

Suggested Citation

  • Niu, Cuizhen & Wong, Wing-Keung & Zhu, Lixing, 2017. "Farinelli and Tibiletti ratio and Stochastic Dominance," MPRA Paper 82737, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:82737
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/82737/1/FT%20ratio%20and%20SD%20WP.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Niu, Cuizhen & Guo, Xu & McAleer, Michael & Wong, Wing-Keung, 2018. "Theory and application of an economic performance measure of risk," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 383-396.
    2. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    3. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    4. Fong, Wai Mun, 2016. "Stochastic dominance and the omega ratio," Finance Research Letters, Elsevier, vol. 17(C), pages 7-9.
    5. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    6. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    7. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    8. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
    9. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    10. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    11. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    12. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    13. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    14. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    15. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2009. "Optimal asset allocation aid system: From "one-size" vs "tailor-made" performance ratio," European Journal of Operational Research, Elsevier, vol. 192(1), pages 209-215, January.
    16. Guo, Xu & Wong, Wing-Keung, 2016. "Multivariate Stochastic Dominance for Risk Averters and Risk Seekers," MPRA Paper 70637, University Library of Munich, Germany.
    17. Xu Guo & Xuejun Jiang & Wing-Keung Wong, 2017. "Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly," Economies, MDPI, vol. 5(4), pages 1-16, October.
    18. Johannes Leitner, 2005. "A Short Note On Second‐Order Stochastic Dominance Preserving Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 649-651, October.
    19. Jean-Luc Prigent & Philippe Bertrand, 2011. "Omega performance measure and portfolio insurance," Post-Print hal-01833064, HAL.
    20. Chun-Kei Tsang & Wing-Keung Wong & Ira Horowitz, 2016. "Arbitrage opportunities, efficiency, and the role of risk preferences in the Hong Kong property market," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 33(4), pages 735-754, October.
    21. Tehranian, Hassan, 1980. "Empirical Studies in Portfolio Performance Using Higher Degrees of Stochastic Dominance," Journal of Finance, American Finance Association, vol. 35(1), pages 159-171, March.
    22. Cuizhen Niu & Wing-Keung Wong & Qunfang Xu, 2017. "Kappa ratios and (higher-order) stochastic dominance," Risk Management, Palgrave Macmillan, vol. 19(3), pages 245-253, August.
    23. Zhuo Qiao & Wing-Keung Wong, 2015. "Which is a better investment choice in the Hong Kong residential property market: a big or small property?," Applied Economics, Taylor & Francis Journals, vol. 47(16), pages 1670-1685, April.
    24. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    25. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    26. Ma, Chenghu & Wong, Wing-Keung, 2010. "Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR," European Journal of Operational Research, Elsevier, vol. 207(2), pages 927-935, December.
    27. Balder, Sven & Schweizer, Nikolaus, 2017. "Risk aversion vs. the Omega ratio: Consistency results," Finance Research Letters, Elsevier, vol. 21(C), pages 78-84.
    28. Homm, Ulrich & Pigorsch, Christian, 2012. "Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2274-2284.
    29. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nguyen Huu Hau & Tran Trung Tinh & Hoa Anh Tuong & Wing-Keung Wong, 2020. "Review of Matrix Theory with Applications in Education and Decision Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(1), pages 28-69, March.
    2. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.
    3. Alkhazali, Osamah M. & Zoubi, Taisier A., 2020. "Gold and portfolio diversification: A stochastic dominance analysis of the Dow Jones Islamic indices," Pacific-Basin Finance Journal, Elsevier, vol. 60(C).
    4. Zhihui Lv & Amanda M. Y. Chu & Wing Keung Wong & Thomas C. Chiang, 2021. "The maximum-return-and-minimum-volatility effect: evidence from choosing risky and riskless assets to form a portfolio," Risk Management, Palgrave Macmillan, vol. 23(1), pages 97-122, June.
    5. Carole Bernard & Massimiliano Caporin & Bertrand Maillet & Xiang Zhang, 2023. "Omega Compatibility: A Meta-analysis," Computational Economics, Springer;Society for Computational Economics, vol. 62(2), pages 493-526, August.
    6. Richard Lu & Chen-Chen Yang & Wing-Keung Wong, 2018. "Time Diversification: Perspectives From The Economic Index Of Riskiness," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 1-15, September.
    7. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    8. Duc Hong Vo, 2021. "Portfolio Optimization and Diversification in China: Policy Implications for Vietnam and Other Emerging Markets," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 57(1), pages 223-238, January.
    9. Wenjing Xie & João Paulo Vieito & Ephraim Clark & Wing-Keung Wong, 2020. "Could Mergers Become More Sustainable? A Study of the Stock Exchange Mergers of NASDAQ and OMX," Sustainability, MDPI, vol. 12(20), pages 1-25, October.
    10. Courtois, Olivier Le & Xu, Xia, 2023. "Semivariance below the maximum: Assessing the performance of economic and financial prospects," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 185-199.
    11. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    12. Zongxin Li & Xinge Li & Yongchang Hui & Wing-Keung Wong, 2018. "Maslow Portfolio Selection for Individuals with Low Financial Sustainability," Sustainability, MDPI, vol. 10(4), pages 1-11, April.

    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. Niu, Cuizhen & Wong, Wing-Keung & Zhu, Lixing, 2016. "First Stochastic Dominance and Risk Measurement," MPRA Paper 75027, University Library of Munich, Germany.
    2. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Documentos de Trabajo del ICAE 2018-09, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    4. Xu Guo & Xuejun Jiang & Wing-Keung Wong, 2017. "Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly," Economies, MDPI, vol. 5(4), pages 1-16, October.
    5. Carole Bernard & Massimiliano Caporin & Bertrand Maillet & Xiang Zhang, 2023. "Omega Compatibility: A Meta-analysis," Computational Economics, Springer;Society for Computational Economics, vol. 62(2), pages 493-526, August.
    6. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    7. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    8. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.
    9. Zhihui Lv & Amanda M. Y. Chu & Wing Keung Wong & Thomas C. Chiang, 2021. "The maximum-return-and-minimum-volatility effect: evidence from choosing risky and riskless assets to form a portfolio," Risk Management, Palgrave Macmillan, vol. 23(1), pages 97-122, June.
    10. Cuizhen Niu & Wing-Keung Wong & Qunfang Xu, 2017. "Kappa ratios and (higher-order) stochastic dominance," Risk Management, Palgrave Macmillan, vol. 19(3), pages 245-253, August.
    11. Nguyen Huu Hau & Tran Trung Tinh & Hoa Anh Tuong & Wing-Keung Wong, 2020. "Review of Matrix Theory with Applications in Education and Decision Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(1), pages 28-69, March.
    12. Richard Lu & Chen-Chen Yang & Wing-Keung Wong, 2018. "Time Diversification: Perspectives From The Economic Index Of Riskiness," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 1-15, September.
    13. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Management Information, Decision Sciences, and Financial Economics: A Connection," Tinbergen Institute Discussion Papers 18-004/III, Tinbergen Institute.
    14. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    15. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2016. "Almost stochastic dominance for risk averters and risk seeker," Finance Research Letters, Elsevier, vol. 19(C), pages 15-21.
    16. Niu, Cuizhen & Wong, Wing-Keung & Xu, Qunfang, 2017. "Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance," MPRA Paper 75948, University Library of Munich, Germany.
    17. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    18. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2016. "Management science, economics and finance: A connection," Documentos de Trabajo del ICAE 2016-07, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    19. Chan, Raymond H. & Chow, Sheung-Chi & Guo, Xu & Wong, Wing-Keung, 2022. "Central moments, stochastic dominance, moment rule, and diversification with an application," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.

    More about this item

    Keywords

    First-order Stochastic Dominance; High-order Stochastic Dominance; Upside Potential Ratio; Farinelli and Tibiletti ratio; Risk Measures.;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    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:82737. 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.