IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v18y2016i4d10.1007_s11009-016-9502-y.html
   My bibliography  Save this article

Asymptotic Multivariate Dominance: A Financial Application

Author

Listed:
  • Sergio Ortobelli Lozza

    (University of Bergamo
    VŠB- Technical University of Ostrava)

  • Tommaso Lando

    (University of Bergamo
    VŠB- Technical University of Ostrava)

  • Filomena Petronio

    (VŠB- Technical University of Ostrava)

  • Tomáš Tichý

    (VŠB- Technical University of Ostrava)

Abstract

We propose a multivariate stochastic dominance relation aimed at ranking different financial markets/sectors from the point of view of a non-satiable risk averse investor. In particular, we assume that the vector of returns of a given market is in the domain of attraction of a symmetric stable Paretian law in order to take into account the asymptotic behaviour of the financial returns. We determine the stochastic dominance rule for stable symmetric distributions, where the stability parameter plays a crucial role. Consequently, the multivariate rule for ordering markets is based on a comparison between i) location parameters, ii) dispersion parameters, and iii) stability indices. Finally, we apply the method to the equity markets of the four countries with the highest gross domestic product in 2013, namely, the US, China, Japan and Germany. In this empirical comparison we examine the ex ante and ex post dominance between stock markets, either assuming that the returns are jointly (or conditionally, for a robust approach) Gaussian distributed, or in the domain of attraction of a stable sub-Gaussian law.

Suggested Citation

  • Sergio Ortobelli Lozza & Tommaso Lando & Filomena Petronio & Tomáš Tichý, 2016. "Asymptotic Multivariate Dominance: A Financial Application," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1097-1115, December.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-016-9502-y
    DOI: 10.1007/s11009-016-9502-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-016-9502-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-016-9502-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rodica Branzei & Sirma Zeynep Alparslan Gok, 2008. "Bankruptcy problems with interval uncertainty," Economics Bulletin, AccessEcon, vol. 3(56), pages 1-10.
    2. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    3. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    4. Sergio Ortobelli Lozza & Enrico Angelelli & Annamaria Bianchi, 2011. "Financial Applications of Bivariate Markov Processes," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-15, October.
    5. R. Branzei & O. Branzei & S. Alparslan Gök & S. Tijs, 2010. "Cooperative interval games: a survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 397-411, September.
    6. Jansen, Dennis W. & Koedijk, Kees G. & de Vries, Casper G., 2000. "Portfolio selection with limited downside risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 247-269, November.
    7. repec:ebl:ecbull:v:3:y:2008:i:56:p:1-10 is not listed on IDEAS
    8. Ortobelli, Sergio & Rachev, Svetlozar T. & Fabozzi, Frank J., 2010. "Risk management and dynamic portfolio selection with stable Paretian distributions," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 195-211, March.
    9. Sebastián Ceria & Robert A Stubbs, 2006. "Incorporating estimation errors into portfolio selection: Robust portfolio construction," Journal of Asset Management, Palgrave Macmillan, vol. 7(2), pages 109-127, July.
    10. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    11. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    12. Hyung, Namwon & de Vries, Casper G., 2007. "Portfolio selection with heavy tails," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 383-400, June.
    13. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    14. Katrin Schöttle & Ralf Werner & Rudi Zagst, 2010. "Comparison and robustification of Bayes and Black-Litterman models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 453-475, June.
    15. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 99-109, March.
    16. Sergio Ortobelli Lozza & Haim Shalit & Frank J. Fabozzi, 2013. "Portfolio Selection Problems Consistent With Given Preference Orderings," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-38.
    17. Sergio Ortobelli & Svetlozar Rachev & Haim Shalit & Frank Fabozzi, 2009. "Orderings and Probability Functionals Consistent with Preferences," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 81-102.
    18. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    19. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    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. Noureddine Kouaissah & Amin Hocine, 2021. "Forecasting systemic risk in portfolio selection: The role of technical trading rules," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 708-729, July.
    2. Kouaissah, Noureddine, 2023. "Robust reward-risk performance measures with weakly second-order stochastic dominance constraints," The Quarterly Review of Economics and Finance, Elsevier, vol. 88(C), pages 53-62.
    3. Kouaissah, Noureddine, 2021. "Using multivariate stochastic dominance to enhance portfolio selection and warn of financial crises," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 480-493.

    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. De Giovanni, Domenico & Ortobelli, Sergio & Rachev, Svetlozar, 2008. "Delta hedging strategies comparison," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1615-1631, March.
    2. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    3. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.
    4. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    5. José Antonio Climent Hernández & Gabino Sánchez Arzate & Ambrosio Ortiz Ramírez, 2021. "Portafolios ?-estables del G20: Evidencia empírica con Markowitz, Tobin y CAPM," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(4), pages 1-28, Octubre -.
    6. Ortobelli, Sergio & Rachev, Svetlozar T. & Fabozzi, Frank J., 2010. "Risk management and dynamic portfolio selection with stable Paretian distributions," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 195-211, March.
    7. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    8. José Antonio Climent Hernández, 2017. "Portafolios de dispersión mínima con rendimientos log-estables," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 12(2), pages 49-69, Abril-Jun.
    9. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, December.
    10. Mouck, T., 1998. "Capital markets research and real world complexity: The emerging challenge of chaos theory," Accounting, Organizations and Society, Elsevier, vol. 23(2), pages 189-203, February.
    11. José Antonio Climent-Hernández, 2017. "Portafolios de dispersión mínima con rendimientos log-estables Minimum dispersion portfolios with log-stable returns," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, March.
    12. Climent-Hernández, José Antonio & Venegas-Martínez, Francisco & Ortiz-Arango, Francisco, 2014. "Portafolio óptimo y productos estructurados en mercados alpha-estables: un enfoque de minimización de riesgo [Optimal Portfolio and Structured Notes in alpha-stable Markets: a Risk Minimization App," MPRA Paper 57740, University Library of Munich, Germany.
    13. Bao, Te & Diks, Cees & Li, Hao, 2018. "A generalized CAPM model with asymmetric power distributed errors with an application to portfolio construction," Economic Modelling, Elsevier, vol. 68(C), pages 611-621.
    14. Lina Mallozzi & Juan Vidal-Puga, 2021. "Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism," Annals of Operations Research, Springer, vol. 301(1), pages 143-159, June.
    15. Sergio Ortobelli Lozza & Enrico Angelelli & Daniele Toninelli, 2011. "Set-Portfolio Selection with the Use of Market Stochastic Bounds," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 47(0), pages 5-24, November.
    16. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    17. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    18. Sabiou M. Inoua & Vernon L. Smith, 2022. "Perishable goods versus re-tradable assets: A theoretical reappraisal of a fundamental dichotomy," Chapters, in: Sascha Füllbrunn & Ernan Haruvy (ed.), Handbook of Experimental Finance, chapter 15, pages 162-171, Edward Elgar Publishing.
    19. François-Éric Racicot & William F. Rentz & Alfred L. Kahl, 2017. "Rolling Regression Analysis of the Pástor-Stambaugh Model: Evidence from Robust Instrumental Variables," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 23(1), pages 75-90, February.
    20. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.

    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:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-016-9502-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.