IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v6y2018i3p76-d162453.html
   My bibliography  Save this article

A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures

Author

Listed:
  • Stanislaus Maier-Paape

    (Institut für Mathematik, RWTH Aachen University, 52062 Aachen, Germany)

  • Qiji Jim Zhu

    (Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA)

Abstract

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the “current” drawdown of the portfolio equity. In contrast to references Chekhlov, Uryasev, and Zabarankin (2003, 2005), Goldberg and Mahmoud (2017), and Zabarankin, Pavlikov, and Uryasev (2014), who used the absolute drawdown, our risk measure is based on the relative drawdown process. Combined with the results of Part I, Maier-Paape and Zhu (2018), this allows us to calculate efficient portfolios based on a drawdown risk measure constraint.

Suggested Citation

  • Stanislaus Maier-Paape & Qiji Jim Zhu, 2018. "A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures," Risks, MDPI, Open Access Journal, vol. 6(3), pages 1-31, August.
  • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:76-:d:162453
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/6/3/76/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-9091/6/3/76/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. 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.
    3. Lisa R. Goldberg & Ola Mahmoud, 2014. "Drawdown: From Practice to Theory and Back Again," Papers 1404.7493, arXiv.org, revised Sep 2016.
    4. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    5. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    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. Sagara Dewasurendra & Pedro Judice & Qiji Zhu, 2019. "The Optimum Leverage Level of the Banking Sector," Risks, MDPI, Open Access Journal, vol. 7(2), pages 1-30, May.
    2. Stanislaus Maier-Paape & Andreas Platen & Qiji Jim Zhu, 2019. "A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach," Risks, MDPI, Open Access Journal, vol. 7(2), pages 1-31, June.
    3. Leonie Violetta Brinker, 2021. "Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model," Risks, MDPI, Open Access Journal, vol. 9(1), pages 1-18, January.

    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. Zabarankin, Michael & Pavlikov, Konstantin & Uryasev, Stan, 2014. "Capital Asset Pricing Model (CAPM) with drawdown measure," European Journal of Operational Research, Elsevier, vol. 234(2), pages 508-517.
    2. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    3. Allen, D.E. & McAleer, M.J. & Powell, R.J. & Singh, A.K., 2015. "Down-side Risk Metrics as Portfolio Diversification Strategies across the GFC," Econometric Institute Research Papers EI2015-32, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Stanislaus Maier-Paape & Andreas Platen & Qiji Jim Zhu, 2019. "A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach," Risks, MDPI, Open Access Journal, vol. 7(2), pages 1-31, June.
    5. Víctor Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, 2017. "“Resolution of optimization problems and construction of efficient portfolios: An application to the Euro Stoxx 50 index"," IREA Working Papers 201702, University of Barcelona, Research Institute of Applied Economics, revised Feb 2017.
    6. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
    7. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2014. "European Market Portfolio Diversifcation Strategies across the GFC," Working Papers in Economics 14/25, University of Canterbury, Department of Economics and Finance.
    8. Palczewski, Andrzej & Palczewski, Jan, 2019. "Black–Litterman model for continuous distributions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 708-720.
    9. Grechuk, Bogdan & Zabarankin, Michael, 2018. "Direct data-based decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 267(1), pages 200-211.
    10. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, M., 2007. "Equilibrium with investors using a diversity of deviation measures," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3251-3268, November.
    11. David E. Allen & Michael McAleer & Shelton Peiris & Abhay K. Singh, 2014. "Hedge Fund Portfolio Diversification Strategies Across the GFC," Working Papers in Economics 14/27, University of Canterbury, Department of Economics and Finance.
    12. Schoch, Daniel, 2017. "Generalised mean-risk preferences," Journal of Economic Theory, Elsevier, vol. 168(C), pages 12-26.
    13. Allen, D.E. & Powell, R.J. & Singh, A.K., 2016. "Take it to the limit: Innovative CVaR applications to extreme credit risk measurement," European Journal of Operational Research, Elsevier, vol. 249(2), pages 465-475.
    14. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2016. "Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(2), pages 1-18, June.
    15. Grechuk, Bogdan & Zabarankin, Michael, 2016. "Inverse portfolio problem with coherent risk measures," European Journal of Operational Research, Elsevier, vol. 249(2), pages 740-750.
    16. R. Tyrrell Rockafellar & Stan Uryasev & Michael Zabarankin, 2008. "Risk Tuning with Generalized Linear Regression," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 712-729, August.
    17. Grechuk, Bogdan & Zabarankin, Michael, 2014. "Inverse portfolio problem with mean-deviation model," European Journal of Operational Research, Elsevier, vol. 234(2), pages 481-490.
    18. Trindade, A. Alexandre & Uryasev, Stan & Shapiro, Alexander & Zrazhevsky, Grigory, 2007. "Financial prediction with constrained tail risk," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3524-3538, November.
    19. Víctor M. Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, "undated". "Portfolios in the Ibex 35 index: Alternative methods to the traditional framework, a comparative with the naive diversification in a pre- and post- crisis context," Documentos de Trabajo del ICAE 2015-07, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Jun 2015.
    20. 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.

    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:gam:jrisks:v:6:y:2018:i:3:p:76-:d:162453. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.mdpi.com/ .

    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: XML Conversion Team (email available below). General contact details of provider: https://www.mdpi.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.