IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v78y2020i3d10.1007_s10898-020-00922-y.html
   My bibliography  Save this article

Portfolio optimization with two coherent risk measures

Author

Listed:
  • Tahsin Deniz Aktürk

    (The University of Chicago)

  • Çağın Ararat

    (Bilkent University)

Abstract

We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio manager is of primary concern, hence, it appears in the objective function, and the risk perception of an external authority needs to be taken into account as well, which appears in the form of a risk constraint. The problem covers the risk minimization problem with an expected return constraint and the expected return maximization problem with a risk constraint, as special cases. For the general case of an arbitrary joint distribution for the asset returns, under certain conditions, we characterize the optimal portfolio as the optimal Lagrange multiplier associated to an equality-constrained dual problem. Then, we consider the special case of Gaussian returns for which it is possible to identify all cases where an optimal solution exists and to give an explicit formula for the optimal portfolio whenever it exists.

Suggested Citation

  • Tahsin Deniz Aktürk & Çağın Ararat, 2020. "Portfolio optimization with two coherent risk measures," Journal of Global Optimization, Springer, vol. 78(3), pages 597-626, November.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:3:d:10.1007_s10898-020-00922-y
    DOI: 10.1007/s10898-020-00922-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00922-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/s10898-020-00922-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. Zinoviy Landsman & Udi Makov, 2016. "Minimization of a Function of a Quadratic Functional with Application to Optimal Portfolio Selection," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 308-322, July.
    2. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. 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. c{C}au{g}{i}n Ararat, 2020. "Portfolio optimization with two quasiconvex risk measures," Papers 2012.06173, arXiv.org.

    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. Tahsin Deniz Akturk & c{C}au{g}{i}n Ararat, 2019. "Portfolio optimization with two coherent risk measures," Papers 1903.10454, arXiv.org, revised Jul 2020.
    2. Taras Bodnar & Mathias Lindholm & Erik Thorsén & Joanna Tyrcha, 2021. "Quantile-based optimal portfolio selection," Computational Management Science, Springer, vol. 18(3), pages 299-324, July.
    3. Bodnar Taras & Schmid Wolfgang & Zabolotskyy Tara, 2012. "Minimum VaR and minimum CVaR optimal portfolios: Estimators, confidence regions, and tests," Statistics & Risk Modeling, De Gruyter, vol. 29(4), pages 281-314, November.
    4. Dias, Alexandra, 2016. "The economic value of controlling for large losses in portfolio selection," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 81-91.
    5. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2007. "Mean-variance portfolio selection with `at-risk' constraints and discrete distributions," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3761-3781, December.
    6. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    7. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    8. Kull, Andreas, 2009. "Sharing Risk – An Economic Perspective," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 591-613, November.
    9. Curtis, John & Lynch, Muireann Á. & Zubiate, Laura, 2016. "The impact of the North Atlantic Oscillation on electricity markets: A case study on Ireland," Energy Economics, Elsevier, vol. 58(C), pages 186-198.
    10. Brian Tomlin & Yimin Wang, 2005. "On the Value of Mix Flexibility and Dual Sourcing in Unreliable Newsvendor Networks," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 37-57, June.
    11. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2014. "Bank regulation and international financial stability: A case against the 2006 Basel framework for controlling tail risk in trading books," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 107-130.
    12. Kolos Ágoston, 2012. "CVaR minimization by the SRA algorithm," 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. 20(4), pages 623-632, December.
    13. Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo.
    14. Harris, Richard D.F. & Mazibas, Murat, 2013. "Dynamic hedge fund portfolio construction: A semi-parametric approach," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 139-149.
    15. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    16. Scheuenstuhl, Gerhard & Zagst, Rudi, 2008. "Integrated portfolio management with options," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1477-1500, March.
    17. 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.
    18. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.
    19. Ben Ameur, Hachmi & Ftiti, Zied & Louhichi, Waël & Yousfi, Mohamed, 2024. "Do green investments improve portfolio diversification? Evidence from mean conditional value-at-risk optimization," International Review of Financial Analysis, Elsevier, vol. 94(C).
    20. Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Papers 2306.14506, arXiv.org.

    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:jglopt:v:78:y:2020:i:3:d:10.1007_s10898-020-00922-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.