IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3766-d1532731.html
   My bibliography  Save this article

Portfolio Selection Based on Modified CoVaR in Gaussian Framework

Author

Listed:
  • Piotr Jaworski

    (Institute of Mathematics, University of Warsaw, 02-097 Warszawa, Poland)

  • Anna Zalewska

    (Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662 Warszawa, Poland)

Abstract

We study a Mean-Risk model, where risk is measured by a Modified CoVaR (Conditional Value at Risk): CoVaR α , β ≤ ( X | Y ) = V a R β ( X | Y + V a R α ( Y ) ≤ 0 ) . We prove that in a Gaussian setting, for a sufficiently small β , such a model has a solution. There exists a portfolio that fulfills the given constraints and for which the risk is minimal. This is shown in relation to the mean–standard deviation portfolio, and numerical examples are provided.

Suggested Citation

  • Piotr Jaworski & Anna Zalewska, 2024. "Portfolio Selection Based on Modified CoVaR in Gaussian Framework," Mathematics, MDPI, vol. 12(23), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3766-:d:1532731
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3766/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3766/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    2. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    3. Bernardi, M. & Durante, F. & Jaworski, P., 2017. "CoVaR of families of copulas," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 8-17.
    4. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    5. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    6. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650, September.
    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. Francisco Peñaranda & Enrique Sentana, 2024. "Portfolio management with big data," Working Papers wp2024_2411, CEMFI.
    2. Michele Costola & Bertrand Maillet & Zhining Yuan & Xiang Zhang, 2024. "Mean–variance efficient large portfolios: a simple machine learning heuristic technique based on the two-fund separation theorem," Annals of Operations Research, Springer, vol. 334(1), pages 133-155, March.
    3. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    4. 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.
    5. Markus Hirschberger & Ralph E. Steuer & Sebastian Utz & Maximilian Wimmer & Yue Qi, 2013. "Computing the Nondominated Surface in Tri-Criterion Portfolio Selection," Operations Research, INFORMS, vol. 61(1), pages 169-183, February.
    6. Gabriel Frahm, 2010. "Linear statistical inference for global and local minimum variance portfolios," Statistical Papers, Springer, vol. 51(4), pages 789-812, December.
    7. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    8. Anders Johansson, 2009. "An analysis of dynamic risk in the Greater China equity markets," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 7(3), pages 299-320.
    9. 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.
    10. 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.
    11. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    12. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Papers 1910.13960, arXiv.org, revised Oct 2020.
    13. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, December.
    14. Michael W. Brandt & Pedro Santa-Clara & Rossen Valkanov, 2009. "Parametric Portfolio Policies: Exploiting Characteristics in the Cross-Section of Equity Returns," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3411-3447, September.
    15. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    16. ,, 2007. "Two-fund separation in dynamic general equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
    17. Jaehyung Choi & Hyangju Kim & Young Shin Kim, 2021. "Diversified reward-risk parity in portfolio construction," Papers 2106.09055, arXiv.org, revised Sep 2022.
    18. Demircioglu, Emre, 2015. "Testing of Capital Assets Pricing Model (CAPM) in Cement Sector & Power Generation and Distribution Sector in Turkey," MPRA Paper 61392, University Library of Munich, Germany.
    19. Nitzan Weiss, 1984. "Reply to a Paradigmatic Comment: Capital Markets, Output, and the Demand for Inputs under Uncertainty," Eastern Economic Journal, Eastern Economic Association, vol. 10(1), pages 79-85, Jan-Mar.
    20. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The RQE-CAPM : New insights about the pricing of idiosyncratic risk," CIRANO Working Papers 2021s-28, CIRANO.

    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:jmathe:v:12:y:2024:i:23:p:3766-:d:1532731. 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: MDPI Indexing Manager (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. RePEc uses bibliographic data supplied by the respective publishers.