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Portfolio Selection Based on Modified CoVaR in Gaussian Framework

Author

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  • 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
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    References listed on IDEAS

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    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.
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