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Global optimization for bilevel portfolio design: Economic insights from the Dow Jones index

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  • González-Díaz, Julio
  • González-Rodríguez, Brais
  • Leal, Marina
  • Puerto, Justo

Abstract

This paper deals with a portfolio selection problem with transaction costs and two levels of decision-making. It is assumed that the decision making structure is twofold: there is a broker-dealer that controls the fees to be charged on the different securities in order to maximize his benefit and there is an investor who chooses his portfolio trying to minimize risk while ensuring a minimum level of return. This structure gives rise to an implicit hierarchical competition that consists in anticipating the rational decision of the other agent in order to optimize the decision-makers’ own criteria. We analyze different situations depending on who is first in the hierarchy: the broker-dealer or the investor. We present different nonlinear and nonconvex mathematical programming models for the different situations and develop an extensive computational study in which we discuss the ensuing economic insights for the models based on Dow Jones index data.

Suggested Citation

  • González-Díaz, Julio & González-Rodríguez, Brais & Leal, Marina & Puerto, Justo, 2021. "Global optimization for bilevel portfolio design: Economic insights from the Dow Jones index," Omega, Elsevier, vol. 102(C).
    • Handle: RePEc:eee:jomega:v:102:y:2021:i:c:s0305048320307076
    DOI: 10.1016/j.omega.2020.102353
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    1. Stambaugh, Fred, 1996. "Risk and value at risk," European Management Journal, Elsevier, vol. 14(6), pages 612-621, December.
    2. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2020. "An optimization–diversification approach to portfolio selection," Journal of Global Optimization, Springer, vol. 76(2), pages 245-265, February.
    3. Benati, Stefano, 2003. "The optimal portfolio problem with coherent risk measure constraints," European Journal of Operational Research, Elsevier, vol. 150(3), pages 572-584, November.
    4. Stefano Benati, 2015. "Using medians in portfolio optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(5), pages 720-731, May.
    5. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    6. Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.
    7. Leal, Marina & Ponce, Diego & Puerto, Justo, 2020. "Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 712-727.
    8. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    9. Maravillo, Héctor & Camacho-Vallejo, José-Fernando & Puerto, Justo & Labbé, Martine, 2020. "A market regulation bilevel problem: A case study of the Mexican petrochemical industry," Omega, Elsevier, vol. 97(C).
    10. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2013. "Portfolio rebalancing with an investment horizon and transaction costs," Omega, Elsevier, vol. 41(2), pages 406-420.
    11. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    12. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    13. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    14. 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.
    15. Philipp Baumann & Norbert Trautmann, 2013. "Portfolio-optimization models for small investors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 345-356, June.
    16. Valle, C.A. & Meade, N. & Beasley, J.E., 2014. "Absolute return portfolios," Omega, Elsevier, vol. 45(C), pages 20-41.
    17. 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.
    18. Qiu, Rui & Xu, Jiuping & Ke, Ruimin & Zeng, Ziqiang & Wang, Yinhai, 2020. "Carbon pricing initiatives-based bi-level pollution routing problem," European Journal of Operational Research, Elsevier, vol. 286(1), pages 203-217.
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