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An analytic derivation of the efficient frontier in biobjective cash management and its implications for policies

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Listed:
  • Francisco Salas-Molina

    (Universitat Politècnica de València)

  • David Pla-Santamaria

    (Universitat Politècnica de València)

  • Juan A. Rodriguez-Aguilar

    (Campus UAB)

Abstract

Cash managers who optimize returns and risk rely on biobjective optimization models to select the best policies according to their risk preferences. In the related portfolio selection problem, Merton (J Financ Quant Anal 7(4):1851–1872, 1972) provided the first analytical derivation of the efficient frontier with all non-dominated return and risk combinations. This first proposal was later extended to account for three or more criteria by other authors. However, the cash management literature needs an analytical derivation of the efficient frontier to help cash managers evaluate the implications of selecting policies and risk measures. In this paper, we provide three analytic derivations of the efficient frontier determining a closed-form solution for the expected returns and risk relationship using three different risk measures. We study its main properties and its theoretical implications for policies. Using the variance of returns as a risk measure imposes limitations due to invertibility reasons.

Suggested Citation

  • Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2023. "An analytic derivation of the efficient frontier in biobjective cash management and its implications for policies," Annals of Operations Research, Springer, vol. 328(2), pages 1523-1536, September.
    • Handle: RePEc:spr:annopr:v:328:y:2023:i:2:d:10.1007_s10479-023-05433-z
    DOI: 10.1007/s10479-023-05433-z
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    References listed on IDEAS

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    1. Merton H. Miller & Daniel Orr, 1966. "A Model of the Demand for Money by Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(3), pages 413-435.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Francisco Salas-Molina & Juan A. Rodriguez-Aguilar & David Pla-Santamaria & Ana García-Bernabeu, 2021. "On the formal foundations of cash management systems," Operational Research, Springer, vol. 21(2), pages 1081-1095, June.
    4. Francisco Salas-Molina, 2020. "Risk-sensitive control of cash management systems," Operational Research, Springer, vol. 20(2), pages 1159-1176, June.
    5. Yue Qi, 2022. "Classifying the minimum-variance surface of multiple-objective portfolio selection for capital asset pricing models," Annals of Operations Research, Springer, vol. 311(2), pages 1203-1227, April.
    6. William J. Baumol, 1952. "The Transactions Demand for Cash: An Inventory Theoretic Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 66(4), pages 545-556.
    7. Yue Qi & Ralph E. Steuer, 2020. "On the analytical derivation of efficient sets in quad-and-higher criterion portfolio selection," Annals of Operations Research, Springer, vol. 293(2), pages 521-538, October.
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    9. Schroeder, Pascal & Kacem, Imed, 2020. "Competitive difference analysis of the cash management problem with uncertain demands," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1183-1192.
    10. Yue Qi & Xiaolin Li, 2020. "On Imposing ESG Constraints of Portfolio Selection for Sustainable Investment and Comparing the Efficient Frontiers in the Weight Space," SAGE Open, , vol. 10(4), pages 21582440209, December.
    11. 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.
    12. Francisco Salas-Molina & Juan A. Rodriguez-Aguilar & Pablo Díaz-García, 2018. "Selecting cash management models from a multiobjective perspective," Annals of Operations Research, Springer, vol. 261(1), pages 275-288, February.
    13. Francisco Salas-Molina & Juan A. Rodríguez-Aguilar & Montserrat Guillen, 2023. "A multidimensional review of the cash management problem," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-35, December.
    14. Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2018. "A multi-objective approach to the cash management problem," Annals of Operations Research, Springer, vol. 267(1), pages 515-529, August.
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