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Risk-Return Trade-off with the Scenario Approach in Practice: A Case Study in Portfolio Selection

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  • B. K. Pagnoncelli

    (Universidad Adolfo Ibañez)

  • D. Reich

    (Universidad Adolfo Ibañez
    Ford Research and Advanced Engineering)

  • M. C. Campi

    (University of Brescia)

Abstract

We consider the scenario approach for chance constrained programming problems. Building on existing theoretical results, effective and readily applicable methodologies to achieve suitable risk-return trade-offs are developed in this paper. Unlike other approaches, that require solving non-convex optimization problems, our methodology consists of solving multiple convex optimization problems obtained by sampling and removing some of the constraints. More specifically, two constraint removal schemes are introduced, one greedy and the other randomized, and a comparison between them is provided in a detailed computational study in portfolio selection. Other practical aspects of the procedures are also discussed. The removal schemes proposed in this paper are generalizable to a wide range of practical problems.

Suggested Citation

  • B. K. Pagnoncelli & D. Reich & M. C. Campi, 2012. "Risk-Return Trade-off with the Scenario Approach in Practice: A Case Study in Portfolio Selection," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 707-722, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0074-x
    DOI: 10.1007/s10957-012-0074-x
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    References listed on IDEAS

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    1. Tanner, Matthew W. & Ntaimo, Lewis, 2010. "IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation," European Journal of Operational Research, Elsevier, vol. 207(1), pages 290-296, November.
    2. Miguel A. Lejeune, 2012. "Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems," Operations Research, INFORMS, vol. 60(6), pages 1356-1372, December.
    3. Yi Wang & Zhiping Chen & Kecun Zhang, 2007. "A CHANCE-CONSTRAINED PORTFOLIO SELECTION PROBLEM UNDERt-DISTRIBUTION," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 535-556.
    4. Miguel Lejeune, 2011. "A VaR Black–Litterman model for the construction of absolute return fund-of-funds," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1489-1501.
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    Cited by:

    1. Ramponi, Federico Alessandro & Campi, Marco C., 2018. "Expected shortfall: Heuristics and certificates," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1003-1013.
    2. Azad, Nader & Hassini, Elkafi, 2019. "Recovery strategies from major supply disruptions in single and multiple sourcing networks," European Journal of Operational Research, Elsevier, vol. 275(2), pages 481-501.
    3. Reich, Daniel, 2013. "A linear programming approach for linear programs with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 230(3), pages 487-494.
    4. Algo Carè & Simone Garatti & Marco C. Campi, 2014. "FAST---Fast Algorithm for the Scenario Technique," Operations Research, INFORMS, vol. 62(3), pages 662-671, June.

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