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

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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.

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Notes

  1. Note that the dimension of our problem is actually n, since once percentages x 1,…,x n are allocated, x n+1 must become the remaining unallocated percentage.

  2. http://finance.yahoo.com/.

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Authors and Affiliations

  1. Escuela de Negocios, Universidad Adolfo Ibañez, Diagonal las Torres 2640 oficina 533-C, Peñalolén, Santiago, Chile

    B. K. Pagnoncelli & D. Reich

  2. Ford Research and Advanced Engineering, Dearborn, MI, 48124, USA

    D. Reich

  3. Department of Information Engineering, University of Brescia, Via Branze 38, 25123, Brescia, Italy

    M. C. Campi

Authors
  1. B. K. Pagnoncelli
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  2. D. Reich
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  3. M. C. Campi
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Corresponding author

Correspondence to B. K. Pagnoncelli.

Additional information

Communicated by Johannes O. Royset.

This research was funded by ANILLO Grant ACT-88 and Basal project CMM, Universidad de Chile.

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Pagnoncelli, B.K., Reich, D. & Campi, M.C. Risk-Return Trade-off with the Scenario Approach in Practice: A Case Study in Portfolio Selection. J Optim Theory Appl 155, 707–722 (2012). https://doi.org/10.1007/s10957-012-0074-x

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  • DOI: https://doi.org/10.1007/s10957-012-0074-x

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