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Notes: A Reformulation of a Mean-Absolute Deviation Portfolio Optimization Model

Author

Listed:
  • Charles D. Feinstein

    (Department of Decision and Information Sciences, Leavey School of Business, Santa Clara University, Santa Clara, California 95053)

  • Mukund N. Thapa

    (Stanford Business Software, Inc., 2672 Bayshore Parkway, Suite 304, Mountain View, California 94043)

Abstract

The purpose of this note is to present a reformulation of the model presented by Konno and Yamazaki (1991). In their paper, it was claimed that (under the assumption that there is no upper limit on the investment in an asset) the number of nonzero assets in the optimal portfolio is at most 2T + 2, where T is the number of time periods in the data base used to approximate the parameters of the return distributions of the assets. The formulation we present, which is shown to be equivalent to that of Konno and Yamazaki, has a bound of T + 2 on the number of nonzero assets in the optimal portfolio.

Suggested Citation

  • Charles D. Feinstein & Mukund N. Thapa, 1993. "Notes: A Reformulation of a Mean-Absolute Deviation Portfolio Optimization Model," Management Science, INFORMS, vol. 39(12), pages 1552-1553, December.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:12:p:1552-1553
    DOI: 10.1287/mnsc.39.12.1552
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    Cited by:

    1. Leon, T. & Liern, V. & Vercher, E., 2002. "Viability of infeasible portfolio selection problems: A fuzzy approach," European Journal of Operational Research, Elsevier, vol. 139(1), pages 178-189, May.
    2. Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
    3. Xidonas, Panagiotis & Mavrotas, George & Zopounidis, Constantin & Psarras, John, 2011. "IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection," European Journal of Operational Research, Elsevier, vol. 210(2), pages 398-409, April.
    4. Guo, Sini & Yu, Lean & Li, Xiang & Kar, Samarjit, 2016. "Fuzzy multi-period portfolio selection with different investment horizons," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1026-1035.
    5. Lozano, Sebastián & Gutiérrez, Ester, 2008. "Data envelopment analysis of mutual funds based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 189(1), pages 230-244, August.
    6. Ralph Steuer & Yue Qi & Markus Hirschberger, 2007. "Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection," Annals of Operations Research, Springer, vol. 152(1), pages 297-317, July.
    7. Li, Xiang & Qin, Zhongfeng, 2014. "Interval portfolio selection models within the framework of uncertainty theory," Economic Modelling, Elsevier, vol. 41(C), pages 338-344.
    8. Panagiotis Xidonas & George Mavrotas & John Psarras, 2010. "Equity portfolio construction and selection using multiobjective mathematical programming," Journal of Global Optimization, Springer, vol. 47(2), pages 185-209, June.
    9. Thorsten Michalik & Leo Schubert, 2009. "Hedging Portfolios with Short ETFs," Economic Analysis Working Papers (2002-2010). Atlantic Review of Economics (2011-2016), Colexio de Economistas de A Coruña, Spain and Fundación Una Galicia Moderna, vol. 8, pages 1-23, December.
    10. Cooper, W. W. & Lelas, V. & Sueyoshi, T., 1997. "Goal programming models and their duality relations for use in evaluating security portfolio and regression relations," European Journal of Operational Research, Elsevier, vol. 98(2), pages 431-443, April.
    11. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    12. X Cai & K L Teo & X Q Yang & X Y Zhou, 2004. "Minimax portfolio optimization: empirical numerical study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 65-72, January.
    13. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.
    14. Liu, Wenbin & Zhou, Zhongbao & Liu, Debin & Xiao, Helu, 2015. "Estimation of portfolio efficiency via DEA," Omega, Elsevier, vol. 52(C), pages 107-118.
    15. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    16. Zhang Peng & Gong Heshan & Lan Weiting, 2017. "Multi-Period Mean-Absolute Deviation Fuzzy Portfolio Selection Model with Entropy Constraints," Journal of Systems Science and Information, De Gruyter, vol. 4(5), pages 428-443, October.

    More about this item

    Keywords

    portfolio optimization; L1 risk function; linear programming; Markowitz model;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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