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Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion

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  • W. Michalowski
  • W. Ogryczak

Abstract

A mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable tradeoff between expected rate of return and risk is sought. In a classical Markowitz model, the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was developed by Konno and Yamazaki, where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is easily transformed into a linear programming problem. An extension to the MAD model proposed in this paper allows us to measure risk using downside deviations, with the ability to penalize larger downside deviations. Hence, it provides for better modeling of risk averse preferences. The resulting m‐MAD model generates efficient solutions with respect to second degree stochastic dominance, while at the same time preserving the simplicity and linearity of the original MAD model. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 185–200, 2001
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Suggested Citation

  • W. Michalowski & W. Ogryczak, 1998. "Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion," Working Papers ir98041, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir98041
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    Cited by:

    1. Diana Barro & Elio Canestrelli, 2014. "Downside risk in multiperiod tracking error models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 263-283, June.
    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    3. James DiLellio, 2015. "A Kalman filter control technique in mean-variance portfolio management," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(2), pages 235-261, April.
    4. Diana Barro & Elio Canestrelli & Fabio Lanza, 2014. "Volatility vs. downside risk: optimally protecting against drawdowns and maintaining portfolio performance," Working Papers 2014:18, Department of Economics, University of Venice "Ca' Foscari".
    5. 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.
    6. Diana Barro & Elio Canestrelli, 2012. "Dynamic tracking error with shortfall control using stochastic programming," Working Papers 2012_18, Department of Economics, University of Venice "Ca' Foscari", revised 2012.
    7. 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.
    8. 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.
    9. Diana Barro & Elio Canestrelli & Giorgio Consigli, 2019. "Volatility versus downside risk: performance protection in dynamic portfolio strategies," Computational Management Science, Springer, vol. 16(3), pages 433-479, July.
    10. Shrey Jain & Siddhartha P. Chakrabarty, 2020. "Does Marginal VaR Lead to Improved Performance of Managed Portfolios: A Study of S&P BSE 100 and S&P BSE 200," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(2), pages 291-323, June.
    11. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.

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