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Downside Risk Approach for Multi-Objective Portfolio Optimization

In: Operations Research Proceedings 2011

Author

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  • Bartosz Sawik

    (AGH University of Science and Technology)

Abstract

This paper presents a multi-objective portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a triple-objectivemixed integer program. One of the problem objectives is to allocate the wealth on different securities to optimize the portfolio return. The portfolio approach has allowed the two popular in financial engineering percentile measures of risk, value-at-risk (VaR) and conditional valueat- risk (CVaR) to be applied. The decision maker can assess the value of portfolio return and the risk level, and can decide how to invest in a real life situation comparing with ideal (optimal) portfolio solutions. The concave efficient frontiers illustrate the trade-off between the conditional value-at-risk and the expected return of the portfolio. Numerical examples based on historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments show that the proposed solution approach provides the decision maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.

Suggested Citation

  • Bartosz Sawik, 2012. "Downside Risk Approach for Multi-Objective Portfolio Optimization," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 191-196, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_31
    DOI: 10.1007/978-3-642-29210-1_31
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    Cited by:

    1. Zunhao Luo & Zexin Li, 2019. "A MAGDM Method Based on Possibility Distribution Hesitant Fuzzy Linguistic Term Set and Its Application," Mathematics, MDPI, vol. 7(11), pages 1-32, November.
    2. Fima Klebaner & Zinoviy Landsman & Udi Makov & Jing Yao, 2017. "Optimal portfolios with downside risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 315-325, March.
    3. Carlo Andrea Bollino & Philipp Galkin, 2021. "Energy Security and Portfolio Diversification: Conventional and Novel Perspectives," Energies, MDPI, vol. 14(14), pages 1-24, July.
    4. Prayut Jain & Shashi Jain, 2019. "Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification," Risks, MDPI, vol. 7(3), pages 1-27, July.
    5. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    6. Emanuel Canelas & Tânia Pinto-Varela & Bartosz Sawik, 2020. "Electricity Portfolio Optimization for Large Consumers: Iberian Electricity Market Case Study," Energies, MDPI, vol. 13(9), pages 1-21, May.
    7. Markellos, Raphael N. & Psychoyios, Dimitris & Schneider, Friedrich, 2016. "Sovereign debt markets in light of the shadow economy," European Journal of Operational Research, Elsevier, vol. 252(1), pages 220-231.
    8. Bartosz Sawik, 2023. "Space Mission Risk, Sustainability and Supply Chain: Review, Multi-Objective Optimization Model and Practical Approach," Sustainability, MDPI, vol. 15(14), pages 1-25, July.
    9. Bartosz Sawik & Adrian Serrano-Hernandez & Alvaro Muro & Javier Faulin, 2022. "Multi-Criteria Simulation-Optimization Analysis of Usage of Automated Parcel Lockers: A Practical Approach," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    10. Mojtaba Borza & Azmin Sham Rambely, 2021. "A Linearization to the Sum of Linear Ratios Programming Problem," Mathematics, MDPI, vol. 9(9), pages 1-10, April.
    11. Gabriel Frahm, 2018. "An Intersection–Union Test for the Sharpe Ratio," Risks, MDPI, vol. 6(2), pages 1-13, April.
    12. X. Liu & Y.L. Gao & B. Zhang & F.P. Tian, 2019. "A New Global Optimization Algorithm for a Class of Linear Fractional Programming," Mathematics, MDPI, vol. 7(9), pages 1-21, September.

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