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Mean-Semivariance Efficient Frontier: A Downside Risk Model for Portfolio Selection

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  • Enrique Ballestero

Abstract

An ongoing stream in financial analysis proposes mean-semivariance in place of mean-variance as an alternative approach to portfolio selection, since segments of investors are more averse to returns below the mean value than to deviations above and below the mean value. Accordingly, this paper searches for a stochastic programming model in which the portfolio semivariance is the objective function to be minimized subject to standard parametric constraints, which leads to the mean-semivariance efficient frontier. The proposed model relies on an empirically tested basis, say, portfolio diversification and the empirical validity of Sharpe's beta regression equation relating each asset return to the market. From this basis, the portfolio semivariance matrix form is strictly mathematically derived, thus an operational quadratic objective function is obtained without resorting to heuristics. Ease of computation is highlighted by a numerical example, which allows one to compare the results from the proposed mean-semivariance approach with those derived from the traditional mean-variance model.

Suggested Citation

  • Enrique Ballestero, 2005. "Mean-Semivariance Efficient Frontier: A Downside Risk Model for Portfolio Selection," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 1-15.
    • Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:1-15
    DOI: 10.1080/1350486042000254015
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    References listed on IDEAS

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    1. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
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    1. Felici, Marco & Kenny, Geoff & Friz, Roberta, 2023. "Consumer savings behaviour at low and negative interest rates," European Economic Review, Elsevier, vol. 157(C).
    2. Ballestero, E. & Gunther, M. & Pla-Santamaria, D. & Stummer, C., 2007. "Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1476-1487, September.
    3. 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.
    4. Cinzia Colapinto & Raja Jayaraman & Simone Marsiglio, 2017. "Multi-criteria decision analysis with goal programming in engineering, management and social sciences: a state-of-the art review," Annals of Operations Research, Springer, vol. 251(1), pages 7-40, April.
    5. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    6. Adam Borovička, 2022. "Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model," 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. 30(2), pages 595-616, June.
    7. Duc Hong Vo, 2021. "Portfolio Optimization and Diversification in China: Policy Implications for Vietnam and Other Emerging Markets," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 57(1), pages 223-238, January.
    8. Marco Corazza & Giovanni Fasano & Riccardo Gusso, 2011. "Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem," Working Papers 2011_10, Department of Economics, University of Venice "Ca' Foscari".
    9. Reus, Lorenzo & Mulvey, John M., 2016. "Dynamic allocations for currency futures under switching regimes signals," European Journal of Operational Research, Elsevier, vol. 253(1), pages 85-93.
    10. D. Pla-Santamaria & M. Bravo, 2013. "Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips," Annals of Operations Research, Springer, vol. 205(1), pages 189-201, May.
    11. Ballestero, Enrique & Bravo, Mila & Pérez-Gladish, Blanca & Arenas-Parra, Mar & Plà-Santamaria, David, 2012. "Socially Responsible Investment: A multicriteria approach to portfolio selection combining ethical and financial objectives," European Journal of Operational Research, Elsevier, vol. 216(2), pages 487-494.
    12. Cumova, Denisa & Nawrocki, David, 2011. "A symmetric LPM model for heuristic mean-semivariance analysis," Journal of Economics and Business, Elsevier, vol. 63(3), pages 217-236, May.
    13. Sebastian, Steffen P. & Steininger, Bertram I., 2021. "Real estate ETNs in strategic asset allocation," Working Paper Series 21/8, Royal Institute of Technology, Department of Real Estate and Construction Management & Banking and Finance.
    14. Beach, Steven L., 2011. "Semivariance decomposition of country-level returns," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 607-623, October.
    15. Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2018. "A multi-objective approach to the cash management problem," Annals of Operations Research, Springer, vol. 267(1), pages 515-529, August.
    16. Trichilli, Yousra & Abbes, Mouna Boujelbène & Masmoudi, Afif, 2020. "Islamic and conventional portfolios optimization under investor sentiment states: Bayesian vs Markowitz portfolio analysis," Research in International Business and Finance, Elsevier, vol. 51(C).
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