IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v12y2005i1p1-15.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000254015
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486042000254015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. J. G. Kallberg & W. T. Ziemba, 1983. "Comparison of Alternative Utility Functions in Portfolio Selection Problems," Management Science, INFORMS, vol. 29(11), pages 1257-1276, November.
    2. Dybvig, Philip H, 1984. "Short Sales Restrictions and Kinks on the Mean Variance Frontier," Journal of Finance, American Finance Association, vol. 39(1), pages 239-244, March.
    3. Shaun Bond & Stephen Satchell, 2002. "Statistical properties of the sample semi-variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(4), pages 219-239.
    4. Porter, R Burr, 1974. "Semivariance and Stochastic Dominance: A Comparison," American Economic Review, American Economic Association, vol. 64(1), pages 200-204, March.
    5. 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.
    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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".
    2. Felici, Marco & Kenny, Geoff & Friz, Roberta, 2023. "Consumer savings behaviour at low and negative interest rates," European Economic Review, Elsevier, vol. 157(C).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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).
    17. Nick James & Max Menzies & Jennifer Chan, 2023. "Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks," Econometrics, MDPI, vol. 11(1), pages 1-33, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sean A. Anthonisz & Tālis J. Putniņš, 2017. "Asset Pricing with Downside Liquidity Risks," Management Science, INFORMS, vol. 63(8), pages 2549-2572, August.
    2. Cumova, Denisa & Nawrocki, David, 2014. "Portfolio optimization in an upside potential and downside risk framework," Journal of Economics and Business, Elsevier, vol. 71(C), pages 68-89.
    3. Luciano de Castro & Antonio F. Galvao & Gabriel Montes-Rojas & Jose Olmo, 2022. "Portfolio selection in quantile decision models," Annals of Finance, Springer, vol. 18(2), pages 133-181, June.
    4. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    5. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    6. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    7. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    8. Yudhvir Seetharam, 2013. "Do Mutual Funds Attract the Right Investor? A Stochastic Dominance Approach," Journal of Economics and Behavioral Studies, AMH International, vol. 5(12), pages 905-914.
    9. Houda Hafsa & Dorra Hmaied, 2012. "Are Downside Higher Order Co-Moments Priced? : Evidence From The French Market," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 65-81.
    10. Wetzstein, Michael E. & Szmedra, Philip I. & McClendon, Ronald W. & Edwards, David M., 1988. "Efficiency Criteria And Risk Aversion: An Empirical Evaluation," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 20(1), pages 1-8, July.
    11. Hassine, Marlène & Roncalli, Thierry, 2013. "Measuring Performance of Exchange Traded Funds," MPRA Paper 44298, University Library of Munich, Germany.
    12. Tamara Ajrapetova, 2018. "Cross-Section of Asset Returns: Emerging Markets and Market Integration," European Financial and Accounting Journal, Prague University of Economics and Business, vol. 2018(1), pages 41-60.
    13. repec:stn:sotoec:1311 is not listed on IDEAS
    14. Amy V. Puelz, 2002. "A Stochastic Convergence Model for Portfolio Selection," Operations Research, INFORMS, vol. 50(3), pages 462-476, June.
    15. Wei Liu & James W. Kolari, 2022. "Multifactor Market Indexes," JRFM, MDPI, vol. 15(4), pages 1-26, March.
    16. B Ritchie & C Brindley, 2007. "An emergent framework for supply chain risk management and performance measurement," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(11), pages 1398-1411, November.
    17. Stephen E. Satchell & Shaun A. Bond, 2004. "Asymmetry, Loss Aversion and Forecasting," Econometric Society 2004 Australasian Meetings 160, Econometric Society.
    18. Zhangxin (Frank) Liu & Michael J. O'Neill, 2018. "Partial moment volatility indices," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(1), pages 195-215, March.
    19. Schmidt, Ulrich, 2003. "The axiomatic basis of risk-value models," European Journal of Operational Research, Elsevier, vol. 145(1), pages 216-220, February.
    20. Olivier Brandouy & Philippe Mathieu & Iryna Veryzhenko, 2012. "Risk Aversion Impact on Investment Strategy Performance: A Multi Agent-Based Analysis," Post-Print halshs-02048765, HAL.
    21. Christis Katsouris, 2021. "Optimal Portfolio Choice and Stock Centrality for Tail Risk Events," Papers 2112.12031, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:1-15. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.