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The Proper Use Of Risk Measures In Portfolio Theory

Author

Listed:
  • SERGIO ORTOBELLI

    (University of Bergamo, Italy)

  • SVETLOZAR T. RACHEV

    (University of California, Santa Barbara and University of Karlsruhe, Germany)

  • STOYAN STOYANOV

    (FinAnalytica Inc., USA)

  • FRANK J. FABOZZI

    () (Yale University, School of Management, 135 Prospect Street, CT 06520-8200, USA)

  • ALMIRA BIGLOVA

    (University of Karlsruhe, Germany)

Abstract

This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor's portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety-risk measures and dispersion measures. We study and describe how the risk could depend on other distributional parameters. Then, we examine and discuss the differences between statistical parametric models and linear fund separation ones. Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter. Thus, we assess and value the impact on the investor's preferences of three different risk measures even considering some derivative assets among the possible choices.

Suggested Citation

  • Sergio Ortobelli & Svetlozar T. Rachev & Stoyan Stoyanov & Frank J. Fabozzi & Almira Biglova, 2005. "The Proper Use Of Risk Measures In Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1107-1133.
  • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003402
    DOI: 10.1142/S0219024905003402
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    Citations

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    Cited by:

    1. Ankit Dangi, 2013. "Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!?," Papers 1301.4194, arXiv.org.
    2. Arreola Hernandez, Jose, 2014. "Are oil and gas stocks from the Australian market riskier than coal and uranium stocks? Dependence risk analysis and portfolio optimization," Energy Economics, Elsevier, vol. 45(C), pages 528-536.
    3. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    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. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2009. "Optimal asset allocation aid system: From "one-size" vs "tailor-made" performance ratio," European Journal of Operational Research, Elsevier, vol. 192(1), pages 209-215, January.
    6. repec:imx:journl:v:12:y:2017:i:2:p:49-69 is not listed on IDEAS
    7. Rosella Giacometti & Sergio Ortobelli & Tomáš Tichý, 2015. "Portfolio Selection with Uncertainty Measures Consistent with Additive Shifts," Prague Economic Papers, University of Economics, Prague, vol. 2015(1), pages 3-16.
    8. Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
    9. Ortobelli, Sergio & Rachev, Svetlozar T. & Fabozzi, Frank J., 2010. "Risk management and dynamic portfolio selection with stable Paretian distributions," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 195-211, March.
    10. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    11. repec:eee:finlet:v:24:y:2018:i:c:p:105-112 is not listed on IDEAS
    12. José Antonio Climent-Hernández, 2017. "Portafolios de dispersión mínima con rendimientos log-estables Minimum dispersion portfolios with log-stable returns," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, March.
    13. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2016. "Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(2), pages 1-18, June.

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