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Grading Investment Diversification Options in Presence of Non-Historical Financial Information

Author

Listed:
  • Clara Calvo

    (Department of Mathematics for Economics and Business, University of Valencia, Avda. dels Tarongers s/n, 46022 Valencia, Spain)

  • Carlos Ivorra

    (Department of Mathematics for Economics and Business, University of Valencia, Avda. dels Tarongers s/n, 46022 Valencia, Spain)

  • Vicente Liern

    (Department of Mathematics for Economics and Business, University of Valencia, Avda. dels Tarongers s/n, 46022 Valencia, Spain)

  • Blanca Pérez-Gladish

    (Department of Economy Quantitative, University of Oviedo, Campus del Cristo, 33006 Oviedo, Spain)

Abstract

Modern portfolio theory deals with the problem of selecting a portfolio of financial assets such that the expected return is maximized for a given level of risk. The forecast of the expected individual assets’ returns and risk is usually based on their historical returns. In this work, we consider a situation in which the investor has non-historical additional information that is used for the forecast of the expected returns. This implies that there is no obvious statistical risk measure any more, and it poses the problem of selecting an adequate set of diversification constraints to mitigate the risk of the selected portfolio without losing the value of the non-statistical information owned by the investor. To address this problem, we introduce an indicator, the historical reduction index, measuring the expected reduction of the expected return due to a given set of diversification constraints. We show that it can be used to grade the impact of each possible set of diversification constraints. Hence, the investor can choose from this gradation, the set better fitting his subjective risk-aversion level.

Suggested Citation

  • Clara Calvo & Carlos Ivorra & Vicente Liern & Blanca Pérez-Gladish, 2021. "Grading Investment Diversification Options in Presence of Non-Historical Financial Information," Mathematics, MDPI, vol. 9(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:692-:d:522666
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    References listed on IDEAS

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    1. Kao, Chiang & Steuer, Ralph E., 2016. "Value of information in portfolio selection, with a Taiwan stock market application illustration," European Journal of Operational Research, Elsevier, vol. 253(2), pages 418-427.
    2. Victor DeMiguel & Francisco J. Nogales, 2009. "Portfolio Selection with Robust Estimation," Operations Research, INFORMS, vol. 57(3), pages 560-577, June.
    3. Toker Doganoglu & Christoph Hartz & Stefan Mittnik, 2007. "Portfolio optimization when risk factors are conditionally varying and heavy tailed," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 333-354, May.
    4. Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    5. Belaid Aouni & Michalis Doumpos & Blanca Pérez-Gladish & Ralph E. Steuer, 2018. "On the increasing importance of multiple criteria decision aid methods for portfolio selection," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(10), pages 1525-1542, October.
    6. Yew Low, Rand Kwong & Faff, Robert & Aas, Kjersti, 2016. "Enhancing mean–variance portfolio selection by modeling distributional asymmetries," Journal of Economics and Business, Elsevier, vol. 85(C), pages 49-72.
    7. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
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