IDEAS home Printed from https://ideas.repec.org/p/lvl/lacicr/1508.html
   My bibliography  Save this paper

Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy

Author

Listed:
  • Benoît Carmichael
  • Gilles Boevi Koumou
  • Kevin Moran

Abstract

This paper extends the use of Rao(1982b)’s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, flexible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio’s RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz’s utility function and Bouchaud’s general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial.

Suggested Citation

  • Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2015. "Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy," Cahiers de recherche 1508, CIRPEE.
    • Handle: RePEc:lvl:lacicr:1508
    as

    Download full text from publisher

    File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2015/CIRPEE15-08.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nayak, Tapan K & Gastwirth, Joseph L, 1989. "The Use of Diversity Analysis to Assess the Relative Influence of Factors Affecting the Income Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 453-460, October.
    2. John L. Evans & Stephen H. Archer, 1968. "Diversification And The Reduction Of Dispersion: An Empirical Analysis," Journal of Finance, American Finance Association, vol. 23(5), pages 761-767, December.
    3. Jean-Philippe Bouchaud & Marc Potters & Jean-Pierre Aguilar, 1997. "Missing information and asset allocation," Science & Finance (CFM) working paper archive 500045, Science & Finance, Capital Fund Management.
    4. William N. Goetzmann & Alok Kumar, 2008. "Equity Portfolio Diversification," Review of Finance, European Finance Association, vol. 12(3), pages 433-463.
    5. William N. Goetzmann & Lingfeng Li & K. Geert Rouwenhorst, 2005. "Long-Term Global Market Correlations," The Journal of Business, University of Chicago Press, vol. 78(1), pages 1-38, January.
    6. Hsuan-Chi Chen & Keng-Yu Ho & Yu-Jen Hsiao & Cheng-Huan Wu, 2010. "The Diversification Effects of Initial Public Offerings," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 37(1-2), pages 171-205.
    7. Ingersoll, Jonathan E, Jr, 1984. "Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-1039, September.
    8. Elton, Edwin J & Gruber, Martin J, 1977. "Risk Reduction and Portfolio Size: An Analytical Solution," The Journal of Business, University of Chicago Press, vol. 50(4), pages 415-437, October.
    9. Klemkosky, Robert C & Martin, John D, 1975. "The Effect of Market Risk on Portfolio Diversification," Journal of Finance, American Finance Association, vol. 30(1), pages 147-154, March.
    10. Merton, Robert C, 1987. "A Simple Model of Capital Market Equilibrium with Incomplete Information," Journal of Finance, American Finance Association, vol. 42(3), pages 483-510, July.
    11. Fernholz, Robert & Shay, Brian, 1982. "Stochastic Portfolio Theory and Stock Market Equilibrium," Journal of Finance, American Finance Association, vol. 37(2), pages 615-624, May.
    12. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    13. Scott Willenbrock, 2011. "Diversification Return, Portfolio Rebalancing, and the Commodity Return Puzzle," Papers 1109.1256, arXiv.org.
    14. Stirling, Andy, 2010. "Multicriteria diversity analysis: A novel heuristic framework for appraising energy portfolios," Energy Policy, Elsevier, vol. 38(4), pages 1622-1634, April.
    15. Cazalet, Zelia & Grison, Pierre & Roncalli, Thierry, 2013. "The Smart Beta Indexing Puzzle," MPRA Paper 48823, University Library of Munich, Germany.
    16. Yueqin Zhao & Dayanand N. Naik, 2012. "Hypothesis testing with Rao's quadratic entropy and its application to Dinosaur biodiversity," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1667-1680, January.
    17. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Econometrics and Statistics 2/11, University of Cologne, Institute of Econometrics and Statistics.
    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. Benoit Carmichael & Gilles Boevi Koumou & Kevin Moran, 2015. "A New Formulation of Maximum Diversification Indexation Using Rao's Quadratic Entropy," Cahiers de recherche 1519, CIRPEE.
    2. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    3. Koumou, Gilles Boevi, 2020. "Mean-variance model and investors’ diversification attitude: A theoretical revisit," Finance Research Letters, Elsevier, vol. 37(C).
    4. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    5. Benoit Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The political reception of innovations," Cahiers de recherche 2107, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    6. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The RQE-CAPM : New insights about the pricing of idiosyncratic risk," CIRANO Working Papers 2021s-28, CIRANO.
    7. Contreras, Javier & Rodríguez, Yeny E. & Sosa, Aníbal, 2017. "Construction of an efficient portfolio of power purchase decisions based on risk-diversification tradeoff," Energy Economics, Elsevier, vol. 64(C), pages 286-297.
    8. Marielle Jong, 2018. "Portfolio optimisation in an uncertain world," Journal of Asset Management, Palgrave Macmillan, vol. 19(4), pages 216-221, July.

    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. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    2. Benoît Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The RQE-CAPM : New insights about the pricing of idiosyncratic risk," CIRANO Working Papers 2021s-28, CIRANO.
    3. Benoit Carmichael & Gilles Boevi Koumou & Kevin Moran, 2021. "The political reception of innovations," Cahiers de recherche 2107, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    4. Dionne, Georges & Koumou, Gilles Boevi, 2018. "Machine Learning and Risk Management: SVDD Meets RQE," Working Papers 18-6, HEC Montreal, Canada Research Chair in Risk Management.
    5. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Econometrics and Statistics 2/11, University of Cologne, Institute of Econometrics and Statistics.
    6. Haensly, Paul J., 2022. "Lessons from naïve diversification about the risk-reward trade-off," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    7. Vafai, Nima & Rakowski, David, 2024. "The sources of portfolio volatility and mutual fund performance," International Review of Financial Analysis, Elsevier, vol. 91(C).
    8. Contreras, Javier & Rodríguez, Yeny E. & Sosa, Aníbal, 2017. "Construction of an efficient portfolio of power purchase decisions based on risk-diversification tradeoff," Energy Economics, Elsevier, vol. 64(C), pages 286-297.
    9. Vitali Alexeev & Francis Tapon, 2014. "The number of stocks in your portfolio should be larger than you think: diversification evidence from five developed markets," Published Paper Series 2014-4, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    10. Gilles Boevi Koumou, 2016. "Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit," Papers 1608.05024, arXiv.org, revised Aug 2016.
    11. Prateek SHARMA, 2017. "Economic value of portfolio diversification: Evidence from international multi-asset portfolios," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(613), W), pages 33-42, Winter.
    12. Dilip B. Madan & King Wang, 2023. "Measuring Dependence in a Set of Asset Returns," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 363-385, June.
    13. Ayub, Usman & Shah, Syed Zulfiqar Ali & Abbas, Qaisar, 2015. "Robust analysis for downside risk in portfolio management for a volatile stock market," Economic Modelling, Elsevier, vol. 44(C), pages 86-96.
    14. Jiawen Xu & Yixuan Li & Kai Liu & Tao Chen, 2023. "Portfolio selection: from under-diversification to concentration," Empirical Economics, Springer, vol. 64(4), pages 1539-1557, April.
    15. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    16. Marie Brière & Bastien Drut & Valérie Mignon & Kim Oosterlinck & Ariane Szafarz, 2013. "Is the Market Portfolio Efficient? A New Test of Mean-Variance Efficiency when all Assets are Risky," Finance, Presses universitaires de Grenoble, vol. 34(1), pages 7-41.
    17. Vitali Alexeev & Mardi Dungey, 2015. "Equity portfolio diversification with high frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1205-1215, July.
    18. Oehler, Andreas & Wanger, Hans Philipp, 2020. "Household portfolio optimization with XTFs? An empirical study using the SHS-base," Research in International Business and Finance, Elsevier, vol. 51(C).
    19. Guiso, Luigi & Sodini, Paolo, 2013. "Household Finance: An Emerging Field," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1397-1532, Elsevier.
    20. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(2), pages 247-267, June.

    More about this item

    Keywords

    Portfolio Diversification; Rao’s Quadratic Entropy; Diversification Return; Diversification Ratio; Portfolio Variance Normalized; Gini-Simpson Index; Markowitz’s Utility Function; Bouchaud’s General Free Utility;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:lvl:lacicr:1508. 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: Manuel Paradis (email available below). General contact details of provider: https://edirc.repec.org/data/cirpeca.html .

    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.