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Note---Naive Diversification and Portfolio Risk---A Note


  • Ron Bird

    (Faculty of Economics and Commerce, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia)

  • Mark Tippett

    (Faculty of Economics and Commerce, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia)


A number of authors have used the portfolio standard deviation to model the risk reduction advantages of naive diversification. Other authors have pointed out that when risk is modelled by the portfolio's variance the modelling process becomes much simpler and is computationally more efficient. In this note we derive an exact parametric relationship between portfolio standard deviation and size and thus highlight the dangers of using the standard deviation in conjunction with O.L.S. regression techniques to model the risk reduction advantages of naive diversification. It is then shown that past empirical studies which have used this methodology are deficient.

Suggested Citation

  • Ron Bird & Mark Tippett, 1986. "Note---Naive Diversification and Portfolio Risk---A Note," Management Science, INFORMS, vol. 32(2), pages 244-251, February.
  • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:2:p:244-251

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    Cited by:

    1. Ravi Jagannathan & Tongshu Ma, 2002. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," NBER Working Papers 8922, National Bureau of Economic Research, Inc.
    2. Tasca, Paolo & Mavrodiev, Pavlin & Schweitzer, Frank, 2014. "Quantifying the impact of leveraging and diversification on systemic risk," Journal of Financial Stability, Elsevier, vol. 15(C), pages 43-52.
    3. Cabrini, Silvina M. & Stark, Brian G. & Irwin, Scott H. & Good, Darrel L. & Martines-Filho, Joao, 2005. "Portfolios of Agricultural Market Advisory Services: How Much Diversification Is Enough?," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 37(1), pages 101-114, April.
    4. repec:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-016-2377-z is not listed on IDEAS
    5. Chia, Rui Ming Daryl & Lim, Kai Jie Shawn, 2012. "The Attenuation of Idiosyncratic Risk under Alternative Portfolio Weighting Strategies: Recent Evidence from the UK Equity Market," MPRA Paper 41455, University Library of Munich, Germany.
    6. Gilles Boevi Koumou, 2016. "Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit," Papers 1608.05024,, revised Aug 2016.
    7. Peter Byrne & Stephen Lee, 2000. "Risk reduction in the United Kingdom property market," Journal of Property Research, Taylor & Francis Journals, vol. 17(1), pages 23-46, January.
    8. repec:eee:dyncon:v:82:y:2017:i:c:p:96-124 is not listed on IDEAS
    9. Paolo Tasca & Stefano Battiston, "undated". "Diversification and Financial Stability," Working Papers CCSS-11-001, ETH Zurich, Chair of Systems Design.
    10. Vitali Alexeev & Mardi Dungey, 2015. "Equity portfolio diversification with high frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1205-1215, July.
    11. repec:spr:annopr:v:272:y:2019:i:1:d:10.1007_s10479-018-2876-1 is not listed on IDEAS
    12. Alexeev, Vitali & Tapon, Francis, 2013. "Equity Portfolio Diversification: How Many Stocks are Enough? Evidence from Five Developed Markets," Working Papers 2013-16, University of Tasmania, Tasmanian School of Business and Economics, revised 20 Nov 2013.
    13. 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.
    14. Groh, Alexander P., 2004. "Risikoadjustierte Performance von Private Equity-Investitionen," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 21382, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    15. Sirapat Polwitoon & Oranee Tawatnuntachai, 2013. "In Search of Optimal Number of Bond Funds," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 3(1), pages 1-5.
    16. repec:imx:journl:v:4:y:2005:i:1:p:65-72 is not listed on IDEAS
    17. Statman, Meir, 1987. "How Many Stocks Make a Diversified Portfolio?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 353-363, September.
    18. S. G. M. Fifield & D. M. Power & C. D. Sinclair, 2002. "Emerging stock markets: a more realistic assessment of the gains from diversification," Applied Financial Economics, Taylor & Francis Journals, vol. 12(3), pages 213-229.
    19. Alexeev, Vitali & Tapon, Francis, 2013. "What Australian investors need to know to diversity their portfolios," Working Papers 2013-17, University of Tasmania, Tasmanian School of Business and Economics, revised 20 Nov 2013.


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