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

Author

Listed:
  • 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)

Abstract

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
    DOI: 10.1287/mnsc.32.2.244
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    Citations

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    Cited by:

    1. Francisco Fernández-Navarro & Luisa Martínez-Nieto & Mariano Carbonero-Ruz & Teresa Montero-Romero, 2021. "Mean Squared Variance Portfolio: A Mixed-Integer Linear Programming Formulation," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    2. 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.
    3. K. Liagkouras & K. Metaxiotis, 2018. "A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem," Annals of Operations Research, Springer, vol. 267(1), pages 281-319, August.
    4. 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.
    5. Vitali Alexeev & Mardi Dungey, 2015. "Equity portfolio diversification with high frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1205-1215, July.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. Paolo Tasca & Stefano Battiston, "undated". "Diversification and Financial Stability," Working Papers CCSS-11-001, ETH Zurich, Chair of Systems Design.
    11. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    12. Haensly, Paul J., 2020. "Risk decomposition, estimation error, and naïve diversification," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    13. 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.
    14. David Bradfield & Brian Munro, 2017. "The number of stocks required for effective portfolio diversification: the South African case," South African Journal of Accounting Research, Taylor & Francis Journals, vol. 31(1), pages 44-59, January.
    15. Florin Aliu & Besnik Krasniqi & Adriana Knapkova & Fisnik Aliu, 2019. "Interdependence and Risk Comparison of Slovak, Hungarian and Polish Stock Markets: Policy and Managerial Implications," Acta Oeconomica, Akadémiai Kiadó, Hungary, vol. 69(2), pages 273-287, June.
    16. Gilles Boevi Koumou, 2016. "Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit," Papers 1608.05024, arXiv.org, revised Aug 2016.
    17. 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.
    18. Tasca, Paolo & Battiston, Stefano & Deghi, Andrea, 2017. "Portfolio diversification and systemic risk in interbank networks," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 96-124.
    19. K. Liagkouras & K. Metaxiotis, 2019. "Improving the performance of evolutionary algorithms: a new approach utilizing information from the evolutionary process and its application to the fuzzy portfolio optimization problem," Annals of Operations Research, Springer, vol. 272(1), pages 119-137, January.
    20. 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.
    21. 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.
    22. Iván Aguayo Guajardo, 2005. "Is Portfolio Diversification Achievable Within The Mexican Stock Market?," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 4(1), pages 65-72, Marzo 200.
    23. 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.
    24. 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.
    25. Grout, Paul A, 1987. "Wider Share Ownership and Economic Performance," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 3(4), pages 13-29, Winter.

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