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

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Author Info

  • 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)

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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.

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File URL: http://dx.doi.org/10.1287/mnsc.32.2.244
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 32 (1986)
Issue (Month): 2 (February)
Pages: 244-251

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Handle: RePEc:inm:ormnsc:v:32:y:1986:i:2:p:244-251

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Keywords: portfolio; standard deviation; variance; naive diversification;

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Cited by:
  1. 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, Southern Agricultural Economics Association, vol. 37(01), April.
  2. 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.
  3. 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.
  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. 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.
  6. Statman, Meir, 1987. "How Many Stocks Make a Diversified Portfolio?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 353-363, September.
  7. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Statistics and Econometrics 2/11, University of Cologne, Department for Economic and Social Statistics.

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