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How to quantify the influence of correlations on investment diversification

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  • Matus Medo
  • Chi Ho Yeung
  • Yi-Cheng Zhang
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    Abstract

    When assets are correlated, benefits of investment diversification are reduced. To measure the influence of correlations on investment performance, a new quantity - the effective portfolio size - is proposed and investigated in both artificial and real situations. We show that in most cases, the effective portfolio size is much smaller than the actual number of assets in the portfolio and that it lowers even further during financial crises.

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    File URL: http://arxiv.org/pdf/0805.3397
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0805.3397.

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    Date of creation: May 2008
    Date of revision: Feb 2009
    Publication status: Published in International Review of Financial Analysis 18, 34-39 (2009)
    Handle: RePEc:arx:papers:0805.3397

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    Web page: http://arxiv.org/

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    References

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    1. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1998. "Noise dressing of financial correlation matrices," Science & Finance (CFM) working paper archive 500051, Science & Finance, Capital Fund Management.
    2. Heston, Steven L. & Rouwenhorst, K. Geert, 1994. "Does industrial structure explain the benefits of international diversification?," Journal of Financial Economics, Elsevier, vol. 36(1), pages 3-27, August.
    3. Paolo Laureti & Matus Medo & Yi-Cheng Zhang, 2010. "Analysis of Kelly-optimal portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 689-697.
    4. Matus Medo & Yury M. Pis'mak & Yi-Cheng Zhang, 2008. "Diversification and limited information in the Kelly game," Papers 0803.1364, arXiv.org, revised Jul 2008.
    5. 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 415-37, October.
    6. Valery Polkovnichenko, 2005. "Household Portfolio Diversification: A Case for Rank-Dependent Preferences," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1467-1502.
    7. Smimou, K. & Bector, C.R. & Jacoby, G., 2008. "Portfolio selection subject to experts' judgments," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 1036-1054, December.
    8. 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.
    9. Myron S. Scholes, 2000. "Crisis and Risk Management," American Economic Review, American Economic Association, vol. 90(2), pages 17-21, May.
    10. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-78, July.
    11. Chris Whitrow, 2007. "Algorithms for optimal allocation of bets on many simultaneous events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(5), pages 607-623.
    12. Markowitz, Harry M, 1976. "Investment for the Long Run: New Evidence for an Old Rule," Journal of Finance, American Finance Association, vol. 31(5), pages 1273-86, December.
    13. Olibe, Kingsley O. & Michello, Franklin A. & Thorne, Jerry, 2008. "Systematic risk and international diversification: An empirical perspective," International Review of Financial Analysis, Elsevier, vol. 17(4), pages 681-698, September.
    14. William N. Goetzmann & Alok Kumar, 2005. "Why Do Individual Investors Hold Under-Diversified Portfolios?," Yale School of Management Working Papers ysm454, Yale School of Management.
    15. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
    16. Medo, Matúš & Pis’mak, Yury M. & Zhang, Yi-Cheng, 2008. "Diversification and limited information in the Kelly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6151-6158.
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    Cited by:
    1. Sophie Brana & Stéphanie Prat, 2009. "The Introduction Of Emerging Currencies Into A Portfolio: Towards A More Complete Diversification Model," Working Papers hal-00616581, HAL.

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