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On the diversification of portfolios of risky assets

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  • Frahm, Gabriel
  • Wiechers, Christof
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    Abstract

    We introduce a measure of diversification for portfolios comprising d risky assets. This measure relates the smallest possible return variance among these d assets to the overall portfolio return variance, yielding the portion of non-diversifiable risk. In the context of normally distributed asset returns, its estimator and finite-sample properties are explored when being applied to the trivial asset allocation strategy. An overview of different previous approaches towards the measurement of diversification is provided, and the shortcomings of some of these approaches are illustrated. A categorization of tests regarding the portfolio return variance is given, especially for comparing naively allocated with minimum-variance portfolios. The empirical part of this work is carried out on monthly return data for the S&P500 constituents, with a return history spanning the last five decades. When measuring the diversification of naively allocated 40-asset portfolios, the average degree of diversification barely exceeds 60%. This result indicates that - for the mutual fund manager as well as for the private investor - well-founded selection of assets indeed leads to better portfolio diversification than naive allocation does. --

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    Bibliographic Info

    Paper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 2/11.

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    Date of creation: 2011
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    Handle: RePEc:zbw:ucdpse:211

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    Related research

    Keywords: Diversification; Portfolio Management; Naive Portfolio; Variance Estimation; Finite-Sample Distribution; S&P500;

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    1. Jean-Philippe Bouchaud & Marc Potters & Jean-Pierre Aguilar, 1997. "Missing Information and Asset Allocation," Papers cond-mat/9707042, arXiv.org.
    2. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
    3. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    4. Ron Bird & Mark Tippett, 1986. "Note---Naive Diversification and Portfolio Risk---A Note," Management Science, INFORMS, vol. 32(2), pages 244-251, February.
    5. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
    6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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