On the diversification of portfolios of risky assets
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.
|Date of creation:||2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 0221 / 470 5607
Fax: 0221 / 470 5179
Web page: http://www.wisostat.uni-koeln.de/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Szilard Pafka & Imre Kondor, 2002.
"Noisy Covariance Matrices and Portfolio Optimization II,"
cond-mat/0205119, arXiv.org, revised May 2002.
- Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
- William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
- Ron Bird & Mark Tippett, 1986. "Note---Naive Diversification and Portfolio Risk---A Note," Management Science, INFORMS, vol. 32(2), pages 244-251, February.
- 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.
- 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.
- Jean-Philippe Bouchaud & Marc Potters & Jean-Pierre Aguilar, 1997.
"Missing information and asset allocation,"
Science & Finance (CFM) working paper archive
500045, Science & Finance, Capital Fund Management.
When requesting a correction, please mention this item's handle: RePEc:zbw:ucdpse:211. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics)
If references are entirely missing, you can add them using this form.