On the diversification of portfolios of risky assets

Gabriel Frahm and Christof Wiechers

No 2/11, Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics

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.

Keywords: Diversification; Portfolio Management; Naive Portfolio; Variance Estimation; Finite-Sample Distribution; S&P500 (search for similar items in EconPapers)
JEL-codes: C13 C16 C58 G11 (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-rmg
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:ucdpse:211

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