Diversification and Generalized Tracking Errors for Correlated Non-Normal Returns

Quantitative Finance, Vol. 2, No. 6, pp. 482-486, December 2002

Posted: 12 Feb 2003

See all articles by Mark B. Wise

Mark B. Wise

California Institute of Technology

Vineer Bhansali

LongTail Alpha, LLC

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Abstract

The probability distribution for the relative return of a portfolio constructed from a subset n of the assets from a benchmark, consisting of N assets whose returns are multivariate normal, is completely characterized by its tracking error. However, if the benchmark asset returns are not multivariate normal then higher moments of the probability distribution for the portfolio's relative return are not related to its tracking error. We discuss the convergence of generalized tracking error measures as the size of the subset of benchmark assets increases. Assuming that the joint probability distribution for the returns of the assets is symmetric under their permutations we show that increasing n makes these generalized tracking errors small (even though n << N). For n >> 1 the probability distribution for the portfolio's relative return is approximately symmetric and strongly peaked about the origin. The results of this paper generalize the conclusions of Dynkin et. al. (Dynkin L, Hyman J and Konstantinovsky V 2002 Sufficient Diversification in Credit Portfolios (Lehman Brothers Fixed Income Research)) to more general underlying asset distributions.

Keywords: Diversification, Non-normal, Returns

JEL Classification: G00, G10, G11

Suggested Citation

Wise, Mark B. and Bhansali, Vineer, Diversification and Generalized Tracking Errors for Correlated Non-Normal Returns. Quantitative Finance, Vol. 2, No. 6, pp. 482-486, December 2002. Available at SSRN: https://ssrn.com/abstract=366940

Mark B. Wise (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States
626-395-6687 (Phone)
626-568-8473 (Fax)

Vineer Bhansali

LongTail Alpha, LLC ( email )

500 Newport Center Drive
Suite 820
Newport Beach, CA 92660
United States

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