Being Naive about Naive Diversification: Can Investment Theory be Consistently Useful

49 Pages Posted: 19 Mar 2008 Last revised: 15 Nov 2013

See all articles by Jun Tu

Jun Tu

Singapore Management University - Lee Kong Chian School of Business

Guofu Zhou

Washington University in St. Louis - John M. Olin Business School; China Academy of Financial Research (CAFR)

Date Written: June 2008

Abstract

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and taught in MBA texts. DeMiguel, Garlappi and Uppal (2007), however, show that, due to estimation errors, existing theory-based portfolio strategies are not as good as we once thought, and the estimation window needed for them to beat the naive $1/N$ strategy (that invests equally across N risky assets) is 'around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets.' In this paper, we modify the modern portfolio theory to account for estimation errors, so that the theory becomes more relevant in practice to yield positive gains over the naive 1/N strategy under realistic estimation windows. In particular, we provide new portfolio strategies that not only perform as well as the 1/N strategy in an exact one-factor model that favors the 1/N, but also outperform it substantially in a one-factor model with mispricing, in multi-factor models with and without mispricing, and in models calibrated from real data without any factor structures. We also find that the usual maximum likelihood (ML) estimator of the true portfolio rule can have Sharpe ratios higher than the 1/N in many cases, and hence, if one is concerned only about Sharpe ratios, the ML estimator is not as bad as one might have once believed.

Keywords: Portfolio choice, parameter uncertainty, shrinkage, admissibility

JEL Classification: G11, G12, C11

Suggested Citation

Tu, Jun and Zhou, Guofu, Being Naive about Naive Diversification: Can Investment Theory be Consistently Useful (June 2008). EFA 2008 Athens Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1099293 or http://dx.doi.org/10.2139/ssrn.1099293

Jun Tu (Contact Author)

Singapore Management University - Lee Kong Chian School of Business ( email )

50 Stamford Road
#04-01
Singapore, 178899
Singapore

Guofu Zhou

Washington University in St. Louis - John M. Olin Business School ( email )

Washington University
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-6384 (Phone)
314-658-6359 (Fax)

HOME PAGE: http://apps.olin.wustl.edu/faculty/zhou/

China Academy of Financial Research (CAFR)

Shanghai Advanced Institute of Finance
Shanghai P.R.China, 200030
China

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