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Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? Victor DeMiguel London Business School Lorenzo Garlappi University of Texas at Austin Raman Uppal London Business School and CEPR

Downloaded from http://rfs.oxfordjournals.org/ at BCV - Research Department on October 26, 2011

We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the sample-based mean-variance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many “miles to go” before the gains promised by optimal portfolio choice can actually be realized out of sample. (JEL G11)

In about the fourth century, Rabbi Issac bar Aha proposed the following rule for asset allocation: “One should always divide his wealth into three parts: a third in land, a third in merchandise, and a third ready to hand.”1 After a “brief” ˇ We wish to thank Matt Spiegel (the editor), two anonymous referees, and Luboˇ P´ stor for extensive comments; s a John Campbell and Luis Viceira for their suggestions and for making available their data and computer code; and Roberto Wessels for making available data on the ten sector portfolios of the S&P 500 Index. We also gratefully acknowledge the comments from Pierluigi Balduzzi, John Birge, Michael Brennan, Ian Cooper, Bernard Dumas, Bruno Gerard, Francisco Gomes, Eric Jacquier, Chris Malloy, Francisco Nogales, Anna Pavlova, Loriana Pelizzon, Nizar Touzi, Sheridan Titman, Rossen Valkanov, Yihong Xia, Tan Wang, Zhenyu Wang, and seminar participants at BI Norwegian School of Management, HEC Lausanne, HEC Montr´ al, London e Business School, Manchester Business School, Stockholm School of Economics, University of Mannheim, University of Texas at Austin, University of Venice, University of Vienna, the Second McGill Conference on Global Asset Management, the 2004 International Symposium on Asset Allocation and Pension Management at Copenhagen Business School, the 2005 Conference on Developments in Quantitative Finance at the Isaac Newton Institute for Mathematical Sciences at Cambridge University, the 2005 Workshop on Optimization in Finance at University of Coimbra, the 2005 meeting of the Western Finance Association, the 2005 annual meeting of INFORMS, the 2005 conference of the Institute for Quantitative Investment Research (Inquire UK), the 2006 NBER Summer Institute, the 2006 meeting of the European Finance Association, and the First Annual Meeting of the Swiss Finance Institute. Send correspondence to Lorenzo Garlappi, McCombs School of Business, University of Texas at Austin, Austin, TX 78712; telephone: (512) 471-5682; fax: (512) 471-5073. E-mail: lorenzo.garlappi@mccombs.utexas.edu. 1

Babylonian Talmud: Tractate Baba Mezi’a, folio 42a.

C The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org. doi:10.1093/rfs/hhm075 Advance Access publication December 3, 2007

The Review of Financial Studies / v 22 n 5 2009

lull in the literature on asset allocation, there have been considerable advances starting with the pathbreaking work of Markowitz (1952),2 who derived the optimal rule for allocating wealth across risky assets in a static setting when investors care only about the mean...
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