A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms

Victor DeMiguel (), Lorenzo Garlappi (), Francisco J. Nogales () and Raman Uppal
Additional contact information
Victor DeMiguel: London Business School, London NW1 4SA, United Kingdom
Lorenzo Garlappi: McCombs School of Business, University of Texas at Austin, Austin, Texas 78712
Francisco J. Nogales: Universidad Carlos III de Madrid, 28911 Leganes, Madrid, Spain

Management Science, 2009, vol. 55, issue 5, 798-812

Abstract: We provide a general framework for finding portfolios that perform well out-of-sample in the presence of estimation error. This framework relies on solving the traditional minimum-variance problem but subject to the additional constraint that the norm of the portfolio-weight vector be smaller than a given threshold. We show that our framework nests as special cases the shrinkage approaches of Jagannathan and Ma (Jagannathan, R., T. Ma. 2003. Risk reduction in large portfolios: Why imposing the wrong constraints helps. J. Finance 58 1651-1684) and Ledoit and Wolf (Ledoit, O., M. Wolf. 2003. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J. Empirical Finance 10 603-621, and Ledoit, O., M. Wolf. 2004. A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Anal. 88 365-411) and the 1/N portfolio studied in DeMiguel et al. (DeMiguel, V., L. Garlappi, R. Uppal. 2009. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Rev. Financial Stud. 22 1915-1953). We also use our framework to propose several new portfolio strategies. For the proposed portfolios, we provide a moment-shrinkage interpretation and a Bayesian interpretation where the investor has a prior belief on portfolio weights rather than on moments of asset returns. Finally, we compare empirically the out-of-sample performance of the new portfolios we propose to 10 strategies in the literature across five data sets. We find that the norm-constrained portfolios often have a higher Sharpe ratio than the portfolio strategies in Jagannathan and Ma (2003), Ledoit and Wolf (2003, 2004), the 1/N portfolio, and other strategies in the literature, such as factor portfolios.

Keywords: portfolio choice; covariance matrix estimation; estimation error; shrinkage estimator; norm constraints (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (371)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:55:y:2009:i:5:p:798-812

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