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

Author

Listed:
  • 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)

  • Raman Uppal

    () (London Business School, London NW1 4SA, United Kingdom)

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.

Suggested Citation

  • Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
  • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:5:p:798-812
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    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
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