A Generalized Approach to Portfolio Optimization: Improving Performance By Constraining Portfolio Norms Articles uri icon

publication date

  • January 2009

start page

  • 798

end page

  • 812


  • 5


  • 55

International Standard Serial Number (ISSN)

  • 0025-1909

Electronic International Standard Serial Number (EISSN)

  • 1526-5501


  • 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
    norm of the portfolio-weight vector be smaller than
    a given threshold. We show that our framework nests as special cases
    shrinkage approaches of Jagannathan and Ma
    (Jagannathan, R., T. Ma. 2003. Risk reduction in large portfolios: Why
    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
    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.