Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps


  • Ravi Jagannathan,

  • Tongshu Ma

    Search for more papers by this author
    • Jagannathan is from the Kellogg School of Management at Northwestern University and the National Bureau of Economic Research and Ma is from the David Eccles School of Business at the University of Utah. We thank Torben Andersen, Gopal Basak, Louis Chan, Gregory Connor, Kent Daniel, Bernard Dumas, Ludger Hentschel, Philippe Henrotte, Ioulia Ioffe, Olivier Ledoit, Ludan Liu, Andrew Lo, Jesper Lund, Robert McDonald, Steve Ross, Jay Shanken, and seminar participants at Copenhagen Business School, HEC, INSEAD, MIT, Norwegian School of Management, Hong Kong University of Science and Technology, University of Rochester, University of Illinois at Urbana-Champaign, University of Utah, and the 2002 AFA meeting in Atlanta, and especially the referees, the editor, Rick Green, and Wayne Ferson for helpful comments. We are responsible for any errors or omissions.


Green and Hollifield (1992) argue that the presence of a dominant factor would result in extreme negative weights in mean-variance efficient portfolios even in the absence of estimation errors. In that case, imposing no-short-sale constraints should hurt, whereas empirical evidence is often to the contrary. We reconcile this apparent contradiction. We explain why constraining portfolio weights to be nonnegative can reduce the risk in estimated optimal portfolios even when the constraints are wrong. Surprisingly, with no-short-sale constraints in place, the sample covariance matrix performs as well as covariance matrix estimates based on factor models, shrinkage estimators, and daily data.