02570cam a22002657 4500001000600000003000500006005001700011008004100028100002300069245013800092260006600230490004100296500001400337520142700351530006101778538007201839538003601911690005501947690009402002700001702096710004202113830007602155856003702231856003602268w8922NBER20150603170746.0150603s2002 mau||||fs|||| 000 0 eng d1 aJagannathan, Ravi.10aRisk Reduction in Large Portfoliosh[electronic resource]:bWhy Imposing the Wrong Constraints Helps /cRavi Jagannathan, Tongshu Ma. aCambridge, Mass.bNational Bureau of Economic Researchc2002.1 aNBER working paper seriesvno. w8922 aMay 2002.3 aMean-variance efficient portfolios constructed using sample moments often involve taking extreme long and short positions. Hence practitioners often impose portfolio weight constraints when constructing efficient portfolios. Green and Hollifield (1992) argue that the presence of a single dominant factor in the covariance matrix of returns is why we observe extreme positive and negative weights. If this were the case then imposing the weight constraint should hurt whereas the empirical evidence is often to the contrary. We reconcile this apparent contradiction. We show that constraining portfolio weights to be nonnegative is equivalent to using the sample covariance matrix after reducing its large elements and then form the optimal portfolio without any restrictions on portfolio weights. This shrinkage helps reduce the risk in estimated optimal portfolios even when they have negative weights in the population. Surprisingly, we also find that once the nonnegativity constraint is imposed, minimum variance portfolios constructed using the monthly sample covariance matrix perform as well as those constructed using covariance matrices estimated using factor models, shrinkage estimators, and daily data. When minimizing tracking error is the criterion, using daily data instead of monthly data helps. However, the sample covariance matrix without any correction for microstructure effects performs the best. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC49 - Other2Journal of Economic Literature class. 7aG11 - Portfolio Choice • Investment Decisions2Journal of Economic Literature class.1 aMa, Tongshu.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w8922.4 uhttp://www.nber.org/papers/w892241uhttp://dx.doi.org/10.3386/w8922