The Dispersion Bias

Lisa R Goldberg, Alex Papanicolaou and Alex Shkolnik

Department of Economics, Working Paper Series from Department of Economics, Institute for Business and Economic Research, UC Berkeley

Abstract: We identify and correct excess dispersion in the leading eigenvector of a sample covariance matrix when the number of variables vastly exceeds the number of observations. Our correction is datadriven, and it materially diminishes the substantial impact of estimation error on weights and risk forecasts of minimum variance portfolios. We quantify that impact with a novel metric, the optimization bias, which has a positive lower bound prior to correction and tends to zero almost surely after correction. Our analysis sheds light on aspects of how estimation error corrupts an estimated covariance matrix and is transmitted to portfolios via quadratic optimization.

Keywords: dispersion bias; optimization bias; eigenvector; minimum variance portfolio; covariance matrix; shrinkage; Applied Mathematics; Statistics; Banking; Finance and Investment (search for similar items in EconPapers)
Date: 2022-06-01
New Economics Papers: this item is included in nep-ecm
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