The Dispersion Bias
SIAM Journal on FInancial Mathematics, forthcoming
34 Pages Posted: 17 Nov 2017 Last revised: 8 Jan 2022
Date Written: January 2, 2022
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 data-driven, 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 previously unknown aspects of how estimation error corrupts an estimated covariance matrix and is transmitted to portfolios via quadratic optimization.
Keywords: Markowitz optimization, eigenvector bias, sample covariance, shrinkage, random matrix theory, dispersion, minimum variance portfolio
JEL Classification: C11, C13, C15, C18, C44,G11
Suggested Citation: Suggested Citation