The Dispersion Bias

SIAM Journal on FInancial Mathematics, forthcoming

34 Pages Posted: 17 Nov 2017 Last revised: 8 Jan 2022

See all articles by Lisa R. Goldberg

Lisa R. Goldberg

University of California, Berkeley; Aperio Group

Alex Papanicolaou

University of California, Berkeley

Alexander Shkolnik

University of California at Berkeley; University of California, Santa Barbara (UCSB)

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

Goldberg, Lisa R. and Papanicolaou, Alex and Shkolnik, Alexander and Shkolnik, Alexander, The Dispersion Bias (January 2, 2022). SIAM Journal on FInancial Mathematics, forthcoming, Available at SSRN: https://ssrn.com/abstract= or http://dx.doi.org/10.2139/ssrn.3071328

Lisa R. Goldberg

University of California, Berkeley ( email )

Department of Statistics
367 Evans Hall
Berkeley, CA 94720-3860
United States

Aperio Group ( email )

3 Harbor Drive
Suite 315
Sausalito, CA 94965
United States

Alex Papanicolaou

University of California, Berkeley ( email )

310 Barrows Hall
Berkeley, CA 94720
United States

Alexander Shkolnik (Contact Author)

University of California, Santa Barbara (UCSB) ( email )

5501 South Hall
Santa Barbara, CA 93106
United States

University of California at Berkeley ( email )

Berkeley, CA 94720
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
323
Abstract Views
1,433
Rank
148,309
PlumX Metrics