Abstract

Estimation of the covariance of a high-dimensional returns vector is well-known to be impeded by the lack of long data history. We extend the work of Goldberg, Papanicolaou, and Shkolnik [SIAM J. Financial Math., 13 (2022), pp. 521--550] on shrinkage estimates for the leading eigenvector of the covariance matrix in the high-dimensional, low sample size regime, which has immediate application to estimating minimum variance portfolios. We introduce a more general framework of shrinkage targets---multiple anchor point shrinkage---that allows the practitioner to incorporate additional information---such as sector separation of equity betas, or prior beta estimates from the recent past---to the estimation. We prove some asymptotic statements and illustrate our results with some numerical experiments.

Keywords

  1. covariance matrix estimation
  2. shrinkage
  3. minimum variance portfolio

MSC codes

  1. 91G60
  2. 91G70
  3. 62H25

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Information & Authors

Information

Published In

cover image SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
Pages: 1112 - 1143
ISSN (online): 1945-497X

History

Submitted: 14 September 2021
Accepted: 6 June 2022
Published online: 24 August 2022

Keywords

  1. covariance matrix estimation
  2. shrinkage
  3. minimum variance portfolio

MSC codes

  1. 91G60
  2. 91G70
  3. 62H25

Authors

Affiliations

Funding Information

Simons Foundation https://doi.org/10.13039/100000893

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