Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Estimation of the global minimum variance portfolio in high dimensions
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32018 (English)In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 266, no 1, p. 371-390Article in journal (Refereed) Published
Abstract [en]

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and optimal in the sense of minimizing the out-of-sample variance. Its asymptotic properties are investigated assuming that the number of assets p depends on the sample size n such that p/n -> c is an element of (0, + infinity) as n tends to infinity. The results are obtained under weak assumptions imposed on the distribution of the asset returns: only the existence of the fourth moments is required. Furthermore, we make no assumption on the upper bound of the spectrum of the covariance matrix. As a result, the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in the financial literature nowadays. This is also documented in a numerical study where the small- and large-sample behavior of the derived estimator is compared with existing estimators of the GMV portfolio. The resulting estimator shows significant improvements and it turns out to be robust if the assumption of normality is violated.

Place, publisher, year, edition, pages
2018. Vol. 266, no 1, p. 371-390
Keywords [en]
Finance, Global minimum variance portfolio, Large-dimensional asymptotics, Covariance matrix estimation, Random matrix theory
National Category
Economics and Business
Identifiers
URN: urn:nbn:se:su:diva-153586DOI: 10.1016/j.ejor.2017.09.028ISI: 000423646500030OAI: oai:DiVA.org:su-153586DiVA, id: diva2:1190772
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-03-15Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Bodnar, Taras
By organisation
Department of Mathematics
In the same journal
European Journal of Operational Research
Economics and Business

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 10 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf