Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory

Taras Bodnar (), Stepan Mazur, Krzysztof Podgórski () and Joanna Tyrcha ()
Additional contact information
Taras Bodnar: Stockholm University, Postal: Stockholm University, Department of Mathematics, SE - 10691 Stockholm, Sweden, https://www.su.se/profiles/tbodn-1.219689
Krzysztof Podgórski: Lund University, Postal: Lund University, Department of Statistics, SE - 22007 Lund, Sweden, https://www.lunduniversity.lu.se/lucat/user/d99b100b63c92a737abe35802ad5812f
Joanna Tyrcha: Stockholm University, Postal: Stockholm University, Department of Mathematics, SE - 10691 Stockholm, Sweden, https://www.su.se/profiles/joanna-1.182691

No 2018:1, Working Papers from Örebro University, School of Business

Abstract: In this paper we derive the nite-sample distribution of the esti- mated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency port- folio where the distribution of the test statistic is obtained under both the null and the alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sam- ple size increase to in nity. The theoretical ndings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.

Keywords: tangency portfolio; singular Wishart distribution; singular covariance matrix; high-dimensional asymptotics; hypothesis testing (search for similar items in EconPapers)
JEL-codes: C10 C44 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2018-02-01
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.oru.se/globalassets/oru-sv/institution ... rs2018/wp-1-2018.pdf Full text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hhs:oruesi:2018_001

Access Statistics for this paper

More papers in Working Papers from Örebro University, School of Business Örebro University School of Business, SE - 701 82 ÖREBRO, Sweden. Contact information at EDIRC.
Bibliographic data for series maintained by ().