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Tangency portfolio weights for singular covariance matrix in small and large dimensions: Estimation and test theory
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 42019 (English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 201, p. 40-57Article in journal (Refereed) Published
Abstract [en]

In this paper we derive the finite-sample distribution of the estimated 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 portfolio where the distribution of the test statistic is obtained under both the null and 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 sample size increase to infinity. The theoretical findings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.

Place, publisher, year, edition, pages
2019. Vol. 201, p. 40-57
Keywords [en]
Tangency portfolio, Singular Wishart distribution, Singular covariance matrix, High-dimensional asymptotics, Hypothesis testing
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-167551DOI: 10.1016/j.jspi.2018.11.003ISI: 000459528700004OAI: oai:DiVA.org:su-167551DiVA, id: diva2:1304455
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically approved

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Bodnar, TarasMazur, StepanTyrcha, Joanna
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