Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory
2019 (English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 201, p. 28p. 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 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 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
Elsevier, 2019. Vol. 201, p. 28p. 40-57
Keywords [en]
Tangency portfolio, singular Wishart distribution, singular covariance matrix, high-dimensional asymptotics, hypothesis testing
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-63498DOI: 10.1016/j.jspi.2018.11.003ISI: 000459528700004Scopus ID: 2-s2.0-85058549449OAI: oai:DiVA.org:oru-63498DiVA, id: diva2:1168298
Funder
Swedish Research Council, 2008-5382
Note
Funding Agencies:
Örebro University, Sweden
Project "Models for macro and financial economics after the financial crisis" - Jan Wallander and Tom Hedelius Foundation, Sweden P18-0201
2017-12-202017-12-202022-10-27Bibliographically approved