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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Paper ; No. 1/2018

Classification and Topics

• Classification: Wirtschaft ; Econometric and Statistical Methods and Methodology: General ; Operations Research; Statistical Decision Theory
• Subject: tangency portfolio ; singular Wishart distribution ; singular covariance matrix ; high-dimensional asymptotics ; hypothesis testing

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Bodnar, Taras ; Mazur, Stepan ; Podgórski, Krzysztof ; Tyrcha, Joanna
• Event: Veröffentlichung
• (who): Örebro University School of Business
• (where): Örebro
• (when): 2018

Further information

• Handle: http://hdl.handle.net/10419/244533
• Last update: 10.03.2025, 11:42 AM CET