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

Bodnar, Taras ; Mazur, Stepan LU ; Podgórski, Krzysztof LU and Tyrcha, Joanna (2019) In Journal of Statistical Planning and Inference 201. p.40-57
Abstract

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.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
High-dimensional asymptotics, Hypothesis testing, Singular covariance matrix, Singular Wishart distribution, Tangency portfolio
in
Journal of Statistical Planning and Inference
volume
201
pages
40 - 57
publisher
North-Holland
external identifiers
  • scopus:85058549449
ISSN
0378-3758
DOI
10.1016/j.jspi.2018.11.003
language
English
LU publication?
yes
id
61fe929c-2cac-4b3f-87bb-25a07ccc9f22
date added to LUP
2019-01-10 08:53:22
date last changed
2022-04-25 20:01:46
@article{61fe929c-2cac-4b3f-87bb-25a07ccc9f22,
  abstract     = {{<p>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&amp;P 500 index.</p>}},
  author       = {{Bodnar, Taras and Mazur, Stepan and Podgórski, Krzysztof and Tyrcha, Joanna}},
  issn         = {{0378-3758}},
  keywords     = {{High-dimensional asymptotics; Hypothesis testing; Singular covariance matrix; Singular Wishart distribution; Tangency portfolio}},
  language     = {{eng}},
  pages        = {{40--57}},
  publisher    = {{North-Holland}},
  series       = {{Journal of Statistical Planning and Inference}},
  title        = {{Tangency portfolio weights for singular covariance matrix in small and large dimensions : Estimation and test theory}},
  url          = {{http://dx.doi.org/10.1016/j.jspi.2018.11.003}},
  doi          = {{10.1016/j.jspi.2018.11.003}},
  volume       = {{201}},
  year         = {{2019}},
}