Singular inverse Wishart distribution and its application to portfolio theory
(2016) In Journal of Multivariate Analysis 143. p.314-326- Abstract
- The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean–variance portfolio weights as well as to derive... (More)
- The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean–variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8228299
- author
- Mazur, Stepan LU ; Bodnar, Taras and Podgorski, Krzysztof LU
- organization
- publishing date
- 2016
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Mean–variance portfolio, Singular Wishart distribution, Sample estimate of precision matrix, Moore–Penrose inverse
- in
- Journal of Multivariate Analysis
- volume
- 143
- pages
- 314 - 326
- publisher
- Academic Press
- external identifiers
-
- wos:000366885300019
- scopus:84945144193
- ISSN
- 0047-259X
- DOI
- 10.1016/j.jmva.2015.09.021
- language
- English
- LU publication?
- yes
- id
- f7f3b194-95b8-4f08-9765-db68184ed5b0 (old id 8228299)
- date added to LUP
- 2016-04-01 13:54:31
- date last changed
- 2025-04-04 15:11:03
@article{f7f3b194-95b8-4f08-9765-db68184ed5b0,
abstract = {{The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean–variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.}},
author = {{Mazur, Stepan and Bodnar, Taras and Podgorski, Krzysztof}},
issn = {{0047-259X}},
keywords = {{Mean–variance portfolio; Singular Wishart distribution; Sample estimate of precision matrix; Moore–Penrose inverse}},
language = {{eng}},
pages = {{314--326}},
publisher = {{Academic Press}},
series = {{Journal of Multivariate Analysis}},
title = {{Singular inverse Wishart distribution and its application to portfolio theory}},
url = {{http://dx.doi.org/10.1016/j.jmva.2015.09.021}},
doi = {{10.1016/j.jmva.2015.09.021}},
volume = {{143}},
year = {{2016}},
}