Singular inverse Wishart distribution and its application to portfolio theory
(2016) In Journal of Multivariate Analysis 143. p.314326 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:
http://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
 0047259X
 DOI
 10.1016/j.jmva.2015.09.021
 language
 English
 LU publication?
 yes
 id
 f7f3b19495b84f089765db68184ed5b0 (old id 8228299)
 date added to LUP
 20151120 15:20:50
 date last changed
 20180107 07:25:33
@article{f7f3b19495b84f089765db68184ed5b0, 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 = {0047259X}, keyword = {Mean–variance portfolio,Singular Wishart distribution,Sample estimate of precision matrix,Moore–Penrose inverse}, language = {eng}, pages = {314326}, 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}, volume = {143}, year = {2016}, }