 Singular inverse Wishart distribution and its application to portfolio theoryTaras Bodnar, Stepan Mazur and Krzysztof Podgórski Journal of Multivariate Analysis, 2016, vol. 143, issue C, 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 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. Keywords: Singular Wishart distribution; Mean–variance portfolio; Sample estimate of precision matrix; Moore–Penrose inverse (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:143:y:2016:i:c:p:314-326 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2015.09.021 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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