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Singular inverse Wishart distribution and its application to portfolio theory
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 3
2016 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 143, 314-326 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 143, 314-326 p.
Keyword [en]
Singular Wishart distribution, Mean-variance portfolio, Sample estimate of precision matrix, Moore-Penrose inverse
National Category
Mathematics Probability Theory and Statistics
Research subject
Mathematical Statistics
URN: urn:nbn:se:su:diva-126185DOI: 10.1016/j.jmva.2015.09.021ISI: 000366885300019OAI: diva2:898775
Available from: 2016-01-29 Created: 2016-01-26 Last updated: 2016-03-03Bibliographically approved

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Bodnar, Taras
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