A test on the location of tangency portfolio for small sample size and singular covariance matrix

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dc.contributor.authorDrin, Svitlanaen_US
dc.contributor.authorMazur, Stepanen_US
dc.contributor.authorMuhinyuza, Stanislasen_US
dc.date.accessioned2025-01-29T06:48:39Z
dc.date.available2025-01-29T06:48:39Z
dc.date.issued2025
dc.description.abstractThe test for the location of the tangency portfolio on the set of feasible portfolios is proposed when both the population and the sample covariance matrices of asset returns are singular. The particular case of investigation is when the number of observations, n, is smaller than the number of assets, k, in the portfolio, and the asset returns are i.i.d. normally distributed with singular covariance matrix Σ such that rank(Σ) = r < n<k +1. The exact distribution of the test statistic is derived under both the null and alternative hypotheses. Furthermore, the high-dimensional asymptotic distribution of that test statistic is established when both the rank of the population covariance matrix and the sample size increase to infinity so that r/n → c ∈ (0, 1). Theoretical findings are completed by comparing the high-dimensional asymptotic test with an exact finite sample test in the numerical study. A good performance of the obtained results is documented. To get a better understanding of the developed theory, an empirical study with data on the returns on the stocks included in the S&P 500 index is provided.en_US
dc.identifier.citationDrin S. A test on the location of tangency portfolio for small sample size and singular covariance matrix / Svitlana Drin, Stepan Mazur, Stanislas Muhinyuza // Modern Stochastics: Theory and Applications. - 2025. - Vol. 12, Issue 1. - P. 43–59. - https://doi.org/10.15559/24-VMSTA261en_US
dc.identifier.issn2351-6054
dc.identifier.issn2351-6046
dc.identifier.urihttps://doi.org/10.15559/24-VMSTA261
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/33360
dc.language.isoenen_US
dc.relation.sourceModern Stochastics: Theory and Applicationsen_US
dc.statusfirst publisheden_US
dc.subjectTangency portfolioen_US
dc.subjectHypothesis testingen_US
dc.subjectSingular Wishart distributionen_US
dc.subjectMoore–Penrose inverseen_US
dc.subjectHigh-dimensional asymptoticsen_US
dc.subjectSingular covariance matrixen_US
dc.subjectarticleen_US
dc.titleA test on the location of tangency portfolio for small sample size and singular covariance matrixen_US
dc.typeArticleen_US
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