A test on the location of tangency portfolio for small sample size and singular covariance matrix
The 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 asset...
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| Language: | English |
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2024-07-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/24-VMSTA261 |
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| author | Svitlana Drin Stepan Mazur Stanislas Muhinyuza |
| author_facet | Svitlana Drin Stepan Mazur Stanislas Muhinyuza |
| author_sort | Svitlana Drin |
| collection | DOAJ |
| description | The 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 $rank(\boldsymbol{\Sigma })=r\lt n\lt k+1$. 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 $r/n\to c\in (0,1)$. 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. |
| format | Article |
| id | doaj-art-7de9abead37942859fe9403ad1a155b3 |
| institution | Kabale University |
| issn | 2351-6046 2351-6054 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj-art-7de9abead37942859fe9403ad1a155b32025-01-10T11:16:08ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542024-07-01121435910.15559/24-VMSTA261A test on the location of tangency portfolio for small sample size and singular covariance matrixSvitlana Drin0Stepan Mazur1Stanislas Muhinyuza2School of Business, Örebro University, 70182 Örebro, Sweden; Department of Mathematics, National University of Kyiv-Mohyla Academy, 04070 Kyiv, UkraineSchool of Business, Örebro University, 70182 Örebro, SwedenSchool of Business and Economics, Linnaeus University, 35195 Växjö, SwedenThe 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 $rank(\boldsymbol{\Sigma })=r\lt n\lt k+1$. 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 $r/n\to c\in (0,1)$. 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.https://www.vmsta.org/doi/10.15559/24-VMSTA261Tangency portfoliohypothesis testingSingular Wishart distributionSingular covariance matrixMoore–Penrose inverseHigh-dimensional asymptotics |
| spellingShingle | Svitlana Drin Stepan Mazur Stanislas Muhinyuza A test on the location of tangency portfolio for small sample size and singular covariance matrix Modern Stochastics: Theory and Applications Tangency portfolio hypothesis testing Singular Wishart distribution Singular covariance matrix Moore–Penrose inverse High-dimensional asymptotics |
| title | A test on the location of tangency portfolio for small sample size and singular covariance matrix |
| title_full | A test on the location of tangency portfolio for small sample size and singular covariance matrix |
| title_fullStr | A test on the location of tangency portfolio for small sample size and singular covariance matrix |
| title_full_unstemmed | A test on the location of tangency portfolio for small sample size and singular covariance matrix |
| title_short | A test on the location of tangency portfolio for small sample size and singular covariance matrix |
| title_sort | test on the location of tangency portfolio for small sample size and singular covariance matrix |
| topic | Tangency portfolio hypothesis testing Singular Wishart distribution Singular covariance matrix Moore–Penrose inverse High-dimensional asymptotics |
| url | https://www.vmsta.org/doi/10.15559/24-VMSTA261 |
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